The whole matter of musical intonation was treated with some

completeness in the early part of this work, and the reader may

be expected to comprehend the principles of the Equal Temperament

upon which the tuning of the pianoforte and of all other fixed tone

instruments is now universally based. It is not within our province,

in the course of a treatise upon the principles of pianoforte

construction, to venture too deeply into the quagmires that surround

the aspirant for the honors of the tuner. The discussion of musical

intonation and the Equal Temperament was made for the principal

purpose of acquainting the student with the reason for the peculiar

construction of scales, as to their string lengths, and to make clear

the _raison d’etre_ of the frequent divergences from theoretical

proportions of strings and tones that we have been obliged to note.

The scale designer is better equipped for his task, however, if he

possess a working knowledge of the principles upon which the science

and art of tuning are based. This is the justification for the space

and time devoted to the exhibition of certain of these principles in

the earlier portion of this book. As a further contribution to this

useful body of knowledge, we shall point out here the general scheme

whereby the tuner proceeds to the execution of his important, indeed

essential, portion of the whole work.

The practical work of tuning is performed by the aid of certain

acoustical phenomena which enable the tuner to distinguish between

sounds that are very nearly in unison. As the Equal Temperament

requires the slight roughening of all the intervals with the exception

of the unison and octave, it is clear that there is great value in a

method of estimating, not only the unisonal or non-unisonal condition

of two sounds, but also the exact amount of difference that may occur

between them. The phenomena mentioned are called “beats,” and it is

well that their physical basis should be described here.

From what has been said before, it is clear that musical sounds,

generated as they are by the periodic agitation of the air according

to fixed laws, are but the audible manifestations of a peculiar form

of air-motion. The particular form of air-motion can best be described

as a wave. Whenever a sonorous body is excited into vibration it

causes the surrounding atmosphere to make motions that correspond to

its own. A vibrating body such as we have described (together with the

segments thereof) partakes of a motion that may be compared to that of

a pendulum. There is a rhythmic swinging back and forth of the body

and its segments, with the result that the immediately adjacent layers

of air are excited into alternate states of compression and expansion;

or, more correctly, of condensation and rarefaction. This rhythmic

motion is imparted by the layers of air adjacent to the sonorous body

to the next adjacent layers, and so on. The result of this is that a

wave is formed, the length of which varies inversely as the number

of vibrations performed by the sonorous body. This wave is called a

sonorous wave.

Now we know that sounds are at the same pitch when they are generated

by sonorous bodies having the same speed of vibration, and it is

easy to perceive that, if two such bodies are sounding together, the

condensations and rarefactions of the layers of air will synchronize

with each other, so that both will be exciting condensations at the

same instant and likewise will generate rarefactions simultaneously.

And even if the two bodies have not exactly the same speed, the result

will be equally simple as long as their speeds bear simple ratios to

each other. Thus two bodies which are emitting sounds at the interval

of an octave or of a fifth or fourth will generate condensations and

rarefactions in such a manner that they will not interfere one with

another. But the case is different where two sounds are separated

by differences in pitch that cannot be expressed by simple ratios.

For example, if one sound be one vibration per second higher than

another, it is clear that by the time that the first sounding body

has completed its given number of vibrations in one second, the other

will be one vibration behind. When, therefore, the vibrations of the

first body are continued into the next second the condensation of one

wave will be completely synchronous with neither the condensation nor

the rarefaction of the other. The obvious result is that at a certain

point the condensations of each wave concur while at another point

the condensation of one crosses the rarefaction of the other. In the

first case we have a considerable augmentation of sound and in the

other case a complete silence. As the waves thus approach and recede

there is a gradual diminution of sound followed by a complete cessation

for a small fraction of a second, and then a gradual increase until

the point of greatest augmentation occurs. This latter happens when

the two condensations concur, and the gradual rise and fall of the

sound correspond to the gradual approach of this concurrence in the

first case and to the similar advance of the point of crossing in the

second. This phenomenon of alternate augmentation and diminution of

sound separated by an almost inappreciable interval of silence occurs

whenever two sounds of nearly the same pitch are heard simultaneously.

These peculiar changes in the intensity of a sound are denominated

“beats.”

This description of the physical nature of “beats” will be sufficient

to make clear to us how a recognition of them is of value to the tuner.

From what we have just said, it will be observed that the number of

beats that may be set up between any two sounds depends upon the

difference in the frequency of the two sonorous bodies. So that the

number of beats form a true guide to the exact amount of difference

between sounds that are nearly in consonance. Thus, if it becomes a

matter of tuning a certain interval a little flat or sharp, in order to

comply with the requirements of Equal Temperament, the operation may

be readily performed by observing the number of beats that are heard

between the two sounds when one of them is sharpened or flattened.

So that all schemes of tuning must necessarily be founded upon a

recognition of this important phenomenon.

At this point it will be well to reiterate the fact that the Equal

Temperament owes its popularity and long prevalence to the wonderful

facility of modulation which it possesses. While it certainly involves

discords and disharmonics that the mesotonic system, for instance,

avoided, yet the fact that it does not limit the expression of

musical ideas to a few scales, but permits the composer to roam at

will through the whole field of tonalities, has given to it a deeply

founded popularity that has not yet been seriously challenged. We

must bear in mind that the Equal Temperament is the first fact, the

“prius,” the “proton hemin,” as it were, of musical performance.

Obviously, therefore, the importance of a proper and close adherence

to this system in the tuning of fixed-tone instruments cannot be

insisted upon too strongly. The reader has already had occasion to

examine a comparative table which showed the pitches of a true and of

a corresponding tempered scale. He will have noted that the tempered

scale errs very greatly in respect to certain intervals. The task of

equalizing the thirteen sounds which a fixed-tone instrument allows

to the octave, involves in each interval a greater or less divergence

from purity, according to the ratio of such interval. Thus we find

that the error of a tempered third is greater than that of a fifth,

and so on. Now, if the four minor thirds within the compass of an

octave be considered, it will be found that the octave to the tonic

which is produced from the last of these is a good deal sharper than

the octave taken direct from the tonic. Again the octave produced from

the building up of the three major thirds within the same compass is

very much flatter than the octave taken direct from the tonic. Again,

it will be remembered that there are twelve fifths within the compass

of seven octaves. The last sound in this progression of fifths is

considerably sharper than the sound that is produced by taking a series

of seven octaves from the tonic. Without going into figures, we may

give the differences thus noted concisely as follows:

In the cases above considered the octaves obtained by building up

intervals differ from the straight octave in the following proportions:

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

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

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

Obviously, therefore, it will be necessary to tune all the minor

thirds, within an octave, flat by one-fourth each of the ratio given

for them. It will also be necessary to tune each of the major thirds

sharp by one-third of the ratio proper to those intervals. Likewise

each of the perfect fifths must be made flat by one-twelfth of the

ratio given above for fifths.

We are thus able to understand just how great divergencies from purity

are involved in the Equal Temperament of major thirds, minor thirds and

fifths. As far as the other intervals are concerned, it is obvious that

if the thirds and fifths are equally tempered and the octaves tuned

quite purely, the other intervals will be subjected simultaneously and

automatically to a similar process of temper.

Now from what we learned of the phenomena of beats, we must conclude

that the tempering process when applied to these intervals will

generate beats between the sounds that compose each interval. We know

that beats must occur when the sounds that form any consonant interval

are not quite in tune with one another. We also know that the frequency

of the beats depends upon the difference in frequency of the generating

sounds. We can, therefore, easily see that those intervals that are

subjected to the greatest amount of tempering will produce the greatest

number of beats. And further, as the actual frequencies of the sounds

increase according to their pitch, it is equally obvious that the

tempering will result in greater differences as to actual frequency

between the true and the corresponding tempered intervals. Therefore

the number of beats that any tempered interval generates varies

directly as the pitch of the sounds that form the interval. The higher

the pitch, the greater the number of beats. Conversely, the lower the

pitch, the smaller the number of beats.

Now we have already noted that the phenomena of beats afford an

absolutely precise test for the consonance or otherwise of an interval.

If we can estimate the number of beats that should occur between the

sounds of any given equally tempered interval, we can always tune such

an interval in the Equal Temperament by noting the number of beats

and adjusting this to the theoretical number in the calculations. It

is not possible accurately to follow the number of beats that are

supposed to be between any given intervals in Equal Temperament even

when the pitch of the tonic of the interval that is being tuned is

precisely similar to the corresponding sound in the calculations. It

is not possible, therefore, in practice, to tune with such accuracy

as theory would demand, but an approximation may be obtained. If we

could secure an absolute standardization of pitch for the pianoforte it

would be possible to construct tables that would show the exact number

of beats that ought to occur between all the equally tempered sounds

within the whole compass. In default of such a method, it is necessary

to resort to a variety of tests and to prove the correctness of the

tempering of each interval by comparison of the different intervals of

various kinds that to which each sound, as it is completed, gives rise.

