Title: Theory and Practice of Piano Construction - With a Detailed, Practical Method for Tuning
Author: White, William B
Language: English
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Transcriber’s Note

The original contains inconsistent hyphenation; this has been preserved.
Obvious printer’s errors have been corrected; a full list is available at
the end of this book. [-] is used for a minus sign.



  William B. White


  Theory and Practice of
  PIANO CONSTRUCTION

  With a Detailed, Practical
  Method for Tuning


  Dover Publications, Inc.
  New York



Published in Canada by General Publishing Company, Ltd., 30 Lesmill
Road, Don Mills, Toronto, Ontario.

Published in the United Kingdom by Constable and Company, Ltd., 10
Orange Street, London WC 2.

This Dover edition, first published in 1975, is an unabridged and
unaltered republication of the work originally published by Edward
Lyman Bill, Publisher, New York, in 1906 under the title _Theory and
Practice of Pianoforte Building_.

  _International Standard Book Number: 0-486-23139-9_
  _Library of Congress Catalog Card Number: 74-78811_

  Manufactured in the United States of America
  Dover Publications, Inc.
  180 Varick Street
  New York, N.Y. 10014



CONTENTS.


                                                           PAGE
  Some Remarks by the Publisher                               5
  Introductory Remarks                                        9
  The Evolution of the Modern Pianoforte                     13
  Description of the Modern Pianoforte                       23
  Acoustical Laws of Sounding Strings                        28
  The Musical Scale and Musical Intonation                   36
  The Equal Temperament                                      44
  Pianoforte Strings and Their Proper Dimensions             48
  Resonance and the Resonance-Apparatus of the Pianoforte    58
  The Casing and Framing of the Pianoforte                   67
  The Iron Frame of the Pianoforte                           79
  The Mechanism of Percussion                                92
  The Touch Mechanism                                        96
  The Regulation of Pianoforte Touch-Mechanism              113
  Tuning and Tone Regulation of the Pianoforte              122
  The Draughting of the Pianoforte Scale                    135
  Conclusion                                                139
  Appendix A--Development of Player Piano                   144
  Appendix B--The Small Grand                               153



SOME REMARKS BY THE PUBLISHER.


For many years we have been receiving at the office of The Music Trade
Review constant inquiries for sources from which information might be
gleaned regarding the theory and practice of tone production as applied
to the piano. It has therefore been obvious to all who have given this
subject the slightest consideration that there has been a lack of book
information which should be at the hand of the student and the seeker
of knowledge regarding scale draughting and other essentials relating
to piano construction. Some years ago, after careful consideration of
this subject, special topics along these lines were assigned to the
author of this work, who was well fitted for the task before him, and
as a result of more than two years of conscientious study and research,
the “Theory and Practice of Pianoforte Building” is put forth as
representing in a concrete form a work of technical knowledge which
hitherto has been unobtainable to the student.

The necessity of acquiring some knowledge of the principles of
mechanics before proceeding to the study of scale design is admitted.
Such knowledge, together with that of the principles of the acoustics
as they apply to musical sounds produced by vibrating strings,
is essential to a correct understanding of the fundamental ideas
underlying true pianoforte design.

To know a piano accurately one must understand the laws governing tone
quality, and how the propagation and transmission of sound is produced
as well as the pitch and intensity of sound. And there are thousands
of men to-day in the various factories who are anxious to obtain
sources of information from which to gain a more correct knowledge of a
profession which should take high rank among industrial pursuits.

Owing to the gradual changes which have been wrought in all industries
through the abandonment of the apprentice system, there is more need
for instruction books than ever before.

A factory operative, according to the present plan, may know thoroughly
but one department of the business, but he can become more useful
to himself and his employers when he possesses a knowledge of all
branches. In the piano trade particularly there must be a correct
knowledge of piano building, else there can be no advance, and with
our old piano makers rapidly passing away there is need for a healthy
school of new inventors, so that wherever possible, improvements may
be made and defects remedied. These can only be accomplished by the
possession of a knowledge of all the intricate principles involved in
piano making.

We feel that in presenting a work of this kind we are offering a
volume which will meet with the approval of those who seek knowledge,
for while there are great trade and technical schools which are the
fountains of inspiration for various trades, the science of piano
making is not included as a branch in any of them. It is therefore
evident that knowledge must be gained outside, for piano schools there
are none. To every mind seeking information there should be knowledge
given, and we believe that a work of this kind must be of value to an
industry wherein there is such a dearth of reliable text books.

It will be seen by examination that all of the practical problems which
are to be considered by the scale draughtsmen have been fairly treated
in this volume and yet the desire of the author has been throughout to
avoid tiresome details. Condensation is one of the recognized laws of
our day, and in producing this technical work the author has labored
to create a volume of convenient size which shall be of service to
the student, and to the advanced thinker as well, on account of the
accuracy with which the subjects are treated.

This book is not in the remotest sense a history of piano building
or development, and it should not be so considered; in fact it has
been deemed wise to dip into historical matters only to the extent of
showing the application of an enduring principle rather than to give
credit to a number of deserving inventors who have worked along special
lines. A treatment of worthy inventions would require a much larger
volume than this; and while there are many inventors who have given to
the world special devices of value, it has not been considered timely
to describe them in this volume or to enter into an exposé of their
merits or demerits. We may say that this is not a critical work but
rather one which we trust may be eminently practical in its mission as
an instructive and an educational force.

We may add in closing that the “Theory and Practice of Pianoforte
Building” is the only work of its kind ever put forth in the English
language, and we have every confidence that it will find a growing
demand among music trade people everywhere.

                                                     EDWARD LYMAN BILL.

       Editorial Rooms,
  _The Music Trade Review_,
      NEW YORK, May, 1906.



THEORY AND PRACTICE OF PIANOFORTE BUILDING.



CHAPTER I.

INTRODUCTORY REMARKS.


The development of the modern American pianoforte presents a most
interesting study to the practical member of the musical industries
as well as to the pianist. For it is possible to view the subject
with equal facility from the standpoints of both. Descended through a
clearly defined line of ancestry from the ancient psaltery, and showing
traces of the various steps in its evolution throughout its entire
modern form, the pianoforte of to-day is essentially the product of all
the ages. There have not been wanting a sufficient number of writers
upon the history and ancestry of the instrument; but an exposition
of the correct principles of design has not hitherto appeared in the
English language, at least in a form that possesses permanent value
to the American manufacturer. The once classic work of Rimbault
is obsolete to-day, even in Europe; while, on the other hand, the
various German treatises have been difficult to obtain and necessarily
limited in their appeal to an English speaking people, nor have any
satisfactory translations of any of them yet been put forth.

Furthermore, the evolution of pianoforte building in this country has
proceeded along characteristically American lines and has resulted in
the existence to-day of a peculiarly national, advanced and complex
type. American pianofortes are universally acknowledged to stand among
the highest developments of applied musical craftsmanship, and artists
of every degree have willingly given their assent to every claim that
has been made for the instruments.

While, however, these facts are easily demonstrable, it would be
by no means correct to suppose that the development of the American
types of pianoforte has been materially assisted by even a respectable
minority of those who have been engaged in constructing them. On the
contrary, the magnificent examples of the musical instrument maker’s
art that grace the homes of musicians and people of culture throughout
the United States owe their present high excellence to the labors and
skill of a small band of enthusiastic and clever workers. The names of
William Hawkins, Jonas Chickering, and Henry Engelhard Steinway should
be written in letters of gold above the doors of all institutions
devoted to the creation of artistic pianofortes. For it is to the
earnest labor and untiring enthusiasm of these men and a few others,
working alone and unassisted, that the modern American instrument owes
its present proud position.

And this state of affairs has continued to exist until the present
day. There are, as there have always been, a few talented and skilful
men who have never been content to rest upon their laurels or to
desist from continual labor along the lines of musical and mechanical
betterment; but such as they stand, and have always stood, alone. The
great majority have been glad to accept the improvements of their
preceding or contemporaneous masters after the commercial value of the
innovations has been demonstrated; but they have always lacked the
audacity or capability to strike out into new fields and untrodden
pathways.

We may, however, discern a sufficient reason for this timidity on the
part of pianoforte makers. The principles that underly the design of
the instrument are primarily acoustical. They have never been very
easily digested, either by the mechanic or by the man of affairs. And
since a knowledge of acoustics has been profoundly developed only
within the last sixty years or so, it follows that its application
to the design of musical instruments has naturally lagged behind the
progress of the science itself. Pianoforte makers are not usually
professing scientists or practical musicians; and they have discerned
little profit in attempting to keep up with the trend of modern
acoustical research, even so far as this has directly affected the
principles of musical instrument construction.

The development of the pianoforte has, in fact, proceeded empirically,
and has been prosecuted inductively rather than from any _a priori_
notions. And while we cannot withhold our admiration from the splendid
success that has attended so much of this empirical research, we
cannot be blind to the fact that very many modern pianofortes exhibit
clearly the inherent defects of such methods. The practical musical
mechanician, if he possess the requisite knowledge, is often able
to remedy existing faults in tone quality and tone-production. And
while studying ways and means for doing this, he cannot but observe
innumerable cases of neglected opportunities, or even of positive
mistakes. The pure empirical method must always produce a large number
of failures. Yet the application of even the elementary principles of
Applied Acoustics would frequently prevent the commission of serious
sins in design. It is not necessary, of course, that every scale
draughtsman or designer should have the results of modern acoustical
discovery at his fingers’ ends; but it is here insisted that such
knowledge, in so far as it relates to musical instruments, is essential
to the correct construction of pianofortes.

Tone-production, otherwise than by the human voice, implies both
scientific and mechanical problems. Especially is this true of
the pianoforte, which, with the exception of the pipe organ, may
properly be considered the most complex of artificial devices for the
performance of music.

Recognition of this truth and a general improvement in the knowledge of
the acoustical and musical principles involved cannot fail to exercise
a most beneficial influence upon the future of the American pianoforte.

As has already been remarked, there is a dearth of convenient treatises
in the English language that can be said to possess a present value
to the earnest student of pianoforte design. The present book is an
attempt in the direction of supplying the deficiency. The author has
aimed at presenting the various problems pertaining to the art of
pianoforte construction with due regard both to their acoustical and
mechanical features. No attempt has been made to delve profoundly into
the mysteries of sound; but the elementary and basic principles of
tone-production have been stated, and their true application to the
various stages of pianoforte construction explained. Each step in the
making of a pianoforte from beginning to completion has been subjected
to analysis, and the correct principles pointed out.

The author believes that the book may be read and comprehended, even
by one to whom the very term acoustics has hitherto been unfamiliar.
While he does not expect that a study of this book can make the
novice a full-fledged scale draughtsman, as it were, overnight, he
does expect, on the other hand, to assist those who have already
investigated, or who intend to investigate the whole problem, to a
clearer and broader comprehension of a beautiful art. If this hope be
gratified, much will have been achieved, and no one who has at heart
the future of musical industry in America can fail to be encouraged, if
nothing else, by the appearance of this condensed work.

The general outline of the book can be explained with little detail.
Recognizing, as has already been suggested, the dependence of all right
pianoforte making upon the observance of the established principles of
acoustics, the author has thought it well, after a short historical
sketch of the pianoforte, to make a general statement of the laws that
govern the propagation and transmission of sound. It is but a step
from this to a concise explanation of the peculiarities of stretched
strings and their behavior under varying conditions of excitation,
and differing phases of tension, etc. This leads us directly to the
discussion of pianoforte strings, their dimensions, and the manner in
which they become the agents of sound-production in the instrument.

Continuing our investigations, we pass to the subject of resonance
and come naturally to a discussion of the resonating apparatus of the
pianoforte.

The framing that holds together these two vital elements is next
subjected to analysis and explanation, and finally the mechanisms
of percussion and touch are brought under our inquiry and their
peculiarities noted and expounded. The remarks upon the draughting of
pianoforte scales, that conclude the volume, are necessarily broad and
general, since it is quite impossible to indicate with exactitude the
actual method to be employed in making mechanical drawings, at least
within the limits that the relative importance of the subject imposes
on us. Attention has been drawn more particularly to the calculations
for shrinkage that are rendered necessary by the vagaries of cast iron,
such as is used in the manufacture of metal frames, and to the details
of hammer-stroke points and string dimensions, the principles of which
have been explained in their proper places within the body of the work.



CHAPTER II.

THE EVOLUTION OF THE PIANOFORTE.


While the present work is by no means intended to serve as an
elaborate analysis of pianoforte development, it seems that a proper
comprehension of the various principles that are laid down in the
course of our argument will be facilitated by a short survey of the
evolution of the instrument, undertaken from an historical viewpoint.
As we recognize in the pianoforte of to-day the culmination of the
musical-mechanical effort of ages, and as a complete study of the
results that have been achieved can best be introduced by a preliminary
knowledge of the manner in which the various steps towards latter-day
excellence have been attained, it seems that we cannot do better than
make an attempt to survey the field of pianoforte evolution in a manner
broad and general, though necessarily brief.

As was incidentally remarked in the last chapter, we may properly
consider the modern pianoforte as essentially the product of all
the ages. The origin of stringed instruments is lost in the mists
of antiquity, but Greek mythology has supplied us with a most
pleasing legend to account for the invention of that pioneer of all
stretched-string instruments, the classic lyre. We are told that
Hermes, walking one day along the shore, found lying at his feet the
shell of a dead tortoise. The intestines of the animal had been dried
in the sun and were stretched along the rim of the shell so that when
Hermes’ foot struck against one of them, a musical sound was given
forth and Lo! the lyre was born. Earlier still are the accounts, in
the shape of cuneiform or other inscriptions, that show a form of lyre
to have been in use among the Assyrians. The biblical descriptions of
various stringed instruments, such as the psaltery, or the harp of
David, are generally familiar.

While doubtless we need not consider it illogical to trace the
beginning of modern stringed instruments, whether they be of the
key-board variety or otherwise, to such misty and vague traditions,
we must look to more modern times for a true understanding of the
causes that operated to produce the key-board. This, the distinguishing
feature of the pianoforte family, first arose through the need for a
facile means of accompanying the voice in the then newly beginning art
of music which required the simultaneous sounding of different tones.
Instruments of the organ type were earlier in the field, for we have
accounts of the water-organ in the writings of the historians of the
later Roman Empire. The earliest form of key-board seems to have been
introduced in Europe in the latter part of the eleventh century A. D.
At about the same period we hear of a stringed instrument called the
organistrum, having three strings, one of which was in connection with
a number of tangents which were adapted to be pushed in upon it so as
to sound different segments and produce different notes. Later we find
that the ecclesiastical musicians were in the habit of using more or
less complicated monochords for the purpose of training their pupils in
the plain-chants of the church. These monochords gradually became more
complex and finally were mounted on a kind of sound board in groups
and thus became no longer monochords but trichords, tetrachords, or
polychords. The next step was obviously to furnish the instrument with
a set of balanced key-levers borrowed from the organ and with tangents
to connect the keys with the strings, these latter coming from the
organistrum. Thus we have at once the famous clavichord.

But this was not the only form of keyed instrument that was thus
early devised. We learn that the psaltery had contemporaneously been
fitted with keys. There were two forms of this famous instrument,
one trapezoid and one triangular. When both of these had been fitted
with keys there were two more distinct forms of keyed instruments;
differences which had a large influence upon the later development of
the type.

These three instruments were thus developed into the accepted forms
that were in general use during the seventeenth century and later;
becoming respectively the clavichord, harpsichord and spinet. It is
from these that the pianoforte is directly sprung. The harpsichord,
as its name implies, resembled a harp laid on its back and enclosed
in a case, while the strings were plucked, by quills set on jacks,
mounted on the keys. The natural shape of the harpsichord, therefore,
was similar to that of the modern grand pianoforte and it derived this
form from its direct relationship to the early keyed forms of the
triangular psaltery. The harpsichord had been a favorite for a long
time when Bartolomeo Cristofori, a maker of Florence, completed in
1709 the invention of a hammer action to replace the quilled jack at
the end of the harpsichord key. Thus was made possible the production
of dynamic effects, of which the harpsichord action had never been
capable except through the employment of various mechanical devices,
such as swells and double or triple banks of keys with jacks and quills
to match. The hammer-action of Cristofori as completed by him in 1726
shows a remarkable similarity to the mechanisms that are still to be
found in certain forms of square pianofortes. He succeeded in producing
an acceptable form of escapement and a damping device as well, although
as the date shows, not until after several years of experimenting and
improving upon the original design. Examination shows that Cristofori’s
action differs in no essential respect from the square pianoforte
actions that we have mentioned. There is the upper and under hammer,
the jack working on a groove in the key, the escapement device to
determine the travel of the jack, the back-check, and the damper.
Every feature that is essential to provide escapement, repetition and
damping is found here. Cristofori was, however, obliged to make many
changes in the construction of his “gravicembalo col piano e forte” to
provide the increased stiffness necessitated by the different manner
of exciting the strings. His work, curiously enough, was not taken up
after his death by any other Italian harpsichord maker, and it remained
for a German to continue his experiments and bring them to a practical
and commercial success. Only two pianofortes by Cristofori are known to
exist, and one of these is in the Metropolitan Museum of Art, New York.

Gottfried Silbermann, who took up the work of Cristofori, built several
grand pianofortes towards the end of the first half of the eighteenth
century, and there still exist at Potsdam some of these that were
sold by him to Frederick the Great. These instruments appear to be
essentially founded upon the work of Cristofori, and the superior
workmanship and better adjustment of them do not serve to disguise
the evident fact that Silbermann, while improving in details, did not
discover any new principles either in action or otherwise.

Somewhat later we hear of Zumpe, who was apparently struck with the
idea of adapting the pianoforte hammer to the square-shaped clavichord,
which was not deep enough to take the Silbermann action, thus producing
a veritable square pianoforte. Zumpe’s device contained no provision
for escapement, which fault was afterwards corrected by the celebrated
inventor Stein. Mozart speaks of the merits of Stein and joyfully
describes how his mechanism prevented the blocking of the hammers.
Mozart used one of Stein’s pianofortes during the rest of his life.

The name of Stein is justly famous among the early pianoforte makers.
He was responsible, with the able assistance of his daughter Nanette,
for the Viennese type of pianoforte, which was for long such a favorite
over the heavier and more solid English style on account of its
surprising delicacy and lightness of touch. After her marriage, Nanette
Stein, in partnership with her husband Streicher, made many other
improvements, and her pianofortes were used by Beethoven and others.
The firm of Streicher still existed in Vienna a few years ago.

At this point, namely at the beginning of the nineteenth century,
we begin to hear of three revolutionary figures; a Frenchman, an
Englishman and an American. These are Erard, Broadwood and Hawkins.

Pierre Sebastian Erard settled in Paris during the latter part of the
eighteenth century as a maker of harps and harpsichords. Shortly before
the breaking out of the French revolution, Erard came to London and
began to make harps and pianofortes. In the meantime he was continually
working to improve his instruments and was responsible for many useful
inventions, such as the up-bearing to the strings by means of the
“agraffe.” His chief claim to the consideration of pianoforte makers
is due, however, to his invention of the “double repetition” action
which was perfected by him in 1821, after many years of unsuccessful
experiment. This action, with slight modification, is used at the
present day in all grand pianofortes, and its manifold excellences have
never been yet surpassed. Erard took out a large number of patents,
which were put into use by his successors, and the house founded by him
is still in existence and one of the most famous in France or indeed in
the world.

John Broadwood, the great English inventor and manufacturer, who also
has his name perpetuated in the continued and flourishing career of the
firm that he founded, was originally a workman in the shop of Tschudi
or Shudi, a London harpsichord maker. He rose from an apprenticeship to
the head of the house of Shudi and finally turned his attention to the
improvement of the pianoforte. He had early been the recipient of the
knowledge of Backers, the inventor of the so-called English action, and
when he came to build pianofortes on his own account, this experience
was made to bear practical fruit. Broadwood’s first achievement was
in the re-designing of the square piano of Zumpe. About the year 1780
he entirely altered its construction, set the tuning pins at the back
of the case, and added dampers and pedals. He next set about the
improvement of the grand, and divided the bridge, giving a separate
bass bridge and permitting the striking point of the hammers on the
strings to be adjusted with correctness, something that had never
been done before. This completed the divorce of the pianoforte from
the harpsichord. With the addition of the action invented by Backers,
Broadwood’s pianofortes became at once a standard of quality and
excellence and until the introduction of iron framing stood alone.

We now come to Hawkins. This remarkable man was an engineer of
Philadelphia, English by birth but American by adoption. In the year
1800 he produced an upright pianoforte, the first of its kind. This
instrument, though it was not a commercial success, was remarkable for
the fact that Hawkins in it anticipated so many of the ideas that have
since become essential to modern instruments. He had an independent
iron frame supporting the sound-board, a mechanical tuning device, and
metal action frames. His action, too, had many features that have since
been adopted. Unfortunately, the tone was so poor that the instrument
was a failure from the start. His ideas in regard to upright pianoforte
construction were not allowed to languish, however, and the labors of
Wornum, who followed Southwell, were at last successful in producing,
in 1826, a practical action which at once settled the destiny of the
upright. This action had as its peculiar feature the “bridle tape,”
which is now such a necessary element of the upright pianoforte. He
also introduced the centre pin and flange.

At this point we begin to come to the great dividing line between the
early and the modern pianoforte. The introduction of metal framing
marks this division and it is from here that the American instrument
begins its independent and extraordinarily successful career. Indeed,
the development of American instruments is bound up with the almost
concurrent progress of ideas as to metal framing.

Although the first application of metal to pianofortes, not
considering the unfortunately abortive invention of Hawkins, may
be credited to William Allen, an Englishman, yet we must look to
the United States for the pioneer in the modern conception of metal
bracing. The man in question, Alpheus Babcock, was a Boston maker and
had been originally an apprentice of Crehore, who appears to have
made the first American pianoforte. Babcock applied his invention in
Boston in the form of a cast metal plate for a square pianoforte about
the year 1822 and this date is most memorable in that it marks the
epoch of the strictly modern conception of the instrument. Continuing
the consideration of this National school of design, we find that
the celebrated Jonas Chickering produced, in 1840, a cast-iron plate
for grand pianofortes, having the string-plate, agraffe-bridge and
resistance-bars cast solid in one piece. This revolutionary invention
unquestionably paved the way for the wonderful American productions
of later years and at once placed the American pianoforte upon a
plane of excellence that has never been altogether reached by its
competitors in other parts of the world. European makers were at first
slow to appreciate the eminently valuable nature of the invention of
Chickering, and until lately the solid cast plate was not extensively
used in Europe outside of Germany. The house of Collard and Collard,
which had the services of Stewart, the assistant of Chickering for
many years, was, however, most progressive in this respect and for
long was the only London firm which made grand pianofortes with the
iron plate cast in one piece. The celebrated house of Broadwood, after
much experimenting, produced a form of iron plate for grands that
was somewhat different in principle from that of Chickering. In this
type, the body of the structure was cast complete, but instead of the
multiplicity of braces, we find only two. One of these runs parallel
with the line of the vertically-strung bass strings at the extreme bass
end of the instrument, while the other crosses the plate in a diagonal
direction from near the middle of the agraffe-bridge to the point of
greatest tension. Both of these bars are cast separate from the body of
the plate and secured to it by means of bolts and nuts. Such a method
has usually been characteristic of European as opposed to American
methods, but the Broadwoods, about fifteen years ago, brought out a
decided novelty in their “Barless Grand.” This remarkable instrument
has a plate of cast steel and is entirely without braces or bars of any
kind, the necessary stiffness being gained through the tensile strength
of the metal employed and the use of a number of turned up flanges
along the sides of the structure, these being screwed into the case of
the pianoforte at equal intervals on its periphery.

As to the further development of the grand pianoforte, we may look
to the progress of the Chickerings and the Steinways in America and
to the Broadwoods in England, the Erards in France and the Bechsteins
and Blüthners in Germany. These makers are considered here because
they have all contributed in no small degree to the development of
the instrument as an artistic product and because they have all
been responsible for some radical improvement that has later become
essential to the make-up of a good pianoforte. We need only mention
the Steinway cupola plate, fan-like disposition of strings, overstrung
bass, duplex scale and capo d’astro bar to give the reader some idea
of the many inventions that have sprung from the fertile brains of the
members of this house. The other houses, notably that of Chickering
in this country, and Broadwood in England, have been prolific in
improvements, and the development of the grand pianoforte has
consequently been rapid and successful from the musical and scientific,
no less than from the commercial view-point. The history of the type in
more recent years is familiar to all, however, and it is unnecessary to
enlarge upon it here.

If we have seemed, hitherto, to have neglected proper consideration of
the upright and square forms of pianoforte, the fault is more apparent
than real. For there are two good reasons why discussion of these types
should have been delayed. In the first place, the square is already
obsolescent if not obsolete, while on the other hand the development
of the upright into a commercially successful and largely produced
instrument has only come about in recent years. This sketch would, of
course, be incomplete without brief consideration of them and we shall
therefore devote some space to this end.

As has already been indicated, the square piano may be considered
as having a genesis quite distinct from the grand or upright. It
was developed, as we know, by Zumpe, whose purpose was to fit the
hammer action to the body of a clavichord. Thus, when we consider the
different roots from which the clavichord and spinet-harpsichord types
were themselves evolved, and the direct descent of the grand pianoforte
from the latter, the entirely separate and distinct growth of the
square is easily discerned. This distinction is most interesting at the
present day, when the glory of the square has departed and its days are
numbered.

The evolution of the square pianoforte in America has been recorded
with faithful detail by Spillane in his “History of the American
Pianoforte,” and the reader will find in that work an abundance of
material to satisfy any curiosity that may possess him. Incidentally
it may be remarked that the idea of cross-stringing the bass had been
applied to clavichords as early as the time of Händel; so that the
overstringing of the square pianoforte came about quite naturally,
especially after the improvements of John Broadwood the First. On the
other hand, this principle was for long overlooked in the design of
the other popular types; so much so, in fact, that European grands
and uprights are still to be found in plenty with straight stringing
throughout.

The chief reasons for the gradual decline in the popularity of the
square may be traced almost as much to social and economic as to
artistic and mechanical causes, although these latter had the greater
influence in shaping the ultimate destiny of the type. The square was
developed in the United States until the native American product left
all imitators and rivals far behind, but even at that the fundamental
defects of construction could never be overcome entirely. The great
gap in the middle of the structure, required for the passage of the
hammers, entailed dangerous weakness, against which no reasonable
weight of iron bracing has ever seemed to prevail. Again, the fact
that the bass keys, where the strength of the blow and the leverage
of the action need to be greatest, were the shortest of all, while
the extreme treble keys were longest, always tended to destroy the
touch proportions and entailed much counter-balancing and other
operations which were, however, but makeshifts at the best. Moreover,
the development of the grand type led to rivalry among those makers
who confined themselves chiefly to the square, with the result that
the latter was made more and more heavy and cumbrous in an effort to
catch up with the fundamental advantage which the grand pianoforte
possessed on account of its superior design. Besides, the square was
never a thing of beauty, and its increasing size was by no means an
advantage in this respect, so that when the rapidly growing population
of the great American cities began to make living room continually
more valuable, the claims of the small, powerful, elegant, and
moderate-priced upright soon were successfully asserted. As a last
consideration, it should be mentioned that the makers of square
pianofortes were never able to apply to it a mechanism having the
elasticity and rapid repetition that belong to the Erard grand action
or the tape-check device of Wornum, which is universal in the upright.

In view of all these disadvantages, it is no longer a matter for
wonderment that the upright pianoforte succeeded the square as a bidder
for domestic favor, while the larger and more highly evolved grand
remained the choice of professional musicians.

The commercial development of the upright pianoforte, as we have
remarked, began at a comparatively recent period. In this country,
owing to the popularity of the square, we find that the upright was
late in coming into favor. Its development, however, had been going on
in Europe since the beginning of the nineteenth century. The “cabinet”
piano of Southwell and the “upright grand” of Hawkins were examples of
early attempts in this line, but it remained for the genius of Robert
Wornum to place the upright instrument on a truly practical footing.
This was accomplished through his invention of “the tape-check action,”
which at once put the upright pianoforte upon an equal plane of
efficiency with the prevailing types and assured its rapid adoption. By
the end of the first half of the nineteenth century the upright piano
had become firmly established as the home instrument throughout Europe,
and about the same time began to appear among American products. As
soon as American manufacturers took hold of it, they set about making
vast improvements upon European models; and we may properly date the
modern development of the upright from this time. Americans were
responsible for the adoption of overstrung iron-framed scales, and for
the increase in size and power which now makes our best instruments of
this class equal, if not superior, to the grands of a few years ago.

The later history of the upright, not less than of the grand, is a
simple record of continuous improvement in details of workmanship and
material, in beauty of case design and in scientific construction of
scale. It is not necessary, for the purpose of this short sketch, to
enter into the familiar modern history of manufacturing the various
types of pianoforte, either in this country or abroad; but we may note,
incidentally, that European makers have adopted more and more American
inventions and improvements, so that the modern, up-to-date pianoforte
owes a great part of its present efficiency to the genius of the great
American makers, although these, of course, have worked along the great
principles that Broadwood, Chickering, Steinway, Weber, Knabe, Erard
and others laid down.

Thus we have surveyed, though truly in a somewhat hurried manner, the
interesting history of the growth and development of the pianoforte of
to-day. The reader will forgive the brief and sketchy nature of this
bird’s-eye view, when he recollects that our purpose in this book is
to lay down the correct principles of modern design, rather than to
analyze those principles from an historical standpoint. Some of the
laws that we shall have occasion to expound have already been noted
here. In the succeeding chapters these and others will be considered in
the light of their scientific and practical application.



CHAPTER III.

DESCRIPTION OF THE MODERN PIANOFORTE.


The pianoforte of to-day is the most complex and ingenious of musical
instruments. With the possible exception of the pipe-organ, there is
no existing tone apparatus that combines within itself the product
of so many varied industries. Both as to the raw material and the
finished parts, this instrument draws its tonal charm, in the ultimate
analysis, as much from the saw-mill, the machine shop and the iron
foundry as from the forest and the mine. Trees of the forest, ore
from the mines--even the wooly coats of the peaceful sheep--alike
contribute their share to the completion of the wonderful product of
musico-mechanical ingenuity that we recognize in the modern pianoforte.

In such circumstances as these, it is easy to understand that the
commercial production of these instruments is a formidable undertaking.
To the musical and technical skill that is essential must now be added
large capital and a great manufacturing plant. The moderate prices
at which it is at present possible to sell pianofortes would not be
maintained for a moment without this modern system of productive
concentration and distributive expansion. The application of such
business systems to the production of an essentially artistic structure
has had the double effect of cheapening the selling price and improving
the quality.

This is not the place to go into details of the organization of a
modern pianoforte factory, but we may very properly devote some
moments to a consideration of the main points of construction that are
observable in the pianofortes of the day. Critical analysis of these
points will be in order later on in the course of the present work. For
the moment we shall be content with obtaining a bird’s-eye view, as it
were, of that which we are later to dissect and criticise.

There are to-day two distinct and prevailing types of pianoforte.
These are the “upright” and the “grand.” Of the once popular “square”
it is unnecessary here to do more than say that the type has passed
into a state of obsolescence and is fast dying out. Both structurally
and tonally, it was most defective; and its popularity was due rather
to the imperfect development of the other types during the period of
its vogue than to any inherent advantages of its own. It has well and
faithfully served its appointed time, and we may properly leave it to
die in peace.

For the last thirty years in this country and for considerably longer
in Europe, the upright, succeeding the square as a home instrument, has
remained victorious. Its small size and great convenience, together
with the surprising tonal capacity that has been developed in it in the
United States, have universally commended it, and only the development
of the very small grand has lately seemed to be threatening its long
unchallenged supremacy.

The exterior form of an upright is familiar to all. If we strip from it
all the outer appendages, and then remove the action and keys, we shall
at once see that the instrument consists essentially of a sound-board
and a frame, the latter partly wooden and partly metallic, upon which
are stretched strings of regularly graduated lengths and thicknesses.
Attached to this framing are two more or less ornate wooden erections
which are denominated the “sides” of the instrument, while a horizontal
wooden shelf, called the “key-bed,” serves to join the sides and
support the keys and their frame.

The strings of an upright are arranged vertically from the top to the
bottom of the framing already described, with the exception of those
which serve the bass notes. These are strung diagonally over the treble
strings. It will also be observed that the strings become progressively
shorter as the scale ascends until the speaking lengths at the highest
notes are two inches or less. The thickness also varies directly as the
length. The material of which the strings are made is cast-steel wire,
and the overstrung bass strings are, in addition, covered with copper
or iron wire. These strings, in order that they may be maintained at
the proper tensions and in the correct positions, must be supported
by suitable framing. The demands of modern construction require that
the framing be most massive. We have already cast a hurried glance at
it, and may now proceed to describe it in more detail. First of all,
however, it is necessary to investigate the apparatus that amplifies
the sound waves projected from the strings and transforms them into
the pleasing tones of the pianoforte. We must, in short, examine the
sound-board.

We shall have occasion later, critically to examine and discuss the
resonance apparatus of the pianoforte. It is sufficient, therefore,
that we glance briefly at it here, so as to familiarize ourselves
with its general form and construction. The sound-board is usually
constructed of a sheet of spruce fir of varying thickness and arched
inwards towards the strings, the crown of the arch being at its middle
portion. It carries wooden bridges, over which pass the strings and
upon which the vibrations of these strings are impressed and which
serve to limit their speaking lengths. The side of the sound-board,
remote from the strings, is strengthened by the addition of a series of
strips of hard wood called “ribs,” which are tightly glued on to it.

