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.

The cover image was created by the transcriber and is placed in the public domain.

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.

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:

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.

Transcriber’s Note: For note 15, 960Hz is slightly below B-natural, not B-sharp.

[[Listen]]

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:

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:

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:

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:

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		Appears in the scales of		C, F, G, B-flat.
2.	“     C	= 521 11⁄54				E-flat
3.	“     C-sharp	= 556 7⁄8				D, B, F-sharp, C-sharp
4.	“     C-sharp	= 550				A, E, G-sharp
5.	“     D	= 594				C-G
6.	“     D	= 586 2⁄3				A, F, B-flat, E-flat
7.	“     D-sharp	= 618 3⁄4				E, B, F-sharp, G-sharp
8.	“     D-sharp	= 626 31⁄64				C-sharp.
9.	“     E-flat	= 625 4⁄9				B-flat
10.	“     E	= 660				C, G, A, E, B-flat
11.	“     E	= 668 1⁄4				D
12.	“     E-sharp	= 696 3⁄32				F-sharp, C-sharp
13.	“     E-sharp	= 687 1⁄2				G-sharp.
14.	“     F	= 704				C, F, B-flat
15.	“     F-sharp	= 742 1⁄2				G, D, E, B, F-sharp, C-sharp
16.	“     F-sharp	= 753 1⁄3				A
17.	“     G	= 792				C, D, F, G
18.	“     G	= 782 4⁄13				B-flat
19.	“     G	= 781 34⁄36				E-flat
20.	“     Fx	= 773 6⁄16				G-sharp
21.	“     G-sharp	= 825				A, E, B, G-sharp
22.	“     G-sharp	= 835 5⁄16				F-sharp, C-sharp
23.	“     A-flat	= 833 25⁄27				E-flat
24.	“     A	= 880				C, E, F, A
25.	“     A	= 881				D
26.	“     A	= 891				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:

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.

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:

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).

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

[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.)

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.

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.

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.

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.

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.

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.

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.