If, for example, we find that any given sound, when tuned, gives the

same number of beats with the tenth below as it does with the third

below, which is one octave above the tenth, then we have some assurance

that the sound in question is properly tempered. If this assurance is

confirmed by a complete absence of beats between the given sound and

its octave, above or below, then we have an almost absolute assurance

as to the correctness of the work.

It is then upon the phenomena of beats that the tuner depends for a

guide to the correctness of the work in which he is engaged. By noting

the frequency of the beats at some places, or their absence at others,

he is able to judge most accurately whether any interval is tuned

too sharp or too flat, or whether any octave is tuned purely or the

reverse. All good tuning depends entirely upon such estimation of the

beats, and the greatest difficulty that the tuner encounters lies in

the fact that he must try to equalize the frequencies of the beats

between all the intervals of the same kind within the compass of each

octave. If this work is well and truly done it properly deserves the

name of art, and, indeed, fine tuning is a fine art, one to be acquired

by the painful and slow processes of manual practice and mental

application. He who overcomes all obstacles to success and masters

thoroughly the principles and practice of tuning is an artist in the

truest sense.

In applying these principles to the tuning of the pianoforte, the

problem that confronts us is to devise a rapid and simple means of

tempering each sound within the seven odd octaves of the instrument,

and to do this in such a manner that the deviation from purity shall be

the same for all similar intervals within the compass of each octave.

Now it follows, from what has gone before, that the tempering of each

separate interval, by itself, and without reference to any other,

would be a very tedious and inaccurate process. It would, in fact, be

quite impracticable to employ such means for intervals that require

relatively large deviations from purity, especially in the higher

pitched registers. There is, however, a method that largely obviates

these difficulties. The middle octave of the instrument, which runs

from F below middle C to F above it, is chosen, and the intervals

within this octave are so tuned that the thirteen semitones which it

contains become equally tempered sounds. The sounds within the next

octave above or below are thereupon tuned from the former, each to its

octave above or below, and this process is continued until all the

sounds upon the key-board have been tuned.

It is easy to see that such a method possesses many and great

advantages. All the difficult tempering of intervals that require large

deviations from purity is confined to that portion of the piano where

beats are most easily estimated; while the rest of the instrument is

tuned by means of octave intervals, in which the test of purity is

absence of beats, rather than the estimation of any number of them.

The tempering of the intervals in the middle octave is called “laying

the bearings” and is the most difficult, as it is the most important,

of the various processes incident to the practice of pianoforte tuning.

The “accumulation of insensible into almost intolerable errors,” as

Mr. Ellis aptly terms it, continually besets the path of the tuner,

especially if his preliminary knowledge be imperfect. The true

estimation of beats, as generated by various intervals, is an art that

is but slowly and painfully acquired, by long practice and training of

the ear.

Examination of the pianoforte key-board shows us thirteen sounds within

the compass of an octave. In proceeding to the conversion of these into

equally tempered sounds, we have more than one method presented to us.

We shall, of course, choose the octave which, as stated above, runs

from F below middle C to F above it, and shall use, for our purposes,

such adjacent sounds as we may consider necessary.

It is usual to take from a tuning-fork the pitch of the sound from

which the tuning is begun. These instruments are tuned either to C, or

A next above middle C. It is usual, in this country, to tune from C,

and we shall, therefore, adopt that method.

Now there are various ways of setting about the “laying of the

bearings.” Some tuners work by thirds, others by fourths and fifths;

others again use a series or circle of fifths joined by octaves.

Whatever intervals are tuned, the idea is to include all the thirteen

sounds within the octave and to use, as far as possible, only one or

two kinds of intervals.

Of all these methods, the shortest, easiest and most accurate is that

which employs fourths and fifths only. It is used in such a manner

that, by tuning a circle of fifths and fourths, the last sound tuned

provides the octave to the first, thus completing the circle and the

octave of tempered sounds.

[Illustration: tuning music notation]

In this method we proceed as follows:

1. Pitch C is tuned by the tuning fork.

2. F below pitch C is tuned, being a tempered fifth.

3. G below pitch C is tuned, being a tempered fourth.

4. D above G is tuned, being a tempered fifth.

5. A below D is tuned, being a tempered fourth.

6. E above A is tuned, being a tempered fifth.

7. B below E is tuned, being a tempered fourth.

8. F sharp below B is tuned, being a tempered fourth.

9. C sharp above F sharp is tuned, being a tempered fifth.

10. G sharp below C sharp is tuned, being a tempered fourth.

11. D sharp above G sharp is tuned, being a tempered fifth.

12. A sharp below D sharp is tuned, being a tempered fourth.

13. F above A sharp is tuned, being a tempered fourth.

This last F is the octave to the first F tuned, and should coincide

exactly with the latter.

The reader will, of course, realize that the tempering of these

various intervals must be tested by means of the generated beats.

Helmholtz, in “Die Lehre der Tonempfindungen,” calculates that the

tempered fifths should average .6 of a beat per second at standard

pitch within the octave that we are treating. This is equivalent to

three beats in five seconds. But it is impracticable to measure the

generated beats upon the pianoforte in this manner. The tone of the

instrument is too evanescent and fleeting. We may, however, attain to

a very fair approximation. If, for example, each fifth be tuned so

that two distinct beats are heard before the sound dies away, it will

be found that the beat-rate is a near approximation to the calculated

average. The two beats that we speak of occur in about three seconds,

while the Helmholtz rate is three and one-third seconds for two beats.

Again Helmholtz gives an average beat-rate for tempered fourths in

the same octave; namely, one per second. If we tune the fourths so

that we hear three distinct beats we shall likewise obtain a very fair

approximation to the calculated beat-rate.

We showed above that the last sound produced by the building up of a

progression of twelve fifths is sharper than the sound produced by the

piling up of seven octaves from the same tonic. The two sounds thus

produced ought to coincide, for the compass of twelve fifths and of

seven octaves is the same. We concluded, therefore, that the Equal

Temperament required the flattening of all the fifths.

The meaning of the discussion is, therefore, that the fifths within

the octave where the “bearings” are being laid must each be tuned flat

by two beats. Or, rather, that the higher sound of every fifth must be

flatter by two beats than if it were in consonance with the lower sound.

Again, if we tune the F below middle C two beats sharp of the latter

(which is equivalent to tuning the fixed pitch sound C two beats flat

of F) we shall obtain a properly tempered fifth. Now, if the octave

above this F be taken it will be found to form a sharp fourth with

middle C. For example, if the pitch of middle C be 264, then the pitch

of F below it, in pure intonation, is two-thirds or 176. Assuming that

the F be then tempered so as to be sharp by two vibrations, it will

have a frequency of 178. The octave to this is 356 But this latter is

a fourth above C 264 and should, therefore, be 352 Consequently we see

that the fourths in Equal Temperament are to be tuned sharp ascending,

or conversely, flat descending. As already explained, the beat-rate in

the “bearings” should be nearly one per second or three beats, while

the sound of the interval remains audible.

When the deviations from purity are as slight as in the cases that we

have been considering, it is by no means easy to determine, at all

times, whether the note that is being tuned is sharp or flat of its

tonic. For the beats occur similarly in either case and few ears can

determine the relative sharping or flatting without some extraneous

aid. Fortunately, however, we have a variety of tests open to us, which

for completeness and accuracy leave nothing to be desired.

To take a concrete example, during the “laying of the bearings” we

first tune the F below middle C, then the G below middle C, and then

the D above G. When we reach this last note, we find that a sixth has

been obtained; namely, F--D. Now if the notes already tuned have been

tempered, so as to be too _flat_, the resultant sixth will beat too

_slowly_, and, conversely, if the tuned notes be too _sharp_ the sixth

will beat too _fast_.

This test may be amplified when we proceed to the next interval, D--A.

When this latter note has been tuned, we have the triad F--A--C. F--A

is a major third, and by referring to previous calculation we see that

as such it must, when properly tempered, be considerably sharp. By

noting the beats of the major third and likewise the beats of the sixth

we may correct the tuning of all the sounds with which we have hitherto

dealt. The same process is, of course, carried on throughout the whole

process of “laying the bearings.” The major thirds and sixths are

tested continually as the tuning proceeds, and thus is provided a sure

guide to the correctness of the fourths and fifths.

The correct beat-rates for the major thirds may be stated as about

eight per second, while that for the major sixths is approximately

eleven in the same period. Of course, as already stated, these rates

per second cannot be measured with accuracy, but with practice one soon

discovers by ear the proper roughness in each case, and is thus enabled

to estimate the beat rates without much trouble. Every opportunity of

examining the work of good tuners should be taken by the observer, who

should note carefully the beat-rates which they assign to each kind of

interval. In this way he will provide himself with practical examples

of tempering of intervals which will be of great value to him.