All of this apparatus is fitted into a wooden frame technically called
the “back.” It consists of two horizontal beams, situated at the
top and bottom of the instrument and joined together with a number
of vertical wooden posts of great strength. Into this structure the
sound-board is secured in such a manner as to produce the arched shape
above described, and in such a manner also as to leave nearly the whole
of its surface free to vibrate. The top beam of the back is covered
with the “wrest-plank,” a wooden block built up of crossed strips of
hard maple into which are driven the tuning pins, or “wrest-pins” as
they used to be called.

The whole structure is then covered by the “iron plate,” which is a
massive affair cast in one piece and bolted all round to the sides of
the sound-board and back, and to the wrest plank at the top and the
bottom beam at the bottom. This plate contains the “hitch-pins,” over
which are looped the waste ends of the strings, and also the iron
bridge, which limits the upper extension of their speaking lengths.
The strings are arranged upon this elaborate foundation, looped over
the hitch-pins, passed over the sound-board--or “belly”--bridges, and
thence through the bearing-bar, up to the tuning-pins.

To the sides of this structure are glued the external walls. A wooden
bed for the keys is provided, and the action is secured partly to the
iron plate and partly to the key-bed. The pedals are placed upon the
bottom board, which is secured between the external walls or sides,
and the pedals are connected with the proper parts of the action. When
this has been done the construction of the instrument is essentially
completed.

The various kinds of upright pianoforte do not vary greatly in size.
In the United States the popular sizes vary between the extremes of
four feet ten inches and four feet in height, with sufficient width
to accommodate the eighty-eight notes that make up the modern compass
of seven octaves and a minor third. The multitude of different scale
arrangements need not be discussed here at all, nor is it necessary to
enter into any investigation of the various individual arrangements
and devices that different manufacturers fit to their instruments. All
these things will be treated in their proper order.

The grand pianoforte has always been the favorite of the composer and
the interpretative artist. In this type alone has it been possible to
combine the highest qualities of tonal beauty and mechanical ingenuity.
To-day the concert grands of our most eminent makers stand unsurpassed,
both as mechanical structures and as musical instruments.

The most obvious dissimilarity between the grand and the upright is,
of course, seen in the difference of their planes. The grand might
properly be called the horizontal pianoforte. Its strings are stretched
parallel to the plane of the floor and the hammers strike upwards at
them from below. The second conspicuous difference is in the function
of the exterior casing. We have already noted that this part of the
upright is chiefly required to complete the exterior ornamentation of
the structure, and secondarily to support the keys and action. The case
of the grand, on the other hand, is an essential part of the resonant
body of the instrument. It consists of a rim, bent to suitable shape
and built up of continuous veneers, running all round in one piece and
glued together at crossed grain until the desired number of layers and
the proper thickness are thus obtained. The whole of what corresponds
to the upright back framing, as well as the sound-board and iron plate,
are rigidly built into this continuous bent rim, and thus the whole
structure forms one complete resonant entity, entirely unified and
interdependent. The rim is made deep enough to permit of the insertion
of action and keys in the front portion, and a gap in the framing is
left for the hammers to strike upwards at the strings. The wrest-plank
is placed on one side of the gap and the sound-board occupies the
remainder of the space on the other side. The iron plate covers the
entire structure, wrest-plank included, and sustains the same relations
to the instrument as in the upright. Its shape, as also that of the
sound-board, is adapted to the peculiar outline of the grand, which
is so aptly implied in the word “fluegel” (wing), used in Germany to
designate the entire grand type.

Until a comparatively recent period the large concert size grand was
practically the only type of these instruments. The revolutionary
improvements initiated by the Steinways in the middle of the nineteenth
century paved the way, however, for the general introduction of smaller
styles. It was found possible to retain the characteristically full and
rich tone of the large grand--at least to a great extent--while its
inherent advantages in the matter of touch and action all combined to
assure the popularity of the smaller instrument among the more critical
and discriminating of the public. Doubtless, also, the remarkable
change in the housing of urban populations that has been so conspicuous
during the last twenty years had much to do with the general desire for
an instrument that should be less common than the ordinary upright and
that should at the same time be less cumbersome than the full-sized
grand. A powerful incentive was therefore given to manufacturers to
strive towards the perfecting of the small types, and we cannot deny
that they have succeeded in a remarkable manner.

It is true that there exists today a tendency to cut the size of these
small grands down to really impossible proportions. There is a limit
to the cutting down process; and it is apparent to the observer that
more than one maker is endeavoring to obtain a true grand tone from a
sound-board area and from string lengths that are such as entirely to
prohibit the attainment of this desirable goal. Of course, it may be
retorted that the term “true grand tone” is subject to variations of
definition. It may even be plausibly said that tone of any kind is too
intangible a thing to be limited by any definitions. Nevertheless, it
would seem that there is a very decided limit, and that when we arrive
at the point where it is no longer possible to obtain the fullness,
richness and volume of tone that we are accustomed to accept as the
distinguishing characteristic of the grand pianoforte, then, indeed, we
no longer have a true grand. Other instruments may have the outline and
the action of a grand, but if they have not the proper sound-board area
and string length, then they are merely (if we may perpetrate a bull)
“horizontal uprights.”

The very general description that we have thus given of the two
prevailing types of pianoforte has not been intended to serve as
more than what it so obviously is--a rapid bird’s-eye view of the
instruments as they appear to the casual observer. The reader may thus
prepare himself for the more definite and critical investigation that
is now about to be begun.



CHAPTER IV.

ACOUSTICAL LAWS OF SOUNDING STRINGS.


Sound is an impression produced upon the brain through the ear by
the motion of air particles excited by an external body. In the
transmission of sound from the vibrating or “sonorous” body to the
ear it is motion that is transferred and not the substance of the air
itself. In the same way there can be no sensation of sound without
the interposition of an elastic fluid such as air or water, and the
production of sound in a vacuum is, therefore, impossible.

Sound, in short, has no objective existence. We know it simply as a
sensation, primarily caused by certain physical processes, the nature
of which is comparatively familiar to us. We are aware of all that goes
on between a sounding body and the ear, but we know nothing of the
processes whereby these physical motions are transformed until they
become, within the brain, sensations of musical sound or of noise.

While so much of mystery clouds our conception of the nature of sound,
we may take comfort in the knowledge that to penetrate the enigma is by
no means necessary. Not even the musician requires such transcendent
knowledge. To the student of musical craftsmanship it is equally
non-essential. It is well, however, to recognize the fact that as
soon as we leave the sure ground of physical investigation, we become
lost in impenetrable mystery and find ourselves face to face with the
ancient, yet ever new, questions of our origin and destination. When
we reflect upon the essentially spiritual and unearthly influence of
music, we cannot but feel that, in the making of instruments to serve
this art, we are ourselves assisting, however blindly, at a more than
Eleusinian mystery.

The ear easily distinguishes between musical and non-musical sounds.
Nor does it fail to recognize differences in relative loudness or
softness of any given musical sound. Again, the relative degree of
acuteness or gravity is distinguished, and, lastly, the quality of the
same musical note when played upon two different instruments or when
sung by two different voices is no less easily observed.

Now we have first to ask ourselves in what the difference between
musical and non-musical sounds consists. We may say that a musical
sound is produced by regularly recurring motions of the sounding body
communicated to the air; or, more technically, a musical sound may
be defined as a sound produced by periodical vibrations. This may be
proved by holding a piece of cardboard against a rapidly revolving
toothed wheel. As long as the revolutions of the wheel are performed
at a comparatively slow speed the noise produced by the impact of the
cardboard is broken and disjointed; but as the wheel is caused to
revolve with greater rapidity the noise becomes gradually continuous
and assumes a definite pitch. By increasing the speed of the wheel we
cause a higher pitched musical sound to be produced. Now, if we arrange
a second card and wheel and cause them to be set in motion together
with the first we shall find that when the two wheels are revolved
at the same speed, they produce sounds of the same pitch. Thus it is
apparent that the pitch of a musical sound depends upon the speed of
vibration, or upon the number of vibrations per second. Without going
too deeply into technicalities it may be said that similar experiments
have enabled investigators to determine the behavior of sonorous
bodies in reference to all the other conditions that pertain to them.
Thus, in the case of strings such as are used in the pianoforte, we
are in possession of facts that make it possible for us to state
accurately the pitches that will pertain to strings of given lengths,
densities and thicknesses, which are stretched at given tensions. It
is unnecessary to go into details of the precise methods employed to
demonstrate these laws, and it will be quite sufficient to quote the
laws themselves. The reader is therefore invited to note carefully that:

  1. The number of vibrations of a string is inversely proportional to
     the length of the string.

  2. The pitch of a musical sound is proportional to the number of
     vibrations per second; the greater the number of vibrations, the
     higher the pitch.

  3. The number of vibrations per second of a string is proportional
     to the square root of its tension. That is to say, if a string is
     stretched with a weight of one pound it will give forth a sound one
     octave lower than the sound that it would emit if stretched with a
     weight of four pounds.

  4. The number of vibrations of a string varies inversely as the
     thickness of the string. So that if there are two strings of the
     same material and length and subjected to the same tension, and if
     the diameter of the first is twice the diameter of the second, the
     first will produce one-half as many vibrations as the second.

  5. The number of vibrations per second of a string varies inversely as
     the square root of its density. Thus, if one string has four times
     the density of another, the first will produce one-half as many
     vibrations as the second.

In addition to these valuable laws, there are certain others which have
reference to the actual musical sounds produced by strings. By means of
them we know the relative proportions of the strings that will, other
things being equal, give the various notes of the musical scale. If a
perfect musical string be stretched and excited into vibration it will
be found that an exact octave above the note that the whole string
gives out may be produced by dividing the string at its precise middle
point and causing one of the halves to vibrate. Now we have already
noted that the number of vibrations of a string is proportional to its
length, and it is therefore obvious that the halves of the given string
each have double the number of vibrations of the whole, and that,
consequently, the octave to a note is produced by either twice or half
the number of vibrations that suffice to produce the given note.

Carrying the experiment further, we may, by dividing the given string
at other points on its surface, obtain all the other notes of the
musical scale. It will not be necessary to repeat the explanation in
each case, and the reader will have no difficulty in comprehending
the following table, which gives the relative string length required
to produce the eight notes of the diatonic scale of C major, taking
the length of the complete string that gives the keynote as 1, and
considering all other pertinent conditions to remain equal:

    C        D    E    F    G    A    B     C
    1       8/9  4/5  3/4  2/3  3/5  8/15  1/2
  Keynote    2d   3d  4th  5th  6th  7th  Octave

At first sight it might appear that the above data ought to give us
all necessary information in regard to the phenomena of vibrating
strings. Undoubtedly, the difficulties that surround the pianoforte
designer would have little power to cause worry if there were nothing
more to learn. Our troubles, however, are but just now beginning, and
the difficulties that still exist are greater than any that we have yet
investigated. These difficulties have their origin in the _nature_ of
the sounds that are emitted by musical strings.

While we have been investigating the relative vibration speeds and
pitches that pertain to the strings under various conditions, we
have not as yet paid attention to any other difficulties that might
have their origin under entirely different circumstances. There are,
however, certain highly important phenomena which are determined
by the nature of the strings themselves, irrespective of all other
conditions. These phenomena affect the constitution of such sounds as
any musical string may produce. Sounds produced through the agency
of musical strings are not and cannot be simple sounds. And this
peculiarity arises from the fact that such strings in common with most
other agencies for the production of musical sounds are incapable of
performing perfectly simple vibrations. If a string vibrated as a
whole uniformly and all the time, its motions might be compared to the
rhythmic swing of a pendulum, and the sounds that it emitted would be
absolutely simple and absolutely pure. The fact, however, is that this
never occurs. No string ever vibrates as a whole without simultaneously
vibrating in segments, which are aliquot parts of the whole. These
segments, when thus vibrating, give out the sounds that pertain to them
according to their relative lengths; while the vibration of the whole
length of the string, at the same time, causes the production of the
sound proper to it, which is called the “prime” or “fundamental” tone.
The sounds produced by the simultaneously vibrating segments are called
“partial tones” or “upper partials.” In the case of sounding strings,
such as we are now investigating, the partials follow each other in
arithmetical progression and are produced by the vibrating of segments
the proportions of which may be expressed by the harmonic series 1,
1/2, 1/3, 1/4, 1/5, 1/6, 1/7, 1/8, 1/9, and so on ad infinitum. Now,
if we examine this series we shall see that the lower of the partial
tones that are represented by the various fractions must bear distinct
harmonic relations to the fundamental tone. It will simultaneously be
observed, however, that as the series is continued, the fractional
quantities become uniformly smaller, and the difference between any
pair of them (for the same reason) is smaller as the position of the
given pair is more remote from unity. Naturally, this means that the
partial tones represented by such fractional quantities are separated
by continually decreasing intervals. If the process is carried far
enough, the time comes when the interval of separation is less than a
semitone. Clearly, then, partial tones in this condition can bear no
proper harmonic relation to the fundamental tone. They are, in fact,
dissonant.

Here, then, we come upon a fact that has a very wide bearing. It is a
demonstrated acoustical truth that tone quality depends upon the number
and intensity of the partial tones that accompany the fundamental
during the sounding of any musical note. If, through any cause, these
high and dissonant partials are excited into undue prominence, they
may, and do, exercise a profound and maleficent influence upon the
quality of musical sounds. We shall later have occasion to confirm
the truth of this statement, and we shall learn, in the course of our
investigation, fully to appreciate its importance in the practical
problems of pianoforte design.

For the purpose of assisting the reader in the comprehension of the
above argument, the following table is given, showing the order of
succession and pitch of the partial tones of the note C (second line
below the staff in the bass clef). Taking the pitch of the octave above
middle C, for convenience of calculation, as 512 vibrations per second,
this gives us 64 for the C in question.

[Illustration:

  NAME OF NOTE
               ORDER OF SUCCESSION
                    VIBRATION PER SECOND
  C1            1     64
  C2            2    128
  G2            3    192
  C3            4    256
  E3            5    320
  G3            6    384
  B-flat3       7    448
  C4            8    512
  D4            9    576
  E4           10    640
  F-sharp4     11    704
  G4           12    768
  A4           13    832
  B-flat4      14    896
  B-natural4   15    960
  C5           16   1024
]

It should be observed that the seventh, eleventh and fourteenth
partials and their multiples cannot more than approximately be
indicated in musical notation, as they do not exactly correspond to the
notes that are written to represent them. We are obliged to be content
with an approximation to the true pitch of these partials and the
notation given here is as near as it is possible to approach.

A brief consideration of the facts thus presented will convince the
reader that a combination of any fundamental tone with its first eight
partials will produce a relatively harmonious effect. At the same time
we must observe that this harmoniousness is more and more obliterated
as the higher partials are permitted to sound simultaneously with the
others. In fact, it may be said that, although we can not and must not
eliminate the dissonant partials altogether, we should attempt to cause
the strings to vibrate with entire freedom only as far as concerns the
first eight partials, and less freely as far as concerns the others.

Now, in what manner can this desirable end be attained? To answer
this question we must first discover what pre-disposing causes, if
any, exist towards the favoring of any combination of partials at the
expense of any other.

In speaking of the automatic sub-division of a string into vibrating
segments, we omitted, at the time, to make mention of a fact which
should, however, be obvious to the reader; namely, that the various
points at which the sub-division occur are themselves motionless.

It would be more correct, perhaps, to say “apparently motionless”; for,
of course, if these dividing points or “nodes,” as they are called,
were entirely without motion, the formation of the vibrating segments
would be impossible. In most cases, however, the “amplitude” or length
of swing of the nodes when in motion is very much smaller than the
amplitude of vibration of the segments. Consequently, as the vibration
of the segments of a string is itself ordinarily invisible, the motion
of the nodes may be considered as inappreciable.

Now, these nodes exercise considerable influence upon the problems that
we are considering. For example, according to the researches of Young,
it appears that when a string is struck at any point all those partials
are obliterated that have their nodes at that point. Curiously enough,
however, it has since been found in the case of the pianoforte, that
those upper partials are not _necessarily_ eliminated that have their
nodes at the striking point. Undoubtedly, however, a properly chosen
node provides the best possible striking point, since its selection
permits the operation of its tendency to suppress those particular
partials that have their nodes at the same place.

A consideration of the phenomena already observed has caused us to
perceive that the highest partials of the compound tone produced by
a musical string do not bear precise harmonic relations to the prime
tone. As the successive sub-divisions of the string approach closer and
closer to each other, the tones thus generated are seen to be distant
by proportionately less intervals, until at length they cease to have a
close similarity to any tone of the musical scale. Consequently, as was
said before, they exercise a generally harsh and dissonant influence
upon the nature of the compound tone. We have already concluded that,
broadly speaking, we should aim to eliminate these dissonant partials
and, conversely, to favor the prominence of those which are more nearly
harmonic. The reasoning which has served to lead us to this conclusion
may profitably be carried a step further. If the highest partials are
non-harmonic, it is obvious that their presence or absence, their
prominence or the reverse, must necessarily exercise much influence
upon the actual quality of a musical sound; upon the individual color
which different generating agencies impart to the same musical note; in
effect, upon all the numerous gradations of what we are accustomed to
call harshness, hollowness or mellowness of tonal quality.

This inevitable conclusion has been fully substantiated by the
results of experiment. The labors of Helmholtz and Koenig have
demonstrated conclusively that the quality of a musical sound depends
upon the number and intensity of the partial tones that accompany
the fundamental. Thus the mystery of the individual tone coloring
that distinguishes the voices of different musical instruments or of
different persons is transferred from the realm of psychology to that
of science. In fine, it becomes clear that if we can govern the number
of the segments into which a vibrating string divides itself, and if we
can also control the amplitude of vibration of these segments, we shall
find it possible to alter the tone quality of a musical instrument at
our pleasure.

It has already been observed that the generation of certain partial
tones is assisted or retarded as the position of the striking point
on a string is changed. It may not be out of place to note that the
various other methods of exciting a string, such as plucking, bowing,
etc., permit the production of equally variable effects as the points
at which they operate are changed. Our inquiry, however, is confined to
the pianoforte, and we shall therefore continue to limit ourselves to
the cases of pianoforte strings as struck by the usual hammers.

The matter of choosing a proper striking point was first systematically
investigated by John Broadwood, founder of the celebrated house of that
name, in the early part of the nineteenth century. Until that time the
pianoforte makers had, apparently, paid no attention to this important
problem and had been content to follow in the steps of the builders of
harpsichords and spinets. Examination of any of the instruments that
are direct ancestors of the pianoforte will show that the strings are
struck, indifferently, at any point from one-tenth to one-half of the
speaking length. The only exceptions appear to be those clavichords in
which the strings are all of the same length and in which the tangents
on the keys impinge upon the strings at different fixed points to give
the corresponding notes of the scale. Since the time of Broadwood,
however, the vast importance of correctness in this particular has come
to be recognized with more or less unanimity.

The investigations undertaken by this eminent maker convinced him that
the ideal striking point lay between one-seventh and one-ninth of the
speaking length of the string. Now, our investigations have shown us
that the most harmonious and agreeable compound tone is that which is
formed by the combination of the first eight partials. It would seem,
therefore, that one-eighth of the speaking length would be more correct
than the approximation that was arrived at by Broadwood. Theoretically,
indeed, the latter is nearer to the ideal point; is, in fact, the
ideal point. For obvious mechanical reasons, however, it is usually
impossible to hit this point with exactitude, and the approximation
suggested and used by Broadwood has been proved, by the practice of the
best makers, to offer the nearest practical solution.

We may, then, lay it down as a rule to be followed that a point as
nearly as possible midway between one-seventh and one-ninth of the
speaking length of the string should be chosen and adhered to as the
proper place where the blow of the hammer should be struck. If this
rule be faithfully followed the greatest obstacle to purity of tone is
removed and the most harmonious and agreeable combination of partials
is in a fair way to be secured. Nevertheless, it is necessary to make
an exception for the highest notes on the piano. Practical experience
has shown that one-tenth is a better striking point for the very
highest and shortest strings.

Thus we have been able to enunciate and discuss the principal laws that
govern the activities of sounding strings, particularly those of the
pianoforte. As the argument is developed, it will often appear that the
theoretical exactitude of the rules here laid down must be modified
in practice. Such a condition is always inevitable as between a body
of laws and the application thereof. It will be found, however, that
the variations to be recorded are not generally very important, and
the reader will be well advised to make the rules enunciated in this
chapter his continual leaning post and guide.

The most conspicuous difference is, perhaps, that which exists between
the theoretical and practical results of halving string lengths to
obtain octaves. In practice it is found that pianoforte strings
generally sound a little flat of the octave when divided at exactly the
middle point. But the variation is the fault of the steel wire and not
of the rule.



CHAPTER V.

THE MUSICAL SCALE AND MUSICAL INTONATION.


We have now considered as much of the phenomena of musical sounds
as may be considered to have a bearing upon the purpose of our
investigations. We may then devote some space to the matter of the
expression of musical ideas, and the intonation which has been devised
in order to reduce the mental products of composers to the limitations
of musical instruments. Music is expressed through the medium of a
scale of tones, all of which bear definite relations to each other as
to pitch. The “diatonic scale,” which is the foundation of musical
intonation, is composed of a series of eight tones which are named
after letters of the alphabet, the last tone having the same name as,
and being the octave to, the first. The frequencies of these tones
always bear the same ratios, one to another, whatever may be their
positions within the compass of any instrument. Now, considering the
frequency of the first tone to be unity, the frequencies of the others
are in the following proportions:

  C   D    E    F    G    A     B   C
  1  9/8  5/4  4/3  3/2  5/3  15/8  2

If we now divide these proportionate numbers each by the other we have
the proportionate intervals that separate them. Doing this, we have the
following result:

  C      D       E        F      G       A      B        C
    9/8    10/9    16/15    9/8    10/9    9/8    16/15

Now, it will be observed that we have in the above table three
different kinds of interval represented by the three ratios, 9/8,
10/9 and 16/15. The first of these is called the major tone and the
second the minor tone, while the third is known as the diatonic
semitone. Following out these ratios, we may obtain the frequencies of
any diatonic series. We shall choose the scale of which C 528 is the
key-note. Its frequencies are as follows:

   C    D    E    F    G    A     B    C
   1   9/8  5/4  4/3  3/2  5/3  15/8  2/1
  528  594  660  704  792  880   990  1056

Knowing as we do the ratios and frequencies already calculated, it
is obvious that we may similarly calculate the ratios and frequencies
for the diatonic scale, of which any given tone is the tonic or
key-note. Before doing this, however, it is well for us to remember
that the diatonic scale is not adequate to all the requirements of
music. Musicians have found it necessary to interpolate other sounds
in between those which form the diatonic progression. The reason for
this is that music, in order that it may have the greatest possible
freedom of expression, must be written in a larger number of keys,
and must contain more distinct sounds than the diatonic scale is able
to afford. For these and other cognate reasons the chromatic scale
was introduced. The addition of five chromatic semitones, obtained by
taking the difference between a minor tone and a diatonic semitone,
gives the chromatic scale thirteen semitones from key-note to octave.
Unfortunately, however, the same number of keys upon the pianoforte
cannot provide us with thirteen pure chromatic sounds in every key.
This may be demonstrated as follows: The ratio of a chromatic semitone
is 25/24. The sharp of C 528 is, therefore, 550. But in the diatonic
scale of D (the major second in scale of C), C sharp has a frequency
of 1113-3/4. The octave below this latter sound is the C sharp, which
is one chromatic semitone above C 528. We know the frequency of the
latter to be 550. The frequency of the octave below C sharp, 1113-3/4,
ought, therefore, to be 550. But we know that the octave below any
given note has a frequency that is one-half that of the given note.
Now, one-half of 1113-3/4 is 556-7/8. Therefore, we see that there is a
difference of 6-7/8 vibrations per second between the C sharp that is a
chromatic semitone above C 528 and the C sharp that is the octave below
the major seventh of the scale of D, and which ought to be the same
sound, as it is in the same position on the key-board as the former.
By carrying the same investigation further we are enabled to perceive
that sounds of the same name are not identical when played in different
keys, or, rather, that the same name does not imply that the sound so
denoted means the same thing when it is considered in its relation to
any tonic different to that to which it was first related. There is
another difficulty also that confronts us in the problem of playing
pure sounds upon the pianoforte; that instrument, as we know, does not
provide us with different keys for the sharp of one sound and the flat
of the sound next above it. There is a general belief that C sharp, for
example, and D flat are identical. But this is not so. The flat of D is
a chromatic semitone below that note, while the sharp of C is the same
interval above the latter. By referring to our former calculations it
will be seen that the chromatic semitone ratio is 25/24. The sharp of
C is, therefore, obtained by multiplying the frequency of C by 25/24,
and the flat of D is likewise evolved by an inverse process, namely, by
dividing the frequency of D by the same ratio. This is equivalent to
adding a chromatic semitone to C and subtracting the same from D. If we
take the notes C and D from the scale of C 528, we have the frequencies
of C and D as 528 and 594 respectively. Effecting the multiplication
and division as above we see that C sharp has a frequency of 550, while
that of D flat is 570-6/25. That is to say that these two notes differ
by no less than 20-6/25 vibrations per second.

It thus becomes obvious that the expression of all the sounds within
the compass of an octave, in such a manner that absolutely correct
sounds in every key may be obtained, is a problem that calls for more
sounds than are provided by the pianoforte. As a correct understanding
of this most important subject is essential, a somewhat elaborate
treatment of it will be given here. The reader who takes the pains
to master the true inwardness of the problem of musical intonation
will have an insight into the matter which few pianoforte makers or
musicians possess.

“Just intonation” is the name given to that system whereby we are
enabled to command the expression of all the sounds that are required
to be heard within the compass of an octave in order that the degrees
of each and every possible scale may be correctly and exactly rendered.
It is not difficult to see that performers upon instruments which
do not have fixed tones should have no difficulty in adjusting the
intonation of every tone to correspond with the variations in pitch
required by the different positions in the scale that such tones may
occupy. Experiments have, in fact, been carried out with violinists
and it has been shown that artists upon this instrument do naturally
play the true diatonic and chromatic intervals when left to themselves
and when not forced to adjust their intonation to that of fixed tone
instruments.

In order to show with accuracy the total number of different sounds
that are required to produce “just intonation” in every possible key
the reader is invited to consider the following table, which shows the
smallest possible number of sounds that will give the true diatonic
intervals in twelve keys. The first note in each row is the key-note
and the last the octave thereto. The frequencies of those key-notes
that are not represented in the first scale (that of C) have been
calculated as follows:

  The key-note to scale of B-flat is the perfect fourth to key-note of
        scale F.
  The key-note to scale of E-flat is the perfect fourth to key-note of
        scale B-flat
  The key-note to scale of F-sharp is the octave below major seventh of
        scale G.
  The key-note to scale of G-sharp is the octave below major seventh of
        scale A.
  The key-note to scale of C-sharp is the octave below major seventh of
        scale D.

We therefore have the following results:

     C        D         E        F        G        A         B        C
    528      594       660      704      792      880       990      1056

  C-sharp  D-sharp   E-sharp  F-sharp  G-sharp  A-sharp   B-sharp  C-sharp
  556-7/8 626-3/64  696-3/32  742-1/2  835-5/16 928-1/8  1044-9/64 1113-3/4

     D        E      F-sharp     G        A        B      C-sharp     D
    594    668-1/4   742-1/2    792      881      990    1113-3/4    1188

  E-flat      F         G      A-flat   B-flat     C         D      E-flat
  625-4/9 703-45/72 781-34/36   833-   938-1/18  1042-     1172-   1250-8/9
                               25/27             11/27     59/72

     E     F-sharp   G-sharp     A        B     C-sharp   D-sharp     E
    660    742-1/2     825      880      990      1100   1237-1/2    1320

     F        G         A      B-flat     C        D         E        F
    704      792       880    938-2/3    1056   1173-1/3   1320      1408

  F-sharp  G-sharp   A-sharp     B     C-sharp  D-sharp   E-sharp  F-sharp
  742-1/2 835-5/16   928-1/8    990    1113-3/4 1237-1/3 1392-3/15   1492

     G        A         B        C        D        E      F-sharp     G
    704      792       880      938      1056     1173     1320      1408

  G-sharp  A-sharp   B-sharp  C-sharp  D-sharp  E-sharp     Fx     G-sharp
    825    928-1/8  1031-3/4    1100   1237-1/2   1375   1546-1/8    1650

     A        B      C-sharp     D        E     F-sharp   G-sharp     A
    880      990      1100    1173-1/3   1320   1466-2/3   1650      1760

  B-flat      C         D      E-flat     F        G         A      B-flat
  938-2/3   1056    1173-1/6  1258-8/9   1408   1564-4/9   1760    1877-1/3

     B     C-sharp   D-sharp     E     F-sharp  G-sharp   A-sharp     B
    990   1113-3/4  1237-1/2    1320     1485     1650   1856-1/4    1980

In order that the different sounds may more easily be separated,
they have been collated in linear progression, together with their
frequencies and the scales in which they or their octaves appear:

   1. The sound C       = 528       \       / C, F, G, B-flat.
   2.    "      C       = 521-11/54  |     |  E-flat
   3.    "      C-sharp = 556-7/8    |  A  |  D, B, F-sharp, C-sharp
   4.    "      C-sharp = 550        |  p  |  A, E, G-sharp
   5.    "      D       = 594        |  p  |  C-G
   6.    "      D       = 586-2/3    |  e  |  A, F, B-flat, E-flat
   7.    "      D-sharp = 618-3/4    |  a  |  E, B, F-sharp, G-sharp
   8.    "      D-sharp = 626-31/64  |  r  |  C-sharp.
   9.    "      E-flat  = 625-4/9    |  s  |  B-flat
  10.    "      E       = 660        |     |  C, G, A, E, B-flat
  11.    "      E       = 668-1/4    |  i  |  D
  12.    "      E-sharp = 696-3/32   |  n  |  F-sharp, C-sharp
  13.    "      E-sharp = 687-1/2    |     |  G-sharp.
  14.    "      F       = 704        |  t  |  C, F, B-flat
  15.    "      F-sharp = 742-1/2     > h <   G, D, E, B, F-sharp, C-sharp
  16.    "      F-sharp = 753-1/3    |  e  |  A
  17.    "      G       = 792        |     |  C, D, F, G
  18.    "      G       = 782-4/13   |  s  |  B-flat
  19.    "      G       = 781-34/36  |  c  |  E-flat
  20.    "      Fx      = 773-6/16   |  a  |  G-sharp
  21.    "      G-sharp = 825        |  l  |  A, E, B, G-sharp
  22.    "      G-sharp = 835-5/16   |  e  |  F-sharp, C-sharp
  23.    "      A-flat  = 833-25/27  |  s  |  E-flat
  24.    "      A       = 880        |     |  C, E, F, A
  25.    "      A       = 881        |  o  |  D
  26.    "      A       = 891        |  f  |  G
  27.    "      A-sharp = 928-1/8    |     |  B, F-sharp, C-sharp, G-sharp
  28.    "      B-flat  = 938-2/3    |     |  F, B-flat, E-flat
  29.    "      B       = 990        |     |  C, G, D, A, E, B, F-sharp
  30.    "      B-sharp = 1031-1/4   |     |  G-sharp
  31.    "      B-sharp = 1044-8/64 /       \ C-sharp

Thus we see that thirty-one different sounds are required to give the
true diatonic intervals in only twelve keys. But it is not necessary to
remind the reader that there are more keys than these used in music.
We have, in fact, not yet considered the keys of A flat, D flat and
G flat. The frequencies of the keynotes of these scales have been
calculated as follows:

 A-flat is the perfect fourth to E-flat, which as calculated above =
    625 therefore A-flat = 833-25/27.

 D-flat is the perfect fourth to A-flat, which as calculated above =
    833-25/27 therefore D-flat = 555-154/162.

 G-flat is the perfect fourth to D-flat, which as calculated above =
    555-154/162 therefore G-flat = 741-130/486.

We are therefore able to construct these following additional scales:

  A-flat   B-flat       C      D-flat   E-flat     F         G      A-flat
   833-     938-      1042-    1111-    1250-    1389-     1563-    1666-
   25/27   26/316    73/236    73/81     8/9     21/52    132/216   50/54

  D-flat   E-flat       F      G-flat   A-flat   B-flat      C      D-flat
   555-     624-      694-      741-     833-     926-     1042-    1111-
  154/162 640/1290   365/648  130/486  150/162  284/486  528/1296  146/152

  G-flat   A-flat    B-flat    C-flat   D-flat   E-flat      F      G-flat
   741-     823-      926-      988-    1111-    1285-     1389-    1482-
  130/486 3600/3888 1136/1944 520/1458 308/456  650/1458 1408/3088 260/486

By examining the last table the reader will perceive that we have
obtained fourteen new sounds. They are shown graphically in this manner:

  In the scale of A-flat the new sounds are B-flat, C, D-flat, F and G.
  In the scale of D-flat the new sounds are E-flat, F, G-flat, and A-flat.
  In the scale of G-flat the new sounds are A-flat, C-flat, D-flat,
        E-flat and F.

None of these sounds had been obtained in the scales given before and,
consequently, we have to consider that there are fourteen more sounds
to be added to the thirty-one that we have already found.

