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THE PHYSICAL BASIS OF
PIANO TOUCH AND TONE
THE EHYSKAL BASIS OF
PIANO TOUCH AND TONE
AN EXPERIMENTAL INVESTIGATION OF THE EFFECT OF
THE PLAYER'S TOUCH UPON THE TONE OF THE PIANO
BY
OTTO ORTMANN
Psychological Laboratory of the Peabody Conservatory of Music
WITH NUMEROUS ILLUSTRATIONS
LONDON
KEGAN PAUL, TRENCH, TRUBNER & CO., LTD.
J. CURWEN & SONS, LTD.
NEW YORK: E. P. DUTTON & CO.
1925
PREFACE
mean * * e ^ me ^ ia ^ suc ^ P oe tic effects
are produced by means of mere variations in
key-speed and in time duration ? " I was asked after
a particularly beautiful performance of Schumann's
Kinderscenen by Harold Bauer. Bauer himself, of
course, would be the first to deny the existence of
any physical agencies other than those of key-speed
and duration. The question, however, is so often
asked and so variously answered that it prompted
a decision to undertake an experimental investigation
of the problem in the hope that such an investigation
might clear up some of these differences of opinion,
and might, at the same time, furnish a stable basis
upon which some of our reactions to music could be
explained. The scope of the work and the method
of procedure adopted in it were far from being as
complete and accurate as I should have liked to
make them ; but they were determined by the fact
that the investigation was made as a minor problem
of a more general one : the development of an adequate
measure of musical talent.
( The work on piano touch and tone, however, yielded
results of sufficient clearness and practicability to
warrant their publication as a separate study;
particularly since this subject is a fundamental
problem of piano pedagogy, in which its efficient applica-
tion has been seriously interfered with by the conflict
of opinions on the basic relationship between piano-
touch and piano-tone. What we actually hear and
what we imagine we hear, what we actually do and
what we imagine we do, when listening to or playing
upon a piano are distinctions urgently needing
PREFACE
a clear exposition. Some affirm that the influence
of touch upon tone must forever remain a mystery ;
others hold that the piano action is but a lot of dead,
wooden sticks, movable up and down, in only one,
fixed way ; still others assert that the most subtle
shades of emotion are actually transmitted to and
through this action by individual spiritual differences
of touch. Such confusion is both harmful and
unnecessary, since the piano is not a psychical but
a physical instrument, and, as such, is entirely obedient
to laws that have been formulated, tested, and proved
long since.
A preliminary study of the problems connected
\vith the effect of touch upon piano-tone brings to
light the facts that the musician rests content with
the total effect and does not analyse this into its
fundamental components ; and that so long as we
depend upon personal opinion, as expressed through
playing, we cannot bring the problem to any satis-
factory solution. Instead of trying to find common
ground in the various views held, it is better to adopt
the experimental method. This method accepts only
those conditions and relationships that can be proved
to exist. The problem is solved when we can
reproduce at will the action and reaction experimented
upon ; when, given the conditions, we can definitely
forecast results ; or, given the results, can determine
the causes. Such a method is entirely free from
personal bias ; it furnishes a permanent record which
may be verified, at any time, by subsequent experiment.
In music such proof is not always easily established.
No language is so difficult to understand as the language
of tones. And no language is so misunderstood ;
for a tone lives but a moment, and when we would
scrutinize it, it is gone. Music, in this respect, differs
from all the other arts : its transiency keeps its nature
obscure and makes its effects subtle. As a result,
vi
PREFACE
truth and error, fact and fancy, have long played
a game of hide-and-seek in musical theory, and will
continue to do so until we catch the elusive tone and
hold it for closer inspection. We must do the same
with touch ; for touch, as here understood, means
movement, and movement means transiency.
Fortunately, both touch and tone can be adequately
recorded. When we have so recorded them, we shall
have taken the fiist step in the solution of our problem :
the separation of the physical from the non-physical.
This division is fundamentally essential. The musician
often objects to it on the ground that it robs music
of its poetry : " Art is not science/' he says. That
is quite true, and yet the objection is not well taken.
Are we the less able to appreciate the art in a painting
because we happen to know, when we chance to think
of it, that the picture consists of various coloured
pigments and a piece of canvas ? Is the poetry of
Shakespeare less beautiful because we know the
process by means of which the book was printed ?
The artist need have no fear that art will suffer from
scientific investigation. The two points of view are
never co-existent. A performance of Tristan is a
world of poetry to the adolescent girl ; it is " worse
than a pig-kill " to a scientist of my acquaintance ;
it is a fitting environment for her new evening gown
to Mrs. Smith ; a study in altered chords to the
harmony student; a reaction experiment to the
psychologist. Moreover, what at one time is the
perfection of musical art, may at another time, to
the same person, ' be rates of vibration, sheep-gut,
and what not. The objection to a scientific analysis
of art is but a reflex of the classical problem of Greek
philosophy, which has pointed out the loss of identity
that accompanies any division into parts. It is,
therefore, an objection outside the field of the scientific
investigation itself.
vii
PREFACE
The division into a physical and a non-physical
element is not at all times easily made, for there
are phases of the one that shade imperceptibly into
phases of the other. These demand separate treat-
ment. Our immediate problem will be limited to
the purely physical elements of touch and tone, and
will exclude all processes which occur before the finger
touches the piano-key, as well as all those which
occur after the sound-wave reaches the ear. It wiU
include each step between the moment of contact
of finger with key, and the impingement upon the
ear of the sound-wave resulting from the touch.