Having thus determined the proper beat-rates for each of the intervals

that are used in the “laying of the bearings,” we may proceed to the

further consideration of that convenient method for tuning the middle

octave that has already been demonstrated.

In order to facilitate comprehension of the argument, the following

table is given, showing graphically the sounds that are tuned in laying

the bearings and the tests and trial chords--

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

already tuned.

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

follows:

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

beats.

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

beats.

Upper notes of major thirds must be sharp so as to give approximately

eight beats per second.

Upper notes of major sixths must be sharp so as to give approximately

eleven beats per second.

If the laying of the bearings has been accurately performed, the

chords that are produced by the combination of the various sounds

will be found to have very nearly the same roughness and to generate

approximately the same number of beats. The best work is that which

most closely approaches this standard.

After the bearings have thus been laid, it is necessary to continue

the tuning of the instrument above and below the octave already

treated. Now, since the octave to any given sound has exactly double

the frequency of the former, and since octaves are to be tuned purely,

it follows that we need only tune the remainder of the instrument by

octaves up and down from the “bearings.” The consonance of an octave is

determined by the absence of beats, and, consequently, we have only to

follow this rule to reproduce, in all parts of the piano, deviations

from purity _relatively_ the same as those which we have been at such

pains to secure.

Of course, the _actual_ number of beats in any given interval varies

as the frequencies, and, consequently, the frequency of the beats

increases regularly in the higher registers, while it similarly

decreases in the lower portions. Thus the deviations from purity become

much greater in the higher portions of the compass and incorrect

laying of the bearings is, therefore, productive of more and more

disagreeable results as the scale ascends. On the contrary, in the

lower register these inaccuracies are less productive of irritation, as

the frequencies of the beats become continually less.

Such, then, is the process of tuning the pianoforte in Equal

Temperament. We have made no attempt to go into those practical details

that are concerned with the ear-training, the manipulation of the

hammer, or other cognate matters. These are entirely “_ex provincia_”

of this work.

Nevertheless the person who digests the foregoing statement of the

laws and methods of the art will be well equipped to pass upon the

correctness of tuning, and this is sufficient for our purpose.

The work of tone-regulation opens up varying but not entirely

dissimilar fields of research. The material of which the pianoforte

hammer is constructed has an important influence upon the coloring of

the sound that it draws from the string. In order that the influence of

the pianoforte hammer in tone-coloring may be understood clearly, we

shall investigate the matter with some completeness.

We have already investigated the compound nature of the sounds excited

by the pianoforte strings. We know that the nature of these sounds

varies as the method of excitement and as the nature of the resonance

apparatus that surrounds the strings. Now the pianoforte strings are

excited by being struck, and we have already noted that the point of

striking must be carefully chosen. Further, we know that the amount

of metal framing, the manner of adjusting the bridges, the nature

of the sound-board and innumerable other details must be taken into

consideration.

But by the time that the pianoforte comes into the hands of the

tone-regulator, it is out of his power to affect the construction in

any fundamental points. He is able to change only two things. These

are the striking point and the condition of the hammer-heads. Even the

former cannot be changed to any great extent. In the highest treble,

however, it often becomes necessary to bend the hammer-shanks slightly

in order that a more correct striking point may be obtained. But this

must be done with great discretion and caution.

The object of tone-regulation is to ensure an agreeable tone and

perfect evenness of quality throughout.

Obviously, this is so intimately bound up with the whole construction

that it may be said that the tone-regulation begins with the drawing

of the scale and is never finished until the pianoforte itself is

completed. This would be a perfectly proper statement, but we have here

to consider the final touches, as it were, that the tone-regulator may

give to the tonal equipment.

When the instrument comes into his hands the hammers are still covered

with the hard outer skin of the felt head. This must be removed with

a sand-paper file. It then is necessary to sound each tone slowly

and carefully, first loudly, and then less so. It will be found that

some of the hammers produce a harsh and disagreeable timbre, while

others may be too soft and mushy. Under all circumstances it is far

better to endow the instrument, as far as is possible, with a quality

that shall be comparatively mellow and round. Brilliancy cannot be

forced artificially without spoiling the whole quality and imparting a

thinness and roughness that is most disagreeable.

If the hammers are too hard at the crown, they have the acoustical

effect upon the strings of exciting the upper dissonant partials to

undue prominence. This occurs from the fact that when the head is hard

it rebounds instantly from the string, and thus does not damp any

of the dissonant partials. On the other hand, if the head be soft,

the felt clings for a fraction of a second longer to the strings and

effects the damping to a greater or less degree, according to the

relative softness or hardness of the head.

It is thus possible, by discreet manipulation of the felt, to influence

the character of the sounds to no small degree. The method is to pick

up the felt, when it is to be softened, with a set of felt needles

mounted in a handle for the purpose. It is essential to note whether

the sound is the same when the hammer strikes with great force as it

is when it strikes gently. If, for example, a gentle pressure on the

key gives an agreeable quality, but harder strokes on the key destroy

this, then we see that the crown of the hammer head is soft enough, but

the felt cushion underneath is too hard. Fine needles are, therefore,

employed to dig into the lower cushion of felt, while disturbing the

consistency of the upper crown as little as possible. On the other

hand, when the quality of sound is hard under all conditions, the upper

surface of the hammer-head must be treated by picking it with heavier

needles. Hardening of the felt may also be undertaken by covering the

hammer-head with a damp cloth and then applying a hot iron.

The whole work is primarily one of practice and experience. No

directions can do more than give an outline of the processes and

the physical reasons for them. It is well, however, to lay down the

laws that underly these processes, in order that practice may be

supplemented and improved with theory.

CHAPTER XV.

THE DRAUGHTING OF THE PIANOFORTE SCALE.

Although, for obvious reasons, we speak of it thus late, yet it is

true that the first and most important step in the designing of a

pianoforte is the draughting of the scale. This process includes a

complete planning of the iron plate and of the bridges, in fact of the

whole arrangements for stretching the strings and maintaining their

tension. This plan must indicate very clearly the exact length both of

the vibratory portion and of the waste ends of each string; it must

show the place on each string where the stroke of the hammer is to be

directed, while the exact positions of each tuning-pin and hitch-pin

must be laid down with equal certitude. Further, the place of the

belly-bridges, their dimensions and manner of pinning, have to be shown

on the drawing. Lastly, the fastening of the iron plate by screws and

bolts must be indicated; together with the precise position of each

individual screw, bolt and pin.

When this plan is in all respects complete, it has to be transferred to

a wooden pattern. The inevitable shrinkage of paper always makes the

retention of the proper measurements a matter of difficulty. This may

be overcome by making the first drawing upon a sheet of wood, varnished

to give a clear surface. If the drawing be made with India ink instead

of with pencil, we shall have a complete and permanent record obtained

in a superior manner.

When the wooden templet is to be made from such a drawing, it will

not be found that there has been the shrinking or swelling caused by

the use of paper, and the first drawing, if made after the method

described, may be laid aside for any length of time.

Let us suppose that it is desired to draught the scale of an upright

pianoforte. Having selected the size of pianoforte that is to be

designed and the wooden “table” which is to serve for the drawing

surface, we proceed as follows:

First lay down the line whereon all the hammers are to strike the

strings. From this line as base we plot out the string lengths and the

direction in which each runs; also the distance of each group from the

immediately adjacent groups.

Having laid down the striking point line, we next proceed to indicate

upon it, by suitable lines, the middle string of each three-string

group. For the two-string groups a line is taken in the middle of the

two strings. We call these lines “running lines.” Then the string

dimensions must be taken into consideration and calculated according to

the rules laid down already. The highest treble strings run at right

angles to the striking point line, and the running lines indicating

the positions of the groups are to be placed accordingly. The distance

between the running lines should be a shade more than one-half of

an inch at the highest portions of the scale. It is found necessary

to draw the running lines with increasing obliquity as their length

increases, until at the end of the treble sections they are running

at an angle of about 110 degrees counting from the treble end or 70

degrees counting from the bass end of the striking point line.

The lengths of the strings as determined by previous calculations mark

the line of the belly-bridge. The bars that are to be cast in the plate

must be allowed for in plotting the string plan. It is usual to place

one of these at about F₂ and another at C, where the over-stringing

customarily begins. The variations of individual scales and the

requirements of particular sizes of instruments sometimes cause changes

in this regard. This is one of the points that the designer must decide

for himself.

The space between the running lines increases gradually as the length

of them, on account of their oblique direction and the necessity for

providing sufficient space for the dampers and hammers. The actual

length of the strings as calculated must be laid down with reference to

the striking point line. As has been pointed out, it is found better

in practice to have the hammers strike the very high strings a little

above the theoretical place. A good average would contemplate one-tenth

of the length for the six highest strings, graduating down to one-ninth

for the rest of the highest octave and the next below it. Before the

lowest string of this last-named octave (C₃) is reached, the striking

point is gradually lowered and two or three strings below C₃ it becomes

one-eighth.