The above calculations would suffice to provide us with the diatonic
intervals in all the keys that are used in music. Harmony demands,
however, certain other intervals. These are minor thirds, minor
sevenths, dominant sevenths and minor sixths. Accordingly, if we desire
to probe the matter of just intonation to its depths, we must calculate
the sounds that are required to make up these intervals in such scales
as are now without them. Examining the tables already prepared, we find
that there are wanting the following members:

 Minor thirds to the key-notes of the scales C, D, E-flat, F, G,
    B-flat, A-flat, D-flat, G-flat.

 Minor sixths to the key-notes of the scale C, E-flat, B-flat, A-flat,
    G-flat, and D-flat.

 Dominant sevenths to the key-notes of the scales E-flat, F and B-flat.

 Minor sevenths to the key-notes of the scales A-flat, D-flat, and
    G-flat.

We shall have no difficulty in calculating the frequencies of the
required notes by the same processes that we have followed heretofore.

                      Minor           Minor       Dominant        Minor
   Key-notes--       thirds--        sixths--     sevenths--    sevenths--
                    6/5 Ratio       8/5 Ratio    16/9 Ratio     9/5 Ratio

        C            E-flat          A-flat
       528          633-3/5         841-4/5

        D               F
       594           712-4/5

     E-flat          G-flat          C-flat        D-flat
     625-4/9        750-4/55       1000-32/45    1111-80/81

        F            A-flat                        E-flat
       704           844-4/5                      1251-5/9

        G            B-flat
       792          950-2/5

     B-flat          D-flat          G-flat        A-flat
     938-2/3       1125-11/15      1501-13/15    1668-20/27

     A-flat          C-flat          F-flat                       G-flat
    833-25/27     1000-106/135     667-38/276                   741-64/243

     D-flat          F-flat      B double flat                    C-flat
   555-146/152     667-66/810     889-358/810                   988-359/810

     G-flat      B double flat   E double flat                    F-flat
   741-124/486   889-1330/2430    593-10/2400                 658-2908/4374


The result of these calculations may now be collated and summarized.
We find that there are no less than sixty-six separate sounds required
for the production of the necessary intervals in all the possible
scales. These sounds are thus classified:

  Different sounds in twelve diatonic scales                        31
  Sounds wanting to complete the diatonic scales of A-flat,
        D-flat, G-flat                                              14
  Minor thirds wanting in scales of C, E-flat, F, G, B-flat          6
  Minor sixths wanting in scales of C, E-flat, and B-flat            3
  Dominant sevenths wanting in scales of E-flat, F and B-flat        3
  Minor thirds wanting in scales of A-flat, D-flat and G-flat        3
  Minor sixths wanting in scales of A-flat, D-flat and G-flat        3
  Minor sevenths wanting in scales of A-flat, D-flat and G-flat      3
                                                                    --
      Total number of sounds in an octave                           66

Now the obvious conclusion to be drawn from this analysis is that
the true sounds of the just musical scales are very different from
any that we hear upon the pianoforte. Indeed, we may properly carry
the reasoning a step further. If the expression of all the degrees
of the true musical scales requires this formidable array of sounds,
then surely, the sounds that are produced upon the piano are not all
of the required true sounds, but are totally unlike any of them. For
it is evident that if the sixty-six true sounds within the compass
of an octave have to be reduced to the thirteen that are found upon
the pianoforte, the process of compression to which the former must
be subjected will force the latter into the position of so many
compromises. In fact, with the exception of the standard tone from
which all calculations and all tuning must start, and its octaves,
there is no tone upon the piano, as it is now tuned, which is identical
with any sound of the justly tuned scale. The process to which we have
alluded, and which is necessary to secure to the piano and all other
instruments with fixed tones the ability to perform music in all keys
which are desired for the proper expression of the composers’ ideas,
is called temperament. Upon the skill and cunning with which this
compromise with natural laws is effected depends the whole beauty of,
and the whole of our pleasure in, music as we are accustomed to hear
it. It would be vain to pretend that tempered intonation is preferable
to that which is pure and just, but it is equally vain and foolish to
decry the accepted system of temperament until the mechanical skill of
manufacturers of musical instruments and the taste of performers have
risen to the point of appreciating the beauties of pure intonation and
of devising mechanical means of attaining it. Until that time arrives
we must fain be content to accept what we have and make the best of
it. There have, of course, been attempts to provide instruments that
could be used to give the pure intervals in every key, but they have
been invariably failures. Most of them have been forced to depend
upon tempered intonation to a certain extent, while others have been
mechanically impossible.

In any case we must remember that the pianoforte, as at present
constructed and played, depends entirely upon an equally tempered
intonation. So strongly has the pianoforte entrenched itself in popular
favor, indeed, that music and tempered intonation have become, to most
people, exactly synonymous. It is proper that we should be able to draw
true distinctions, however, as the practical work of piano building
ought to be largely guided by the considerations induced from the
necessity and fact of temperament.



CHAPTER VI.

THE EQUAL TEMPERAMENT.


As was suggested in the last chapter, it becomes necessary to effect
a compromise between the demands of true musical intonation and the
limitations of musical instruments, in order that the performance of
music may be made practicable. The equal temperament, now universally
employed, has only risen to its present commanding position within the
last century. It seems to have been first used by Johann Sebastian
Bach. Händel did not know it, and it struggled throughout the whole of
the eighteenth century with the mean-tone system.

Temperament systems were, however, invented and used long before this
period. Pythagoras, the Greek pre-Christian philosopher, was one of the
earliest experimenters along these lines. The method that he devised
has come down to us, and we are thus able to see wherein lies the
difference between it and the modern diatonic scale. Without going into
too much detail, we may note that the Pythagorean system recognizes
only two intervals; namely, the tone and semitone. The diatonic scale,
as we know, has a major tone, a minor tone and a diatonic semitone. The
Pythagorean scale contemplates perfect fifths and sharped thirds, and
is incapable of the effects of modern harmony.

The next attempt to adapt the necessary compromise in the interests
of practical music was introduced after the modern diatonic scale
had become the standard method of octave-division; that is to say,
some time in the fifteenth century. It has been variously called the
“mean-tone,” “mesotonic” and “vulgar” temperament. In this method
the tone is a mean or average between the major and minor tones of
the diatonic scale. The fifths are all flattened, while the thirds
are justly tuned. Such a system possesses both advantages and
disadvantages. On the one hand, the nearer and more frequently used
scales are purer and more agreeable; on the other hand, the remoter
scales are exceedingly dissonant; so much so, in fact, that they cannot
be employed with pleasure to either the performer or the hearer. So
long, however, as the music is written in the commoner scales the
mean-tone temperament, possessing the great advantage over other
methods of having pure thirds, is far more agreeable to the ear. In
fact, up till a few years ago it was not uncommon to find organs in
village churches in Europe that were still tuned according to this
system. The mean-tone system first made harmony, as we understand it,
practicable, but as the knowledge and imagination of composers widened,
the desire naturally arose to take advantage of the greater powers for
harmony that could alone be afforded by the unrestricted possession
of all possible scales. A substitute for the mean-tone system had,
therefore, to be found, and thus arose the modern and accepted method,
universally known as the Equal Temperament. By this method, which is at
the present time universal, the octave is divided into thirteen equally
distant semitones or half-steps. All distinctions between major and
minor tones and diatonic and chromatic semitones are swept away, and
it is assumed that the sound between any two sounds in the scale is
equally sharp and flat respectively to the sound immediately preceding
and following it.

This method, of course, implies a rearrangement of the whole scale,
for it is necessary to alter the precise pitch of every sound within
the compass of the octave in order that the equalization may be
effected. Thus it comes about that the equally tempered scale has only
one interval tuned purely. This interval naturally is the octave. All
the others require to be sharped or flatted in varying degrees. Every
chord, every interval, with one exception, therefore, is more or less
out of tune. The effect of this system of tempering cannot very well
be noted accurately upon the pianoforte, owing to the evanescence of
that instrument’s tone; but the organ often shows the dissonance of
certain intervals and chords in a most distressing manner. Perhaps
the worst of the defects of the Equal Temperament are exhibited in
the inability clearly to distinguish between true consonances and
true dissonances. Where the actual distinctions between the true
intervals are fused together it is impossible that there should be such
distinctions between them as the true scale shows, and, consequently,
we often are obliged to miss many delicate shades of comparative
consonance or dissonance that would be clearly exhibited in a scale in
which the intervals were represented with fidelity. We already know,
however, that no such method is at present possible, and we must fain
resign ourselves to the compromise that we have, and hope for better
things in the future. But at the same time, the Equal Temperament
possesses not a few positive virtues. As explained above, there can be
no difference between the sharp of a given tempered sound and the flat
of the tempered sound one whole step above the former. In other words,
the sharp of C in the Equal Temperament must be the same as the flat
of D, for these two sounds are assumed to be equally distant from the
sound which is between them, and the three are simply part of a series
of equal semitones. This being the case, the ambiguity that arises from
the identity of these sounds is very often found to be invaluable for
the purposes of quick and convenient modulation. There are instances
in which the connecting link between two modulations would entirely
be lost without the peculiar intonation that is afforded by equally
tempered sounds. It seems, in short, that the equal temperament,
imperfect and artificial as it is, cannot easily be replaced in the
existing states of our acoustical knowledge and of the mechanical
musical industries.

In order that the reader may more clearly realize the actual effects
of the Equal Temperament upon musical intonation, the following table
has been prepared, showing the differences of frequency between the
true sounds of the just chromatic scale and the corresponding tempered
sounds: (We are already familiar with the identity, in tempered
intonation, of the sharps and flats of adjacent degrees of the scale.)
C = 528 (Philharmonic Pitch).

      True Scale.                 Equally Tempered Scale.
  C              528            C                      528
  B              495            B                      498-7/32
  B flat         475-1/5        B flat--A sharp        470-7/20
  A sharp        458-1/3        A                      440
  A              440            A flat--G sharp        417-1/20
  A flat         422-2/5        G                      391-11/20
  G sharp        412-1/2        G flat--F sharp        373-7/20
  G              396            F                      342-4/10
  G flat         380-4/25       E                      332-17/20
  F sharp        366-2/3        E flat--D sharp        313-19/20
  F              352            D                      296-7/20
  E              330            D flat--C sharp        279-14/20
  E flat         316-4/5        C                      264
  D sharp        309-11/24
  D              297
  D flat         285-3/25
  C sharp        275
  C              264

It would be without the province of our immediate purpose to enter
into any special discussion of the possibility of manufacturing
pianofortes that shall give pure intonation, as distinguished from
the tempered sounds that we have thus exhibited. We have already had
occasion to mention that the Equal Temperament has become so strongly
and intimately bound up with the performance of music, that the
majority of musicians are probably incapable of distinguishing between
the idea of pure as opposed to that of tempered musical sounds.

We have already pointed out, and reference to the various tables will
confirm the assertion, that the Equal Temperament imposes excessive
roughness of intonation upon very few of the musical intervals. Thus
the octave is pure, the fourths and fifths nearly so, and only the
seconds, thirds, sixths and sevenths are so rough as to be noticeable
to other ears than those of the professional pianoforte tuner.
Indeed it is very doubtful whether the musical public could ever be
universally educated to the point of appreciating the differences
between pure and equally-tempered fourths and fifths; while at the same
time it must be remembered that the second and seventh, at least, are
dissonances whether purely intoned or not.

We may properly question the actual advantage that the mechanical
attainment of just pianoforte intonation would produce; we may ask
ourselves what would be gained thereby for the cause of art, and the
answer does not appear to be other than that any conceivable benefit
must be so slight as to be practically negligible.



CHAPTER VII.

PIANOFORTE STRINGS AND THEIR PROPER DIMENSIONS.


The strings of a modern pianoforte are made of cast steel and possess
a relatively great thickness and stiffness. That is to say, they enjoy
these characteristics to a far greater degree than do the strings of
any other musical instruments that employ such agents for the purpose
of generating musical sounds. The strings of any member of the viol
family, for example, are so totally unlike those of the pianoforte that
no comparison of their respective behavior when subjected to tension
can be of interest to any save the scientist. In dealing with the
strings of the pianoforte then, we face an isolated and unusual problem
which we shall have to consider at some length. We shall investigate
the peculiar effects produced by the high tension, great thickness
and great stiffness of the strings, as well as the singular phenomena
exhibited in the case of the covered bass strings. We shall note that
the strings are responsible for many unpleasant things of which they
are seldom accused, and that their proportions as to length and tension
do not comprehend in themselves the whole problem that the scaling of
them presents to the designer. This matter of the internal nature of
the steel and other wire has not, unhappily, received that attention to
which its importance justly entitles it. No treatment of the principles
of pianoforte design could be considered complete, however, without
some discussion of the phenomena thus presented. The investigation
which we shall undertake will lead us to the development of more of
those general principles that we are now engaged in enunciating, and we
shall then be able to formulate certain rules of wide application which
may be employed in the practical consideration of the problems with
which the whole matter of pianoforte design abounds.

As is generally known, the strings that are charged with the duty of
emitting the sounds comprehended within the two lowest octaves on the
pianoforte are customarily constructed of a combination of steel wire
and some other, usually copper or iron. The latter is wound over a core
of the former wire, and this winding is graduated, as to the amount and
thickness of the material employed, according to the pitch to which it
is desired that each string shall be tuned. There is an obvious reason
for this procedure. For, as we have already shown, two strings whose
lengths are as 2:1 will, other things being equal, emit musical sounds
separated by the interval of an octave. Consequently, under perfect
mechanical conditions, the length of each string of a pianoforte should
conform to the rule thus indicated, and should be one-half or double
the length of that which produces the octave above or below it; the
absolute application of this rule, however, being subject to certain
practical modifications throughout the entire compass. These will be
discussed later.

Even in the absence of such considerations, however, this ideal
condition could not be attained. The mechanical difficulties presented
would always operate to forbid the carrying out of such an arrangement
throughout the whole compass of the instrument. For, to follow the
rule with entire consistency would necessitate a length of 256 inches
for the lowest C, on an assumed length of 2 inches for the highest
note of the same denomination. As this would imply a length or height
of the instrument of nearly 24 feet it is not difficult to see that
such construction is impossible. Furthermore, evenness of tone quality
would be seriously hindered if the lowest strings were of any such
dimensions. To secure equality of tonal result it is necessary, as
has been noted above, that we should be able to equalize, as far as
possible, the particular forms of vibration that pertain to each
string. Obviously, the nature of the blow that would produce a given
form of vibration in a string of 256 inches in length must be very
different from that which would produce similar forms in a string only
one-tenth as long. Again, to maintain such long strings at the required
tension involves mechanical problems that savor more of engineering
than of pianoforte building.

For these and cognate reasons, therefore, the practice has arisen
of artificially slowing the rate of vibration in the bass strings by
wrapping them with brass, iron or copper wire. Naturally, the form of
the vibrations excited in these wrapped strings is entirely different
from any that the plain steel wire is capable of producing. The iron
or copper wire is itself thrown into vibration both independently of
and together with the cord of steel, so that we have the phenomenon of
one string emitting two separate series of vibrations, with resultant
disarrangement of the generated upper partials and concomitant
production of beats in a more or less appreciable quantity. Now
if, in addition, the bass strings are not scaled with approximate
correctness as to their relative lengths, thicknesses, and other
dimensions, it follows that there will be two distinct and different
causes of dissonance and unevenness of tone-quality, either of which is
sufficient, in itself, to produce very unpleasant tonal results. It is
clear, then, that particular attention must be paid to the designing of
the string arrangement, if excellence of tone-quality is to be anywhere
approached.

It is, fortunately, possible to give quite precise directions for the
calculating of string dimensions. As a preliminary, we must remind the
reader of the rules that were laid down in Chapter IV, relating to the
behavior of stretched strings. It will be recalled that we had occasion
to observe that these rules would require certain modifications in
practice, as they referred only to ideal musical strings which are of
perfect flexibility and perfect uniformity, and are stretched at an
absolutely constant tension.

The first modification that appears upon investigation has reference
to the division of string-lengths. It has already been pointed out
that, in practice, we cannot obtain the octave above the fundamental
tone of a given pianoforte string by dividing it exactly in the middle.
Conversely, an exact doubling of the length does not produce the exact
octave below the given fundamental tone. This discrepancy occurs on
account of the fact that the shortening or lengthening of a given
string causes a corresponding change in the tension at which it is
maintained and in the density of adhesion of its molecules.

Now if we double the length of a string in order to obtain the octave
below its fundamental tone, we decrease its tension, and this causes
a slowing of the frequency of vibration. Then again, the increased
resiliency of the string brought about by the lengthening tends also to
decrease the frequency. The frequencies of vibration of a string vary
directly as the square root of the tension, inversely as the thickness,
and directly also as the stiffness. These axioms being admitted, we
observe that to obtain an octave lower than a given fundamental tone,
we must obtain one-half the frequency that produces the fundamental.
Therefore, as we see from above, the double length must be decreased
by one-fourth to allow for the automatic decrease of stiffness which
varies directly as the frequency. And this modification must itself be
modified to compensate for the increase in frequency produced by the
very act of shortening. Therefore we must consider the tension, and
we find that to reduce this tends again to decrease the stiffness in
exactly the same proportions as it was before increased. But frequency
of vibration varies as the square root of the tension; therefore we
take the square root of one-fourth, which was the fraction first
arrived at. This root is one-sixteenth and is the differential factor
that must be subtracted from the ideal octave lengths, in order to
obtain the practical lengths.

It will be found of course, as must be apparent to the reader, that
the differential factor here suggested does not provide a complete
solution to the problem of allowing for the exhibited differences
between theory and practice. It does, however, provide a true guide to
the lengths. There is of course a difference of produced frequency to
be allowed for yet. Fortunately, however, this is provided for by the
graduated thicknesses of pianoforte wire. By taking advantage of this
almost geometrically proportioned graduation of diameter we are able to
calculate a stringing scale that, if adhered to, will give the nearest
possible approximation to complete harmony between theory and practice.
That is to say, we can proceed with a string-length calculation based
upon the differential factor already obtained, and then by arranging
the distribution of the string thicknesses according to the diameters
that are provided by the manufacturers of music wire, we may obtain a
true estimation, not only as to the thickness of wire to be used at
each place, but also as to the lengths proper to each string. Of course
the reader will remember that the matter of pitch is of considerable
importance in all calculations of this kind. A difference in pitch
implies difference of tension when the other factors remain equal, and
we therefore have calculated the following tables on the assumption
that the pitch to be used is that known as the International or C 517.
Attention is, therefore, directed to the following

TABLE SHOWING TRUE LENGTHS OF OCTAVE STRINGS FROM THE HIGHEST C STRING
TO THE LAST C STRING THAT IS USUALLY LEFT UNWRAPPED.

  C⁵                   =  2.048 in. = 2-1/25  + ... Approx.
  C⁴ =  2.048 × 1.9375 =  3.968 in. = 3-24/25 + ...    "
  C³ =  3.968 × 1.9375 =  7.688 in. = 7-17/25 + ...    "
  C² =  7.688 × 1.9375 = 14.875 in. = 14-7/8  + ...    "
  C¹ = 14.875 × 1.9375 = 28.820 in. = 28-4/5  + ...    "
  C  = 28.820 × 1.9375 = 55.828 in. = 55-4/5  + ...    "

[NOTE.--The length of the first string is chosen arbitrarily,
but as given is a very close approximation to the practice of the best
American makers. The vulgar fractions are calculated from the decimals
and the error in no case exceed about one-fiftieth of an inch. The
differential factor is, as we know, 1/16. Therefore we multiply by (2
[-] 1/16) or 1-15/16; in decimals 1.9375.]

The above table, then, affords us a reliable guide to the scaling of
the unwrapped strings. At the same time, however, it is not by any
means complete, for the reason that there is no method shown as yet for
the calculation of the other and intermediate string-lengths. We are,
however, able to accomplish this task by the aid of a very ingenious
rule proposed by the late Professor Pole, F.R.S. It is as follows:

The proper length of any string may be determined from that of any
other string, provided that the length and frequency of the second
string be known. Given these factors: Then,

(1) Take the logarithm of the length of the known string.

(2) Multiply the number .025086 by the number of semitones that the
sound to be given by the required string length is above or below the
sound produced by the given string.

(3) If the required string is below the given string, add together the
two numbers obtained; if it be above, subtract the second number from
the first; the result in both cases is the logarithm of the required
length.

For example, we have calculated already the proper length of C. In
hundredths of an inch this length is expressed as 2882. The log. of
this number is 45943. (This may be verified by any table of logarithms.)

    It is required to obtain the length of the string that,
    _caeteris paribus_, will produce one semitone above C.

                  45943      = log. of 2882
                  02508 (6)  = .02508 (6) × the number (1) of
                               semitones that required string
                               sounds above given string
                -------------
  By subtraction, 43435      = log. of 2718 = length of required
                               string in hundredths of an inch

                ∴ Required length for C-sharp = 27-18/100 inches

By reversing the process described above, and adding instead of
subtracting, the proper lengths for the semitone below and all others
in descending progression may be calculated with accuracy.

Having thus settled the matter of string lengths, we may proceed to
consider the questions of diameter. But it is first of all necessary to
warn the reader that the lengths that have here been calculated refer
only to such pianofortes as are capable, by reason of their size, of
taking the ideal string-lengths. Very small uprights, for example,
cannot be brought within that classification, except as regards the
highest of their strings. In all pianofortes, no matter what their
size, the higher strings are practically identical in length; but it
will be found that shortness of height in an upright or of length
in a grand begins, towards the middle of the scale, disastrously to
affect the string proportions. As already pointed out, there are
only two ways in which these disproportions can be overcome. These
are through alterations in the tension or in the thickness. But such
alterations necessarily disturb the whole tonal balance; and here we
find a very strong reason for the poor tone that the average atrophied
grand or upright possesses. Moreover, it must not be forgotten that
disproportionate thickness or unduly slackened tension affect the
actual nature of the vibrations that are set up within the string.
And the affections are operative both as to frequency and to form.
Therefore, naturally, bad tone and inability to stand in tune. This is
not intended as an argument against the small pianoforte; but it is
desired here to show that these little instruments, whether horizontal
or vertical, must not be expected to perform impossibilities. If we are
obliged to build small instruments, we must revise our calculations
and tabulate the string-lengths according to a different basis of
apportionment. For the purpose of the present work, however, the
calculations have been made on the assumption that the standard size of
pianoforte is to be designed.

Turn we then to the consideration of string diameters. The cast
steel wire that is used for the pianoforte strings is supplied in
definitely numbered and graded thicknesses. The numbers that are used
generally run from No. 13 to No. 24. According to the tests made at
the Chicago World’s Fair by the aid of Riehle Bros.’ testing machine,
the wire of these numbers was of the following diameters and broke at
the following strains. The wire manufactured by the firm of Moritz
Poehlmann, Nuremberg, Germany, has been selected from among the various
products that were subjected to these tests, on account of its superior
durability and evenness of gradation.

  Number   Diameter in fractions of an inch  Broke at strain of
    13                 .030                       325 lbs.
    14                 .031                       335  "
    15                 .032                       350  "
    16                 .035                       400  "
    17                 .037                       415  "
    18                 .040
    19                 .042
    20                 .044

Now it is a well known fact, and, indeed, obvious from what has
already been said, that the proportional relations as to length,
tension, diameter and breaking strain do not permit any other
arrangement for the scaling of wire than that which is universally
accepted by piano makers. That is to say, the shortest wires are taken
from the thinnest numbers, and vice-versa, the whole scaling being so
arranged as to secure for each tone that its strings shall be stretched
at approximately the same tension. Experience and the observations
of the most eminent manufacturers seem to have established that the
strain upon each of the uncovered strings should be maintained, as
nearly as possible, at 160 lbs. If this be done it will be found that a
pianoforte so constructed will produce the proper pitch at each string
when the lengths are as calculated in the tables referred to. It will,
of course, be necessary to arrange with due proportion the number of
strings that are to be taken from the wire of each number. It will be
found that the best practice takes into account the half sizes not
shown here and strings the instrument with an average of five tones
to each thickness of wire, beginning at 13 or 13-1/2 and continuing
down to the end of the unwrapped strings according to the general
directions suggested. Experience and the individual ideas of the
designer, assisted by such knowledge as this work aims to impart, are
the best guides that can be followed. Empirical induction, based upon
observation and experience, provides the only possible and practical
means for arriving at the true and proper arrangements to be made for
each individual instrument. This empiricism extends with particular
force to all string arrangements and is seen nowhere so conspicuously
as in the variety of methods that are adopted by manufacturers in
determining the number of strings within the unwrapped sections of the
scale. Thus, certain makers carry the wrapping over to the beginning
of the treble strings and have two or three string-groups provided
with wrapped wire before the overstringing is begun. The idea here
is either to correct original defects of scale design or to shade
down the break in tone that so often occurs at the point where the
overstringing usually begins. From observation of the practice of the
best makers, it may be said that the tone C below middle C is usually
the first overstrung tone. Of course, when the instrument is very small
it will often be found that it is impossible to give the last unwrapped
strings their proper lengths. In this case these offending strings may
either be covered with light wrapping or may be put bodily over into
the overstrung portion of the scale, in which latter case they will be
wrapped anyway.

Supposing then that the matter of the number of overstrung strings has
been determined, we may proceed to the consideration of the dimensions,
number and covering of the strings that are to serve here. We are
obliged to confess that the problem of attaining to good tone in the
bass is, indeed, difficult. It is by no means hopeless, however, as the
success of more than one eminent maker has already demonstrated.

The simplest, most obvious, and easiest way out of the inherent
difficulties of the scaling of bass strings is to be found in the
consideration of their proper lengths. It does not require very much
thought to perceive the truth that the longer the strings the less
weight need be imposed upon them. If, in fact, we make the bass strings
to approach as far as may be to the lengths that they would require
to have if unwrapped, we shall be able to reduce proportionally
the amount of artificial control that has to be exercised over the
vibration speed. Not only this, but the greater length thus attained
implies greater tension. That is to say that, as we saw before, the
tension at which a string is stretched acts to overcome the slowness
of vibration-speed induced by its greater length, and, consequently,
tends to generate a more regular progression of the upper partials (as
experiment has demonstrated), with resultant tendency to greater purity
of tone-quality.

We may, in fact, accept it as an axiom that the bass strings should be
as long and, simultaneously, as lightly weighted as possible, and that
the weight of them should be strictly proportioned to the pitch of the
musical tone that they are desired, at a given tension, to emit. As far
as the second clause of these conditions is concerned it is well to
remind the reader that limitations of space within the body of a piano
usually determine the possible lengths of the bass strings. So much so
is this the case, indeed, that it is not often possible to make any
great difference in their respective lengths. The best makers appear to
be agreed in a method of treating the problem that is at once simple
and effective. They recognize the great advantage of scaling the bass
strings at the greatest possible length, and then they take care that
the descending increase of length is no greater than to make the lowest
bass string one-fifth longer than the highest. At the same time they so
graduate the weight of the wrapping material that the same results are
attained as would naturally follow if they were as accurately scaled,
in proportionate length, as are the plain wire strings.

This equalization is, of course, only approximate. For the forms of
vibration excited in two strings of the same pitch will be different
whenever the various factors that govern the emission of sound by
them are variable. Thus when the factor of length is varied, no
counter-adjustment of tension, thickness or density can restore to
the string so modified the exact form of vibration that it may have
originally possessed. Consequently it becomes impossible to induce from
artificially weighted strings precisely the same series of partial
tones that a plain wire filament will emit, even when the tones
generated by the two strings are of the same pitch.

The lesson of this is plain. As perfection of tonal quality can only
be attained in part, it especially behooves us to pay strict attention
to such scaling of the bass strings as will furnish a complement of
sound producing agencies that may be relied upon to induce as nearly
as possible the same successions of partials as are habitually emitted
throughout the higher sections of the piano. Thus it becomes evident
that the greatest practicable length and the least practicable weight
are the chief factors that must govern the designer in laying out the
scale for the bass strings.

The relative densities of the wrapping material employed in the
manufacture of bass strings have been the subject of considerable
study. Brass, which was the earliest object of experiment, has long
been superseded by either copper or iron. As to the relative advantages
possessed by these two materials, it can be said at once that the chief
and almost the only advantage presented by the latter lies in its
relative cheapness. Acoustically, however, copper forms by all means
the most suitable material for the winding of bass strings, and this
for the following reasons: The specific gravity of copper is 8.78,
while that of iron is but 7.78. Again, the former metal, while inferior
in tenacity to the latter, possesses, on the other hand, the great
advantage of higher ductility, so that its elastic qualities are very
marked. It is thus evident that copper is a more suitable material for
the generation of musical sound than is iron, and the qualities which
we have just noted as pertaining to it are precisely those most useful
in the production of harmonic progressions of partial tones. It is
therefore clear that as between copper and iron all the advantages lie
with the former.

The thickest wire used for the uncovered strings is generally No.
24. In beginning the scaling of the bass strings, however, we choose
No. 17 or No. 18 for the notes nearest to the treble. The covering
is usually from No. 25 to No. 28 (standard, not music, wire gauge)
according to the size of the piano and the practicable string-length.
Of course, longer strings may be covered with lighter wire. The first
covered string is generally approximately one-sixth shorter than the
string immediately above it. This proportion, as suggested above,
may, however, be profitably disregarded, if it thereby be possible to
lengthen the bass strings. There are always two of these strings to
each tone and the thickness of covering wire must be progressively
increased as the scale descends. A descending increase of one number in
thickness of the covering wire for each pair of strings may properly be
allowed, unless the lengths are too closely alike, or vice-versa, in
which cases suitable modifications may be made. But assuming that the
descending lengths are arranged in arithmetical progression with a mean
of 3/4 of an inch, and supposing the highest covered string to be 45
inches long; then the suggested increase of thickness should under all
circumstances hold good. It may often be found, however, that the space
limitations of an instrument or other practical considerations make it
impossible to follow out these rules with exactitude. In any case, we
must remember that all such rules are themselves the fruit of empirical
observation and to such observations we must look, when it becomes
necessary to revise them in order to satisfy the requirements of some
particular situation.



CHAPTER VIII.

RESONANCE AND THE RESONANCE-APPARATUS OF THE PIANOFORTE.


We have now made a somewhat lengthy and thorough investigation into the
nature and behavior of the various materials and substances that are
employed in the construction of pianoforte strings. From this inquiry
we have been able to deduce a set of rules which, when practically
applied, will furnish us with a guide to the solution of many
perplexing problems which take their root in the conditions imposed
upon the designer by the limitations of space and the other mechanical
conditions of pianoforte construction. It would not be proper, however,
to proceed forthwith to the practical questions of support for the
strings. For we must still find the correct solutions of another series
of problems that spring, not from the strings themselves, but from
their important and necessary accessories, the sound-board and belly
bridges.

The belly-bridge is the medium of connection between the strings and
the sound-board. Through it the vibrations excited in the strings are
conveyed to the freely vibrating surface of the sound-board, and the
sonority of the generated sounds is thereby enormously increased. This
is the process in bare outline, but, in order to obtain a proper view
of the matter under discussion it will be necessary to examine the
phenomena to which the juxtaposition of strings, bridge and sound-board
give rise. We must, in fact, make another brief excursion into the
realms of acoustics.

The property which the sound-board possesses of reinforcing and
emphasizing the sounds generated by the strings is called “resonance.”
Important as this property of sonorous bodies is to musicians and the
makers of musical instruments, the fact remains that it is a matter
very little understood by the mass of them. This is the more remarkable
when one considers that, without resonant properties, no musical
instruments would be possible. For it is not difficult to perceive that
music, as we know it, could not exist were the means of expressing it
limited to the actual and immediate bodies that perform the motions
which are the direct causes of musical sounds. This fact is most
clearly illustrated in the case of the pianoforte. The unaided sound
of a pianoforte string is ridiculously feeble; in fact, it is quite
inaudible at the distance of a few feet. Yet we are all familiar with
the wonderfully harmonious and powerful sounds that the same string
will be the means of producing when aided by the sound-board.

Resonance may be defined as the property which one sonorous body
possesses of impressing its vibrations upon another sonorous body. The
existence of this power may be demonstrated in a variety of ways. The
most simple proofs are afforded by the pianoforte itself. For example,
if we strike any key upon the instrument and at the same time gently
press down the corresponding key one octave higher, so as to raise the
damper without at the same time raising the hammer, we shall find that
if the first key be released while the other is held open, the string
corresponding to the latter will continue to give its proper sound. In
this case the vibrations excited in the first string travel along the
belly-bridge until they reach the nearest open string whose vibration
rate is synchronous with that of the original sounding string. When
such a string is reached it is immediately impressed with the motions
excited in the former string, with the results above described. This
is a case of resonance of two attached bodies. Peculiar as it may
seem, however, it is not _essential_ as a preliminary condition to
the existence of resonance between them that two sonorous bodies be
tangibly connected. For instance, the foregoing experiment may be
varied by employing two pianofortes and choosing one of the sounds
from each. The result will be precisely the same. It will, however,
be noted that only such sounds as have either synchronous or nearly
synchronous rates of vibration will exhibit the phenomena of resonance
when separated from each other. Where they are connected, however,
especially when the connecting body is a sound-board prepared for
the purpose, synchronism is not necessary. In fact, it is a matter
of common observation that the sound-board of the pianoforte, in
conjunction with the belly-bridge, operates to set up more or less
intense vibration in every string within the compass of the instrument
when the dampers are raised, even if only one string be struck.
When the damper pedal is raised in playing, every string throughout
the instrument is immediately thrown into a state of vibration, and
begins to sound. The result is a large augmentation of the total
volume of sound produced. Of course, the sound of any one string thus
sympathetically excited is relatively feeble, but the total volume is
considerable, with especial strength in the particular partials of each
string that are more or less synchronous, as to their vibration rates,
with the sounds originally produced by striking the keys. When the
dampers are permitted to rest in their normal positions, on the other
hand, the sound-board exercises its resonant powers in a different
manner. Whenever a string or group of strings are struck, the board
is thrown into a state of vibration which affects only itself and not
the strings that remain damped. The result of this excitement is to
expose a relatively great vibrating surface to the atmosphere, with the
immediate consequence that the quantity of air impelled into a state of
periodic motion is multiplied many times. Thus the size of the impelled
layers of air, and the resultant sonorous waves is augmented until we
obtain sounds of the intensity and richness which we are accustomed to
associate with the pianoforte.

Now, from what we have already learned of the laws of tone-quality,
it is obvious that the resonant medium must be capable of reinforcing
not only the fundamental but the partials of all the tones which it
influences. To this end we must provide a substance that combines
elasticity with the freedom of vibration that is, of course, essential.
It is not possible to employ metal on account of its excessive
stiffness and consequent resistance to the influence of impressed
vibrations; while on the other hand a wooden body will not be
sufficiently stiff and rigid unless artificially strengthened. For this
reason it is customary to construct sound-boards of a freely-vibrating
wood (the spruce-fir is generally employed for this purpose) and to
strengthen them by fastening to one side bars of hard wood called
“ribs.” In this manner the requisite stiffness is imparted to the
board, which at the same time is sufficiently susceptible to the
impressed vibrations from the strings.

It is a fact that this accepted and universal form of resonance
table is essentially similar to that which was used in the ancient
harpsichord and spinet. While there has been much experimentation along
these lines, it does not appear that any lasting improvements have been
devised as yet, at least in the governing principles of sound-board
construction. We may then confine ourselves to a description of the
accepted styles.

The wood used in the construction of sound-boards is the spruce-fir,
which, as stated above, has been found to be the best possible for the
purpose. It is prepared in a sheet of suitable size, and is arranged so
that the grain runs approximately at right angles to the plane of the
belly-bridge.

It can easily be understood that the thickness of the board must vary
according to the dimensions of the strings that act upon it. In other
words, we can perceive that more resonating power is required for the
relatively weaker treble strings than for the relatively stronger bass
strings. The actual thicknesses vary with individual makers. From 3/8
inch in the treble to 1/4 of an inch in the bass may be regarded as
a fair approximation. Nevertheless, it is necessary to bear in mind
that these dimensions are subject to modification according to the
variations in the total amount of tension that the instrument is made
to bear. Other things being equal, an increased tension load implies a
thicker board, and vice-versa.

After the dimensions and material of the board are thus determined, it
remains to consider the bridging, the reinforcement, and the adjustment
of the board. We shall consider these in their natural order, as given
above.

The belly-bridges are placed upon the surface of the board, as we know,
for the purpose of conveying to the latter the minute blows that are
inflicted by the vibrating strings, in order that the vibrations may
be impressed upon the board and there amplified and intensified as
described at the beginning of this chapter. A secondary duty is that of
delimiting the lower boundaries of the speaking length of the strings.
The bridges must naturally be constructed with a curved outline that
is determined during the draughting of the scale. The actual shape of
this curve has no effect _per se_, upon the activities of the bridge,
but has to do entirely with the string lengths. The bridge which
carries the overstrung portion of the scale may be considered as being
similarly affected, as to outline, by the exigencies of the bass string
dimensions. The bridges are made of hard wood, and their sizes are
usually from one inch and one-quarter to one inch and one-half high,
and in width about one-eighth of an inch less all round. The variations
occur principally on account of the necessity which arises of giving a
bearing to the strings as they cross over the bridges.

It is necessary that the strings be raised at the bridges in order
that they may be firmly held at the points of contact by means of the
strain imposed by them on the surface of the bridge when they are
stretched at proper tension. Of course it is most essential that this
bearing be not too high, as in that case the strain becomes too much
for the board to bear with facility and its durability is thereby
impaired. The necessary immobility of the portions of the strings that
lie upon the bridge is secured by diverting the line of travel, and
causing them to bear against pins placed on either edge of the bridge,
so as to slant the line of the string as it passes over. The waste ends
should run parallel to the speaking-length after the bridge has been
crossed.

It may be further properly remarked that there are interesting and
complicated problems to be overcome in choosing the material and the
exact method of building the belly-bridges. It is desired to combine
extreme facility of vibration with the requisite resisting power. In
other words, the bridge must allow the fullest possible scope to the
impressed vibrations from the strings and, at the same time, must
possess such strength that it can successfully resist the torsions
imposed upon it by the pull of the strings. The only method that
appears to be thoroughly practical and, at the same time, acoustically
correct is one which most manufacturers have already had the acuteness
to adopt. The bridge, according to this method, is built up of a number
of layers of hard wood (generally maple) which are glued together in
such a way that the grain of each layer crosses that of the other.
In this way both the requisite strength and more or less facility of
vibration are obtained. But it has remained for one distinguished piano
maker to go a step further, and to apply thoroughly scientific methods
to the design of the belly-bridges. In the instruments made by him, he
has built the bridges in such a way that the impressed vibrations will
travel _in the line of_ the grain instead of across it. The bridges,
in fact, are built of end-grain and not, as is general, of cross-grain
wood. This ingenious and simple device facilitates the passage of the
impressed vibrations and, in consequence, tends to impart a greater
clarity to the various partials of the compound tones. Some existing
pianofortes might be greatly improved as to their clarity of speech if
a similar device for increasing the power of resonance were fitted to
them.

There is another point to be emphasized in reference to the bridges.
In some makes of pianos the line of the bridge construction is
permitted to be broken wherever there is a corresponding break in the
hammer line caused by the interposition of the various braces of the
iron frame. The obvious result of such a method of construction is that
the resonance of the board is much interfered with and the consequent
tonal efficiency of the instrument lessened. For it is easy to see
that if the bridge line be broken at any point, the vibrations that
are carried from any sounding string along the bridge to the surface
of the sound-board will be stopped at the break and will be unable to
reach those parts of the board that are remote from its path, with
rapidity and ease. Incontestably, therefore, the bridge line should, if
possible, be continuous. Many manufacturers, however, while apparently
recognizing the force of this proposition, seem to be afraid to follow
it out to its logical conclusion. They are willing to make the line of
bridge continuous until the end of the plain wire strings is reached.
After that point they seem to think that it is no longer necessary that
continuity of communication between the various sounding members of the
scale should subsist. This idea is, of course, quite fallacious. The
bass strings are simply a continuation of the higher ones, and are, in
fact, precisely similar except in regard to the details of thickness
and length. Moreover, it is quite as important that the portions of
the board over which the bass bridge exercises control should be made
freely resonant, as it is that this process should be applied to the
others. The bass bridge ought invariably, therefore, to be connected
with the bridges that serve the rest of the strings.

The reinforcement of the board is accomplished by gluing ribs of
wood across its back surface in a direction crossing the grain of
the board. These ribs are usually made about one inch square in the
middle portions. This size is continued until near the edge of the
board on each side, when they are gradually pared down in a graceful
curve until at the actual edge the thickness is no more than about
one-thirty-second of an inch. According to the most approved modern
practice it is found advisable to pocket these ribs into the wooden
framing of the instrument, by continuing them past the edge of the
sound board and making suitable apertures in the framing, into which
the extensions are adjusted and fastened. This has the effect of
holding the board more firmly in its fastenings and also of preventing
the early loosening of the ribs from their places; an occurrence which
causes much rattling, and complete impairment of tonal quality. It is
usual to have twelve ribs upon the surface of the board, but the number
may be varied whenever it is considered necessary. If it is required to
give specially ample support to the board on account of unusually great
strain, or for any other reason, the number may be increased, but such
procedure must be taken with caution, as too many ribs weight the board
to such an extent as to deaden its power of molecular and undulatory
vibration. This must at all costs be avoided.

It is usual to glue the ribs upon the surface of the board first--that
is before the bridges--and good practice dictates that the surface
of the board be dried out in a hot-box for at least 24 hours before
either of these processes take place. If this be carried out properly,
the resultant shrinking of the wood will be taken up after the board
has become thoroughly cooled, and if the process is repeated when the
board is glued into the framing of the instrument, the result will be
to endow it with a natural “crown,” or arch, caused by the re-active
swelling that takes place after the artificially induced shrinking.

Although the above methods of ribbing are to be considered the best and
as representing the most advanced practice, yet it will be found that
some makers dispose the ribs in a fan-like manner, having the diverging
points of the fan at the upper end of the board, while others adopt an
oblique disposition and arrange them as before described. Also, we find
a straight up-and-down arrangement whereby the ribs are glued parallel
to the plane of the treble strings. We term these three styles the fan
form, the oblique form, and the vertical form respectively.

As for the comparative advantages of the three types of construction
thus described, it may be said that they all represent individual
features that are more or less beneficial. For example, the fan-like
disposition gives a greater number of long ribs, while the oblique form
provides more of separate units. The vertical system may be considered
as a mean between the other two.

In general, we shall be well advised in remembering that the prime
function of ribbing is to increase the tension of the board and its
elasticity, and thus to promote the power of resonance. A secondary
function is that of providing extra resisting power. Now it is obvious
that both of these duties can be better performed by a multiplicity
of ribs, and consequently a system is to be recommended that permits
the employment of the largest total area of ribbing. At the same time
unduly long ribs are not good, for they have a greater tendency to
become loose and to spring up from the surface of the board, with
dire results to tone and durability. It would therefore seem that the
oblique disposition has more to recommend it than the others, since it
provides enough total ribbing area without imposing inconveniently long
ribbing units upon the surface of the board.

When the ribbing of the sound-board and the fixing of the bridges has
been accomplished, it remains to adjust the completed structure within
the wooden back-framing of the instrument. It is necessary that the
board be so secured that it shall acquire a position analogous to that
of a stretched membrane--at least as far as concerns the rigidity with
which its edges are fixed to the framing. There are several methods for
obtaining the required rigidity of the edges of the board. The natural
or artificial crowning of the board’s surface is best attained through
the medium of particularly rigid edge fastening; and the adoption of a
continuous closing rim for the board, as in certain grand pianofortes,
together with the use of a system of screw compression, alike indicate
the various directions in which the ideas of experimenters have led
them. The underlying notion in all these devices is to endow the
vibrating surface with both elasticity and durability to an extent that
could not be attained with the unaided wood.

The gluing of the sound-board to the framing is a process that demands
the greatest skill and care. It is essential that the board be warmed,
and that the glue which is used be in just the proper condition;
neither too thick nor too thin, and, above all, boiling hot. If the
fastening be done when the board is in the shrunken condition described
above, and with the required skill and care, it will be found that
the fibres of the wood have been squeezed together so as to raise
the center part of the board somewhat above the level of the edges.
This gives what we have denominated the “crown,” and is important as
affecting the durability and resisting power of the entire board. It
must be remembered that by relieving the sound-board of as much as
possible of the strain imposed by the strings, we are able to increase
its durability and to preserve its tone-producing quality more surely
than is otherwise possible. Boards that are not so protected must
inevitably become entirely flattened out in the course of a few years.
When this happens the level of the belly-bridge sinks and the bearing
of the strings upon the latter is destroyed. Hence an immediate and
inevitable deterioration of tone quality. For the altering of the
level in this manner affects the impression of the vibrations of the
strings upon the bridges and hence upon the board itself. If the
height of the bridges be too great, the bearing of the strings upon
them will likewise be excessive, and the board will be crushed down in
the same manner. If, however, the directions as to bridging, ribbing
and adjustment that have been given are followed with discretion, the
troubles outlined here are likely at least to be minimized.

Of course, the later care of the pianoforte after it is sold has much
to do with the manifold troubles that occur within the entire resonance
apparatus. These things cannot be foreseen, and it is, therefore,
most essential to guard against them as much as possible by careful
attention to the details of construction and adjustment.

Lastly, we may observe that the practice of screwing the bridges down
on to the board by screws driven in from the rear is to be condemned.
While it is undoubtedly advantageous to take some measure to increase
the permanency of the fastening, it will be found that it is far
better, acoustically, to provide the bridge with wooden dowels and glue
these into suitable holes in the board. Thus the conducting power of
the bridge is increased and the vibrating surface of the sound-board is
not broken up by the insertion of foreign metallic substances. Another
and concomitant advantage is the absence of the wooden washers under
the heads of these bridge-screws. Such devices are too often, as they
become loose, a source of rattling and jingling.

It is well to be rid of them, as of all possible things that are
likely to be similarly affected by wear or atmospheric conditions.



CHAPTER IX.

THE CASE AND FRAMING OF THE PIANOFORTE.


The grand pianoforte is distinguished conspicuously from the upright,
as far as concerns the principles of its construction, by the different
function which its exterior casing exercises. As was stated in Chapter
III, the exterior walls of the upright have no part in the bearing or
resisting work that the iron and wooden framing performs. They exist
chiefly for the purpose of giving support to the key-board and action,
and of affording a foundation whereon may be constructed the elaborate
architectural and decorative structure that, in its entirety, is
denominated the pianoforte case.

The synonymous portions of the grand pianoforte, on the contrary,
have a far more important duty to fulfill. While they are equally
charged with the support of the key-frame and action, they are also an
essential part of the wooden framing, are one and homogeneous with it,
and, in fact, occupy much the same position as what is known as the
“back” of the upright, as well as being the external and decorative
coverings of the instrument.

The case of the grand is constructed of a series of continuous
veneers, glued one upon another, and each extending completely around
the periphery of the case. These veneers are glued at cross grain to
prevent splitting and are applied to the pianoforte and bent into
shape when in a heated state. The complete outline thus obtained is
denominated the “continuous bent rim” and is a distinguishing feature
of the modern grand pianoforte as made in America. Several eminent
German makers, as Bechstein, also employ similar means of constructing
the external walls. In England, on the contrary, the case is usually
made out of one thickness of wood bent into the required shape by
steam and joined in several places. This system provides for separate
moldings for the bent and straight sides and for the rear portion.

The advantage claimed for the continuous bent rim is that the whole
case, by this means, becomes so closely bound up with the rest of
the structure as to become part of one homogeneous resonant whole,
thus improving the general resonance and imparting a _sostenuto_ and
_cantabile_ that can in no other manner be attained.

While data are lacking for the precise investigation of this claim, it
is significant that the bent rim method has not only become universal
among American makers--by one of them it was first devised--but has
even made its way into European favor.

The case, after it has been bent in this manner into the proper shape,
has to be decoratively veneered according to the style of ornamentation
that is intended for it. The work of veneering these cases, whether
for uprights or grands, need not be gone into here in detail. There
are so many specialists in this department who confine themselves to
the turning out of such veneered cases, and the whole matter is so far
away from the principles of pianoforte construction, that it is not
considered necessary to go into it here.

It is, of course, required to provide the case of the grand pianoforte
with a system of wooden struts which bind it together and give it
strength and resisting power. These struts are set into the case in the
general form of the letter A, having the apex at the forward end of the
case. At this apex they are crossed by another wooden strut running
parallel to the key-board, which serves to bind them together and to
mark the limit of the space to be occupied by the sound-board. These
struts are not, as we may thus see, carried into the very front of the
case, but are confined to that portion which is directly underneath
the sound-board. In front of this space is left the gap through which
the action is later to strike, and underneath is provided a key-bed to
carry the action and keys. The key-bed joins the front portions of the
bent rim and closes the casing in the front, thus providing a definite
and uniform structure. Above the key-bed and in front of the gap is one
of the most important parts of the entire instrument. It is called the
“wrest-plank,” and is situated at the foremost portion of the case.
This wrest-plank is built of a series of hard wooden layers, glued
together at cross grain and adapted to be bored with holes in which are
placed the “wrest-pins,” or tuning-pins, that control the tension of
the strings. This block or plank must necessarily be of great solidity
and be capable of holding the pins frictionally, so that they will not
pull round under the immense strains that are imposed upon them.

[Illustration: MODERN METHOD OF GRAND PIANOFORTE CASE CONSTRUCTION.

  A. Continuous bent rim.
  B. Wooden struts.
  C. Iron shoe holding struts and connecting with iron plate.
  D. Main beam.
]

The gap which is necessary in the grand pianoforte between the
sound-board and the tuning-pins makes it impossible to join the former
to the wrest-plank. This state of affairs undoubtedly constitutes a
weakness inherent in the grand and, besides, exceedingly unfortunate.
For an interruption of the continuity of communication between
the various sound-conducting materials of which the instrument is
constructed entails a corresponding loss of resonance. The tone of the
pianoforte is inevitably fleeting and evanescent; lack of continuity
in the construction only increases this fault. It has somewhere been
stated that the construction of the grand pianoforte implies greater
resisting strength of the wrest-plank on account of its being entirely
supported by the iron frame and not dependent upon a wooden back as
in the upright. This view seems to be incorrect. A properly supported
back on an upright affords a very strong support to the wrest-plank and
in combination with the iron frame supplies all necessary rigidity,
and in a manner more direct and efficient. But the wrest-plank of the
grand pianoforte may and should possess a sufficient strength. Various
makers have adopted several different methods to secure this strength.
One very good device supplies a rear truss to the lower surface of the
wrest-plank by means of a downward projecting shoulder cast in the iron
frame. There are other methods more or less similar. The arrangement
of the tuning-pins within the body of the wrest-plank also requires
considerable care. Of course, their disposition depends ultimately
upon the string arrangement, but there are problems to be considered
in connection with the manner in which they are arranged with relation
to their mutual positions as considered apart from the strings. For
example, it is most important that they should be so placed that the
strings do no rub against each other in their passage between the pins
and the agraffes. The frequent neglect of this matter is a cause for
regret. Much loss of tonal purity would be avoided and the tuner’s work
greatly simplified if all designers took the proper amount of care
in this important matter. Further, it may be remarked that the best
practice accords with this suggestion in every respect. It will also
be found that a slight tilting back of the pins in a direction that is
remote from the strings tends to lighten the pull of the latter and to
assist the resisting power of the wrest-plank.

When the iron plate is fastened over the entire structure, it is fixed
on to the wrest-plank by means of heavy iron bolts that should be
sufficiently long to go entirely through it and be closed with a nut on
the other side. By this means the wrest-plank is secured against lack
of rigidity, and its durability immensely increased.

The hardest kind of maple should be used in the construction of the
wrest-plank. No other wood appears to have so many of the required
qualities, and its use for this purpose has become, in America at
least, universal.

The general details of the external case of the grand pianoforte are
not unfamiliar. The standard full size of nine feet and the miniature
of six feet or less, as well as intermediate parlor sizes, are familiar
to all. The shape of the fall-board that covers the keys is well known,
and the design of the lid and supporting legs sufficiently common to
make further description superfluous. It is proper, however, to note
briefly the general change that has come about in the conception of the
decorative function of the grand pianoforte case.

Formerly, the aim of pianoforte manufacturers was entirely different
from that of the early harpsichord and spinet makers. Instead of
doing their utmost to improve the external æsthetic value of their
instruments, they seemed too much occupied in providing means for
internal improvement to pay proper attention to appearance. Thus we see
that the sombre and hideous decorative ideas which prevailed in the
furniture of the last generation were long faithfully imitated in the
external design of the grand pianoforte. The ugly and cumbersome carved
legs, the inartistic curving of the lid and arms, and the general look
of ponderosity and hugeness all combined to give to the instrument of
that era the general appearance of a hypertrophied coffin on legs.

Modern makers, however, animated by a truer appreciation of decorative
values, and recognizing the refining influence of beautiful things,
in themselves, and apart from their other properties, have gone far
towards consigning the more crude and hideous designs to the limbo of
obscurity. It has become generally recognized that the coffin-like look
of the concert grand may be largely modified, if not wholly removed. By
altering the design of the legs and by regarding them rather as a part
of the case than as mere supports, it has been possible to combine the
proportions of legs and case so as to make them appear one harmonious
entity. Of course, the actual method of attaining to this end has
varied largely among different makers, and, likewise, the greater
number of successful efforts in the direction suggested have been
made upon grand pianofortes designed to order to fit the furnishings
and decorative schemes of music rooms in the homes of the wealthy.
Nevertheless it is a healthy sign of the general æsthetic development
of the American people that the number of these specially ordered and
designed cases increases yearly. In this way we are going back to the
ideals that possessed the ancient makers of the virginals, clavichords
and other instruments, who were wont to call in the services of the
most famous artists in color and the most cunning carvers in wood to
compass their beautiful and costly designs.

It is true that the stock styles of grand pianoforte cases are usually
plain as to contour and decoration, but no one now can deny to them
grace and purity of outline or beauty and richness of material. On the
other hand, the practice increases yearly of keeping in stock cases
made in such styles as the Chippendale, the Sheraton and the Empire, to
say nothing of the perennial and truly American Colonial designs. The
fact that these numerous varieties all find purchasers is a striking
commentary on the growing taste and refinement of the general public.

In considering the case construction of the upright pianoforte, we
are led to observe that this type exhibits, in these matters, certain
important advantages over the grand. It is true that the case is not
so homogeneously fitted into the resonant structure, and it is equally
true that the grand has hitherto had much the better of it in the fight
for tonal quality and volume. Nevertheless, considering the upright in
the light of its own peculiar fitness for popular use, we are bound to
observe, in considering the construction of its case and back-framing,
the special advantages over the grand that we mentioned as existing.

The chief and most obvious of the inherent advantages of the upright
pianoforte lies in the position which the instrument takes up. The
hammers strike in front of the strings and tend to force them down
upon the bridges, so that the full energy of the blow is impressed
upon them. Further, there is none of that tendency of the strings to
fly off from the belly bridge which is always present in the square
and to a certain extent in the grand. Again the vertical position of
the sound-board would seem to be more favorable to the free vibration
of the wooden fibres of which it is composed; while the simplicity of
the general outline of the upright permits the employment of a larger
sound-board area than is possible with either the square or the small
grand. Lastly, the wrest-plank is greatly strengthened by the omission
of the gap between it and the sound-board, which permits the use of
lighter framing and a consequent gain in portability.

While recognizing these facts, however, we are bound to recognize many
other features that go far to destroy the great initial advantage here
described. It cannot be doubted that today the upright is pre-eminently
the popular type. Whether this fact is entirely a matter for
congratulation is doubtful, for the upright form lends itself readily
to cheap and trashy production. The conditions of modern domestic life
are such, on the other hand, that the portability and convenience of
the popular type, no less than the possibility of producing it cheaply,
have given it a hold upon the public fancy which its own inherent and
undoubted advantages might never have secured for it.

The upright form is capable of the highest artistic and mechanical
development, and there is no good reason why it should not be so
improved as to produce tones equal in volume, purity and richness to
those of the grand.

In considering the details of back and case construction in the
upright, we are compelled to observe instances of faulty method. For
example, it is usual to fasten the sides of the case to the back
by gluing after the latter has been fitted with the sound-board,
iron frame and strings. This method is obviously faulty. It is not
difficult to understand that, although the back partially sustains the
tensions imposed by the strings, the sides when glued to the former are
constantly subjected to a modification of these tensions. Now, gluing,
while convenient, is not the best possible process to give to the sides
the necessary strength to bear such strains, for it is a familiar
fact that pianofortes that are not of the highest class invariably
develop in the course of a few years, more or less serious cracks and
breaks in the continuity of the joins between the glued surfaces. When
this happens, the equilibrium of the instrument is disturbed and its
strength diminished. In addition, the breaks in continuity have, of
course, a serious effect upon the power of resonance. Furthermore, the
glue method is subject to various mechanical defects. It is absolutely
necessary that the surfaces that are to be united should be maintained,
during the process of gluing, at an absolutely uniform temperature.
And this temperature must be high. Consequently it is not hard to see
that in the haste and confusion of construction in the factory, the
large sides and backs may not be so carefully handled as to insure
the continual maintenance of the ideal temperature conditions. If,
in short, the surfaces to be glued together are permitted to become
cold, it is obvious that the adhesion will be imperfect, that the wear
and tear of constant usage will complete what carelessness in the
factory began, and that the value of the instrument will be permanently
impaired.

Before suggesting a remedy for these regrettable conditions, or a
substitute for the faulty methods described, it will be well to examine
carefully the principles that underlie the construction of the upright
pianoforte back. It will thus become less difficult to find some better
method of uniting the sides and back, so as better to conserve the
strength and durability of the instrument.

The back of the upright pianoforte might almost be considered as the
foundation of the instrument. Indeed, before the general introduction
of iron framing, this part of the construction deserved such a
description. Its position, however, is now somewhat subordinate, since
the wooden framing of which it is composed is quite inadequate to the
task of supporting the tension of the strings. As generally built, this
back consists of a number (usually six) of wooden posts arranged in an
upright position and joined at the top and bottom by braces, also of
wood and of similar dimensions. Thus is provided a compact frame that
may be made to possess great strength and resisting power. But, in
order to accomplish properly the duties for which it is designed, the
construction of this frame must be very carefully planned and carried
out. At its upper end it must give proper support to the wrest-plank
and the sound-board must rest easily and securely within its embrace.
The iron frame must then be fastened upon and over the structure.

It would be absurd to suppose that the back is not subjected to
modifications of the strains imposed upon the sound-board, wrest-plank,
and iron frame, and it is equally certain that carelessness in working
out the details of construction will tend materially to reduce the
coefficient of resistance.

An important detail is the joining of the upright posts to the top and
bottom rails. If these rails are made continuous and the posts are
tenoned into them, the frame will possess the maximum of strength that
is possible to such a structure, and if, in addition, the joints are at
all places made more secure by the use of screws and other devices as
supplements to the gluing, then we may consider that we have a properly
made back.

Unfortunately, however, examination of any considerable number of
pianofortes of various makes will soon convince the reader that these
details of construction are seldom given enough attention. Many
instruments will be found to have the back posts joined at top and
bottom by short pieces of wood which do not extend further than the
two posts which each unites. Such a method of construction, especially
when combined with careless gluing and an absence of other fastenings,
provides a frame that possesses none of the desiderata of homogeneity,
compactness and strength.

[Illustration: BACK VIEW OF UPRIGHT PIANOFORTE, KNABE PATENTS, SHOWING
RIBBING OF SOUND-BOARD AND CONSTRUCTION OF BACK FRAMING.]

The upright wrest-plank differs somewhat from the synonymous
structure used in the grand. It does not suffer under the disadvantage
of an involuntary and inevitable separation from the sound-board and
the lower portion of the back, but, when constructed with a due regard
for correct principles, forms one homogeneous and uniform structure.
The upright wrest-plank should, therefore, possess rigidity and
resisting power of the highest order, and should form an unyielding
support for the tuning-pins. The general construction of such a
wrest-plank will not differ materially from that which has already
been discussed in reference to the grand pianoforte. That is to say,
the building up of the body of the structure from crossed layers of
hard maple and the bolting of it into the iron frame (when the latter
is made so as to extend over the whole surface of the back frame) will
be done in the same way. But the upright wrest-plank derives from the
peculiar form of construction that is proper to the upright pianoforte
a further element of strength that is lacking in the grand. For it
is in direct and solid connection with the sound-board and the other
parts of the back-framing, and thus obtains a considerable addition of
strength. Indeed, the wrest-plank should be so constructed as to form
an integral part of the top rail of the back, and should be, in fact,
the front portion of this rail. Further, its connection with the rest
of the back-frame should be as close and binding as possible, and it is
most essential that a sufficient number of lag screws should be driven
into the wrest-plank and through the latter into the further and remote
parts of the back-frame top-rail.

Having thus analyzed the construction of the back in all its parts
and divisions, we may return to the discussion of the sides of the
case and the best methods of uniting them with the back. The reader
has now a good working knowledge of the construction, prior to the
putting on of the sides, and he cannot have failed to come to the
conclusion that gluing is a poor method for joining heavy sides to the
elaborate structure known as the back. Nor does there seem to be any
good practical reason why some other method should not be substituted
for the antiquated gluing. There is no good mechanical reason why a
system of screws should not be devised that would not only not mar the
outer appearance of the case, but also afford a more certain and secure
manner of uniting the sides to the rest of the instrument. Moreover,
such a method would largely increase portability by making possible
the removal of the sides when conditions of transport required this.
Manufacturers might profitably spend a little time in estimating the
saving that a detachable side would enable them and the dealers to
effect in their annual shipping and trucking bills.

The various sizes of upright pianofortes that are customarily found
range from nearly five feet in height down to about ten inches less.
Some very small models are made no more than four feet high. But
the public appears to prefer the larger styles, and in this they
are entirely right. For the very small pianofortes, no matter how
cunningly they be scaled, cannot be equipped with strings of the proper
lengths, nor with sound-boards of sufficient area. Hence their tonal
possibilities are very limited. The full sized upright, on the other
hand, approaches closely to the tonal excellence of the grand.

The styles of case decoration that are and have been applied to the
upright are even more striking and varied than those of the grand.
For the upright lends itself more readily to that kind of decorative
treatment that considers the whole case as one single entity, and
thus harmoniousness of design and unity of treatment are more easily
obtained. At the same time, we are bound to confess that the outline
of the upright is essentially box-like, and that this defect operates
continually to nullify the efforts of the designer to conceal it. It
is a fact that over-elaboration of decorative treatment is usually
accompanied by most unfortunate effects; while the larger styles at
least are little adapted to sustain the burden of meretricious exterior
adornment. In fact, we may well say that the upright is decoratively
at its best in the small sizes. Since, however, there is a public
demand for large models, which are indeed mechanically and acoustically
superior, we must be content to observe the progress of decorative
ideas as applied to the beautifying of these.

One of the most striking features of the modern decorative movement,
as applied to furniture, is seen in the great popularity of rare and
beautiful woods. These are much prized, and it has come to be popular
to finish them in such a manner as plainly to exhibit the natural
figurings and markings. We have even seen a craze for plain rubbing
with wax, which leaves the wood in absolutely its natural appearance.
Red and White Mahogany, Burled and Circassian Walnut, Satin Wood,
Bird’s-Eye Maple, Golden and Flemish Oak, and many other beautiful and
costly varieties are constantly made up into rich and elaborate pieces
of furniture. In this development the upright has had a large part.
While the large size and great first cost of the grand has made the
purchasing of specially decorated cases a matter to be avoided by all
except the wealthy, the same obstacle has not so largely existed to
frighten away the artistic would-be-purchaser of an upright. In fact,
the decorative movement has shown its best manifestations through the
medium of the upright pianoforte, and this in spite of the unfortunate
outline of the instrument that resists all efforts to conceal its
excessive crudity.

Models of the English schools have been produced with great success,
and the inlaying of rich woods, after the manner of Chippendale, has
resulted in some very beautiful specimens of this particular art.
Again, we find the so-called Renaissance, the Colonial, the Empire
(more elaborate than the other two), the Doric (severely simple), and
last but not least, the Mission. The latter, extraordinary perversion
of the handicraft of the Spanish fathers as it usually is found to
be, has nevertheless been the cause of one great good. It has begun
to popularize the dull finish, and to teach the public that the high,
glassy, fragile, and unreliable varnish finish is not the only possible
way of putting a surface upon wood. The Mission craze has taught many
people to admire the natural figure and markings of a fine veneer
or piece of lumber, without regard to the fact that it is or is not
covered with a mirror-like finish that cracks as soon as the room
becomes cold.

In fact we may discern the encouraging signs of a growing sanity
and refinement in the demand for, and production of, suitable designs
for the decorative treatment of pianoforte cases. It has come to be
recognized that a truly chaste and beautiful exterior is the fitting
complement to richness and nobility of tone. The growth of this feeling
deserves the highest encouragement from all. American makers may well
congratulate themselves upon being the foremost exponents of this
movement.



CHAPTER X.

THE IRON FRAME OF THE PIANOFORTE.


In the historical portion of the present work, ample reference has
been made to the genesis and early development of metallic framing in
the construction of pianofortes. We took occasion to point out that
the independent development of the American pianoforte is intimately
connected with the rise and improvement of the system. It is a matter
of no little pride to recall that in the universal recognition of
the value of metallic adjuncts to the framing devices of the modern
pianoforte, the Americans, as became their traditions, blazed the
trail. It is unnecessary to repeat the observations that were made in
Chapter II as to the controversies that have raged over the question
of priority of invention. It is sufficient to refer the reader back
to that portion of the present work where these questions have been
treated in a sufficiently copious manner.

We may therefore proceed directly to the task of investigating the
nature of the universal metallic framing that has been demonstrated to
be so essential in modern constructional systems. Following the plan
that we have adopted throughout, we shall first consider the nature and
application of this kind of framing to the grand pianoforte.

As to the form, then, of the iron framing, its weight and size. Ever
since the first grand pianoforte was produced with an iron plate cast
in one piece, designers have been busy with attempts to improve upon
the original invention. They have met with but moderate success. There
have been multifarious changes in the details of bracing and of fitting
the plate to the case, but the general form of the original design
remains the same. It may be described in general terms as follows:
A plate of iron cast in one piece, which follows the outline of the
instrument and is so arranged that it may be secured to the case and
to the wooden framing that underlies and knits together the latter and
the sound-board. A gap is left in this plate at the point where the
hammers strike the strings, and the resultant weakness is overcome
by a system of bracing by means of resistance bars, also of iron and
cast in the same piece with the main body. At its front end, nearest
to the key-board, the plate is extended so as to cover the wrest-plank
in which are driven the tuning-pins; and at the end remote from the
key-board it is provided with a number of hitch-pins, to which are
secured the waste ends of the strings. This plate, further, is so
arranged that the sound-board is not covered by it except at the edges,
and at the place where the bass bridge is constructed another gap is
left in its surface.