If we follow out this scheme we obtain the place where the scale

rib intervenes at the pressure bar by taking one-tenth, one-ninth

or one-eighth, as the case may be, of the length of each string.

The remaining fraction of the length represents the correct

distance between the striking point line and the nearest pin on

the belly-bridge. Thus the belly-bridge and pressure bar lines are

automatically formed as we go along.

[Illustration: METHOD OF PLOTTING STRING PLAN BY MEANS OF STRIKING

POINT LINE AND RUNNING LINES.

The sketch is intended merely as a general guide to the method outlined

above, and only a few of the running lines are shown. The dark lines

show the direction and position of the bars.]

When the scale rib and pressure bar line has been obtained, it is

necessary to make provision for the tuning pins, and particular care

must be taken that the strings shall not rub against each other owing

to incorrect placing of the pins.

When the drawing has thus been completed, we may take up the design of

the iron plate. It will be remembered that we calculated a compensation

factor for the shrinkage. This factor is 51/50, and all dimensions

where shrinkage may have effect must be multiplied by this amount.

Such dimensions are those of the height and width of the plate. Hence

the lengths of the bars, the distances between them, and the positions

of the bolts and screws as well as the string lengths must all be

modified according to the shrinkage factor.

The wooden templet may be taken directly from the wooden table drawing

by filling in the outlines and details of the iron plate on the latter

and then copying these on to the templet subject to the shrinkage

modifications required. It is well to regard one top side and also that

at the treble as immovable, and to consider the shrinkage as coming

from the bottom to the top and from the bass to the treble.

When the dimensions of the proposed plate are thus laid out on the

surface of the templet, the bars, screw-sockets and bolt holes must be

copied in wood and laid on the templet in the exact places that they

will occupy in the finished plate. Thus we gradually evolve a complete

wooden model of the iron plate, so that the iron founders may readily

obtain a correct casting.

When the first casting comes back from the foundry, it should be

carefully punched for the tuning-pin, bolt and screw holes. The first

casting must be considered in reference to the fact that it represents

only one shrinkage.

After the second casting is made from the first, the correctness of

the calculations may be judged. But not until the first pianoforte is

turned out according to the new scale can the designer find out how

well his efforts have been rewarded.

Of course, the foregoing directions are but outlines of the method.

The true inwardness of scale draughting cannot be explained here, or,

indeed, otherwise than by practical experience. A certain facility in

mechanical draughtsmanship is essential, and also close attention to

the methods that have been laid down in regard to striking points,

number of covered strings, number and place of bars, compensation for

shrinkage, and the various other points that have been mentioned.

For the convenience of the plate-finisher, wooden patterns are

provided, showing the position of hitch-pins, tuning-pin holes,

screw-holes and bolt holes, corrected for shrinkage.

The belly-man must have patterns for the position of the bridges and

for the bridge-pin boring. A wooden pattern is also required for the

pressure bar.

When these details are completed, the draughtsman must possess himself

in patience until his completed instrument is turned out.

If the rules so carefully demonstrated throughout this treatise are

fully digested, the designer will be far on the way towards correct

scale draughting. His native cunning, however, must be relied upon to

carry him through when written directions fail.

CHAPTER XVI.

CONCLUSION.

If the present treatise has convinced the reader that the making of

pianofortes is a very serious matter, and one not to be attacked in a

spirit of levity, then one of its immediate objects has been attained.

Indeed there has been an abiding fear in the breast of the author that

he might presently be charged with piling on the agony too strongly

and searching with excessive zeal for scientific causes and rules when

the shortest solutions may be found by empirical methods. This is not

really the case, however, for the whole problem of the construction

of pianofortes is naturally acoustical. While it is doubtless true

that many pianofortes have been and are continually made, not merely

with indifference to, but in defiance of, every law that has been

expounded in these pages, it nevertheless remains that none of these

have been good pianofortes. Of the making of thump-boxes there is no

end. Unfortunately for the public, musical ignorance is well-nigh

universal, and the impostor finds it easy to palm off shoddy in place

of the real article. Of course, it is quite true that bad pianofortes

are soon found out, but when the inevitable discovery comes, the

mischief has been done and the purchaser is, as usual, the victim.

A student of the construction of good instruments cannot fail to be

astonished that anyone should wish to turn out anything but the best.

For, as one continues to investigate the multifarious problems that

are continually suggested, the desire to overcome them and to produce

perfect instruments becomes almost irresistible. Perhaps this is why

the clever designer, if left to himself, often develops into a crank.

And, indeed, there is not an industry on the face of the globe that has

produced more cranks.

The files of the patent office are full of the ideas of unrewarded

genius that has spent its time, its money and its enthusiasm in the

unenviable task of producing innovations in pianofortes. No feature of

construction has been left unimproved; yet how many of these inventions

ever see the light? Few, indeed; and the fact is a sad commentary on

the unpractical nature of genius in general.

These reflections lead one to the feeling that a fitting conclusion to

a treatise on pianoforte construction may be made by giving particulars

of some of the most famous and revolutionary inventions that at one

time and another have been launched upon the unfeeling world of

piano-making. Not all of these by any means can be denominated freaks;

indeed there are the germs of most valuable developments in many of

them. We shall consider a few of the really valuable ideas at least.

Among these primacy must be given to the screw-stringing device of

Mason & Hamlin. This invention was intended to substitute a positive

mechanical fastening for the tuning-pin, in place of the wooden

wrest-plank. It consisted of a screw, threaded vertically in a socket,

which was cut in a projecting shoulder on the iron-plate. As it

extended below its socket, it was provided with an universal joint

which ended in a hook. On this hook the string was wound, and was then

free to pass on to the agraffe. A small T-hammer sufficed to turn the

screw and the string was tightened or slackened as the screw turned

in the threaded socket. The action was slow but sure, and the strings

had the curious property of sharping under a test blow instead of the

opposite, as is usual. The method of tuning was the same except that

the screw turned in the opposite direction to the ordinary style and

required much more turning to bring the string to the desired point.

On the other hand, however, setting the pin was unnecessary, and the

evils engendered by bad wrest-planks and sticking or twisting pins were

unknown. Moreover, the turning of the screw involved very slight effort.

With all these advantages, however, the reverse motion and the slowness

of action were fatal; and after several years of effort Mason & Hamlin

gave up the attempt to popularize their invention, and let it drop. It

is, indeed, unfortunate that this device did not become more popular,

as in that case its many inherent advantages would doubtless have been

emphasized and the bad points in it eliminated. Prejudice and the

tuners, however, were against it, and it died.

The well-known house of Brinsmead in London has also experimented

with a similar device, but it is not known with what success. One of

the advantages held out by the makers of such string devices was the

supposed facilitation of the work of tuning--that is to say, it was

alleged that every musician could become his own tuner as soon as he

had learned the theoretical principles of the Equal Temperament. The

hope was delusive, however. Perhaps the professional tuners attended to

this point.

Another similar but more successful device is being manufactured by the

Wegman Piano Co. This is in the form of a fastening for the pin in the

iron plate. The appearance of the plate and pin is not different from

the usual design, but the tapered end is done away with and the pin,

instead of being driven into the wooden wrest-plank, is fastened in

the plate by means of the friction set up between the peculiarly bored

hole and the back of the pin. A special twist is needed to fasten the

pin when a string is drawn up to pitch, but otherwise the method of

operation is not unusual. The device appears to be of value.

The sound-board has ever afforded a fertile field for inventive

genius. It has been altered in every conceivable manner, but the old

style continues to flourish with all its pristine activity. This is

not to say that it is ideal and insusceptible of improvement. On the

contrary, one cannot deny that many praiseworthy ideas have been

patented for the purpose of improving it. The ribbing has been the

subject of much attention from inventors. It is true that this method

of giving strength and tension to the board is by no means perfect. Yet

we find that the various devices proposed for the abolition of ribbing

have almost uniformly failed. A large number of these failures owe

their conditions to the lack of acoustical knowledge of the inventors.

It has often been supposed that the enormous relative resonance power

of the violin belly was connected in some way with the duplicate

nature of the resonance table and the consequent hollow shape of the

resonating body. This has been conclusively disproved, however, for it

has been shown that the violin’s special shape is given to it merely

for the purpose of bearing the strain of its strings. Moreover, the

tone and resonance of a violin have been reproduced by means of a

vibrating diaphragm and a horn. This device, known after its inventor

as the Stroh violin, satisfactorily disproves many cherished theories

in regard to violin resonance. In spite of these facts we find that

several patents have been taken out for pianoforte sound-boards, of

which the guiding principles have been ingenious applications of the

violin idea. The “_equilibre_” pianoforte of Frederic Mathushek was an

example of this type. It seems passing strange that experimenters have

not all become aware long ago of the essential differences between the

resonance apparatus required for struck and for bowed strings.