[Illustration: JONAS CHICKERING’S FULL SOLID CAST GRAND METAL PLATE.]

The above general description comprehends in bare outline the
essential features of the iron framing. There are, of course, many
variations of detail, and in seeking for the best methods of designing
this important part of the pianoforte we shall have occasion to examine
the greater number of these with some care.

[Illustration: SKETCH OF IRON PLATE FOR CONCERT GRAND, SHOWING GENERAL
ARRANGEMENT OF BRACES, BELLY-BRIDGES AND SYSTEM OF BOLTS FOR FASTENING
TO CASE.

  A--B. Hammer line.
  1. Body of plate.
  2. Bass bridge.
  3. Continuous treble bridge.
  4. Agraffes.
  5. Capo d’astro bar.

  Plate is cast in one piece and scale is overstrung.
]

Of the various differences of detail that designers have effected
in the construction of iron framing, one of the most important is
presented in the so-called “cupola” style of construction. In this
form the surface of the plate is raised at the edges of the case in
such a manner as to give the general outline of a cupola or semi-dome.
The result of this method is to increase the resonance of the framing
and, at the same time, greatly to enhance the tensile strength of the
whole construction. The “cupola” style was the subject of a patent by
Steinway & Sons of New York some years ago, but has been extensively
copied since that time. The same celebrated house was the originator of
another variation upon the classic manner of plate building. Instead
of arranging the strings in the usual manner, a fan-like disposition
was adopted, with the result of distributing the strain more evenly
throughout the entire surface and thus improving the tensile qualities
of the whole plate. All these methods of construction, however, have
failed to avoid that breaking up of the scale which is made necessary
by the interposition, between the string groups, of bars and bracings.
It has appeared impossible to obtain the requisite resisting power
without the assistance of a number of heavy iron braces cast into the
plate and designed to increase the tensile strength, which is weakened
by the gap at the striking points of the hammers.

[Illustration: ARRANGEMENT OF IRON PLATE, BRACES AND SCALE OF PARLOR
SIZE GRAND PIANOFORTE.]

There has, however, appeared an invention which would seem to overcome,
in an effective manner, the objections to a multiplication of bracings.
The inventor is a member of the celebrated house of Broadwood, and
his device is called the “Barless” or “open scale” grand pianoforte.
By this invention the barred iron frame is replaced by a plate of
mild steel, which is entirely free from bracings, is constructed
with a continuous turned-up flange and is bolted in the usual manner
into the bottom framing. This flange provides the necessary tensile
strength and apparently sustains the tension of the strings in a
perfectly satisfactory manner. The advantages presented by a method
of construction that avoids the breaking up of the string groups into
three or four divisions are obvious and need not be explained in detail.

It may be stated, however, that the principal and conspicuous advantage
presented by this method of construction is found in the fact that the
absence of the usual barring and bracing tends to subdue the metallic
and tinkling quality of tone that is so often found to be induced
by the presence of heavy masses of cast iron. At the same time, the
material employed is so much more elastic than iron that there is no
perceptible loss of resonance, nor is the tensile strength lessened
to any appreciable degree. No one who has tested the pianofortes thus
constructed has failed to be delighted with the singularly beautiful
tone-quality and remarkable evenness that is shown throughout the whole
compass. It is indeed a most difficult task to overcome the tendency to
production of unduly prominent dissonant partials in those parts of the
scale where the bracing is especially heavy, particularly in the lower
portions, and consequently we must regard with admiration so successful
an attempt to do away with these difficulties by removing their cause.

It may be noted at this point that the eminent firm referred to before
as having introduced the “cupola” form of construction, also employ
steel in the making of their metal frames, and it seems curious that
this example has not been more generally followed.

The two types thus described are the most radical exceptions to
the common style of metal framing. It is a matter of regret that
manufacturers in general have been content to follow so closely in the
footsteps of the pioneers, and have not experimented more energetically
with a view to effecting other improvements in the accepted methods.
The problem of sustaining the necessary tensions would undoubtedly
be simplified by the adoption, at least in part, of the ideas of the
eminent firms who have already been mentioned.

In order thoroughly to understand the actual advantages and
disadvantages of the various styles of framing that have been
described, we must consider how great are the tensions that they are
compelled to bear. A concert grand pianoforte of a standard American
make is so constructed that it bears a total strain, when tuned at
concert pitch, of not less than 30 tons. The requirements of increased
tone and the weight and bulk of strings tend constantly to augment
rather than to decrease these tremendous strains, and at the same time
more and more to induce the production of those dissonant partials that
have such a maleficent influence upon tone-quality. Obviously, then,
if we are to satisfy the popular demand for greater volume, and at the
same time to maintain the highest standards of quality, we must seek
for some method that will obviate the employment of yet heavier masses
of cast iron and at the same time preserve the necessary strength and
rigidity. The methods of construction that have been noticed at some
length above seem to present manifold advantages over the older styles.
Steel has greater tensile strength than iron, and consequently a
smaller bulk of it is required. Again, its elasticity is higher and the
vibrations impressed upon it traverse its surface with greater facility
and in a shorter period of time. Whether, therefore, we prefer the
barless or the cupola style of construction, we must recognize the fact
that steel is a better material than iron in any form.

Foremost among the requirements of a successful framing system are
that it shall sustain its burden with such rigidity that the strings
shall stand in tune and the wooden case of the instrument shall not
be twisted out of shape. Even if the material be the best possible, a
faulty method of securing the metal frame to the case will not only
prevent the consummation of these desires, but will tend to weaken the
sound-board and hasten its splitting. It is essential, in fact, that
the board should be relieved of strain, and great care must therefore
be exercised in fitting the framing. The approved method is as follows:
The framing is connected with the system of wooden posts that extend
below the sound-board and bind together the sides of the case. The
latter connection is made by means of long bolts that extend through
the bracings of the frame and are sunk into the posts at convenient
places. The sound-board is secured to the sides of the case by means
of its ribs, which are continued beyond its edges and pocketed into
the sides and the posts, and also by being glued to the bottom surface
of the case and to the system of posts. Lastly, the frame is connected
both with the board and the posts, by a series of heavy screws that
pass through the board and into the posts at regular intervals along
its outer edges.

This method of securing the frame and sound-board to the case ensures
that the former shall be incorporated within the body of the instrument
as rigidly as is possible, and that the latter shall have the fullest
protection against those twisting strains that the metal frame alone
ought to bear.

With such a method as has been described we can find no great fault.
It should be noted, however, that in the barless or open scale
construction the bolts that were described as passing through the
braces into the posts below are omitted, and the whole frame is
supported within the case by a series of bolts driven through the
turned-up steel flange at equal intervals in its surface.

Having thus considered the forms of framing that are employed by
various makers we may turn our attention to the matter of suspending
the strings across the frame and over the sound-board. The upward
stroke of the hammer of the grand pianoforte tends to drive the string
away from its bridge and thus to lessen the energy with which the
vibrations imparted to the string are impressed upon the latter. We
may note that all makers are agreed in giving to the strings of a
grand pianoforte an upward thrust or “bearing” in order that the blow
of the hammer may throw the strings against the upper surface of the
bearing-bridge instead of away from it. There are two devices that are
generally employed for this purpose. They are known as the “agraffe”
and the “capo d’astro bar.”

The first of these was the invention of the celebrated Erard of Paris.
It consists of a brass stud screwed into the iron framing (or into the
wrest-plank where the plate does not extend over the latter), at the
beginning of the speaking length of each string or group of strings.
This stud is bored with the required number of holes--one for each
string in the group. These holes are bored at such an angle that the
ends nearest to the tuning-pins are higher than the other ends, while
the pins are placed at a higher elevation than the agraffes. In this
manner the string is given an upward thrust as it proceeds toward the
tuning-pin, and the blows of the hammer force it against the upper
surface of the agraffe, which, being solid, conveys the impressed
vibrations through the medium of its own surface to the framing.

The “capo d’astro bar” performs the same functions in a slightly
different manner. It is practically a continuous “agraffe,” and
consists of a metal bar which is cast into the metal frame at the
beginning of the speaking length of the strings. It is fitted,
according to the best practice, with an under edge of tool steel, and
the strings are caused to pass underneath it on their way toward the
tuning-pins, which are higher than the bar, as before. The up-bearing
is thus imparted to the strings in a manner similar to that which is
followed in the case of the agraffes.

As to the advantages of the two systems, it may be said that the “capo
d’astro” undoubtedly overcomes those objections to agraffes which are
based upon their tendency to pull out from their places. It provides
an absolutely rigid resistance, and is therefore stronger and more
reliable.

On the other hand, however, the mass of metal employed is considerably
greater than in the “agraffe” method, and the resultant influences upon
tone-quality are clearly disadvantageous.

Further, the work of tuning is rendered more difficult by reason of
the fact that the strings cannot so readily and correctly be pulled
through the space intervening between the bar and the tuning-pin.
It is debatable whether the greater rigidity and resonance offered
by the “capo d’astro” method are not too dearly bought at the cost
of inconvenience in tuning and deterioration of tone-quality. It is
noteworthy that most manufacturers confine the “capo d’astro” bar to
the high treble register of their instruments, where brilliancy and a
somewhat metallic quality of tone are a desideratum.

The iron framing of an upright piano follows the same general lines of
construction as have already been noted in the previous discussion of
the grand. The functions of the frame are precisely the same and its
construction differs outwardly but little. There are, however, certain
divergencies from the grand forms that must be noted carefully. For
example, it will be remembered that the form of the upright pianoforte
is such that the framing has no direct and positive connection with the
outside case. It is thus impracticable to consider the sides of the
iron plate as homogeneous with the sides of the case, nor is it possible
to give to it that consistency of form that, in the grand, results from
the shaping of the plate to correspond with the curved outline of the
case. This, however, is no reason why the upright iron plate should not
be as strong and secure as that of the grand.

[Illustration: IRON PLATE FOR UPRIGHT PIANOFORTE FITTED WITH CAPO
D’ASTRO BAR.]

Among the various differences of detail that we observe to exist
between these two forms of plate is the device adopted to secure
the bearing and rigidity of the strings at their upper end deserves
notice. The practice is entirely different in this respect as regards
the upright, and we are therefore introduced to a new feature: the
“pressure bar.” This device has superseded both the old-fashioned
pinned bearing bridge and the later agraffe forms. It consists,
essentially, of a bar of heavy metal that is screwed into the
wrest-plank through the metal plate and is placed so that the strings
pass under it on the way to the tuning pins. In fact it occupies the
same position as do the agraffes or capo d’astro bar on the grand. Its
function is also similar; namely, accurately to delimit the speaking
lengths of the strings at the upper end and to assist in the formation
of a thrust or bearing whereby the latter may more advantageously be
secured.

[Illustration: IRON PLATE FOR UPRIGHT PIANOFORTE WITH AGRAFFES (MEHLIN
PATENTS).]

This form of building the bearing bridge possesses important
advantages. It does not require to be cast into the plate, nor is it
weakened, as in the agraffe system, by being broken up into a large
number of units. Moreover, the bearing for the strings is formed much
more smoothly and easily between the pressure bar and its attendant
ribs on the plate than is possible when either the agraffes or the capo
d’astro bar are used. This is an important point, for such construction
tends to make the task of tuning much more rapid and correct.

There are, however, several points to be considered in the designing
of pressure bars. As a general thing, it is impracticable to apply this
form to the bass strings on account of the fact that the overstringing
requires of them a slanting direction. On this account the pressure bar
cannot be made properly to maintain the obliquely-running strings in
their respective places. It is therefore usual to build the bass bridge
after the old pinned type and thus to secure the bass strings by much
the same device as is employed in the belly bridges.

As far as the designing of pressure bars is concerned, it will be found
that care should be exercised in arranging the space that the bar must
occupy and its position with regard to the scale ribs that are placed
on each side of it and that support the strings before and after their
passage under it. In general it may be said that the pressure bar must
be screwed in such a position that its lower curved surface is lower
than the upper surfaces of the scale ribs by about one-half of the
height of the latter. It must also describe a curve that corresponds
to the dip or angle of the scale and must be secured by enough screws
(one between each three string-groups is usual), to ensure that the
pull of the strings will have no injurious effect upon its rigidity.
It is also essential that the curve into which the string is bent
during its passage under the pressure-bar and over the scale-ribs be
not too deep or sudden. The bearing surface of the bar should be gently
rounded until very near its middle point where the string exercises its
greatest pulling strain. Here the surface must be curved a little more
sharply.

The iron plate of the upright is the chief supporter of the strains
imposed upon the structure by the strings. It is necessary, as in the
grand, that it should be built so as to have absolute rigidity under
these strains, and that it should be always capable of withstanding
any others that may by any chance be imposed upon it. Remembering
this, what shall we say of the designs that we sometimes see where
the iron is cut and shaved away at every possible point in order to
save a few pounds of weight? There are pianofortes in existence where
the iron framing is so much cut down that the treble can never be
depended upon to stay in tune for a reasonable length of time, and
where the unevenness of the distribution of metal throughout the body
of the frame has caused a warping of the whole instrument out of its
proper shape. All this is unnecessary, but it will continue so long as
manufacturers are willing to effect small savings at the expense of the
future reliability of their product.

It is certainly much better to have the plate of the upright
pianoforte so arranged that the total volume of iron, if it is to be
decreased, may have this process applied evenly and all through. The
most correct design would consider a moderately heavy plate of iron, or
better, of steel. This plate would be so arranged that the hitch-pin
plate (the portion which carries the hitch-pins) covers the entire
surface of the instrument at its bottom end and is bolted into the back
with as many and as heavy bolts as are employed at the other end. The
upper portion of the proposed plate need not extend over the surface
of the wrest-plank, for such a construction can add little to the
resisting power of the frame, while it inevitably tends, for reasons
that have already been described, to the production of dissonant
partials and the consequent emission of a metallic tone. If it is
desirable, for any reason, to cut down the weight of a frame, it can
better be done at the upper end than at the lower, where diminution of
the resisting power of the frame is most severely felt.

We may, then, contemplate a form of iron frame which covers that
portion of the back-framing whereon the edges of the sound-board
are glued, and that is not continued up and over the wrest-plank.
It will be cut away in the centre, as in the grand, and will thus
expose a large part of the sound-board to view. It will be provided
with a certain number of bracings for the purpose of taking up the
strains that are imposed upon the structure at the points of greatest
resistance, such as those where the over-stringing begins and ends, and
those around the middle registers of the scale. There must not be more
of these bracings, however, than is necessary, as it is very important
that the scale should be broken up into the least possible number
of divisions. The bracings will be so designed that no one of them
interferes with the true curve of the belly-bridge. The whole structure
will be solidly bolted into the back-framing through the sound-board by
a series of long and heavy screws and bolts that will be inserted at
frequent intervals along the edges.

We cannot conclude this survey of plate-construction without taking
note of a property that is common to all cast-iron structures. We refer
to shrinkage. The calculations of the designer, no matter how carefully
worked out, must take into consideration the fact that cast-iron
shrinks largely in the cooling. It must be noted that the design for
the iron plate is the chief portion of the work of scale draughting.
As will be explained later on, this work is first done on paper and
then transferred to a wooden pattern. From this pattern the casting is
made. After the first casting is thus completed it is taken in hand
by the designer, who marks and punches it for the boring and pinning
and corrects it where necessary. The corrected casting is then used as
a model for the future plates that are to be turned out for the same
scale. But these also shrink; so that we are compelled to take into
account both shrinkages, and allow for each. Fortunately, however,
there is no difficulty in arranging this.

The method is as follows: After the string-lengths have been calculated
and the size of the iron plate thus determined, a complete drawing is
made, showing the exact dimensions, shape, and other features of the
proposed plate. This is to be used as the guide for the wooden templet.
But this difference exists between the two paper drawings; namely,
that the second is multiplied as to every dimension of the plate by a
quantity that represents the amount of shrinkage that is known to occur
in the two castings.

The average shrinkage of cast-iron in the form of pianoforte plates is
estimated at about one per cent. Consequently to account for the double
shrinkage it becomes necessary to multiply by the square of 101/100;
that is approximately 51/50.

A great deal of trouble will be avoided if the shrinkage is carefully
worked out in this manner. Every dimension of the plate is affected,
and the greatest care must be taken to ensure that the corrected
calculations are accurate. Only thus will it be possible for the ideas
of the designer to be brought out in the completed instrument as he
expects to see them.



CHAPTER XI.

THE MECHANISM OF PERCUSSION.


The pianoforte hammer is perhaps the most striking of the many and
various features of that instrument. Although it is a comparatively
simple device, its historical and musical interest is supreme. For
while the strings, the framing, and even the action that we see in
the instruments of today are but the modern developments of their
clavichord and harpsichord ancestors, the hammer, on the contrary, is
the one revolutionary device that, at a single step, separated the
pianoforte from all other stringed instruments and endowed it with its
own peculiar and powerful attributes.

It was the hammer, in fact, that made the pianoforte. As soon as it was
fitted into a harpsichord, the pianoforte was born, and no refinement
of stringing or framing could have effected the fundamental nature
of key-board instruments in the same manner. For we must recognize
the fact, sometimes overlooked, that the pianoforte is essentially an
instrument of percussion. It is necessary that there be a more or less
violent blow from the hammer to excite the sound-producing vibrations
of the strings. The tone of the instrument, under the most favorable
circumstances, cannot fail to partake of the character peculiar to
sounds produced in this manner. The importance of the hammer as a
tone-producer cannot, then, be underestimated. It stands upon a plane
of importance equal to that occupied by the scale-designing, the
stringing and the resonance apparatus. We are therefore justified in
devoting space to consideration of the construction of this essential
feature.

We cannot say with absolute surety what was the nature of the
material with which the hammers of Cristofori’s original invention
were covered. But we may presume that it was leather. We know that the
hammers were exceedingly small and apparently all of the same size.
Neither Silbermann nor Zumpe can be said to have perfected any special
improvements in the form of hammer construction, and we find that the
revolutionary genius, John Broadwood the First, and also Sebastian
Erard, were the pioneers in the work of adapting the hammers to the
more strenuous styles of playing that the improved touch mechanism
invented by them permitted and encouraged.

Broadwood, who first perceived the necessity of adopting a
scientifically correct striking point, likewise began to fit his
pianofortes with hammers graduated in size, and under him the
leather-covered hammer arrived at its full development.

But leather as a covering material soon began to be decried. It was
discovered that the kind of tone demanded by the rising pianoforte
masters could not be obtained from such material. After much experiment
on the part of pianoforte makers, the German-Frenchman, Pape, of Paris,
tried the use of felt. His success was immediate and conspicuous, and
it was discovered that not only did this kind of covering produce
finer tone quality, but there was little difficulty in regulating
that quality through the hammers within certain well-defined limits.
Nevertheless, we find square pianofortes to-day in which the felt
covering upon the higher hammers is overlaid with strips of buckskin.
This practice, however, represented the last dying struggles of the
leather-covered hammer, and now we use it no longer.

It is true that the use of felt is not unattended with conspicuous
disadvantages. It wears out rapidly, and unless constantly kept in good
condition by use of the felt-needles, the iron, and the sand-paper
file, soon comes to produce a harsh and unpleasant tone-quality. This
defect arises from the fact that as usually constructed, the continual
pounding of the hammer head upon the strings causes the felt on the
crown of the hammer head to become tightly packed and compressed,
and the shaping of the head to be lost. As will be explained later,
this change in the manner in which the head is originally made up
causes a modification in the nature of the vibrations set up in the
strings, and, as we have already learned, this change in the nature
of the produced excitement is the cause of unpleasant tone-quality.
Nevertheless, and in spite of these real disadvantages, the use of
felt as a covering material for pianoforte hammers is now universal.
Nor does it seem at present that we are very likely to find a superior
substitute. As we shall shortly see, however, a simple change in the
manner of securing the felt to the wooden foundation of the hammer-head
may be depended upon to add largely to the durability and efficiency
of the whole structure, both as a tone-producing medium and as a
mechanical device.

As will be surmised by the reader, early covering of pianoforte hammers
with felt was a tedious operation. The material was cut up separately
for each hammer, and glued on to the wooden head by hand. But this
method suffered under the grave disadvantage of affording no correct
guide to the true thicknesses and no means other than furnished by
hand-cutting, of graduating these thicknesses with exact evenness.
It remained for an American (or Americanized German) inventor to
devise a machine that should glue up and finish an entire set of
hammers from one continuous sheet of felt, of which the thickness was
graduated in the making and which could be relied upon to contain
the correct amount of felt, of any desired total weight, the whole
graduated with great evenness. Not merely was this so, but the methods
of manufacturing felt for other special purposes connected with the
manufacture of pianofortes has been entirely revolutionized, so that
today we have dampers, punchings, and many other parts of the mechanism
of pianofortes successfully manufactured out of various kinds of felt,
which vary greatly in consistency, thickness, and other properties.

To return, however, to the special case of hammer-felt. We find that
the original methods of working together the layers of carded wool
has been much improved, chiefly through the efforts of the inventor
mentioned above. It is now a matter of slight difficulty to turn out
sheets of felt for the making of piano hammers that shall have any
desired weight, size and graduation of thickness.

The weight of the sheets of felt varies largely according to the nature
of the hammers that are to be produced. Thus it is customary, as may be
guessed, to provide full-size concert grands with hammers of greater
thickness, while the smaller styles of instrument have progressively
smaller hammers. The actual weights vary according to the caprice or
calculation of manufacturers and designers. An average weight of felt
for hammers suitable to be placed in a nine-foot concert grand is from
16 to 18 lbs. per sheet. This does not include the “underfelt,” which
is glued directly to the wooden head of the hammer and is used to give
greater resiliency to the lower hammers. It is generally omitted at the
higher treble end.

Upright pianofortes frequently are hammered with felt weighing not
more than 8 lbs. to the sheet, but this seems to be too light for
really efficient results. 10 lbs. is quite light enough in most cases.

As has already been indicated, the foundation of the hammer is a wooden
molding. Over this is glued, in the machine, a strip of “underfelt,”
which is long enough to cover about five and a half or six octaves of
hammers, counting from the bass end upwards. The main felting is then
laid over this, the thickest end being at the lowest bass. By means of
the machines, now so generally used, it is possible to glue the entire
underfelt and also the topäfelt, in one piece. The moldings are then
separated and the operation is complete. It is customary to insert a
small piece of wire, doubled over in a loop, through each hammer, in
order to ensure further strength to the fastening.

As may well be imagined, the details of manufacture, of the quality of
the felting, and of the dimensions of the completed hammers, require
much care in their execution. Long practice, study, and experience
have combined to render the specialists, who devote themselves to the
preparation of hammers and hammer-felt, most excellently fitted to
place upon the market the very finest productions of this kind.

There have been attempts made at various times to provide a hammer
head, and a method of felting it, that would obviate the somewhat rapid
deterioration caused by the pounding of the glued and compressed felt
against the stiff steel wire strings. The felt, which requires to be
compressed before it is glued on to the wooden molding, rapidly becomes
altogether too hard. Moreover, the fastening of the felt to the molding
is by no means really permanent. It has been suggested that the felt
might properly be contained within a wooden shell which would extend
as far along the sides of the felt as the wooden molding now reaches
within it. The compressed sheet of felt would be forced into this shell
and fastened therein so that it would always be protected by an outer
wooden covering. Thus, not only would the fastening of the felt to the
wood be reduced more secure, but the pounding upon the strings would
not so rapidly assure the undue hardening of the felt. For there would
not be the hard wooden base between which the strings and the felt is
continually subjected to compression. The idea is good and undoubtedly
will yet be recognized.

Details of the adjustment of the hammers to the rest of the action
and of the preparation of them by the tone-regulator, for the better
production of good and even tone, will be dealt with in the chapters
upon action-and tone-regulating.



CHAPTER XII.

THE TOUCH MECHANISM.


As the hammer-idea evolved itself in the mind of Cristofori and
the other experimenters who were contemporaneously bending their
efforts towards the improvement of the dynamic possibilities of
keyed instruments, we may be certain that much perplexity was caused
them by the problem of providing some mechanism that should form the
connecting link between the hammer and the key. We may understand
how the ingenious Italian must have labored, with the picture of the
dulcimer and its player continually in his mind, to obtain an efficient
mechanical substitute for the uncertain stroke of the hand operated
dulcimer-hammer, as well as the dynamically incapable harpsichord jack
and quill. It is surprising to note, indeed, how early the present
ruling principles of action-mechanism were elaborated by these pioneer
workers. Cristofori, as we have already mentioned, obtained, ere he
died, a complete check to the rebound of the hammer and a form of
escapement that may be seen unaltered in essentials in surviving square
pianofortes of the “English action” variety. We may further reflect
that the invention of Backers, as improved by John Broadwood the
First, remains today the approved mechanism of many English and other
European grands. Not only is this so, but until the general adoption
of the Steinway overstrung model, there existed German makers who were
content to fit their moderate priced grands with a slightly modified
form of the Viennese action invented by that remarkable woman Nanette
Stein, afterwards Madame Streicher, the conspicuous feature of which
was the mobility of the hammer-butt and the stationary condition of
the jack. The fact that these early mechanisms remained satisfactory
to performers until recent years is the best proof of the thorough and
sure mechanical basis upon which they were designed.

It is not necessary to go into elaborate detail in describing these
early actions. Reference to the accompanying cuts will be sufficient
to lay bare their actuating principles. We may, however, observe that
the radical difference of touch between the Viennese (Streicher) models
and those of Broadwood (known as the English grand action) continued
to be a source of annoyance to performers until the increasing
technical demands of the modern virtuoso school and the improvements
in wire-drawing and iron casting made inevitable the supersession of
the very light Streicher action by the heavier, more durable and more
efficient Broadwood English model, which continued in favor until
within recent years.

[Illustration: CRISTOFORI’S ACTION IN ITS FINAL FORM.

   1. Key.
   2. Jack.
   3. Jack-operating spring.
   4. Cushion limiting rebound of jack.
   5. Under-hammer.
   6. Hammer-butt.
   7. Hinge of hammer-butt.
   8. Hammer-shank.
   9. Hammer head.
  10. Check.
  11. Damper-lifter.
  12. Damper-head.
  13. Action-beam.
  14. Wrest-plank.
  15. Tuning pins.
  16. Bearing-bridge.
  17. String.
]

[Illustration: ACTION BY ANDREAS AND NANETTE (STEIN), STREICHER
VIENNESE ESCAPEMENT (1794).

   1. Key.
   2. Jack.
   3. Jack-operating spring.
   4. Cushion limiting rebound of jack.
   5. Button and screw regulating escapement of hammer.
   6. Hammer-butt and operating face.
   7. Hammer-butt pivot.
   8. Hammer-shank.
   9. Hammer-head.
  10. Check.
  11. Damper-lifter.
  12. Damper-head.
  13. Action-rails.
]

[Illustration: ENGLISH DIRECT LEVER GRAND ACTION, DEVELOPED BY
BROADWOOD FROM BACKERS (1884).

   1. Key.
   2. Jack.
   3. Jack operating spring.
   4. Rail and cushion limiting travel of jack.
   5. Button and screw regulating escapement of hammer.
   6. Hammer-butt with operating notch.
   7. Hammer-butt flange.
   8. Hammer-shank.
   9. Hammer-head.
  10. Check.
  13. Action-rails.
]

[Illustration: DOUBLE REPETITION ACTION OF SEBASTIAN ERARD AS USED BY
S. & P. ERARD, PARIS.

   1. Key.
   2. Wippen.
   3. Jack.
   4. Escapement lever.
   5. Hammer-shank.
   6. Roller.
   7. Hammer-head.
   8. Jack regulating button.
   9. Regulating button to limit rise of escapement lever.
  10. Hammer-butt.
  11. Check.
  12. Felt cushion to engage with check.
  13. Sticker connecting key and wippen.
  14. Action-rails.
  15. Damper-head.
  16. Damper operating device.
  17. Device to limit travel of jack.
  18. String.
  19. Spring (v-shaped) for escapement lever and jack.
]

Shortly before the general adoption of the Broadwood model, however,
there was brought forward a new type of grand action, which was
destined in its turn entirely to supersede the then favorite English
type. This was the invention of Sebastian Erard, of Paris, founder of
the still existing house of S. & P. Erard. His new action was termed
the “double repetition action,” and it fully deserves the name. By
the use of this device the leverage that exists between the hammer
and the key is so manipulated that the very slightest touch upon the
keys is sufficient to cause the hammer to deliver a blow. It will be
observed by reference to the cut that the Erard action differs very
largely from that of Broadwood. In the first place, we observe that
the hammer heel is no longer provided with a notch in which the jack
works, but that this heel is reduced to the smallest dimensions and
acts merely as a pivot. Upon the shank of the hammer is fastened a
felt-covered roller. The jack acts upon this roller. Between the jack
and the roller, however, we observe a long lever, one end of which has
a slot through which the jack passes, while the other end is pivoted
on to a rail projecting from the wippen. This is the “escapement” or
repetition lever, and forms the main improvement of Erard. It will
be observed that the repetition lever bears against the roller, and
indeed lifts it before the jack can come into engagement with it.
The jack, working through the slotted portion of the lever, is not
brought into play until the lever has raised the hammer a little way.
The long, double spring that acts both upon the lever and the jack
gives them their motions, and the result of the depression of the key
is that the repetition lever is always in engagement, and when the
angular key-motion is not sufficient to bring the jack into play, the
work will be done by aid of the lever. Furthermore, the lever operates
to maintain the hammer-shank in precisely the proper position for
striking, at all times, and without reference to the angular position
of the key.

It can easily be understood that such a vital change in action
mechanism did not become popular at once. Many pianists objected to
double escapement. Notable among these were Chopin and Kalkbrenner;
these two being the greatest pianists of their day in Paris. Chopin
preferred pianofortes fitted with the Broadwood action.

[Illustration: THE ERARD GRAND ACTION MODIFIED BY HERZ.

   1. Key.
   2. Wippen.
   3. Jack.
   4. Escapement lever.
   5. Hammer-shank.
   6. Hammer-butt notch.
   7. Hammer-head.
   8. Jack regulating button.
   9. Regulating button to limit rise of escapement lever.
  10. Hammer-butt.
  11. Check.
  12. Molded tail of hammer-head to engage with check.
  13. Capstan-screw connecting key and wippen.
  14. Action-rails.
  15. Damper-head.
  16. Damper-operating device.
  17. Device to limit travel of jack.
  18. Regulating device for escapement lever.
  19. Springs (2) for escapement lever and jack.
  20. String.
  21. Flange.
]

Nevertheless, the merits of Erard’s invention continued to impress
themselves upon the musical world, although Pierre Erard, who had
patented his uncle’s invention in 1821, was obliged to obtain an
extension of the English patent in 1835, on the ground of the loss
occasioned in working it. It did not become generally adopted,
even after the expiration of the extended patent, until modified
and simplified by Henri Herz, the famous pianist and pianoforte
manufacturer. Then its merits, in the modified form, were so generally
recognized that it is now in use by Steinway, Chickering, Knabe and all
manufacturers of grand pianofortes in the United States; by Broadwood,
Collard & Collard, Brinsmead, and others in England; by Bechstein
& Bluthner in Germany, and by most French makers of eminence with
the sole exception of the house of Erard itself. This eminent firm
continues to employ the pure and original form of action as patented in
1821, with improvements only in details of workmanship and material.

Whatever we may say as to the general adoption of the Erard action
only after it had been considerably modified, we must not withhold
admiration from the Erards, whose genius and courage gave to us the
enduring double-escapement principle that has never yet been superseded.

The main features of the Herz-Erard mechanism may be seen at a glance.
The roller is replaced by the notch, once more restored to favor, and
the repetition lever is made more effective by being pivoted centrally
with two free ends, and by having means provided to limit its up and
down motion. Moreover, the wippen is shortened and made straight, the
single spring is replaced by two, and the damper is once more permitted
to fall down on the strings by its own weight without recourse to
artificial springs.

The Herz-Erard action has been taken up by American makers, but we find
that they have modified it again, after their own ideas. For example,
if we look at the accompanying cut showing a modern American grand
action of the highest class, we shall observe that the original roller
of Erard is restored, the damper mechanism simplified and additional
means of controlling the movements of the jack introduced. These two
latter improvements combine to make the present American grand action
most perfect, and the achievements of the specialist action makers must
ever command our respectful admiration.

The reader has now been able to take a comparatively complete survey
of the progress of invention in grand pianoforte action mechanism. We
shall therefore turn to a critical examination of the modern standard
grand action here illustrated, in order that the adjustment of it
within the instrument may be understood.

[Illustration: STANDARD MODERN AMERICAN GRAND ACTION.

   1. Key.
   2. Wippen.
   3. Jack.
   4. Escapement lever.
   5. Hammer-shank.
   6. Roller.
   7. Hammer-head.
   8. Jack-regulating button.
   9. Regulating button to limit rise of escapement lever.
  10. Hammer-butt.
  11. Check.
  12. Molded tail of hammer-head to engage with check.
  13. Key-rocker and sticker connecting wippen and key.
  14. Action-rails.
  15. Damper-head.
  16. Damper operating device.
  17. Device to limit travel of jack.
  18. Regulating device for escapement lever.
  19. Separate springs for jack and escapement lever.
  20. String.
  21. Flanges.
]

It will be observed that the key (1) is supported upon a key-frame,
part of which is clearly shown in the drawing. This frame is provided
with a cloth strip at its rear end, also shown, and with a “balance
rail” upon which the key is pivoted by means of a pin. The position
of this balance rail must be such that the divisions of the key thus
made are to one another as 3:2. The part nearest to the player’s
finger is the longer. But such a proportion as this holds good only
for the actual operative lengths of the keys from the front to the
point where the sticker, or capstan screw is placed. For otherwise we
have a distinct change in the mechanical relations of the parts of the
lever-system, and this, of course, entails a corresponding change in
the forces that are brought into operation. It is therefore necessary
to have a standard length of key, as between the points mentioned, and
this length is placed at 15-3/4 inches. But, in order to maintain the
mechanical relations between the dimensions of the lever we must also
consider the depth to which the key sinks in front, and also the height
to which it rises at the back. If, then, we arrange that the depth in
front shall be 3/8-inch full and the rise in the rear 1/4-inch full, we
shall be able to maintain the position of the balance pin as already
calculated. Such a proportion supplies the very best arrangement. In
order to fix the proportions in the reader’s mind we repeat them in
tabular form, as follows:

                                                               Inches
  Length between front of key and balance pin                  9-9/20
  Length between balance pin and capstan or sticker            6-3/10
  Total length of key between front and capstan or sticker     15-3/4
  Depth of fall of front portion of key                       3/8 full
  Height of rise of back portion of key                       1/4 full

The front portion of the key is mounted upon a rail of the key-frame
which is provided with a pin. This pin works in a mortise cut in the
bottom of the front portion of the key and bushed with cloth. The pin
is oval in form and adapted to be turned so as partially to increase
the amount of space occupied by it whenever wear or age tend unduly to
enlarge the size of the mortise.

The exact size of all the various action parts that are mounted
above and in connection with the keys depends largely upon the exact
interior dimensions of the grand pianoforte case. So that it becomes
necessary carefully to measure the height from the key-bed to the level
of the strings, and also the distance from the front of the keys to
the line of damper lifter wires, and from there to the extreme rear
end of the key-bed. Likewise the exact position of the middle string
of each three-string group, the middle point of each two-string group
and the position of each single string must be marked upon a stick
for the guidance of the action-maker. The latter will then be able to
effect the correct alignment of the hammers, the rise of the escapement
lever and jack, and the exact position, in reference to these, of the
other parts of the action. It will, of course, be understood that
the proportionate dimensions of all the action parts depend upon the
measurements that we mentioned just now, as well as upon the dimensions
of the keys. The greatest care is therefore necessary in making these
measurements.

[Illustration: GRAND PIANOFORTE ACTION WITH METALLIC ACTION AND
DAMPER FRAMES, SOSTENUTO PEDAL DEVICE AND HAMMER SWINGING SOFT PEDAL
ATTACHMENT.

  22. Sostenuto pedal-rod.
  23. Attachment to damper-lever engaging with sostenuto pedal-rod.
  24. Metallic action and damper-brackets.
  25. Hammer swing-rail and cushion.
  26. Hammer swing-rail rod.
  27. Hammer swing-rail lifter.
  28. Lifter-rod.
  29. Lost motion compensating levers.
  30. Lost motion compensating levers.
]

The junction of these parts with the damper mechanism lies within the
province of the action finisher and regulator and will therefore be
treated in the chapter on action regulation.

It will be observed then, to return to the consideration of the action
in its actual movements, that the depression of the key causes the
wippen to rise at its forward end. This brings the escapement lever (4)
to bear upon the roller (6), with which it is in continual contact,
and raises the hammer-shank and hammer-head (5) and (7). At the same
time the jack (3) is raised and its tail end is brought nearer to
the button (8), which it finally touches. As soon as this happens
the jack is tripped up and its head comes out of contact with the
roller. The latter in the meantime, having been raised away from the
escapement lever by the action of the jack, falls back into contact
with the former and is then borne up on the lever so that the hammer is
maintained in position near to the strings. The result of this is that
so long as the finger is held on the front of the key, the whole action
is continually in proper position to actuate the hammer. The jack is
not permitted to fall away, for the roller is maintained in the right
place by the escapement lever and it thus happens that a very small
angular motion of the key obtained by slightly raising and depressing
the finger, is sufficient to cause the whole action to be set in
motion, and the operation of actuating the hammer to be gone through as
often and as rapidly as required.

The pedal motions of the grand action are simple. The whole action and
keys, as we know, are mounted upon the key-frame together, and thus
form a homogeneous structure. The “_piano_” pedal is caused to shift
this frame so that the hammers each strike only two of the members of
each three-string group and only one of each two-string group. This
is effected by the use of a heavy spring that is set in the side of
the interior case and bears against the key-frame, and by a lever that
operates from a hole cut in the bottom of the key-bed and engages with
one of the bars of the key-frame. The pedal is connected with this iron
lever so as to shift the key-frame, and the spring operates to push the
key-frame back into place whenever the foot-pressure is removed from
the pedal.

The “_forte_” pedal simply pushes up the whole line of damper levers
(16) each of which is pivoted on flanges (21) for that purpose. The
lifting is effected by means of a rod connecting with the pedal which
is projected through the bottom of the key-bed and engages with a rail
set under the line of damper levers and adapted to raise them when
operated by the pedal-rod.

There are, however, two variations to the pedal mechanism of grand
pianofortes that require some attention on account of their mechanical
interest. These are clearly illustrated and described in the cut and
specifications shown on adjoining page.

The working of the sostenuto pedal and of the new soft pedal device
will be readily comprehended by reference to the cut.

It will be noted, in the first place, that the metallic action brackets
which were omitted in the previous drawing for the sake of exhibiting
the working parts more clearly, are now shown.

The “sostenuto pedal” is devised to permit the sustaining of a chord
while the fingers of the performer, for the purpose of continuing the
melody, are withdrawn from the keys. It will be observed that the
action is provided with a rod (22) which is connected with a pedal and
is adapted to be brought into contact with an additional damper-lever
(23). This additional lever is provided with a tongue of felt, and
when the rod is turned on its axis, this tongue engages with a similar
metallic device on the rod, thus holding the damper up as long as the
rod is kept in the position of contact. When the key is pressed down,
the damper rises to clear the string, and brings the additional lever
up with it, so that, if the rod is now caused to revolve, the tongues
on each engage one with another and the damper is held up as long as
the pedal is pressed down and irrespective of the position of the key.
Provided that the keys are first depressed, the pedal will always hold
up as many of the dampers as are thus raised. The result is to sustain
the sound of the strings after the hand has been removed from the key.
This gives a more permanent character to the harmonization of a melody,
without the dissonance that comes from the releasing of all the dampers
by the ordinary “_forte_” pedal. The “sostenuto pedal” is generally
situated between the others in the lyre or pedal case at the level of
the player’s feet.

The second device is also most interesting. It consists of a method for
softening the sound of the string, by a method similar to that which is
employed in the upright. It is claimed, and with some justice, that the
use of the shifting key-frame is attended with various complications,
and that the motion tends to hinder the adjustment of the action to the
strings. Moreover the hammers become unevenly worn by being continually
caused to strike two, instead of three, strings and this operates to
cause loss of directness in the hammer-strokes.

In this new device, the hammer is provided with a swing-rail (25),
having a cushion for the hammer-rebound similar to the ordinary cushion
that is supported upon the wippen in most actions, and a rod (26) for
pivoting it to the metallic action frame (24). The swing-rail also is
fitted with a lifter (27), which is operated by the soft pedal through
a lifter-rod (28). So far the process is simple. The effect of the
motion of the swing-rail is to bring the hammer closer to the string
and to soften the tone. But this is only accomplished at the cost of
lost motion between the capstan-screw and the key. To avoid the loss
of touch thus brought about, the lifter-rod is connected with two
compensating levers (29) and (30), which are so adjusted that they form
a continuous link between the parts where the lost motion would occur,
and thus preserve the continuity of touch and the weight that is lost
by the different actuating positions of the hammer. The ingenuity of
this device commends it to the student of pianoforte mechanism, and the
makers are entitled to great praise for the successful achievement of
this important modification.

We may conclude our survey by giving a list of the materials of which
grand actions are constructed.

  Various Woods--
    Pear tree        Damper heads.
    Holly            Jacks and other small parts.
    Sycamore         Jacks and other small parts.
    Ebony            Tops of black keys.
    Maple            Hammer moldings and shanks.
    Mahogany         Hammer moldings, buttons, etc.
    White pine       Key-frames.

  Felts and Cloths--
    Baize            On key-frames, hammer-rails, etc.
    Baize            Punchings.
    Flannel cloth    Bushing centre pin holes, damper lifter holes, etc.
    Tone felt        Upper and under felt for hammer.
    Hard felt        Bass damper wedges.
    Soft felt        Treble dampers, etc.
    Flannel          Sundry action parts.

  Leathers and Skins--
    Doeskin
    Buckskin         Various parts of action, operating faces of
    Elkskin              hammer-butts, etc.

  Ivory              Tops of white keys.
  Celluloid          Fronts of white keys.
  Graphite           Lubrication of working parts.
  Iron               Action frames, screws, etc.
  Brass              Centre pins, springs, pedal-feet, etc.

[Illustration: STANDARD AMERICAN UPRIGHT ACTION.

   1. Key-rocker.
   2. Abstract.
   3. Abstract-lever.
   4. Flange.
   5. Action-rail.
   6. Wippen.
   7. Jack.
   8. Jack-spring.
   9. Check.
  10. Check-wire.
  11. Bridle-wire.
  12. Tip of bridle-tape.
  13. Bridle-tape.
  14. Back-stop.
  15. Regulating rail.
  16. Regulating button.
  17. Regulating screw.
  18. Hammer-butt.
  19. Hammer-shank.
  20. Hammer-molding.
  21. Hammer-head.
  22. Hammer-rail.
  23. Hammer-butt spring.
  24. Hammer-spring rail.
  25. Damper-spoon.
  26. Damper-lifting rod.
  27. Damper-lever.
  28. Damper-lever spring.
  29. Damper-wire.
  30. Damper-block.
  31. Damper-head.
  32. String.
  33. Continuous brass hammer-butt flange.
]

We are now able to turn our attention to the action mechanism of the
upright pianoforte. The historical chapter of this work contains a
short description of the early history of the upright form. Of course,
it will at once be seen that the only real mechanical difficulty
in designing a vertical type of pianoforte was to be found in the
department of touch-mechanism. The problem was indeed primarily of
the action. As such it is interesting to note the efforts of Hawkins,
Southwell and Loud, to produce an action that would approach in
efficiency that of the grand. It was Robert Wornum, however, who found
the solution, though not until nearly the end of the first quarter
of the nineteenth century. The principle applied by Wornum possessed
such value that it has never been superseded, and remains today the
distinguishing feature of the upright action.

We refer, of course, to the tape. As applied to the action of
uprights, this device has become universal, and all upright actions
in consequence have for years been everywhere similar as to general
design. Thus we do not find those radical differences of actuating
principle that to this day distinguish American from certain European
grand pianofortes. This is partly due to the fact that the great
battles had already been fought out when the first successful upright
actions were made. At present, the only remaining types of the ancient
“sticker” leather-hinged action are to be found in old-fashioned and
obsolete European pianofortes of the cheaper grade. None are made now,
however, except in the case of a very few worthless commercial English
instruments. In the United States the “sticker” action has hardly been
heard of.

Thus it seems unnecessary to give detailed drawings of any but the
accepted type of upright action. The reader’s attention is immediately
called, therefore, to the drawing herewith given.

The method of operation may be seen very clearly. Depression of the
key, to which is screwed the key-rocker (1), causes the Abstract (2)
and the Wippen (6) to rise. This brings the Jack (7) to bear against
the butt (18), which is raised, forcing the hammer (20) and (21)
through the shank (19) against the string (32). As the hammer strikes,
the rise of the jack has brought its tail against the regulating-button
(16), which trips it up so that it falls towards the back-stop (14).
The butt, being thus left free, drops back, assisted by the pull of
the tape (13), until the back-stop is caught and held by the check
(9), thus leaving time for the jack to get back under the hammer butt
through the aid of the spring (8). Repetition of the hammer is thus
assured, and while the rapidity of stroke cannot be so great as that of
the grand, it is sufficiently so to satisfy ordinary users. Sometimes a
spring is fastened to the front of the jack in connection with a silk
loop and cord which stretches back and engages with the hammer spring
(23). The latter is then fastened to the hammer butt instead of to a
rail (24). This arrangement gives a far more rapid repetition to the
action and causes it to approach the delicacy of the double escapement
of the grand.

[Illustration: UPRIGHT ACTION SHOWING LOST-MOTION DEVICE, METALLIC
REGULATING RAIL SUPPORT, CAPSTAN SCREW, JACK REGULATING RAIL AND
METALLIC ACTION BRACKETS.

  34. Hammer-rail lifter-wire.
  35. Hammer-rail swing-lever.
  36. Hammer-rail lifter rod.
  37. Lifter-rod lever.
  38. Compensation-lever.
  39. Capstan-screw.
  40. Rail for limiting return movement of jack.
  41. Metallic regulating rail support.
]

The pedal mechanism is the same as in the grand. The “_piano_” effect
is obtained by pushing forward the hammer-rail (22), so that the
hammers approach nearer to the strings. The “_forte_” pedal effect
is obtained by use of the damper lifting rod (26) which is turned
rearwards and forces back the whole line of damper heads so that they
leave the strings.

The lost motion that occurs in the action when the “_piano_” pedal is
used has been overcome in a most ingenious manner, and by means similar
to those already described in the discussion of the grand action.
The trouble to be overcome is the same, namely the lifting up of the
abstract from the rocker or capstan screw caused by the forcing of the
hammers towards the strings. This causes loss of touch and is very
irritating to the performer.

The drawing given herewith also shows the metallic action bracket
for supporting the action and the capstan screw that is used as an
alternate to the key-rocker.

The lost motion attachment operates through the rod (36) which lifts
the hammer rail and at the same time brings into play the compensation
lever (38), which takes up the space between the abstract and the
key that would otherwise intervene. Thus the touch remains true
irrespective of the position of the hammer.

The materials that are required for the manufacture of the upright
action do not differ from those, which we have already classified as
pertaining to the grand.

The adjustment of the upright action requires that the same precautions
be taken in the measurement of the key-bed, of the height of the action
between the keys and striking-point of hammers, the distance of hammer
from strings when at rest and so on. All these assist the action maker
to adjust the alignment of the hammers and the height of the abstracts.
The size of the pianoforte sometimes requires the omission of the
abstracts, in which case the bottom of the wippen is felted and brought
into contact with the capstan or rocker direct. All these details are
attended to by the action maker when the proper measurements are given.
The marking on a stick of the run of the strings is done just as was
suggested for the grand scale.

In conclusion, it may be mentioned that much similarity exists between
certain parts of the action of both types of instrument. It has become
customary to make the length of the hammer shank and hammer butt, when
fitted together, about five inches, counting from the center pin of
the butt to the middle of the hammer molding. This measurement will be
found correct for both grands and uprights.

The length of the hammer blow is always as nearly as possible 1-24/25
inches for the bass end, graduating to 1-9/10 scant in the treble.
These dimensions should be maintained at all costs. The key lengths
that we gave before are applicable to all forms of uprights. When
provided with these data the action maker will be able to put out a
mechanism that will fulfill the individual requirements of each kind of
instrument.



CHAPTER XIII.

REGULATION OF PIANOFORTE TOUCH MECHANISM.


We may presume that the reader is by this time quite familiar with
the appearance and use of the various parts of the grand and upright
pianoforte action, both as assembled and detached. We may therefore
proceed to give general instructions for the adjustment of these within
the instrument and the regulation of the various working parts into
proper harmony with one another.

We say “general instructions” advisedly; for it is quite out of the
question to teach action finishing and regulating by means of written
directions. Experience and the practical routine of the shop must
be gone through by anyone who hopes to be able to do this kind of
work well. For there are few departments of mechanical endeavor that
demand such skill, care, and patience as the regulation of pianoforte
mechanism.

Nevertheless the directions that we shall give in this chapter will
be sufficient to make him who reads and digests them a very efficient
critic. It is much to the employer to be able to estimate correctly the
value of each practical detail of the construction, and the correctness
of the manner in which it is executed. This chapter is intended to
provide as much of this knowledge as may be imparted by means of
written words.

We shall begin with the grand action, following the method that has
been pursued throughout this work.

The first step in the regulating and adjustment of the grand action
is taken by the “action-finisher.” He receives the action and keys
separately. The former is without hammers or dampers and the latter
without rockers or capstan screws. The action has to be placed within
the space destined for it in the instrument and the proper position
for it noted. If the action has been well made there should be no
difficulty in seeing that it fits its place correctly. The action is
screwed on to the key-frame through its metallic brackets and the
capstan screws are put into the keys at the proper points so that they
engage with the cushions on the bottom of the wippens. When this has
been done the weight of the action upon any one of the keys should be
noted and the action may then be removed. A piece of lead should then
be taken and fastened to the back of each key. This lead must have the
same weight as the action has upon each key. The keys will then remain
in their proper positions when the action is removed, and the work of
leveling them may then be begun. Remembering the depth of touch that
was prescribed in the last chapter, let the extreme bass and treble
keys be adjusted to an equivalent height by wooden blocks through their
front rail pins. Then run a straight edge over the keys and proceed
to adjust their levels by means of the thin paper punchings that are
provided for the purpose. These come in various thicknesses and are
laid over the balance rail pins and under the cloth punchings that must
first have been placed in position both on the balance rail and the
front rail. When the leveling is accomplished let the action be screwed
on again. Then let the hammers be glued on. The striking point of the
hammers must be carefully measured and the directions already given
as to the striking of the highest hammer must be observed. It will be
remembered that one-tenth of the string was recommended for the highest
hammers, graduating down to the ideal one-ninth and one-eighth. The
scale draughtsman will prepare a marking stick showing the true hammer
line. The hammers are glued on absolutely at right angles to the plane
of the strings. After they are dry, they must be adjusted to the proper
position by the capstan screws or rockers. They must lie just over and
not quite touching the wippen cushions. Let them also be aligned to
each other, horizontally, with great exactness. Be sure that the keys
work easily and that the depth of touch is roughly adjusted as already
provided for.

It next becomes necessary to fix the damper mechanism. This is chiefly
situated in the back of the action and the damper levers are to be so
adjusted that they rest a little above the backs of the keys, ready
to be engaged with them when the fronts of the keys are depressed.
The dampers must fit on to the strings straight and must drop with
sufficient force to effect an instantaneous damping. The damper levers
are leaded for this purpose.

The instrument is then taken in hand by the action regulator. His work
is most important. He first sees that the level of the keys is perfect
and that they are properly balanced when suspended without the action.
If any defects are found here they are remedied by changes in the
leading. The keys should be so leaded that they balance when tested on
a scale and the weight of touch with the action fitted must not be more
than two and one-quarter ounces.

The alignment of the hammers is then corrected and the length of the
hammer stroke, as laid down in Chapter XII, is adjusted by means of the
capstan screw or rocker. The jack is so regulated by its button and
screw that the trip up of the jack occurs when the hammer is 5/32 of an
inch from the string. The checks must catch the hammers when they have
fallen three-quarters of an inch away from the strings. The tails of
the hammer-moldings must be roughened and the checks be so slanted that
the catch is sure and tight.

The escapement lever is then considered. The spring that governs it
requires adjustment. It must be sufficiently strong to cause the hammer
to dance and jump a little on the lever when the key is released. The
escapement lever must also be regulated by means of the hook that is
found at its rear end. There must be space enough between the hook and
the lever to ensure that the catch of the hammer by the check is at all
times free. The screw that regulates the rise of the escapement lever
must also be attended to. It is necessary that the movement of the
lever be arrested before the hammer has quite risen to the point of the
trip up of the jack.

The after-touch under the front of the keys is regulated by means of
paper punchings. If enough punchings are placed under the keys to make
very hard pressure necessary to force a release of the hammer, then
punchings of 1/32 of an inch in thickness must be removed to make the
after touch correct.

The keys must also be made to descend evenly as judged from the top.
Unevenness is corrected also by the judicious use of punchings. In
regulating the dampers there are many small details to be watched. The
lifter-wires must work freely in the bushings and the heads must lie
straight upon the strings. This is especially important as regards the
bass wedge-dampers. There must be a small space between the damper
levers and the felted backs of the keys and the rise of the damper
heads when the levers are lifted must be even and facile. The height of
ascent of the damper heads must not exceed one-fifth of an inch, and
a little more when the whole of them are lifted by the pedal-rod. The
sostenuto rod must also be adjusted so that the damper lever tongues
are caught when the rod is revolved. Care must be taken that the rod
does not catch the tongues when the pedal is not in use.

The pedal mechanism is simple. It is essential to see that the feet
work in the lyre without scraping; hence lubrication with graphite and
tallow is necessary. The rods that connect with the action levers must
so engage as to be just in contact without bearing too much. The soft
“_piano_” pedal must engage with the shifting lever so as to allow a
small space between it and the point of contact with the key-frame.
The strength of the reaction spring in the case must be arranged so
that the key-board is pushed back with promptness upon the release of
the pedal. The “_forte_” pedal must be adjusted so that its connecting
rod is in contact with the damper lever lifting rail, but not enough
to operate without the depression of the pedal. The sostenuto pedal
requires to be arranged to revolve the sostenuto rod instantly. Here
the rod has to be revolved its entire distance before it operates and
the adjustment may therefore be made quite close.

These directions will enable one at least to be sure that the
regulation of a grand pianoforte action has been properly done;
although it is not to be expected that the innumerable small details
of practical work are to be learned other than practically. It must
especially be borne in mind that the use of tools and facility in
handling them and making definite adjustments with them is a matter of
long and patient practice. The above instructions are intended merely
to set the routine method before the reader, so that he may approach
the subject with a correct knowledge of principles.

The regulation and adjustment of the upright action is precisely
similar as to principles. The differences occur through the somewhat
dissimilar method whereby repetition is attained and the great
variation in the general position of the parts with reference to the
strings.

The action of the upright is fastened, by means of the metallic
brackets, to iron bolts which are set up in the key-bed. The height
of these bolts depends upon the dimensions of the instrument and the
striking point of the strings. In setting the action in place great
care must be exercised in seeing that the hammer line lies truly in
regard to the run of the strings. Errors in the casting of the plate
often lead to a distortion of the true string-line and the action
finisher must take care to set the action with due regard to these
matters. When the action, which is minus hammers and dampers, is thus
set in, the keys may be placed under it for the purpose of marking the
points where the capstan screws or rockers must be set. The hammers and
dampers are then glued in and adjusted for position with regard to the
strings. If the action and keys are truly proportioned, it is always
possible to make the length of the key just as recommended in the last
chapter. Sometimes the size of the pianoforte makes impossible the
employment of capstans or rockers with abstracts. In this case it is
customary either to use a dowel prop or to lay the wippen directly upon
the key. When the dowel prop is used it is driven firmly into the key,
and its upper end, which is a wooden rod into which the lower spike is
screwed, impinges against the wippen. In laying the place for the dowel
to be driven, it must be remembered that it is necessary for the head
of the dowel to hit the bottom of the wippen squarely. But the dowel
describes a curve at its head when the key is moving, and the wippen
has to be provided with a felted foot, curved so as to accommodate this
circular motion of the dowel. This motion must be observed carefully,
so that the dowel does not lay too far forward or back of the wippen
foot when the key is at either of its extreme positions. The regulation
proper now begins.

Abstracts, or dowels, are always regulated by a screw. This is either
in the form of a capstan or of a rocker, or of the movable part of
the dowel itself. The adjustment must be made with reference to the
position of the jack under the hammer butt. It is necessary that the
jack be just in contact with the notched heel of the butt. After the
hammers and dampers have been put in and their positions with reference
to the keys adjusted, it becomes necessary to regulate the escape
of the hammer by means of the regulating buttons and the jacks. The
directions given for grands apply here. The hammer springs must be put
in place and the fall of the hammers noted. If they stick, the bushings
are too tight or some cognate trouble exists which can be easily
remedied with a drop of oil on the affected part.

The checks must be adjusted to the back-stops and made to stand square
to them and they must also be arranged to catch the back-stops when the
hammer has recovered about two-thirds of an inch from the string. We
know that the length of the hammer blow should be from 1-24/25 of an
inch in the bass to 1-9/10 of an inch in the treble.

The tapes must be adjusted so that they begin to exercise their
pull when the hammer is started away from the strings. They must not
be strained too tight, but should be left just a little loose, so
that when the soft pedal pushes the hammers towards the strings the
abstracts or dowels do not at once leave the keys.

The dampers are adjusted, as to position, like those of the grand--that
is, they must lie square on the strings and be in a straight line with
one another. Their movements are directed by the spoons and these must
be so bent that the damper begins to move when about one-third of the
angular motion of the key has taken place. When actuated by the pedal,
they must fall against the back of the hammer spring rail, which is
felted for the purpose, and their motion must be instantaneous when
the pedal is depressed. The pedal mechanism is concealed behind the
bottom frame of the case and will be found to be precisely similar
to that of the grand, except as regards the mounting and pivoting of
the levers. These must be kept lubricated with graphite and tallow to
prevent squeaking. The connection of the soft pedal with the hammer
rail must be close so that instantaneous action results when the pedal
is operated. The motion of the pedal may push the hammers one-half of
their stroke length towards the strings, not more.

The leveling of the keys and the regulation of touch have already been
described; nothing further need be said except that these operations
are more easily performed in the upright owing to the open way in which
everything is set in.

It is unnecessary to go further into detail in regard to the regulation
of actions. Enough has been said to lay bare the general principles,
and, as was stated before, the rest comes from experience only. A
text-book can never replace an apprenticeship, but we cannot deny its
value in laying down correct principles for the man who wants to know
how things should be done.

As a fitting conclusion to the present discussion, we may now note the
order of the various processes which combine to make up the manufacture
of a pianoforte, from the cutting of the lumber to the final tuning in
the wareroom.

The various kinds of lumber that are to be used are exposed, after
cutting and rough dressing, in a lumber-yard. Here they remain from
three to ten years according to the kind of wood and the degree of care
that is taken by the manufacturer. The best makers take the greatest
care in seasoning their lumber.

The first operations to be considered are those of the saw-mill.
Here the rough work for the case-making is done, and the moldings for
actions and cases are turned out. The rough cases are then sent to the
case department and made up into shape. The bent rims are there glued
together for the grands, and the sides and frames of the uprights are
shaped. The back framing, wrest-planks and other parts of the case and
back construction are also put together in the case department.

In the meantime, the machine work has gone in the rough from the
saw-mill to the “action department,” where it is cut, shaped and
made up into the delicate action parts. These have to be leathered,
felted, provided with brackets, springs and the other accessories and
assembled. The hammers are covered, dampers, prepared, and the whole of
the action work is thus made ready against the time when the case shall
be in condition to receive it. This action and hammer work is generally
done by specialists, who supply many different makers with actions
according to their particular scales and patterns.

Meanwhile the cases have been sent to the varnish room and are here
prepared with filler and stain to receive the varnish finish. The best
instruments have their cases left about four months in the varnish
room, receiving eight or ten coats at intervals of ten days or more.

While this is going on, the sound-board department is occupied in
preparing the sheets of spruce for manufacture into sound-boards. Here
great care and skill are necessary to obtain the proper gradation of
thickness at all parts of the board’s surface. When the boards are
finished, they are put into drying rooms, to remain until wanted for
ribbing, bridging and insertion within the instruments.

The first operation in the assembling of the parts is performed by the
“bellyman.” He takes the sound-board, ribs it and affixes the bridges
according to pattern, bores the tuning pin holes in the wrest-plank,
and fastens on the iron plate, which was cast to pattern in the iron
foundry, to the back, upon which the completed sound-board has by this
time been glued.

Then the “stringer” receives the bellied back, puts on the strings and
pressure bar (if the latter is used instead of agraffes). The first
rough approximation to pitch is then made by the “chipper,” who pulls
the strings up roughly two or three times in succession at intervals of
about twenty-four hours.

The case is then turned over to the “side-gluer,” if the instrument
be an upright. The case of the grand is incorporated with the back and
is put together before the bellying. The side-gluer affixes the sides
and key-bed of the upright and also the bottom-board, which contains
the trap-work for the pedal mechanism. If the instrument be a grand
this department confines itself to the fitting and adjustment of the
lyre. After the sides are thus affixed the case is returned to the
“flowing-room,” where the final coat of “flowing” varnish is carefully
applied. This requires ten days to dry hard.

The case is now ready for the “action finisher.” His work of setting
in the action and keys and putting the instrument into rough playing
condition has been described in detail.

The pianoforte is then given its first rough tuning by the
“rough-tuner,” who surrenders it in turn to the “fly-finisher.” In this
department the top and bottom frames, fall-board, panels, key-blocks,
name-board, key-slip, hinges, music desk and other parts of the cabinet
work are adjusted and fitted. After fitting they are removed from the
case and sent to the “polishing department” to be made ready for the
final setting up.

The next operation is performed by the “action regulator.” His work,
which includes the finishing touches to the adjustments made by the
action-finisher and side-gluer, has already been gone over in detail.

The instrument is by this time ready for another and somewhat more
careful tuning. Here appears the “second tuner.” The instrument then is
permitted to remain in its existing condition until two more tunings
have been given at intervals of a week.

The “fine-regulator” next takes the instrument and proceeds to review
the work of the action-regulator and correct any deficiencies in touch
or repetition that may have been effected by the pounding of the rough
tuners.

The “tone-regulator” is next called upon, and his delicate work is
needed to give to the pianoforte evenness of tone throughout and an
agreeable quality.

Then the polishers rub down the sides, the smaller parts being already
polished as noted before, and give to the instrument its glossy and
mirror-like finish. The “setter-up” then puts the various cabinet work
parts together and the “fine-tuner” gives the final tuning. Lastly, the
superintendent looks over the whole work, and woe betide the unlucky
wight who has slurred or skimped his part.

The details listed above are, of course, subject to variations in the
order in which they are performed. The variations are according to the
practice of individual shops. Of course, it may at any time be required
to give more tunings, especially if the pianoforte is left on the floor
of the factory very long. But there should never be less than four or
five.

When the instrument is sent to the wareroom or shipped to the dealer
extra tunings are given according to the caprice or knowledge of both.



CHAPTER XIV.

TUNING AND TONE REGULATION OF THE PIANOFORTE.


The art of tuning the pianoforte is one of considerable complexity and
obscurity. During all the time that has elapsed since the key-board
instrument first came into being, controversies innumerable have raged
over the multifarious questions that the practice of the art implies.
This distressing state of affairs is primarily due to the fact that a
system of “tempering” the sounds produced by key-board instruments is
necessary, in order that playing in more than one key may be possible.

The whole matter of musical intonation was treated with some
completeness in the early part of this work, and the reader may
be expected to comprehend the principles of the Equal Temperament
upon which the tuning of the pianoforte and of all other fixed tone
instruments is now universally based. It is not within our province,
in the course of a treatise upon the principles of pianoforte
construction, to venture too deeply into the quagmires that surround
the aspirant for the honors of the tuner. The discussion of musical
intonation and the Equal Temperament was made for the principal
purpose of acquainting the student with the reason for the peculiar
construction of scales, as to their string lengths, and to make clear
the _raison d’etre_ of the frequent divergences from theoretical
proportions of strings and tones that we have been obliged to note.

The scale designer is better equipped for his task, however, if he
possess a working knowledge of the principles upon which the science
and art of tuning are based. This is the justification for the space
and time devoted to the exhibition of certain of these principles in
the earlier portion of this book. As a further contribution to this
useful body of knowledge, we shall point out here the general scheme
whereby the tuner proceeds to the execution of his important, indeed
essential, portion of the whole work.

The practical work of tuning is performed by the aid of certain
acoustical phenomena which enable the tuner to distinguish between
sounds that are very nearly in unison. As the Equal Temperament
requires the slight roughening of all the intervals with the exception
of the unison and octave, it is clear that there is great value in a
method of estimating, not only the unisonal or non-unisonal condition
of two sounds, but also the exact amount of difference that may occur
between them. The phenomena mentioned are called “beats,” and it is
well that their physical basis should be described here.

From what has been said before, it is clear that musical sounds,
generated as they are by the periodic agitation of the air according
to fixed laws, are but the audible manifestations of a peculiar form
of air-motion. The particular form of air-motion can best be described
as a wave. Whenever a sonorous body is excited into vibration it
causes the surrounding atmosphere to make motions that correspond to
its own. A vibrating body such as we have described (together with the
segments thereof) partakes of a motion that may be compared to that of
a pendulum. There is a rhythmic swinging back and forth of the body
and its segments, with the result that the immediately adjacent layers
of air are excited into alternate states of compression and expansion;
or, more correctly, of condensation and rarefaction. This rhythmic
motion is imparted by the layers of air adjacent to the sonorous body
to the next adjacent layers, and so on. The result of this is that a
wave is formed, the length of which varies inversely as the number
of vibrations performed by the sonorous body. This wave is called a
sonorous wave.