There have been other and saner variations of sound-board construction.

It has been suggested that the use of a double board composed of

two cross-grained thicknesses glued to each other would obviate the

necessity of ribbing and increase the power of resonance. There seems

to be little doubt that there is the germ of a valuable idea in this,

and if the notion is properly worked out, it will very likely produce

valuable additions to our knowledge of the phenomena of resonance.

Unusual ideas have been less frequent in the domain of action-making.

There have been several praiseworthy attempts to get rid of the

troublesome, but hitherto necessary, tape in the upright action. The

patent of Leo Battalia is one of these. He abolishes the tape and

bridle wire, and substitutes a two-branched spring fork projecting from

the jack. One branch works in a slot cut in the hammer butt and the

other bears against the back check. The back stop is done away with and

excellent repetition is assured, superior to that which is obtained by

ordinary methods.

In the domain of pure scale design, we note the ever present and

perennial notion of sympathetic strings. This idea has taken various

forms. The most conventional development is, of course, the “duplex

scale” of Steinway and others. This utilizes the waste ends of the

strings and scales off lengths of them that correspond to aliquot parts

of the vibrating length of each string, thus obtaining the advantage

of sympathetic partial tones. Most of the ideas in this direction have

gone further than this, however. Some makers have gone so far as to

have a fourth string tuned to the octave of every three-string group.

But this is surely unnecessary when we consider that the octave is, on

the pianoforte, the strongest partial tone of any musical sound, and

least of all needs adventitious aid.

There are many other similar devices used and unused that we should

waste our time in considering. In any case the true test of the utility

of an invention is use, and each one of these unusual notions that have

been put on the market would have been universal long ago had they been

uniformly practical and valuable.

We cannot close this hasty survey without mention of the remarkable

innovation in action mechanism devised by Mr. Morris Steinert. Here

the forcible hammer-blow is superseded by a gradual push on the hammer

at the strings, executed through the interposition of an articulated

double lever between the hammer and the jack. The result is to produce

a different form of hammer attack and a noticeable modification in

the coloring of the tone produced from the string. While the claims

of the inventor are somewhat exaggerated, there is no doubt that Mr.

Steinert has hit upon a valuable variation in the method of actuating

the hammer, and his invention opens up new prospects of pleasure to the

pianist.

If all these and the innumerable others have no other value, they

at least teach that inventive genius and the hunger for improvement

do not entirely sleep; that the pianoforte is continually being

improved, and that many are spending their time in finding new ways of

improvement. It shows that the value of the pianoforte to the community

is sufficiently great to cause the expenditure of much valuable thought

upon its mechanical and musical betterment. The fact that these things

happen should console anyone who has ever thought that the limit of

mechanical excellence had been reached.

The designing of a pianoforte is art with a big A. It demands of

its practitioners the temperament of an artist and the skill of an

excellent mechanic. There is no greater pleasure and no nobler work

than the construction of an instrument equipped to give forth lovely

tone and to interpret the inspired works of the masters of music. May

the advancing years bring the pianoforte as much more of mechanical and

musical excellence as the last two centuries have so richly imparted.

And now our task is done. It has been a labor of love to place the

results of long study and much practical experience before those to

whom this exposition of the principles of pianoforte construction might

be expected to appeal. It has been far from easy to put into really

intelligible and concise English an explanation of certain of these

laws; and if the reader finds here aught of vagueness or obscurity, may

he blame the subject rather than the author. The latter has, as best

he might, laid down the principles that underly the right building of

the noblest musical instrument that man has yet devised. And in the

contemplation of these principles he may properly be content to leave

his patient readers.

THEORY AND PRACTICE OF PIANOFORTE BUILDING.

APPENDIX A.

THE DEVELOPMENT OF THE PLAYER-PIANO.

Events are moving quickly in these latter days, and the conservative

pianoforte trade is feeling the effect of the extraordinarily active

spirit of constructive commercialism that is so pronounced a feature

of the contemporary industrial movement. When the first chapters of

the present work were in course of preparation, some two years ago,

the pianoforte equipped with an interior playing mechanism was just

beginning to be heard of; to-day its manufacture and marketing are

recognized features in the policy of nearly all pianoforte houses. It

would therefore be unwise to conclude the present treatise without

certain observations on the player-piano question, although a truly

philosophic temper would probably prefer that some further time elapse

before any feature of the player-piano problem be considered in a

work of the same scope and character as this. Abandoning the strict

scientific view of our duty in this matter, however, we may better

adopt a more popular _point d’appui_ and round off this work with a few

observations on the more important and essential underlying problems

connected with this new and remarkable movement in the pianoforte world.

Had the exterior type of pianoforte playing device--the so-called

cabinet-player, in fact--remained alone and supreme in the territory

that it first opened to exploration and development, this work would

contain no notice of any mechanism of the kind. But since the movement

has spread until it comprehends the pianoforte itself, since, in

the nature of things, such a development must profoundly affect the

solution of the problems that confront the pianoforte maker in the

construction of his instrument, it seems to be not only natural, but

imperative, that we should devote some space to certain notes on the

player-piano problem and its relation to the application of such

acoustical and mechanical principles as are germane to the theory of

pianoforte construction.

We are under no obligation to delve into the history of these ingenious

devices. The plan of this work requires nothing of the sort. We may

say, however, that the first impetus towards the production of a piano

playing mechanism came about through the success of the self-playing

organ which began to appear about fifteen years ago. Meanwhile various

inventors had experimented with electrical devices and had succeeded

in producing a mechanism that could be placed within the case of

the instrument without entailing any great distortion of form. Such

devices, however, were, with some exceptions, exceedingly mechanical in

effect, and did little to show the possibility of adequately rendering

pianoforte music through artificial means.

It was, however, through the successful development of mechanism

for the automatic operation of organs that the true principles

for piano-player construction began to come to light. Two leading

manufacturers had both produced reed organs of a very superior kind,

equipped with mechanical playing devices. The principle was pneumatic,

and was applied through the medium of compressed air. The organs

themselves were also operated on this principle, this being a return

to the old force bellows system, adopted in the European harmonium,

and always used in connection with the pipe organ. When developed to

their highest point, these pneumatic self-playing organs produced

superior musical effects, so that they became, and still are, well

known and popular. The latest styles, indeed, rival the orchestra in

their versatility and coloring, especially when operated by a skillful

musician.

The pneumatic principle thus applied, and the success of the attempts

to adapt it to the organ, led experimenters to emulate, and if possible

improve upon, the early attempts at the practical manufacture of

pianoforte-playing mechanism. Without going too much into details,

it may be recorded that the two concerns previously referred to were

nearly ready in 1896 to come out with such an instrument, and patents

were granted in 1897 for a complete piano-player of the cabinet style,

attachable to any piano, and easily detachable therefrom. Other patents

soon followed, and other manufacturers fell into line, with the result

that the great piano-player movement had soon begun in earnest. The

productions of the different firms, of course, varied in details, but

only two widely separated schools have developed, and inasmuch as both

of these employ the pneumatic principle, which has triumphed over all

others, and is now adapted unanimously by manufacturers who desire to

render possible an approximation to artistic rendition of pianoforte

music, it will be unnecessary to treat of any instruments constructed

on other lines.

In the meantime it will be well to note that the above short sketch

of the preliminary skirmishing, as it were, is intended to be nothing

more than an outline, as the policy adopted throughout this entire

work has been to avoid the historical view-point, as much as possible,

and to confine ourselves strictly to the business in hand; namely,

constructional principles and their application.

The pneumatic principle has been adopted in all the piano-players that

we have occasion to survey, and its application has been in all cases

essentially similar. Indeed, the two schools of construction differ,

not in the application of the pneumatic principle, but in certain

details of construction, which are important but not vital. One general

description will be quite sufficient to acquaint the reader with the

make-up of these instruments, and it will be easy to undertake any

further explanations of important variations.

The underlying idea, upon which the whole player is built, may be

described as arising from the knowledge that a bag or bellows of

suitable material will collapse whenever the air is exhausted from it,

and become inflated again when the air is permitted to rush into it,

which happens as soon as the vacuum is destroyed. Now it is obvious

that here, in these two processes, we have the possibility of producing

a reciprocating motion, and the value of this is evident when it is

remembered that the process of pianoforte playing, when reduced to its

lowest terms, is essentially the combination of the alternate manual

motions required to depress and release a key. Consequently, the matter

of designing a pianoforte-playing machine is reduced to the problem of

placing a bellows over a key, or in mechanical connection with it, in

such a way that the inflation and deflation of the bellows will operate

levers to depress and release the key. Thus far, it may be understood,

we are dealing with elementary mechanical principles. But the questions

arising from consideration of the control of these bellows are far more

delicate, and require for their solution a high degree of mechanical

talent. Let us see how the problem has been worked out.