Now we know that sounds are at the same pitch when they are generated
by sonorous bodies having the same speed of vibration, and it is
easy to perceive that, if two such bodies are sounding together, the
condensations and rarefactions of the layers of air will synchronize
with each other, so that both will be exciting condensations at the
same instant and likewise will generate rarefactions simultaneously.
And even if the two bodies have not exactly the same speed, the result
will be equally simple as long as their speeds bear simple ratios to
each other. Thus two bodies which are emitting sounds at the interval
of an octave or of a fifth or fourth will generate condensations and
rarefactions in such a manner that they will not interfere one with
another. But the case is different where two sounds are separated
by differences in pitch that cannot be expressed by simple ratios.
For example, if one sound be one vibration per second higher than
another, it is clear that by the time that the first sounding body
has completed its given number of vibrations in one second, the other
will be one vibration behind. When, therefore, the vibrations of the
first body are continued into the next second the condensation of one
wave will be completely synchronous with neither the condensation nor
the rarefaction of the other. The obvious result is that at a certain
point the condensations of each wave concur while at another point
the condensation of one crosses the rarefaction of the other. In the
first case we have a considerable augmentation of sound and in the
other case a complete silence. As the waves thus approach and recede
there is a gradual diminution of sound followed by a complete cessation
for a small fraction of a second, and then a gradual increase until
the point of greatest augmentation occurs. This latter happens when
the two condensations concur, and the gradual rise and fall of the
sound correspond to the gradual approach of this concurrence in the
first case and to the similar advance of the point of crossing in the
second. This phenomenon of alternate augmentation and diminution of
sound separated by an almost inappreciable interval of silence occurs
whenever two sounds of nearly the same pitch are heard simultaneously.
These peculiar changes in the intensity of a sound are denominated
“beats.”

This description of the physical nature of “beats” will be sufficient
to make clear to us how a recognition of them is of value to the tuner.
From what we have just said, it will be observed that the number of
beats that may be set up between any two sounds depends upon the
difference in the frequency of the two sonorous bodies. So that the
number of beats form a true guide to the exact amount of difference
between sounds that are nearly in consonance. Thus, if it becomes a
matter of tuning a certain interval a little flat or sharp, in order to
comply with the requirements of Equal Temperament, the operation may
be readily performed by observing the number of beats that are heard
between the two sounds when one of them is sharpened or flattened.
So that all schemes of tuning must necessarily be founded upon a
recognition of this important phenomenon.

At this point it will be well to reiterate the fact that the Equal
Temperament owes its popularity and long prevalence to the wonderful
facility of modulation which it possesses. While it certainly involves
discords and disharmonics that the mesotonic system, for instance,
avoided, yet the fact that it does not limit the expression of
musical ideas to a few scales, but permits the composer to roam at
will through the whole field of tonalities, has given to it a deeply
founded popularity that has not yet been seriously challenged. We
must bear in mind that the Equal Temperament is the first fact, the
“prius,” the “proton hemin,” as it were, of musical performance.
Obviously, therefore, the importance of a proper and close adherence
to this system in the tuning of fixed-tone instruments cannot be
insisted upon too strongly. The reader has already had occasion to
examine a comparative table which showed the pitches of a true and of
a corresponding tempered scale. He will have noted that the tempered
scale errs very greatly in respect to certain intervals. The task of
equalizing the thirteen sounds which a fixed-tone instrument allows
to the octave, involves in each interval a greater or less divergence
from purity, according to the ratio of such interval. Thus we find
that the error of a tempered third is greater than that of a fifth,
and so on. Now, if the four minor thirds within the compass of an
octave be considered, it will be found that the octave to the tonic
which is produced from the last of these is a good deal sharper than
the octave taken direct from the tonic. Again the octave produced from
the building up of the three major thirds within the same compass is
very much flatter than the octave taken direct from the tonic. Again,
it will be remembered that there are twelve fifths within the compass
of seven octaves. The last sound in this progression of fifths is
considerably sharper than the sound that is produced by taking a series
of seven octaves from the tonic. Without going into figures, we may
give the differences thus noted concisely as follows:

In the cases above considered the octaves obtained by building up
intervals differ from the straight octave in the following proportions:

The octave produced from minor thirds is sharper in the ratio 1296:1250.

The octave produced from major thirds is flatter in the ratio 125:128.

The octave produced from fifths is sharper in the ratio 531441:524288.

Obviously, therefore, it will be necessary to tune all the minor
thirds, within an octave, flat by one-fourth each of the ratio given
for them. It will also be necessary to tune each of the major thirds
sharp by one-third of the ratio proper to those intervals. Likewise
each of the perfect fifths must be made flat by one-twelfth of the
ratio given above for fifths.

We are thus able to understand just how great divergencies from purity
are involved in the Equal Temperament of major thirds, minor thirds and
fifths. As far as the other intervals are concerned, it is obvious that
if the thirds and fifths are equally tempered and the octaves tuned
quite purely, the other intervals will be subjected simultaneously and
automatically to a similar process of temper.

Now from what we learned of the phenomena of beats, we must conclude
that the tempering process when applied to these intervals will
generate beats between the sounds that compose each interval. We know
that beats must occur when the sounds that form any consonant interval
are not quite in tune with one another. We also know that the frequency
of the beats depends upon the difference in frequency of the generating
sounds. We can, therefore, easily see that those intervals that are
subjected to the greatest amount of tempering will produce the greatest
number of beats. And further, as the actual frequencies of the sounds
increase according to their pitch, it is equally obvious that the
tempering will result in greater differences as to actual frequency
between the true and the corresponding tempered intervals. Therefore
the number of beats that any tempered interval generates varies
directly as the pitch of the sounds that form the interval. The higher
the pitch, the greater the number of beats. Conversely, the lower the
pitch, the smaller the number of beats.

Now we have already noted that the phenomena of beats afford an
absolutely precise test for the consonance or otherwise of an interval.
If we can estimate the number of beats that should occur between the
sounds of any given equally tempered interval, we can always tune such
an interval in the Equal Temperament by noting the number of beats
and adjusting this to the theoretical number in the calculations. It
is not possible accurately to follow the number of beats that are
supposed to be between any given intervals in Equal Temperament even
when the pitch of the tonic of the interval that is being tuned is
precisely similar to the corresponding sound in the calculations. It
is not possible, therefore, in practice, to tune with such accuracy
as theory would demand, but an approximation may be obtained. If we
could secure an absolute standardization of pitch for the pianoforte it
would be possible to construct tables that would show the exact number
of beats that ought to occur between all the equally tempered sounds
within the whole compass. In default of such a method, it is necessary
to resort to a variety of tests and to prove the correctness of the
tempering of each interval by comparison of the different intervals of
various kinds that to which each sound, as it is completed, gives rise.
If, for example, we find that any given sound, when tuned, gives the
same number of beats with the tenth below as it does with the third
below, which is one octave above the tenth, then we have some assurance
that the sound in question is properly tempered. If this assurance is
confirmed by a complete absence of beats between the given sound and
its octave, above or below, then we have an almost absolute assurance
as to the correctness of the work.

It is then upon the phenomena of beats that the tuner depends for a
guide to the correctness of the work in which he is engaged. By noting
the frequency of the beats at some places, or their absence at others,
he is able to judge most accurately whether any interval is tuned
too sharp or too flat, or whether any octave is tuned purely or the
reverse. All good tuning depends entirely upon such estimation of the
beats, and the greatest difficulty that the tuner encounters lies in
the fact that he must try to equalize the frequencies of the beats
between all the intervals of the same kind within the compass of each
octave. If this work is well and truly done it properly deserves the
name of art, and, indeed, fine tuning is a fine art, one to be acquired
by the painful and slow processes of manual practice and mental
application. He who overcomes all obstacles to success and masters
thoroughly the principles and practice of tuning is an artist in the
truest sense.

In applying these principles to the tuning of the pianoforte, the
problem that confronts us is to devise a rapid and simple means of
tempering each sound within the seven odd octaves of the instrument,
and to do this in such a manner that the deviation from purity shall be
the same for all similar intervals within the compass of each octave.

Now it follows, from what has gone before, that the tempering of each
separate interval, by itself, and without reference to any other,
would be a very tedious and inaccurate process. It would, in fact, be
quite impracticable to employ such means for intervals that require
relatively large deviations from purity, especially in the higher
pitched registers. There is, however, a method that largely obviates
these difficulties. The middle octave of the instrument, which runs
from F below middle C to F above it, is chosen, and the intervals
within this octave are so tuned that the thirteen semitones which it
contains become equally tempered sounds. The sounds within the next
octave above or below are thereupon tuned from the former, each to its
octave above or below, and this process is continued until all the
sounds upon the key-board have been tuned.

It is easy to see that such a method possesses many and great
advantages. All the difficult tempering of intervals that require large
deviations from purity is confined to that portion of the piano where
beats are most easily estimated; while the rest of the instrument is
tuned by means of octave intervals, in which the test of purity is
absence of beats, rather than the estimation of any number of them.

The tempering of the intervals in the middle octave is called “laying
the bearings” and is the most difficult, as it is the most important,
of the various processes incident to the practice of pianoforte tuning.
The “accumulation of insensible into almost intolerable errors,” as
Mr. Ellis aptly terms it, continually besets the path of the tuner,
especially if his preliminary knowledge be imperfect. The true
estimation of beats, as generated by various intervals, is an art that
is but slowly and painfully acquired, by long practice and training of
the ear.

Examination of the pianoforte key-board shows us thirteen sounds within
the compass of an octave. In proceeding to the conversion of these into
equally tempered sounds, we have more than one method presented to us.
We shall, of course, choose the octave which, as stated above, runs
from F below middle C to F above it, and shall use, for our purposes,
such adjacent sounds as we may consider necessary.

It is usual to take from a tuning-fork the pitch of the sound from
which the tuning is begun. These instruments are tuned either to C, or
A next above middle C. It is usual, in this country, to tune from C,
and we shall, therefore, adopt that method.

Now there are various ways of setting about the “laying of the
bearings.” Some tuners work by thirds, others by fourths and fifths;
others again use a series or circle of fifths joined by octaves.
Whatever intervals are tuned, the idea is to include all the thirteen
sounds within the octave and to use, as far as possible, only one or
two kinds of intervals.

Of all these methods, the shortest, easiest and most accurate is that
which employs fourths and fifths only. It is used in such a manner
that, by tuning a circle of fifths and fourths, the last sound tuned
provides the octave to the first, thus completing the circle and the
octave of tempered sounds.

[Illustration: tuning music notation]

In this method we proceed as follows:

   1. Pitch C is tuned by the tuning fork.
   2. F below pitch C is tuned, being a tempered fifth.
   3. G below pitch C is tuned, being a tempered fourth.
   4. D above G is tuned, being a tempered fifth.
   5. A below D is tuned, being a tempered fourth.
   6. E above A is tuned, being a tempered fifth.
   7. B below E is tuned, being a tempered fourth.
   8. F sharp below B is tuned, being a tempered fourth.
   9. C sharp above F sharp is tuned, being a tempered fifth.
  10. G sharp below C sharp is tuned, being a tempered fourth.
  11. D sharp above G sharp is tuned, being a tempered fifth.
  12. A sharp below D sharp is tuned, being a tempered fourth.
  13. F above A sharp is tuned, being a tempered fourth.

This last F is the octave to the first F tuned, and should coincide
exactly with the latter.

The reader will, of course, realize that the tempering of these
various intervals must be tested by means of the generated beats.
Helmholtz, in “Die Lehre der Tonempfindungen,” calculates that the
tempered fifths should average .6 of a beat per second at standard
pitch within the octave that we are treating. This is equivalent to
three beats in five seconds. But it is impracticable to measure the
generated beats upon the pianoforte in this manner. The tone of the
instrument is too evanescent and fleeting. We may, however, attain to
a very fair approximation. If, for example, each fifth be tuned so
that two distinct beats are heard before the sound dies away, it will
be found that the beat-rate is a near approximation to the calculated
average. The two beats that we speak of occur in about three seconds,
while the Helmholtz rate is three and one-third seconds for two beats.

Again Helmholtz gives an average beat-rate for tempered fourths in
the same octave; namely, one per second. If we tune the fourths so
that we hear three distinct beats we shall likewise obtain a very fair
approximation to the calculated beat-rate.

We showed above that the last sound produced by the building up of a
progression of twelve fifths is sharper than the sound produced by the
piling up of seven octaves from the same tonic. The two sounds thus
produced ought to coincide, for the compass of twelve fifths and of
seven octaves is the same. We concluded, therefore, that the Equal
Temperament required the flattening of all the fifths.

The meaning of the discussion is, therefore, that the fifths within
the octave where the “bearings” are being laid must each be tuned flat
by two beats. Or, rather, that the higher sound of every fifth must be
flatter by two beats than if it were in consonance with the lower sound.

Again, if we tune the F below middle C two beats sharp of the latter
(which is equivalent to tuning the fixed pitch sound C two beats flat
of F) we shall obtain a properly tempered fifth. Now, if the octave
above this F be taken it will be found to form a sharp fourth with
middle C. For example, if the pitch of middle C be 264, then the pitch
of F below it, in pure intonation, is two-thirds or 176. Assuming that
the F be then tempered so as to be sharp by two vibrations, it will
have a frequency of 178. The octave to this is 356 But this latter is
a fourth above C 264 and should, therefore, be 352 Consequently we see
that the fourths in Equal Temperament are to be tuned sharp ascending,
or conversely, flat descending. As already explained, the beat-rate in
the “bearings” should be nearly one per second or three beats, while
the sound of the interval remains audible.

When the deviations from purity are as slight as in the cases that we
have been considering, it is by no means easy to determine, at all
times, whether the note that is being tuned is sharp or flat of its
tonic. For the beats occur similarly in either case and few ears can
determine the relative sharping or flatting without some extraneous
aid. Fortunately, however, we have a variety of tests open to us, which
for completeness and accuracy leave nothing to be desired.

To take a concrete example, during the “laying of the bearings” we
first tune the F below middle C, then the G below middle C, and then
the D above G. When we reach this last note, we find that a sixth has
been obtained; namely, F--D. Now if the notes already tuned have been
tempered, so as to be too _flat_, the resultant sixth will beat too
_slowly_, and, conversely, if the tuned notes be too _sharp_ the sixth
will beat too _fast_.

This test may be amplified when we proceed to the next interval, D--A.
When this latter note has been tuned, we have the triad F--A--C. F--A
is a major third, and by referring to previous calculation we see that
as such it must, when properly tempered, be considerably sharp. By
noting the beats of the major third and likewise the beats of the sixth
we may correct the tuning of all the sounds with which we have hitherto
dealt. The same process is, of course, carried on throughout the whole
process of “laying the bearings.” The major thirds and sixths are
tested continually as the tuning proceeds, and thus is provided a sure
guide to the correctness of the fourths and fifths.

The correct beat-rates for the major thirds may be stated as about
eight per second, while that for the major sixths is approximately
eleven in the same period. Of course, as already stated, these rates
per second cannot be measured with accuracy, but with practice one soon
discovers by ear the proper roughness in each case, and is thus enabled
to estimate the beat rates without much trouble. Every opportunity of
examining the work of good tuners should be taken by the observer, who
should note carefully the beat-rates which they assign to each kind of
interval. In this way he will provide himself with practical examples
of tempering of intervals which will be of great value to him.

Having thus determined the proper beat-rates for each of the intervals
that are used in the “laying of the bearings,” we may proceed to the
further consideration of that convenient method for tuning the middle
octave that has already been demonstrated.

In order to facilitate comprehension of the argument, the following
table is given, showing graphically the sounds that are tuned in laying
the bearings and the tests and trial chords--

The white notes are those to be tuned. The black notes are those
already tuned.

The kind of deviation from purity of interval and the beat-rates are as
follows:

Upper notes of fifths must be tuned flat so as to give two distinct
beats.

Lower notes of fourths must be tuned flat so as to give three distinct
beats.

Upper notes of major thirds must be sharp so as to give approximately
eight beats per second.

Upper notes of major sixths must be sharp so as to give approximately
eleven beats per second.

If the laying of the bearings has been accurately performed, the
chords that are produced by the combination of the various sounds
will be found to have very nearly the same roughness and to generate
approximately the same number of beats. The best work is that which
most closely approaches this standard.

After the bearings have thus been laid, it is necessary to continue
the tuning of the instrument above and below the octave already
treated. Now, since the octave to any given sound has exactly double
the frequency of the former, and since octaves are to be tuned purely,
it follows that we need only tune the remainder of the instrument by
octaves up and down from the “bearings.” The consonance of an octave is
determined by the absence of beats, and, consequently, we have only to
follow this rule to reproduce, in all parts of the piano, deviations
from purity _relatively_ the same as those which we have been at such
pains to secure.

Of course, the _actual_ number of beats in any given interval varies
as the frequencies, and, consequently, the frequency of the beats
increases regularly in the higher registers, while it similarly
decreases in the lower portions. Thus the deviations from purity become
much greater in the higher portions of the compass and incorrect
laying of the bearings is, therefore, productive of more and more
disagreeable results as the scale ascends. On the contrary, in the
lower register these inaccuracies are less productive of irritation, as
the frequencies of the beats become continually less.

Such, then, is the process of tuning the pianoforte in Equal
Temperament. We have made no attempt to go into those practical details
that are concerned with the ear-training, the manipulation of the
hammer, or other cognate matters. These are entirely “_ex provincia_”
of this work.

Nevertheless the person who digests the foregoing statement of the
laws and methods of the art will be well equipped to pass upon the
correctness of tuning, and this is sufficient for our purpose.

The work of tone-regulation opens up varying but not entirely
dissimilar fields of research. The material of which the pianoforte
hammer is constructed has an important influence upon the coloring of
the sound that it draws from the string. In order that the influence of
the pianoforte hammer in tone-coloring may be understood clearly, we
shall investigate the matter with some completeness.

We have already investigated the compound nature of the sounds excited
by the pianoforte strings. We know that the nature of these sounds
varies as the method of excitement and as the nature of the resonance
apparatus that surrounds the strings. Now the pianoforte strings are
excited by being struck, and we have already noted that the point of
striking must be carefully chosen. Further, we know that the amount
of metal framing, the manner of adjusting the bridges, the nature
of the sound-board and innumerable other details must be taken into
consideration.

But by the time that the pianoforte comes into the hands of the
tone-regulator, it is out of his power to affect the construction in
any fundamental points. He is able to change only two things. These
are the striking point and the condition of the hammer-heads. Even the
former cannot be changed to any great extent. In the highest treble,
however, it often becomes necessary to bend the hammer-shanks slightly
in order that a more correct striking point may be obtained. But this
must be done with great discretion and caution.

The object of tone-regulation is to ensure an agreeable tone and
perfect evenness of quality throughout.

Obviously, this is so intimately bound up with the whole construction
that it may be said that the tone-regulation begins with the drawing
of the scale and is never finished until the pianoforte itself is
completed. This would be a perfectly proper statement, but we have here
to consider the final touches, as it were, that the tone-regulator may
give to the tonal equipment.

When the instrument comes into his hands the hammers are still covered
with the hard outer skin of the felt head. This must be removed with
a sand-paper file. It then is necessary to sound each tone slowly
and carefully, first loudly, and then less so. It will be found that
some of the hammers produce a harsh and disagreeable timbre, while
others may be too soft and mushy. Under all circumstances it is far
better to endow the instrument, as far as is possible, with a quality
that shall be comparatively mellow and round. Brilliancy cannot be
forced artificially without spoiling the whole quality and imparting a
thinness and roughness that is most disagreeable.

If the hammers are too hard at the crown, they have the acoustical
effect upon the strings of exciting the upper dissonant partials to
undue prominence. This occurs from the fact that when the head is hard
it rebounds instantly from the string, and thus does not damp any
of the dissonant partials. On the other hand, if the head be soft,
the felt clings for a fraction of a second longer to the strings and
effects the damping to a greater or less degree, according to the
relative softness or hardness of the head.

It is thus possible, by discreet manipulation of the felt, to influence
the character of the sounds to no small degree. The method is to pick
up the felt, when it is to be softened, with a set of felt needles
mounted in a handle for the purpose. It is essential to note whether
the sound is the same when the hammer strikes with great force as it
is when it strikes gently. If, for example, a gentle pressure on the
key gives an agreeable quality, but harder strokes on the key destroy
this, then we see that the crown of the hammer head is soft enough, but
the felt cushion underneath is too hard. Fine needles are, therefore,
employed to dig into the lower cushion of felt, while disturbing the
consistency of the upper crown as little as possible. On the other
hand, when the quality of sound is hard under all conditions, the upper
surface of the hammer-head must be treated by picking it with heavier
needles. Hardening of the felt may also be undertaken by covering the
hammer-head with a damp cloth and then applying a hot iron.

The whole work is primarily one of practice and experience. No
directions can do more than give an outline of the processes and
the physical reasons for them. It is well, however, to lay down the
laws that underly these processes, in order that practice may be
supplemented and improved with theory.



CHAPTER XV.

THE DRAUGHTING OF THE PIANOFORTE SCALE.


Although, for obvious reasons, we speak of it thus late, yet it is
true that the first and most important step in the designing of a
pianoforte is the draughting of the scale. This process includes a
complete planning of the iron plate and of the bridges, in fact of the
whole arrangements for stretching the strings and maintaining their
tension. This plan must indicate very clearly the exact length both of
the vibratory portion and of the waste ends of each string; it must
show the place on each string where the stroke of the hammer is to be
directed, while the exact positions of each tuning-pin and hitch-pin
must be laid down with equal certitude. Further, the place of the
belly-bridges, their dimensions and manner of pinning, have to be shown
on the drawing. Lastly, the fastening of the iron plate by screws and
bolts must be indicated; together with the precise position of each
individual screw, bolt and pin.

When this plan is in all respects complete, it has to be transferred to
a wooden pattern. The inevitable shrinkage of paper always makes the
retention of the proper measurements a matter of difficulty. This may
be overcome by making the first drawing upon a sheet of wood, varnished
to give a clear surface. If the drawing be made with India ink instead
of with pencil, we shall have a complete and permanent record obtained
in a superior manner.

When the wooden templet is to be made from such a drawing, it will
not be found that there has been the shrinking or swelling caused by
the use of paper, and the first drawing, if made after the method
described, may be laid aside for any length of time.

Let us suppose that it is desired to draught the scale of an upright
pianoforte. Having selected the size of pianoforte that is to be
designed and the wooden “table” which is to serve for the drawing
surface, we proceed as follows:

First lay down the line whereon all the hammers are to strike the
strings. From this line as base we plot out the string lengths and the
direction in which each runs; also the distance of each group from the
immediately adjacent groups.

Having laid down the striking point line, we next proceed to indicate
upon it, by suitable lines, the middle string of each three-string
group. For the two-string groups a line is taken in the middle of the
two strings. We call these lines “running lines.” Then the string
dimensions must be taken into consideration and calculated according to
the rules laid down already. The highest treble strings run at right
angles to the striking point line, and the running lines indicating
the positions of the groups are to be placed accordingly. The distance
between the running lines should be a shade more than one-half of
an inch at the highest portions of the scale. It is found necessary
to draw the running lines with increasing obliquity as their length
increases, until at the end of the treble sections they are running
at an angle of about 110 degrees counting from the treble end or 70
degrees counting from the bass end of the striking point line.

The lengths of the strings as determined by previous calculations mark
the line of the belly-bridge. The bars that are to be cast in the plate
must be allowed for in plotting the string plan. It is usual to place
one of these at about F₂ and another at C, where the over-stringing
customarily begins. The variations of individual scales and the
requirements of particular sizes of instruments sometimes cause changes
in this regard. This is one of the points that the designer must decide
for himself.

The space between the running lines increases gradually as the length
of them, on account of their oblique direction and the necessity for
providing sufficient space for the dampers and hammers. The actual
length of the strings as calculated must be laid down with reference to
the striking point line. As has been pointed out, it is found better
in practice to have the hammers strike the very high strings a little
above the theoretical place. A good average would contemplate one-tenth
of the length for the six highest strings, graduating down to one-ninth
for the rest of the highest octave and the next below it. Before the
lowest string of this last-named octave (C₃) is reached, the striking
point is gradually lowered and two or three strings below C₃ it becomes
one-eighth.

If we follow out this scheme we obtain the place where the scale
rib intervenes at the pressure bar by taking one-tenth, one-ninth
or one-eighth, as the case may be, of the length of each string.
The remaining fraction of the length represents the correct
distance between the striking point line and the nearest pin on
the belly-bridge. Thus the belly-bridge and pressure bar lines are
automatically formed as we go along.

[Illustration: METHOD OF PLOTTING STRING PLAN BY MEANS OF STRIKING
POINT LINE AND RUNNING LINES.

The sketch is intended merely as a general guide to the method outlined
above, and only a few of the running lines are shown. The dark lines
show the direction and position of the bars.]

When the scale rib and pressure bar line has been obtained, it is
necessary to make provision for the tuning pins, and particular care
must be taken that the strings shall not rub against each other owing
to incorrect placing of the pins.

When the drawing has thus been completed, we may take up the design of
the iron plate. It will be remembered that we calculated a compensation
factor for the shrinkage. This factor is 51/50, and all dimensions
where shrinkage may have effect must be multiplied by this amount.

Such dimensions are those of the height and width of the plate. Hence
the lengths of the bars, the distances between them, and the positions
of the bolts and screws as well as the string lengths must all be
modified according to the shrinkage factor.

The wooden templet may be taken directly from the wooden table drawing
by filling in the outlines and details of the iron plate on the latter
and then copying these on to the templet subject to the shrinkage
modifications required. It is well to regard one top side and also that
at the treble as immovable, and to consider the shrinkage as coming
from the bottom to the top and from the bass to the treble.

When the dimensions of the proposed plate are thus laid out on the
surface of the templet, the bars, screw-sockets and bolt holes must be
copied in wood and laid on the templet in the exact places that they
will occupy in the finished plate. Thus we gradually evolve a complete
wooden model of the iron plate, so that the iron founders may readily
obtain a correct casting.

When the first casting comes back from the foundry, it should be
carefully punched for the tuning-pin, bolt and screw holes. The first
casting must be considered in reference to the fact that it represents
only one shrinkage.

After the second casting is made from the first, the correctness of
the calculations may be judged. But not until the first pianoforte is
turned out according to the new scale can the designer find out how
well his efforts have been rewarded.

Of course, the foregoing directions are but outlines of the method.
The true inwardness of scale draughting cannot be explained here, or,
indeed, otherwise than by practical experience. A certain facility in
mechanical draughtsmanship is essential, and also close attention to
the methods that have been laid down in regard to striking points,
number of covered strings, number and place of bars, compensation for
shrinkage, and the various other points that have been mentioned.

For the convenience of the plate-finisher, wooden patterns are
provided, showing the position of hitch-pins, tuning-pin holes,
screw-holes and bolt holes, corrected for shrinkage.

The belly-man must have patterns for the position of the bridges and
for the bridge-pin boring. A wooden pattern is also required for the
pressure bar.

When these details are completed, the draughtsman must possess himself
in patience until his completed instrument is turned out.

If the rules so carefully demonstrated throughout this treatise are
fully digested, the designer will be far on the way towards correct
scale draughting. His native cunning, however, must be relied upon to
carry him through when written directions fail.



CHAPTER XVI.

CONCLUSION.


If the present treatise has convinced the reader that the making of
pianofortes is a very serious matter, and one not to be attacked in a
spirit of levity, then one of its immediate objects has been attained.

Indeed there has been an abiding fear in the breast of the author that
he might presently be charged with piling on the agony too strongly
and searching with excessive zeal for scientific causes and rules when
the shortest solutions may be found by empirical methods. This is not
really the case, however, for the whole problem of the construction
of pianofortes is naturally acoustical. While it is doubtless true
that many pianofortes have been and are continually made, not merely
with indifference to, but in defiance of, every law that has been
expounded in these pages, it nevertheless remains that none of these
have been good pianofortes. Of the making of thump-boxes there is no
end. Unfortunately for the public, musical ignorance is well-nigh
universal, and the impostor finds it easy to palm off shoddy in place
of the real article. Of course, it is quite true that bad pianofortes
are soon found out, but when the inevitable discovery comes, the
mischief has been done and the purchaser is, as usual, the victim.
A student of the construction of good instruments cannot fail to be
astonished that anyone should wish to turn out anything but the best.
For, as one continues to investigate the multifarious problems that
are continually suggested, the desire to overcome them and to produce
perfect instruments becomes almost irresistible. Perhaps this is why
the clever designer, if left to himself, often develops into a crank.
And, indeed, there is not an industry on the face of the globe that has
produced more cranks.

The files of the patent office are full of the ideas of unrewarded
genius that has spent its time, its money and its enthusiasm in the
unenviable task of producing innovations in pianofortes. No feature of
construction has been left unimproved; yet how many of these inventions
ever see the light? Few, indeed; and the fact is a sad commentary on
the unpractical nature of genius in general.

These reflections lead one to the feeling that a fitting conclusion to
a treatise on pianoforte construction may be made by giving particulars
of some of the most famous and revolutionary inventions that at one
time and another have been launched upon the unfeeling world of
piano-making. Not all of these by any means can be denominated freaks;
indeed there are the germs of most valuable developments in many of
them. We shall consider a few of the really valuable ideas at least.

Among these primacy must be given to the screw-stringing device of
Mason & Hamlin. This invention was intended to substitute a positive
mechanical fastening for the tuning-pin, in place of the wooden
wrest-plank. It consisted of a screw, threaded vertically in a socket,
which was cut in a projecting shoulder on the iron-plate. As it
extended below its socket, it was provided with an universal joint
which ended in a hook. On this hook the string was wound, and was then
free to pass on to the agraffe. A small T-hammer sufficed to turn the
screw and the string was tightened or slackened as the screw turned
in the threaded socket. The action was slow but sure, and the strings
had the curious property of sharping under a test blow instead of the
opposite, as is usual. The method of tuning was the same except that
the screw turned in the opposite direction to the ordinary style and
required much more turning to bring the string to the desired point.
On the other hand, however, setting the pin was unnecessary, and the
evils engendered by bad wrest-planks and sticking or twisting pins were
unknown. Moreover, the turning of the screw involved very slight effort.

With all these advantages, however, the reverse motion and the slowness
of action were fatal; and after several years of effort Mason & Hamlin
gave up the attempt to popularize their invention, and let it drop. It
is, indeed, unfortunate that this device did not become more popular,
as in that case its many inherent advantages would doubtless have been
emphasized and the bad points in it eliminated. Prejudice and the
tuners, however, were against it, and it died.

The well-known house of Brinsmead in London has also experimented
with a similar device, but it is not known with what success. One of
the advantages held out by the makers of such string devices was the
supposed facilitation of the work of tuning--that is to say, it was
alleged that every musician could become his own tuner as soon as he
had learned the theoretical principles of the Equal Temperament. The
hope was delusive, however. Perhaps the professional tuners attended to
this point.

Another similar but more successful device is being manufactured by the
Wegman Piano Co. This is in the form of a fastening for the pin in the
iron plate. The appearance of the plate and pin is not different from
the usual design, but the tapered end is done away with and the pin,
instead of being driven into the wooden wrest-plank, is fastened in
the plate by means of the friction set up between the peculiarly bored
hole and the back of the pin. A special twist is needed to fasten the
pin when a string is drawn up to pitch, but otherwise the method of
operation is not unusual. The device appears to be of value.

The sound-board has ever afforded a fertile field for inventive
genius. It has been altered in every conceivable manner, but the old
style continues to flourish with all its pristine activity. This is
not to say that it is ideal and insusceptible of improvement. On the
contrary, one cannot deny that many praiseworthy ideas have been
patented for the purpose of improving it. The ribbing has been the
subject of much attention from inventors. It is true that this method
of giving strength and tension to the board is by no means perfect. Yet
we find that the various devices proposed for the abolition of ribbing
have almost uniformly failed. A large number of these failures owe
their conditions to the lack of acoustical knowledge of the inventors.
It has often been supposed that the enormous relative resonance power
of the violin belly was connected in some way with the duplicate
nature of the resonance table and the consequent hollow shape of the
resonating body. This has been conclusively disproved, however, for it
has been shown that the violin’s special shape is given to it merely
for the purpose of bearing the strain of its strings. Moreover, the
tone and resonance of a violin have been reproduced by means of a
vibrating diaphragm and a horn. This device, known after its inventor
as the Stroh violin, satisfactorily disproves many cherished theories
in regard to violin resonance. In spite of these facts we find that
several patents have been taken out for pianoforte sound-boards, of
which the guiding principles have been ingenious applications of the
violin idea. The “_equilibre_” pianoforte of Frederic Mathushek was an
example of this type. It seems passing strange that experimenters have
not all become aware long ago of the essential differences between the
resonance apparatus required for struck and for bowed strings.

There have been other and saner variations of sound-board construction.
It has been suggested that the use of a double board composed of
two cross-grained thicknesses glued to each other would obviate the
necessity of ribbing and increase the power of resonance. There seems
to be little doubt that there is the germ of a valuable idea in this,
and if the notion is properly worked out, it will very likely produce
valuable additions to our knowledge of the phenomena of resonance.

Unusual ideas have been less frequent in the domain of action-making.
There have been several praiseworthy attempts to get rid of the
troublesome, but hitherto necessary, tape in the upright action. The
patent of Leo Battalia is one of these. He abolishes the tape and
bridle wire, and substitutes a two-branched spring fork projecting from
the jack. One branch works in a slot cut in the hammer butt and the
other bears against the back check. The back stop is done away with and
excellent repetition is assured, superior to that which is obtained by
ordinary methods.

In the domain of pure scale design, we note the ever present and
perennial notion of sympathetic strings. This idea has taken various
forms. The most conventional development is, of course, the “duplex
scale” of Steinway and others. This utilizes the waste ends of the
strings and scales off lengths of them that correspond to aliquot parts
of the vibrating length of each string, thus obtaining the advantage
of sympathetic partial tones. Most of the ideas in this direction have
gone further than this, however. Some makers have gone so far as to
have a fourth string tuned to the octave of every three-string group.
But this is surely unnecessary when we consider that the octave is, on
the pianoforte, the strongest partial tone of any musical sound, and
least of all needs adventitious aid.