A musical composition which is to be performed on the pianoforte

by means of one of these “players,” as they are called colloquially,

is first reduced to a series of perforations on a long sheet, the

perforations being of uniform width, but varying in length according to

the duration of the musical tone for which each stands. The sheet is

then wound upon a spool and is connected with motor mechanism which is

adapted to draw it across a “tracker-board” pierced with holes, each

of which corresponds to some hole in the sheet. The latter, when so

drawn across the plane of the “tracker-board,” is wound up on another

spool, and the motor mechanism of the player is so arranged that the

sheet can be re-wound on to its own spool when the whole composition

has been played, so that it may be withdrawn from the “player,” and

another substituted in its place. The actual process of operation is

as follows: The “player” is provided with foot pedals, which operate

exhaust bellows, and thus maintain a reservoir bellows in a state of

exhaust, on the same principle as in the reed organ. As long as the

exhaust bellows are operated, and the reservoir is kept in a state of

vacuum, it is possible to maintain an “exhaust chamber” within the

“player” also in a state of vacuum. This exhaust chamber communicates

with a “diaphragm chamber,” in connection with the “tracker-board”

hole, and with an “inflation and deflation channel” in connection with

the striking pneumatic or bellows which depresses the pianoforte key.

The connection with the “diaphragm chamber” is by means of a very small

hole pierced in a leather diaphragm which is stretched between the

“exhaust chamber” and the “diaphragm chamber,” so that the latter will

be in a state of partial vacuum. Resting on the leather diaphragm is

a button, attached to an upright spindle which stretches through an

orifice into the inflation and deflation chamber, and there operates

a poppett valve which, in one position of the spindle, will close the

chamber against the exhaust chest, while opening itself and therefore

also the pneumatic to the outer air, and in another position will

reverse the process, opening the chamber to the power of the vacuum

in the exhaust and simultaneously closing itself and therefore the

pneumatic to the vacuum, which will cause the latter to collapse, and

thus bring down the key. Now, when a hole in the perforated sheet comes

opposite a hole in the “tracker-board,” an atmospheric communication is

opened with the “diaphragm chamber,” and air will immediately rush down

into the “diaphragm chamber” and at once destroy the partial vacuum

which existed there. As a consequence of this, the leather diaphragm

will immediately rise to its fullest extent, influenced by the vacuum

in the chamber above it, and will therefore push up the poppett valve.

This action will open communication between the exhaust and inflation

and deflation chambers and will expose the latter to the vacuum, while

shutting off the outer air which has kept the pneumatic inflated. Thus

the pneumatic will collapse, and the piano key will be held down until

the closing of the “tracker-board” hole once more restores the partial

vacuum in the “diaphragm chamber,” thus permitting the poppett valve to

sink, and reopening the connection between the pneumatic and the outer

air, which re-inflates it and releases the key.

As will have been anticipated, there are endless small variations of

detail in the construction of different “players,” but they all work

on the same principle, and the above description will be sufficient to

give an idea of what goes on inside the “player” when the perforated

sheet is put into position and drawn over the “tracker-board.”

Variations on the mechanical carrying out of these principles are

dependent upon the ideas of the different makers. It can easily be

understood that there is plenty of room for endless changes in details,

and that every maker of “players” has his own special notions on the

subject.

We have spoken above of the motor mechanism designed to move the

perforated sheet across the “tracker-board,” and to rewind it when

required. It is clear that such a motor device must be very sensitive

to changes in speed control, very light and very easily operated. In

the search for the ideal device manufacturers have gradually separated

themselves into two schools of practice, each being champions of one

particular type of motor. These two schools of opinion and practice

have adopted respectively the pneumatic and the clock-work motors. Both

have virtues; neither are free from vices. It is no part of our plan to

enter into didactic discussion of the relative merits and demerits of

the two styles, but we shall confine ourselves to an exposition of the

method whereby each is adapted to its required work, and shall point

out the more obvious of the good and bad features of both.

The pneumatic motor has the initial advantage of simplicity and

lightness. It consists of a number of bellows, usually three or five,

which are arranged in series on a board and connected by passages

with the exhaust chest. They are adapted to be collapsed and inflated

alternately by means of the exhaust from the bellows of the “player,”

and are governed by valves so arranged as to cause one bellows to be

open to the atmospheric air, and therefore inflated, while the next to

it is simultaneously closed to the atmospheric air and exposed to the

vacuum from the wind-chest, and therefore collapsed. This alternate

process produces a motion which can, of course, easily be transferred

by means of connecting rods to a crank-shaft, which by reciprocation

produces a rotary motion, and also permits the take-up spool of the

“player” to be connected with it by suitable gearing. The controlling

valves are generally connected with the crank-shaft somewhat after

the manner of the valves of a steam cylinder, and are operated by the

motion of the shaft through suitable connecting rods. The reverse

motion of the spool, for rewinding, is accomplished by gearing between

the motor and spool, and the reversing lever, while operating this

gear, also closes the valve between the exhaust reservoir bellows

and exhaust chamber so as to permit the full power of the exhaust to

be exercised on the motor when the rewinding is required. The speed

control of the pneumatic motor is governed by another finger lever

adapted to operate a valve which can entirely close the passage between

the exhaust chest and motor board, the gradual opening or closing of

which increases or diminishes the power of the exhaust upon the motor

bellows and hence the rapidity with which they collapse and reinflate.

This speed control combines simplicity and effectiveness.

In considering the less agreeable qualities of the pneumatic motor we

have to note that a great deal of the alleged deficiency of the type

arises from the fact that its operation depends upon the same agency

as is employed for the striking pneumatics; namely, the exhaustion

of air from the exhaust bellows reservoir. This means, of course,

that the striking pneumatics and the motor are artificially brought

into relations which would never naturally subsist between them. In

consequence, there is a continual tendency on the part of one of the

elements to monopolize the power reserve, to the detriment of the

other. Thus, a fortissimo passage will tend to use up so much power

that the motor will be slowed down; while, contrariwise, the latter,

when driven at its highest speed, will take too much power from the

pneumatics and prevent the expression of their highest dynamic forces.

Here we touch upon the most serious defect of the pneumatic motor, and

while we find the practical workings of these devices quite excellent,

there is no doubt that they would be far more responsive and far

lighter in operation if these fundamental defects did not exist.

The clock-work motor, on the other hand, is entirely separated from

the striking mechanism, except as far as it is sometimes connected

with the pedals for the purpose of winding the spring. Even this,

however, is not a real interference with the striking pneumatics. The

chief advantages of the clock-work motor are that it is built of steel

and brass, instead of wood and leather; that it is independent of the

rest of the player, and therefore always self-contained and free from

extraneous influences; that rewinding is effected by the reserve power

of the spring, and that the use of the pedals as in the pneumatic

motor, is therefore not necessary.

Its disadvantages, as alleged by its critics, may be considered as

follows: That it requires oiling and cleaning frequently, and that if

neglected will rapidly become impaired; that it is sometimes slow in

acceleration and retarding; that it is heavy and complicated, and that

the winding, when done by pedals, is wasteful, and when effected by a

handle, is tiresome.

The above tables of vices inherent in both types are by no means as

terrible as they look, however, and experience seems to show that many

of them do not appear in practical work. On the whole, the clock-work

motor seems to have much in its favor, although the question still

remains open, and time alone can show which is practically better.

It is neither necessary nor profitable to go into any considerable

detail as to the pianoforte pedal operating devices, the soft stops,

or other details of the sort. We may better employ the space at our

command in a short discussion of the movement which has resulted in

incorporating the mechanism described above into the case of the

pianoforte itself. This movement is, of course, a natural outcome

of the successful introduction of the exterior “player.” The public

soon began to find fault with the latter on account of the space it

occupied, and also because of the annoyance incidental to its removal

from the instrument for manual playing. It was not long before the

makers of “players” were experimenting, with a view to using the

waste space in the upright pianoforte for the purpose of including

the “player” therein. The advantages of such a plan are obvious,

provided that the actual mechanical difficulties can be overcome.

These difficulties proved very stubborn at first, and it is not to be

supposed that all are entirely overcome, even now.

It has been very hard, indeed, to arrange the mechanism in such a

manner as to make all parts accessible for adjustment and repair.

The results of any neglect of this important requisite are very

serious. Makers should bend their first energies to the removal of

all difficulties incidental to the obtaining of access to the playing

mechanism or to the rest of the pianoforte, before they consider

anything else. For example, it should be possible to remove the action

or keys of the pianoforte without having to detach pipes and tubes. Nor

should it be difficult to disconnect the pumping apparatus, or some

individual valve or pneumatic which may need attention.