There are many other similar devices used and unused that we should
waste our time in considering. In any case the true test of the utility
of an invention is use, and each one of these unusual notions that have
been put on the market would have been universal long ago had they been
uniformly practical and valuable.

We cannot close this hasty survey without mention of the remarkable
innovation in action mechanism devised by Mr. Morris Steinert. Here
the forcible hammer-blow is superseded by a gradual push on the hammer
at the strings, executed through the interposition of an articulated
double lever between the hammer and the jack. The result is to produce
a different form of hammer attack and a noticeable modification in
the coloring of the tone produced from the string. While the claims
of the inventor are somewhat exaggerated, there is no doubt that Mr.
Steinert has hit upon a valuable variation in the method of actuating
the hammer, and his invention opens up new prospects of pleasure to the
pianist.

If all these and the innumerable others have no other value, they
at least teach that inventive genius and the hunger for improvement
do not entirely sleep; that the pianoforte is continually being
improved, and that many are spending their time in finding new ways of
improvement. It shows that the value of the pianoforte to the community
is sufficiently great to cause the expenditure of much valuable thought
upon its mechanical and musical betterment. The fact that these things
happen should console anyone who has ever thought that the limit of
mechanical excellence had been reached.

The designing of a pianoforte is art with a big A. It demands of
its practitioners the temperament of an artist and the skill of an
excellent mechanic. There is no greater pleasure and no nobler work
than the construction of an instrument equipped to give forth lovely
tone and to interpret the inspired works of the masters of music. May
the advancing years bring the pianoforte as much more of mechanical and
musical excellence as the last two centuries have so richly imparted.

And now our task is done. It has been a labor of love to place the
results of long study and much practical experience before those to
whom this exposition of the principles of pianoforte construction might
be expected to appeal. It has been far from easy to put into really
intelligible and concise English an explanation of certain of these
laws; and if the reader finds here aught of vagueness or obscurity, may
he blame the subject rather than the author. The latter has, as best
he might, laid down the principles that underly the right building of
the noblest musical instrument that man has yet devised. And in the
contemplation of these principles he may properly be content to leave
his patient readers.



THEORY AND PRACTICE OF PIANOFORTE BUILDING.



APPENDIX A.

THE DEVELOPMENT OF THE PLAYER-PIANO.


Events are moving quickly in these latter days, and the conservative
pianoforte trade is feeling the effect of the extraordinarily active
spirit of constructive commercialism that is so pronounced a feature
of the contemporary industrial movement. When the first chapters of
the present work were in course of preparation, some two years ago,
the pianoforte equipped with an interior playing mechanism was just
beginning to be heard of; to-day its manufacture and marketing are
recognized features in the policy of nearly all pianoforte houses. It
would therefore be unwise to conclude the present treatise without
certain observations on the player-piano question, although a truly
philosophic temper would probably prefer that some further time elapse
before any feature of the player-piano problem be considered in a
work of the same scope and character as this. Abandoning the strict
scientific view of our duty in this matter, however, we may better
adopt a more popular _point d’appui_ and round off this work with a few
observations on the more important and essential underlying problems
connected with this new and remarkable movement in the pianoforte world.

Had the exterior type of pianoforte playing device--the so-called
cabinet-player, in fact--remained alone and supreme in the territory
that it first opened to exploration and development, this work would
contain no notice of any mechanism of the kind. But since the movement
has spread until it comprehends the pianoforte itself, since, in
the nature of things, such a development must profoundly affect the
solution of the problems that confront the pianoforte maker in the
construction of his instrument, it seems to be not only natural, but
imperative, that we should devote some space to certain notes on the
player-piano problem and its relation to the application of such
acoustical and mechanical principles as are germane to the theory of
pianoforte construction.

We are under no obligation to delve into the history of these ingenious
devices. The plan of this work requires nothing of the sort. We may
say, however, that the first impetus towards the production of a piano
playing mechanism came about through the success of the self-playing
organ which began to appear about fifteen years ago. Meanwhile various
inventors had experimented with electrical devices and had succeeded
in producing a mechanism that could be placed within the case of
the instrument without entailing any great distortion of form. Such
devices, however, were, with some exceptions, exceedingly mechanical in
effect, and did little to show the possibility of adequately rendering
pianoforte music through artificial means.

It was, however, through the successful development of mechanism
for the automatic operation of organs that the true principles
for piano-player construction began to come to light. Two leading
manufacturers had both produced reed organs of a very superior kind,
equipped with mechanical playing devices. The principle was pneumatic,
and was applied through the medium of compressed air. The organs
themselves were also operated on this principle, this being a return
to the old force bellows system, adopted in the European harmonium,
and always used in connection with the pipe organ. When developed to
their highest point, these pneumatic self-playing organs produced
superior musical effects, so that they became, and still are, well
known and popular. The latest styles, indeed, rival the orchestra in
their versatility and coloring, especially when operated by a skillful
musician.

The pneumatic principle thus applied, and the success of the attempts
to adapt it to the organ, led experimenters to emulate, and if possible
improve upon, the early attempts at the practical manufacture of
pianoforte-playing mechanism. Without going too much into details,
it may be recorded that the two concerns previously referred to were
nearly ready in 1896 to come out with such an instrument, and patents
were granted in 1897 for a complete piano-player of the cabinet style,
attachable to any piano, and easily detachable therefrom. Other patents
soon followed, and other manufacturers fell into line, with the result
that the great piano-player movement had soon begun in earnest. The
productions of the different firms, of course, varied in details, but
only two widely separated schools have developed, and inasmuch as both
of these employ the pneumatic principle, which has triumphed over all
others, and is now adapted unanimously by manufacturers who desire to
render possible an approximation to artistic rendition of pianoforte
music, it will be unnecessary to treat of any instruments constructed
on other lines.

In the meantime it will be well to note that the above short sketch
of the preliminary skirmishing, as it were, is intended to be nothing
more than an outline, as the policy adopted throughout this entire
work has been to avoid the historical view-point, as much as possible,
and to confine ourselves strictly to the business in hand; namely,
constructional principles and their application.

The pneumatic principle has been adopted in all the piano-players that
we have occasion to survey, and its application has been in all cases
essentially similar. Indeed, the two schools of construction differ,
not in the application of the pneumatic principle, but in certain
details of construction, which are important but not vital. One general
description will be quite sufficient to acquaint the reader with the
make-up of these instruments, and it will be easy to undertake any
further explanations of important variations.

The underlying idea, upon which the whole player is built, may be
described as arising from the knowledge that a bag or bellows of
suitable material will collapse whenever the air is exhausted from it,
and become inflated again when the air is permitted to rush into it,
which happens as soon as the vacuum is destroyed. Now it is obvious
that here, in these two processes, we have the possibility of producing
a reciprocating motion, and the value of this is evident when it is
remembered that the process of pianoforte playing, when reduced to its
lowest terms, is essentially the combination of the alternate manual
motions required to depress and release a key. Consequently, the matter
of designing a pianoforte-playing machine is reduced to the problem of
placing a bellows over a key, or in mechanical connection with it, in
such a way that the inflation and deflation of the bellows will operate
levers to depress and release the key. Thus far, it may be understood,
we are dealing with elementary mechanical principles. But the questions
arising from consideration of the control of these bellows are far more
delicate, and require for their solution a high degree of mechanical
talent. Let us see how the problem has been worked out.

A musical composition which is to be performed on the pianoforte
by means of one of these “players,” as they are called colloquially,
is first reduced to a series of perforations on a long sheet, the
perforations being of uniform width, but varying in length according to
the duration of the musical tone for which each stands. The sheet is
then wound upon a spool and is connected with motor mechanism which is
adapted to draw it across a “tracker-board” pierced with holes, each
of which corresponds to some hole in the sheet. The latter, when so
drawn across the plane of the “tracker-board,” is wound up on another
spool, and the motor mechanism of the player is so arranged that the
sheet can be re-wound on to its own spool when the whole composition
has been played, so that it may be withdrawn from the “player,” and
another substituted in its place. The actual process of operation is
as follows: The “player” is provided with foot pedals, which operate
exhaust bellows, and thus maintain a reservoir bellows in a state of
exhaust, on the same principle as in the reed organ. As long as the
exhaust bellows are operated, and the reservoir is kept in a state of
vacuum, it is possible to maintain an “exhaust chamber” within the
“player” also in a state of vacuum. This exhaust chamber communicates
with a “diaphragm chamber,” in connection with the “tracker-board”
hole, and with an “inflation and deflation channel” in connection with
the striking pneumatic or bellows which depresses the pianoforte key.
The connection with the “diaphragm chamber” is by means of a very small
hole pierced in a leather diaphragm which is stretched between the
“exhaust chamber” and the “diaphragm chamber,” so that the latter will
be in a state of partial vacuum. Resting on the leather diaphragm is
a button, attached to an upright spindle which stretches through an
orifice into the inflation and deflation chamber, and there operates
a poppett valve which, in one position of the spindle, will close the
chamber against the exhaust chest, while opening itself and therefore
also the pneumatic to the outer air, and in another position will
reverse the process, opening the chamber to the power of the vacuum
in the exhaust and simultaneously closing itself and therefore the
pneumatic to the vacuum, which will cause the latter to collapse, and
thus bring down the key. Now, when a hole in the perforated sheet comes
opposite a hole in the “tracker-board,” an atmospheric communication is
opened with the “diaphragm chamber,” and air will immediately rush down
into the “diaphragm chamber” and at once destroy the partial vacuum
which existed there. As a consequence of this, the leather diaphragm
will immediately rise to its fullest extent, influenced by the vacuum
in the chamber above it, and will therefore push up the poppett valve.
This action will open communication between the exhaust and inflation
and deflation chambers and will expose the latter to the vacuum, while
shutting off the outer air which has kept the pneumatic inflated. Thus
the pneumatic will collapse, and the piano key will be held down until
the closing of the “tracker-board” hole once more restores the partial
vacuum in the “diaphragm chamber,” thus permitting the poppett valve to
sink, and reopening the connection between the pneumatic and the outer
air, which re-inflates it and releases the key.

As will have been anticipated, there are endless small variations of
detail in the construction of different “players,” but they all work
on the same principle, and the above description will be sufficient to
give an idea of what goes on inside the “player” when the perforated
sheet is put into position and drawn over the “tracker-board.”
Variations on the mechanical carrying out of these principles are
dependent upon the ideas of the different makers. It can easily be
understood that there is plenty of room for endless changes in details,
and that every maker of “players” has his own special notions on the
subject.

We have spoken above of the motor mechanism designed to move the
perforated sheet across the “tracker-board,” and to rewind it when
required. It is clear that such a motor device must be very sensitive
to changes in speed control, very light and very easily operated. In
the search for the ideal device manufacturers have gradually separated
themselves into two schools of practice, each being champions of one
particular type of motor. These two schools of opinion and practice
have adopted respectively the pneumatic and the clock-work motors. Both
have virtues; neither are free from vices. It is no part of our plan to
enter into didactic discussion of the relative merits and demerits of
the two styles, but we shall confine ourselves to an exposition of the
method whereby each is adapted to its required work, and shall point
out the more obvious of the good and bad features of both.

The pneumatic motor has the initial advantage of simplicity and
lightness. It consists of a number of bellows, usually three or five,
which are arranged in series on a board and connected by passages
with the exhaust chest. They are adapted to be collapsed and inflated
alternately by means of the exhaust from the bellows of the “player,”
and are governed by valves so arranged as to cause one bellows to be
open to the atmospheric air, and therefore inflated, while the next to
it is simultaneously closed to the atmospheric air and exposed to the
vacuum from the wind-chest, and therefore collapsed. This alternate
process produces a motion which can, of course, easily be transferred
by means of connecting rods to a crank-shaft, which by reciprocation
produces a rotary motion, and also permits the take-up spool of the
“player” to be connected with it by suitable gearing. The controlling
valves are generally connected with the crank-shaft somewhat after
the manner of the valves of a steam cylinder, and are operated by the
motion of the shaft through suitable connecting rods. The reverse
motion of the spool, for rewinding, is accomplished by gearing between
the motor and spool, and the reversing lever, while operating this
gear, also closes the valve between the exhaust reservoir bellows
and exhaust chamber so as to permit the full power of the exhaust to
be exercised on the motor when the rewinding is required. The speed
control of the pneumatic motor is governed by another finger lever
adapted to operate a valve which can entirely close the passage between
the exhaust chest and motor board, the gradual opening or closing of
which increases or diminishes the power of the exhaust upon the motor
bellows and hence the rapidity with which they collapse and reinflate.
This speed control combines simplicity and effectiveness.

In considering the less agreeable qualities of the pneumatic motor we
have to note that a great deal of the alleged deficiency of the type
arises from the fact that its operation depends upon the same agency
as is employed for the striking pneumatics; namely, the exhaustion
of air from the exhaust bellows reservoir. This means, of course,
that the striking pneumatics and the motor are artificially brought
into relations which would never naturally subsist between them. In
consequence, there is a continual tendency on the part of one of the
elements to monopolize the power reserve, to the detriment of the
other. Thus, a fortissimo passage will tend to use up so much power
that the motor will be slowed down; while, contrariwise, the latter,
when driven at its highest speed, will take too much power from the
pneumatics and prevent the expression of their highest dynamic forces.
Here we touch upon the most serious defect of the pneumatic motor, and
while we find the practical workings of these devices quite excellent,
there is no doubt that they would be far more responsive and far
lighter in operation if these fundamental defects did not exist.

The clock-work motor, on the other hand, is entirely separated from
the striking mechanism, except as far as it is sometimes connected
with the pedals for the purpose of winding the spring. Even this,
however, is not a real interference with the striking pneumatics. The
chief advantages of the clock-work motor are that it is built of steel
and brass, instead of wood and leather; that it is independent of the
rest of the player, and therefore always self-contained and free from
extraneous influences; that rewinding is effected by the reserve power
of the spring, and that the use of the pedals as in the pneumatic
motor, is therefore not necessary.

Its disadvantages, as alleged by its critics, may be considered as
follows: That it requires oiling and cleaning frequently, and that if
neglected will rapidly become impaired; that it is sometimes slow in
acceleration and retarding; that it is heavy and complicated, and that
the winding, when done by pedals, is wasteful, and when effected by a
handle, is tiresome.

The above tables of vices inherent in both types are by no means as
terrible as they look, however, and experience seems to show that many
of them do not appear in practical work. On the whole, the clock-work
motor seems to have much in its favor, although the question still
remains open, and time alone can show which is practically better.

It is neither necessary nor profitable to go into any considerable
detail as to the pianoforte pedal operating devices, the soft stops,
or other details of the sort. We may better employ the space at our
command in a short discussion of the movement which has resulted in
incorporating the mechanism described above into the case of the
pianoforte itself. This movement is, of course, a natural outcome
of the successful introduction of the exterior “player.” The public
soon began to find fault with the latter on account of the space it
occupied, and also because of the annoyance incidental to its removal
from the instrument for manual playing. It was not long before the
makers of “players” were experimenting, with a view to using the
waste space in the upright pianoforte for the purpose of including
the “player” therein. The advantages of such a plan are obvious,
provided that the actual mechanical difficulties can be overcome.
These difficulties proved very stubborn at first, and it is not to be
supposed that all are entirely overcome, even now.

It has been very hard, indeed, to arrange the mechanism in such a
manner as to make all parts accessible for adjustment and repair.
The results of any neglect of this important requisite are very
serious. Makers should bend their first energies to the removal of
all difficulties incidental to the obtaining of access to the playing
mechanism or to the rest of the pianoforte, before they consider
anything else. For example, it should be possible to remove the action
or keys of the pianoforte without having to detach pipes and tubes. Nor
should it be difficult to disconnect the pumping apparatus, or some
individual valve or pneumatic which may need attention.

Again, the manner in which the pneumatics strike the keys or action is
very important. The earlier player-pianos generally had the pneumatics
placed below the key-bed, so that they operated from the rear end of
the latter, striking them upwards. This had the double disadvantage of
inflicting a hard, rigid kind of blow, and of making the pneumatics
very inaccessible. A better plan has lately been devised, which puts
the pneumatics over the keys, so that they operate at the front ends,
just back of the ivories. Some such method as this is excellent always,
since it permits a considerable concentration of the mechanism and a
consequent curtailment of the inconveniently long tubes leading from
the “tracker-board” to the valve chambers. All these matters, however,
are in process of practical development, and the future holds the key
to the ultimate solution of any such problems.

In considering the influence of the “player” mechanism upon the
pianoforte itself, we may note that the general adoption of these
devices, if it occurs, will inevitably produce certain modifications
in the action mechanism, as well as in the general design. There is no
doubt that the ordinary action mechanism of the pianoforte will not
prove strong enough to endure the furious onslaught of the “player,”
and it is questionable whether pianofortes constructed on the old plan
will not more rapidly deteriorate when exposed to this wear and tear.
The precise direction in which this modification is likely to come may
not now be accurately determined, but it is probable that a general
strengthening of centres and flanges will be the first result.

As for the distortion of the pianoforte case, this, as far as it
now exists, may very easily be corrected. But it will not be easy to
arrange the playing mechanism so as to avoid interference with the
acoustical or mechanical forces of the pianoforte. For one thing, there
is a great deal of machinery to put into a very small space, and for
another there are certain parts of the pianoforte that must under no
circumstances be touched. Thus the sound-board, the strings and the
iron plate must be left severely alone. But the elimination of the
Boston or double-rolling fall-board, and its replacement by something
that will take less room, will provide a sufficient space to house the
pneumatics and exhaust chamber above the keys. This is where they ought
to be, and the only possible place where they can be reached without
trouble or damage. The pumping apparatus must be kept away from the
sound-board, and placed where it will do no harm; under the key-bed,
necessarily, but not so as to interfere with the piano pedals or the
resonance apparatus. Some portion of the bottom frame can usually
be eliminated with advantage, and this will assist in providing the
necessary space.

The position of the motor should be such that the minimum of waste
occurs between the crank-shaft and the take-up spool. Thus, if
possible, the motor ought to be above the key-bed. If it be of the
clock-work type, it can hardly be placed anywhere else. Lastly, the
whole of the exterior apparatus, such as levers, pedals, spool, etc.,
should be arranged to fold away or be covered up out of sight when the
instrument is in use for manual playing.

While it has only been possible in this appendix to give the barest
outline of the player-piano problem, the reader is besought to
recollect that the industry is still new, and that the “present state
of the art” hardly admits of any didactic assertions on principles
of construction. We do not even know, today, whether the pneumatic
principle will continue to prevail, or whether some new refinement of
electric mechanism will not eventually surpass every device now known,
both in responsiveness and convenience.



APPENDIX B.

THE SMALL GRAND.


It is a curious fact, but none the less characteristic of that
most curious of industries--the pianoforte craft--that in it the
development hypothesis, so familiar to all other branches of human
endeavor here, appears not to be fully applicable. While the aim of
the present treatise has been to systematize and codify, as it were,
the laws that underly all right constructional methods, we have been
forced to recognize that there is no appearance of any accurate and
uniform generalization which may be applicable to the future guidance
of pianoforte builders in their efforts to attain to the greatest
perfection in later types. Although we have succeeded in laying down
the broad and universal principles that govern intelligent practice of
the art, yet we cannot fail to note that a progressive evolution is not
yet possible. That is to say, there is no progressive synthesis in the
art which shall carry us continually further from the original types,
so that the ancient models shall become in time quite unrecognizable in
the light of modern improvement. Rather would it seem that the course
of improvement is leading us back to reversions towards the original
types, and of this tendency the rise of the small grand pianoforte is
one of the most striking illustrations.

It is not to be supposed that this reversionary movement is to be taken
as implying a dissatisfaction with the methods that have grown up in
the course of the last hundred years, and the systematization of which
has been our task in the present work; it is rather that the tendency
today is in the direction of utilizing the most modern methods in the
resuscitation and further development of the type of pianoforte that
was earliest in the field.

In other words, as the reader well knows, the last few years have seen
a general tendency towards a revival of the grand, in forms suitable
for modern ways of life, and with the advantages carried by the wealth
of experience and practice on which the modern pianomaker can make
unlimited drafts. This resuscitation has not taken the form of any
attempt to bring the large-sized concert instrument into more popular
use, but it has rather been a matter of evolving a new type out of the
old, and of developing this latter along comparatively original lines.
With the commercial success of such an experiment we are not here
immediately concerned, but we have great and lively interest in the
question of its constructional value and in the possibilities that are
implied in its future development.

Without entering into wearisome detail, it may be stated that the last
five years have seen a most systematic attempt on the part of leading
manufacturers to construct and popularize a very small style of grand
pianoforte, and to endow this new instrument, as far as possible, with
the musical advantages possessed by the larger and older horizontal
forms. The dimensions of the “small grand,” as it has come to be
known, range from a length of five feet to one of six, with width in
proportion, and the smallest sizes are continually attracting greater
attention on the part of experts. The idea is to reduce the dimensions
to the very lowest point compatible with something approaching to grand
pianoforte tone, and to make the general outline as beautiful to the
eye as possible. The latter of these desires is easier of consummation
than the former, and it has therefore appeared that some of the makers
of these instruments have been somewhat apt to overlook truly musical
results in deference to a public sentiment in favor of something that
is graceful, if nothing else. In fact, when considering the small grand
we are obliged to note that it has been developed, and is now being
produced rather to appeal to that portion of the pianoforte-buying
public that demands something for its homes more beautiful than the
upright and less bulky than the large parlor or concert grand than in
answer to any general cry for the better musical development of the
instrument itself.

If we bear this fact in mind, and its truth is obvious to the student
of pianoforte history, we can the more easily understand and appreciate
the essential features of this latest development.

The small grand has been produced, we repeat, to please the public, and
the public at large is not exclusively composed of musicians.

But even while acknowledging the probability of this statement, we
need not conceal from ourselves that the small grand can thus fulfill a
very useful function. Reduced to its lowest terms, it remains a grand
pianoforte, with the action and touch so essentially associated with
the horizontal form, and so immeasurably superior to anything that
is found in even the best uprights. And here the small grand has an
enormous advantage, nor does it appear that its truly musical and tonal
development need be permanently stationary, if only the limitations of
the instrument be appreciated, and work on it be directed with especial
reference to its own size, and without dependence upon the traditions
that have supported the building of larger forms.

In a word, the builders of small grands have the opportunity, if
they care to avail themselves of it, to produce a form of miniature
horizontal pianoforte that shall possess all the advantages of the
large concert instruments, with the exception of the great tonal volume
peculiar to the latter, and none of the disadvantages of bulkiness
and ungracefulness. They can never hope to obtain the same tonal
results from a 5-foot as from a 9-foot instrument; but they have the
opportunity to popularize a touch and technique that is impossible of
achievement for players of the upright, and a quality of tone that is
equally unattainable on vertical instruments. Under all circumstances,
it must be borne in mind that the results of small grand building, even
when most carefully and skilfully executed, are essentially different
from anything that has yet been produced in the tonal development of
the pianoforte, and that no attempt to imitate the tonal properties
of the large grand can be successful. The action and the touch are
fit subjects for this kind of imitation, but such tonal quality as
is susceptible of development is entirely original and indigenous
to the miniature grand. The only legitimate field of inquiry along
these lines, then, is that which has reference to the development and
constructional principles of the small grand considered as a distinct
type, and needing particular and definitely differentiated principles
and methods.

Assuming the correctness of these premises (and their truth would
appear to be obvious), we have to ask ourselves what is the exact
nature of the problem which is set for solution, and wherein it differs
from any that we have had to consider as yet. Bearing in mind that we
are dealing with what is known as the “small grand,” although it is
marketed under various other names selected by different manufacturers,
we can state the constructional problem in fairly definite and exact
terms.

It is required to build a pianoforte in horizontal form, of which the
extreme length shall preferably not exceed five feet and six inches,
and which shall be compensated for shortening by means of extra
widening; which shall have the lines of a larger grand, refined to the
highest degree, and within which the greatest possible tonal value
shall be contained.

Viewed thus, it appears that the principal factors to be considered are
string-length and sound-board area. It is obvious that the diminution
of the former and restriction of the latter are inevitable; and the
net result must be seen in a radical alteration, if not deterioration,
of the tonal property of the instrument. It remains to be seen how we
shall set about to transform this disadvantageous condition into one
that shall work for us, and in accordance with our desires. In other
words, as we cannot get a sound-board containing, say “_n_” square feet
of superficial area into a case that only contains 3/4 “_n_” square
feet of space, we must resign ourselves to the inevitable, and search
for ways and means whereby the difficulty of putting into a quart
bottle more than it will hold may be evaded, if not explained away.

And first, then, let it be remembered that the only line where-from we
can safely base any calculation is that which leads in the direction
of a continual refinement of the means of applying sound-board
construction to the instrument. We must utilize every inch of the
superficies; we must discover and apply methods for opening up the
vibratory area to the impressions received from the strings in a manner
superior to that which has been deemed sufficient when space has been
at a discount. We must arrange bridges and bearing-bars so that the
string-lengths may be stretched to the utmost, and, lastly, we must use
such minute care in the treatment of the hammer-striking line that the
inevitable “breaks” in the tone shall be minimized.

The intelligent reader will not fail to observe that we have put forth
here a tolerably difficult set of requirements. But he will likewise be
equally quick to note that ultimate success in small grand designing
depends entirely upon the manner in which these conditions are met. If
they are slighted or slurred, if the designer attempts to ignore them,
he will find that failure will surely follow. On the other hand, it
would be too much to say that even the most faithful and conscientious
effort applied to the elucidation of the problem will under all
circumstances have the desired effect. The conditions are unusual; in
some cases they do not admit of any direct and positive settlement.
But in so far as these conditions can be met, in so far as they are
susceptible of solution, the designing of the small grand can properly
be made successful.

It must be recollected that the “striking-point” of the hammers is a
vitally important element in the success of pianoforte building. It
is the one factor that cannot be trifled with, and in treating which
there must be rigid adherence to rule. Now it is well known that the
correct striking distance has been ascertained (as shown in the body of
this work) to be at a point between one-seventh and one-ninth of the
speaking length of the string, the exact place for each string being
calculated with reference to the actual speaking length. As worked out
in the best practice, the shortest and highest pitched strings have
their striking points at about one-tenth of the speaking lengths, while
the longer and lower pitched elements further down the scale are made
to conform more closely to rule. Now it is obvious that the application
of this law to the very much shortened strings of a small grand will
result in distinctly unsatisfactory quantity and quality of tone. But
it will not do for us arbitrarily to change the actual striking point,
for that would change the position of the hammer line, and experience
has amply demonstrated that no such idea will work. Inasmuch,
therefore, as we are estopped from interfering with the striking point,
as far as concerns the actual hammer line, it becomes necessary to
discover some means for obtaining a somewhat greater length of string
in proportion to the dimensions of case. Careful measurement will
show that the higher strings do not fall under the classification
of “dangerous.” It is only when we approach the point where the
overstringing begins that the disadvantage of decreased case length
becomes apparent. The treble string-lengths at or near this place will
be too great, if carried out according to the well-known and practiced
laws of scale designing; while, if they are unduly shortened, the
tensions and thicknesses will require to be submitted to such radical
alteration as to make most unpleasant changes in the tonal quality and
volume.

But while an absolute solution is out of the question, there is no
doubt that we are able to find a fairly satisfactory substitute. There
are two courses open to us. We are not permitted to make any great
change in the tension, but, within certain limits, we may weight the
string, and we may even stretch out its length, if we be very careful
and watch out for every inch. The first method must always be used
with caution. It is susceptible, and very easily, too, of improper
application, and when abused becomes an enemy rather than a friend. In
fact, the weighting of treble strings with iron or copper wire should
be undertaken with the greatest caution, and only indulged in when the
designer is absolutely unable in any other manner to obtain a proper
vibrating length. The last two or three strings above the overstrung
portion of the pianoforte may usually be wrapped without troublesome
complications, but under no circumstances should the highest of these
have a frequency greater than 128. On the other side, where the bass
strings begin, this condition does not apply, for it is possible by
means of suspension belly bridges, to increase the actual speaking
lengths several inches. These suspension or extension bridges, as they
are called, may also be used, though with caution, for the lowest
treble strings. We have never advocated the splitting up of bridges,
but there are cases, such as these, where unusual methods are quite
unavoidable.

In the several ways thus sketched out, the designer of small grands
may do something to overcome the manifest difficulties of his task.
He may likewise take heart of grace when he approaches the matter of
sound-board area, for in treating the string-lengths there appears
a partial solution of the latter problem. In speaking of the use of
suspension bridges we omitted to note that the position of these may be
modified so as to give greater length to the speaking portions of the
strings, by increasing the obliquity of the angle of the overstringing.
Of course, this would be obvious, but it is perhaps not quite so clear
that such adaptation will result in an opening out of spaces on the
sound-board that are usually left severely alone. Moreover, if the
necessary splitting up of the bridges be avoided by means of connecting
strips of the same material, it is clear that the opening up of the
sound-board may thus be carried up to the highest possible value.

Along such lines as these, it would seem, must the course of small
grand designing be laid, at least as far as concerns the vital elements
of string-length and sound-board area. There remains the question of
the metal plate, and this deserves separate treatment.

We have taken pains already to insist upon the necessity for
compromise in the building of small grands. Regarding the iron plate,
we have to observe that great care must be taken to avoid undue
massiveness, for this will entirely spoil the tone quality, as the
other dimensions are not capable of supporting a large mass of metal
without tonal deterioration. On the other hand, it is equally certain
that we can afford to sacrifice nothing in the way of strength, as we
purpose to have the highest tensions and the greatest lengths possible
within the space limitations of our instrument. The ordinary form of
plate, copied from the large grand, may very advantageously be modified
by the adoption of a truss or arch construction, which will enable a
large amount of metal to be cut away from the treble sides without
sacrificing any strength.

Along such lines, as we have already said, the design of small grands
must of necessity proceed. We feel that it would not be improper to
repeat our formerly expressed opinion as to the nature and functions
of the small grand. It has come into existence in answer to a public
demand for something differentiated from the upright, possessing great
beauty of outline, and yet adapted to the confined surroundings of
contemporary domestic life. It is not and cannot be a rival of larger
horizontal forms; it is physically estopped from the realization of
such ambitions. But it has a place in the economy of the musical world,
and such a place as nothing else would satisfactorily fill. Wielding
the mighty influence of the name “grand pianoforte” and with the
initial advantages over the upright that its form, touch and action
imply, it would indeed be remarkable if the production of the small
grand did not become more and more a part of the regular routine of
all pianoforte manufacturing establishments. The design of its case
will always, surely, be above criticism. It is out of our province to
enlarge upon the details of case architecture, but it may be pointed
out that such details as graceful trusses, well-designed lyre, and
carefully molded curves do much to make or mar the future of a small
grand, entirely apart from the excellence of its scale. The general
effect should be that of lightness and grace; a touch of frivolity
even will not be out of place. The little instrument is likely to find
its way into homes where money is not always an object, and where the
ability to enjoy the best that life contains is usually present. The
designer will make no mistake if he keeps this in mind.


UNUSUAL METHODS OF CONSTRUCTION.

As the reader is well aware, the greater part of the present work has
been devoted to an exposition of the broad principles underlying all
right methods of pianoforte construction. We have devoted little space
therefore to the elaboration of features without this classification,
or to the consideration even of such ideas and methods as do not fall
within the lines laid down in the theoretical portion of this treatise.
Busily occupied, as we have been, with the development of acoustical
and mechanical principles and their application along the most obvious
and natural lines, we have been forced to neglect one of the most
interesting studies that can be taken up by the investigator; to wit:
the ideas, inventions and devices that have sprung from the brains of
the numerous mechanical and acoustical geniuses who have illuminated
the course of pianoforte history and development. Many of these ideas
have proved impracticable under the stress of use; others, again, have
been shown to be commercially unprofitable; a still larger number have
flourished during a longer or shorter period or have been neglected by
all others than their original inventors. The true place for a study
of these neglected children of enthusiastic, if not always practical,
brains is in a history of the pianoforte rather than in a technical
treatise on construction.


[THE END.]



The following corrections have been made to printer’s errors in this
text:

  Page  Correction                   Location in Text
   20  Handel to Händel             time of Händel;
   20  pianforte to pianoforte      which the grand pianoforte
   27  begin to begun               now about to be begun.
   32  closing parenthisis inserted  staff in the bass clef)
   32  B-sharp to B-Natural         note 15 in harmonic series table
   41  B double F-flat to B double flat  minor sixths table
   42  clasisfied to classified     These sounds are thus classified:
   49  of to or                     imply a length or height of
   53  asumption to assumption      made on the assumption
   68  veenered to veneered         turning out of such veneered cases,
   77  missing comma inserted       (more elaborate than the other two),
   86  homogenous to homogeneous    plate as homogeneous with the sides
   87  is to it                     In fact it occupies
   99  REPETITON to REPETITION      DOUBLE REPETITION ACTION
  109  fough to fought              already been fought out
  113  any one to anyone            through by anyone who hopes
  123  synchromize to synchronize   will synchronize with each other,
  124  mesontonic to mesotonic      that the mesotonic system,
  125  period added                 in the ratio 1296:1250.
  131  turned to tuned              conversely, if the tuned notes
  148  closing quote added          vacuum in the “diaphragm chamber,”
  154  Wtihout to Without           Without entering into wearisome detail,
  154  possesed to possessed        musical advantages possessed
  155  circustances to circumstances  Under all circumstances,





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