Again, the manner in which the pneumatics strike the keys or action is

very important. The earlier player-pianos generally had the pneumatics

placed below the key-bed, so that they operated from the rear end of

the latter, striking them upwards. This had the double disadvantage of

inflicting a hard, rigid kind of blow, and of making the pneumatics

very inaccessible. A better plan has lately been devised, which puts

the pneumatics over the keys, so that they operate at the front ends,

just back of the ivories. Some such method as this is excellent always,

since it permits a considerable concentration of the mechanism and a

consequent curtailment of the inconveniently long tubes leading from

the “tracker-board” to the valve chambers. All these matters, however,

are in process of practical development, and the future holds the key

to the ultimate solution of any such problems.

In considering the influence of the “player” mechanism upon the

pianoforte itself, we may note that the general adoption of these

devices, if it occurs, will inevitably produce certain modifications

in the action mechanism, as well as in the general design. There is no

doubt that the ordinary action mechanism of the pianoforte will not

prove strong enough to endure the furious onslaught of the “player,”

and it is questionable whether pianofortes constructed on the old plan

will not more rapidly deteriorate when exposed to this wear and tear.

The precise direction in which this modification is likely to come may

not now be accurately determined, but it is probable that a general

strengthening of centres and flanges will be the first result.

As for the distortion of the pianoforte case, this, as far as it

now exists, may very easily be corrected. But it will not be easy to

arrange the playing mechanism so as to avoid interference with the

acoustical or mechanical forces of the pianoforte. For one thing, there

is a great deal of machinery to put into a very small space, and for

another there are certain parts of the pianoforte that must under no

circumstances be touched. Thus the sound-board, the strings and the

iron plate must be left severely alone. But the elimination of the

Boston or double-rolling fall-board, and its replacement by something

that will take less room, will provide a sufficient space to house the

pneumatics and exhaust chamber above the keys. This is where they ought

to be, and the only possible place where they can be reached without

trouble or damage. The pumping apparatus must be kept away from the

sound-board, and placed where it will do no harm; under the key-bed,

necessarily, but not so as to interfere with the piano pedals or the

resonance apparatus. Some portion of the bottom frame can usually

be eliminated with advantage, and this will assist in providing the

necessary space.

The position of the motor should be such that the minimum of waste

occurs between the crank-shaft and the take-up spool. Thus, if

possible, the motor ought to be above the key-bed. If it be of the

clock-work type, it can hardly be placed anywhere else. Lastly, the

whole of the exterior apparatus, such as levers, pedals, spool, etc.,

should be arranged to fold away or be covered up out of sight when the

instrument is in use for manual playing.

While it has only been possible in this appendix to give the barest

outline of the player-piano problem, the reader is besought to

recollect that the industry is still new, and that the “present state

of the art” hardly admits of any didactic assertions on principles

of construction. We do not even know, today, whether the pneumatic

principle will continue to prevail, or whether some new refinement of

electric mechanism will not eventually surpass every device now known,

both in responsiveness and convenience.

APPENDIX B.

THE SMALL GRAND.

It is a curious fact, but none the less characteristic of that

most curious of industries--the pianoforte craft--that in it the

development hypothesis, so familiar to all other branches of human

endeavor here, appears not to be fully applicable. While the aim of

the present treatise has been to systematize and codify, as it were,

the laws that underly all right constructional methods, we have been

forced to recognize that there is no appearance of any accurate and

uniform generalization which may be applicable to the future guidance

of pianoforte builders in their efforts to attain to the greatest

perfection in later types. Although we have succeeded in laying down

the broad and universal principles that govern intelligent practice of

the art, yet we cannot fail to note that a progressive evolution is not

yet possible. That is to say, there is no progressive synthesis in the

art which shall carry us continually further from the original types,

so that the ancient models shall become in time quite unrecognizable in

the light of modern improvement. Rather would it seem that the course

of improvement is leading us back to reversions towards the original

types, and of this tendency the rise of the small grand pianoforte is

one of the most striking illustrations.

It is not to be supposed that this reversionary movement is to be taken

as implying a dissatisfaction with the methods that have grown up in

the course of the last hundred years, and the systematization of which

has been our task in the present work; it is rather that the tendency

today is in the direction of utilizing the most modern methods in the

resuscitation and further development of the type of pianoforte that

was earliest in the field.

In other words, as the reader well knows, the last few years have seen

a general tendency towards a revival of the grand, in forms suitable

for modern ways of life, and with the advantages carried by the wealth

of experience and practice on which the modern pianomaker can make

unlimited drafts. This resuscitation has not taken the form of any

attempt to bring the large-sized concert instrument into more popular

use, but it has rather been a matter of evolving a new type out of the

old, and of developing this latter along comparatively original lines.

With the commercial success of such an experiment we are not here

immediately concerned, but we have great and lively interest in the

question of its constructional value and in the possibilities that are

implied in its future development.

Without entering into wearisome detail, it may be stated that the last

five years have seen a most systematic attempt on the part of leading

manufacturers to construct and popularize a very small style of grand

pianoforte, and to endow this new instrument, as far as possible, with

the musical advantages possessed by the larger and older horizontal

forms. The dimensions of the “small grand,” as it has come to be

known, range from a length of five feet to one of six, with width in

proportion, and the smallest sizes are continually attracting greater

attention on the part of experts. The idea is to reduce the dimensions

to the very lowest point compatible with something approaching to grand

pianoforte tone, and to make the general outline as beautiful to the

eye as possible. The latter of these desires is easier of consummation

than the former, and it has therefore appeared that some of the makers

of these instruments have been somewhat apt to overlook truly musical

results in deference to a public sentiment in favor of something that

is graceful, if nothing else. In fact, when considering the small grand

we are obliged to note that it has been developed, and is now being

produced rather to appeal to that portion of the pianoforte-buying

public that demands something for its homes more beautiful than the

upright and less bulky than the large parlor or concert grand than in

answer to any general cry for the better musical development of the

instrument itself.

If we bear this fact in mind, and its truth is obvious to the student

of pianoforte history, we can the more easily understand and appreciate

the essential features of this latest development.

The small grand has been produced, we repeat, to please the public, and

the public at large is not exclusively composed of musicians.

But even while acknowledging the probability of this statement, we

need not conceal from ourselves that the small grand can thus fulfill a

very useful function. Reduced to its lowest terms, it remains a grand

pianoforte, with the action and touch so essentially associated with

the horizontal form, and so immeasurably superior to anything that

is found in even the best uprights. And here the small grand has an

enormous advantage, nor does it appear that its truly musical and tonal

development need be permanently stationary, if only the limitations of

the instrument be appreciated, and work on it be directed with especial

reference to its own size, and without dependence upon the traditions

that have supported the building of larger forms.

In a word, the builders of small grands have the opportunity, if

they care to avail themselves of it, to produce a form of miniature

horizontal pianoforte that shall possess all the advantages of the

large concert instruments, with the exception of the great tonal volume

peculiar to the latter, and none of the disadvantages of bulkiness

and ungracefulness. They can never hope to obtain the same tonal

results from a 5-foot as from a 9-foot instrument; but they have the

opportunity to popularize a touch and technique that is impossible of

achievement for players of the upright, and a quality of tone that is

equally unattainable on vertical instruments. Under all circumstances,

it must be borne in mind that the results of small grand building, even

when most carefully and skilfully executed, are essentially different

from anything that has yet been produced in the tonal development of

the pianoforte, and that no attempt to imitate the tonal properties

of the large grand can be successful. The action and the touch are

fit subjects for this kind of imitation, but such tonal quality as

is susceptible of development is entirely original and indigenous

to the miniature grand. The only legitimate field of inquiry along

these lines, then, is that which has reference to the development and

constructional principles of the small grand considered as a distinct

type, and needing particular and definitely differentiated principles

and methods.

Assuming the correctness of these premises (and their truth would

appear to be obvious), we have to ask ourselves what is the exact

nature of the problem which is set for solution, and wherein it differs

from any that we have had to consider as yet. Bearing in mind that we

are dealing with what is known as the “small grand,” although it is

marketed under various other names selected by different manufacturers,

we can state the constructional problem in fairly definite and exact

terms.

It is required to build a pianoforte in horizontal form, of which the

extreme length shall preferably not exceed five feet and six inches,

and which shall be compensated for shortening by means of extra

widening; which shall have the lines of a larger grand, refined to the

highest degree, and within which the greatest possible tonal value

shall be contained.

Viewed thus, it appears that the principal factors to be considered are

string-length and sound-board area. It is obvious that the diminution

of the former and restriction of the latter are inevitable; and the

net result must be seen in a radical alteration, if not deterioration,

of the tonal property of the instrument. It remains to be seen how we

shall set about to transform this disadvantageous condition into one

that shall work for us, and in accordance with our desires. In other

words, as we cannot get a sound-board containing, say “_n_” square feet

of superficial area into a case that only contains 3/4 “_n_” square

feet of space, we must resign ourselves to the inevitable, and search

for ways and means whereby the difficulty of putting into a quart

bottle more than it will hold may be evaded, if not explained away.

And first, then, let it be remembered that the only line where-from we

can safely base any calculation is that which leads in the direction

of a continual refinement of the means of applying sound-board

construction to the instrument. We must utilize every inch of the

superficies; we must discover and apply methods for opening up the

vibratory area to the impressions received from the strings in a manner

superior to that which has been deemed sufficient when space has been

at a discount. We must arrange bridges and bearing-bars so that the

string-lengths may be stretched to the utmost, and, lastly, we must use

such minute care in the treatment of the hammer-striking line that the

inevitable “breaks” in the tone shall be minimized.

The intelligent reader will not fail to observe that we have put forth

here a tolerably difficult set of requirements. But he will likewise be

equally quick to note that ultimate success in small grand designing

depends entirely upon the manner in which these conditions are met. If

they are slighted or slurred, if the designer attempts to ignore them,

he will find that failure will surely follow. On the other hand, it

would be too much to say that even the most faithful and conscientious

effort applied to the elucidation of the problem will under all

circumstances have the desired effect. The conditions are unusual; in

some cases they do not admit of any direct and positive settlement.

But in so far as these conditions can be met, in so far as they are

susceptible of solution, the designing of the small grand can properly

be made successful.

It must be recollected that the “striking-point” of the hammers is a

vitally important element in the success of pianoforte building. It

is the one factor that cannot be trifled with, and in treating which

there must be rigid adherence to rule. Now it is well known that the

correct striking distance has been ascertained (as shown in the body of

this work) to be at a point between one-seventh and one-ninth of the

speaking length of the string, the exact place for each string being

calculated with reference to the actual speaking length. As worked out

in the best practice, the shortest and highest pitched strings have

their striking points at about one-tenth of the speaking lengths, while

the longer and lower pitched elements further down the scale are made

to conform more closely to rule. Now it is obvious that the application

of this law to the very much shortened strings of a small grand will

result in distinctly unsatisfactory quantity and quality of tone. But

it will not do for us arbitrarily to change the actual striking point,

for that would change the position of the hammer line, and experience

has amply demonstrated that no such idea will work. Inasmuch,

therefore, as we are estopped from interfering with the striking point,

as far as concerns the actual hammer line, it becomes necessary to

discover some means for obtaining a somewhat greater length of string

in proportion to the dimensions of case. Careful measurement will

show that the higher strings do not fall under the classification

of “dangerous.” It is only when we approach the point where the

overstringing begins that the disadvantage of decreased case length

becomes apparent. The treble string-lengths at or near this place will

be too great, if carried out according to the well-known and practiced

laws of scale designing; while, if they are unduly shortened, the

tensions and thicknesses will require to be submitted to such radical

alteration as to make most unpleasant changes in the tonal quality and

volume.

But while an absolute solution is out of the question, there is no

doubt that we are able to find a fairly satisfactory substitute. There

are two courses open to us. We are not permitted to make any great

change in the tension, but, within certain limits, we may weight the

string, and we may even stretch out its length, if we be very careful

and watch out for every inch. The first method must always be used

with caution. It is susceptible, and very easily, too, of improper

application, and when abused becomes an enemy rather than a friend. In

fact, the weighting of treble strings with iron or copper wire should

be undertaken with the greatest caution, and only indulged in when the

designer is absolutely unable in any other manner to obtain a proper

vibrating length. The last two or three strings above the overstrung

portion of the pianoforte may usually be wrapped without troublesome

complications, but under no circumstances should the highest of these

have a frequency greater than 128. On the other side, where the bass

strings begin, this condition does not apply, for it is possible by

means of suspension belly bridges, to increase the actual speaking

lengths several inches. These suspension or extension bridges, as they

are called, may also be used, though with caution, for the lowest

treble strings. We have never advocated the splitting up of bridges,

but there are cases, such as these, where unusual methods are quite

unavoidable.

In the several ways thus sketched out, the designer of small grands

may do something to overcome the manifest difficulties of his task.

He may likewise take heart of grace when he approaches the matter of

sound-board area, for in treating the string-lengths there appears

a partial solution of the latter problem. In speaking of the use of

suspension bridges we omitted to note that the position of these may be

modified so as to give greater length to the speaking portions of the

strings, by increasing the obliquity of the angle of the overstringing.

Of course, this would be obvious, but it is perhaps not quite so clear

that such adaptation will result in an opening out of spaces on the

sound-board that are usually left severely alone. Moreover, if the

necessary splitting up of the bridges be avoided by means of connecting

strips of the same material, it is clear that the opening up of the

sound-board may thus be carried up to the highest possible value.

Along such lines as these, it would seem, must the course of small

grand designing be laid, at least as far as concerns the vital elements

of string-length and sound-board area. There remains the question of

the metal plate, and this deserves separate treatment.

We have taken pains already to insist upon the necessity for

compromise in the building of small grands. Regarding the iron plate,

we have to observe that great care must be taken to avoid undue

massiveness, for this will entirely spoil the tone quality, as the

other dimensions are not capable of supporting a large mass of metal

without tonal deterioration. On the other hand, it is equally certain

that we can afford to sacrifice nothing in the way of strength, as we

purpose to have the highest tensions and the greatest lengths possible

within the space limitations of our instrument. The ordinary form of

plate, copied from the large grand, may very advantageously be modified

by the adoption of a truss or arch construction, which will enable a

large amount of metal to be cut away from the treble sides without

sacrificing any strength.

Along such lines, as we have already said, the design of small grands

must of necessity proceed. We feel that it would not be improper to

repeat our formerly expressed opinion as to the nature and functions

of the small grand. It has come into existence in answer to a public

demand for something differentiated from the upright, possessing great

beauty of outline, and yet adapted to the confined surroundings of

contemporary domestic life. It is not and cannot be a rival of larger

horizontal forms; it is physically estopped from the realization of

such ambitions. But it has a place in the economy of the musical world,

and such a place as nothing else would satisfactorily fill. Wielding

the mighty influence of the name “grand pianoforte” and with the

initial advantages over the upright that its form, touch and action

imply, it would indeed be remarkable if the production of the small

grand did not become more and more a part of the regular routine of

all pianoforte manufacturing establishments. The design of its case

will always, surely, be above criticism. It is out of our province to

enlarge upon the details of case architecture, but it may be pointed

out that such details as graceful trusses, well-designed lyre, and

carefully molded curves do much to make or mar the future of a small

grand, entirely apart from the excellence of its scale. The general

effect should be that of lightness and grace; a touch of frivolity

even will not be out of place. The little instrument is likely to find

its way into homes where money is not always an object, and where the

ability to enjoy the best that life contains is usually present. The

designer will make no mistake if he keeps this in mind.

UNUSUAL METHODS OF CONSTRUCTION.

As the reader is well aware, the greater part of the present work has

been devoted to an exposition of the broad principles underlying all

right methods of pianoforte construction. We have devoted little space

therefore to the elaboration of features without this classification,

or to the consideration even of such ideas and methods as do not fall

within the lines laid down in the theoretical portion of this treatise.

Busily occupied, as we have been, with the development of acoustical

and mechanical principles and their application along the most obvious

and natural lines, we have been forced to neglect one of the most

interesting studies that can be taken up by the investigator; to wit:

the ideas, inventions and devices that have sprung from the brains of

the numerous mechanical and acoustical geniuses who have illuminated

the course of pianoforte history and development. Many of these ideas

have proved impracticable under the stress of use; others, again, have

been shown to be commercially unprofitable; a still larger number have

flourished during a longer or shorter period or have been neglected by

all others than their original inventors. The true place for a study

of these neglected children of enthusiastic, if not always practical,

brains is in a history of the pianoforte rather than in a technical

treatise on construction.

[THE END.]

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

text:

Page Correction Location in Text

20 Handel to Händel time of Händel;

20 pianforte to pianoforte which the grand pianoforte

27 begin to begun now about to be begun.

32 closing parenthisis inserted staff in the bass clef)

32 B-sharp to B-Natural note 15 in harmonic series table

41 B double F-flat to B double flat minor sixths table

42 clasisfied to classified These sounds are thus classified:

49 of to or imply a length or height of

53 asumption to assumption made on the assumption

68 veenered to veneered turning out of such veneered cases,

77 missing comma inserted (more elaborate than the other two),

86 homogenous to homogeneous plate as homogeneous with the sides

87 is to it In fact it occupies

99 REPETITON to REPETITION DOUBLE REPETITION ACTION

109 fough to fought already been fought out

113 any one to anyone through by anyone who hopes

123 synchromize to synchronize will synchronize with each other,

124 mesontonic to mesotonic that the mesotonic system,

125 period added in the ratio 1296:1250.

131 turned to tuned conversely, if the tuned notes

148 closing quote added vacuum in the “diaphragm chamber,”

154 Wtihout to Without Without entering into wearisome detail,

154 possesed to possessed musical advantages possessed

155 circustances to circumstances Under all circumstances,