This defines the problem clearly, and permits aa
effective application of experimental procedure.
The present investigation is addressed primarily
to the musician ; the physicist will necessarily find
in it much that is repeated and apparently superfluous.
He, however, who 'knows the reluctance with which
musicians, both professional and amateur, accept
the limitation of all tone-colour on the piano to
key-speed and duration, will readily understand
the necessity for both repetition and detail. If this
book contributes a little to the acceptance of this
limitation, its object will have been attained. This
it proposes to do by using as a starting point proved
laws ; by employing, in the experimental procedure,
both the affirmative and the negative method of
proof; and by presenting graphically the essential
physical attributes of piano touch and tone.
I take this opportunity to express my gratitude
to Harold Randolph and May G. Evans for the co-
operation that made the investigation possible; to
George P. Hopkins for assistance in conducting the
tests ; and to the many teachers who kindly contributed
the necessary records for the study.
0. O.
BALTIMORE.
viii
INTRODUCTION
PHYSICAL PRINCIPLES
analysis demands accuracy of expression.
If some of the contradictory opinions now current
with regard to certain phases of piano-tone and touch
are to be readjusted advantageously, the meaning"
of the terms and principles involved must be made
as definite and clear as possible. Obviously, all
analysis is useless if we continue to use momentum,
elasticity, and similar terms in the usual confusing
and loose manner. The following list of definitions-
and axioms is an attempt to define clearly certain,
properties of matter and laws of dynamics upon
which the conclusions drawn in later pages are based.
They form the theoretical basis of which the actual
experiments described in succeeding chapters are
the practical application and the verification.
WEIGHT. That force which a body exerts upon any
support which keeps it from falling to the earth.
The greater this force, the greater the weight.
MASS. The amount of matter (number of particles)
which a body contains irrespective of its volume or
shape.
INERTIA. The property possessed by a body by
means of which a force is necessary to change the
motion of the body.
ELASTICITY. The property of matter by means-
of which it returns to its original size and shape after
deformation under the action of some force. Steel,
water, rubber, compressed felt, and all gases are
elastic ; clay, lead, and similar substances are inelastic.
RIGIDITY. That property of matter permitting:
ix
INTRODUCTION
its shape to be changed only by a great force.
Equivalent to stiffness. Applied to muscles it means
a contraction preventing motion among the parts
of the body.
COMPRESSIBILITY. The property of matter by
means ot which its volume may easily be diminished.
The opposite of expansibility.
DENSITY. The mass per unit volume of the
substance.
FORCE. An interaction between two bodies (or
parts of the same body) causing or tending to cause
a change in the motion of each, either in direction
or in magnitude.
We measure all physical phenomena in one or more
of three ways : mass, length, and time. Or, in the
words of Maxwell, our whole civilized life may be
symbolized by a set of weights, a footrule, and a clock.
If a particle or body is moving with a constant
velocity, no resultant force is acting.
To produce a change in the velocity or direction
of a moving body, a force is required.
If F = the force, and t = the time, the product
Ft = the impulse.
If m = the mass, and v = the velocity, the product
mv = the momentum.
When a body is under the influence of several
forces, the action of each one is independent of the
action of the others.
When two bodies receive acceleration from the
same force, their accelerations vary inversely as their
masses.
Conversely, the accelerations impaited to the same
mass by two different forces vary directly as the
forces.
There are two kinds of acceleration, change of
speed and change of direction.
INTRODUCTION
When two bodies, A and B, interact on each other,
the force exerted by A on B is equal and opposite
to the one exerted by B on A.
The effect of a force on a material body depends
upon three things : its numerical value (intensity),
its direction, and its point of application.
The effect of a force on a rotating body is measured
by the product of the force by its lever arm, and is
known as the moment of the force. The lever arm
is the length of the perpendicular dropped from the
axis to the line of direction of a force.
The idea of work involves both force and motion
in the direction of the force.
The power to strike a blow is due to the momentum
of the moving body.
The work done by a purely mechanical force during
a displacement from one point to another depends
upon the initial and final positions and not upon
the path followed.
A force, at any moment, can have but one quantity ;
this is independent of the manner in which it has been
attained.
The general law of mechanical action is stated by
the equation f s = rs 1 +w, in which f force applied,
s, the distance through which force acts, r, the resistance
overcome, s 1 , the distance through which its point
of application moves, and w, the wasted work.
There are two ways of doing work : first, by pro-
ducing acceleration, which means increase of kinetic
energy ; and secondly, by overcoming resistance,
which means increase of potential energy. If a system
has both potential and kinetic energy, an increase in
one is accompanied by a decrease in the other. As
matter cannot be destroyed, so energy cannot be
destroyed. The principle of the conservation of
energy states that in the transfer of energy there is
no loss ; what one body loses the other gains.
XI
INTRODUCTION
Change of velocity due to uniform acceleration is
equal to the product of the acceleration and the units
of time ; v = V + at.
The speed at any instant is the distance which the
point would travel during the next unit of time, if
the motion were to remain uniform.
The law of the lever is expressed by the equation
p x ca = Q x cb, in which P is the power, Q the
resistance, ca and cb the lever arms respectively.
That is, in the lever, the power is to the weight in
the inverse ratio of the arms.
A moving body has three and only three funda-
mental properties : mass, speed, and direction.
The fundamental law of force is F = ma, where
F = force, m = mass, and a = acceleration.
Work = force x displacement in the direction of
force.
Kinetic energy = one-half the mass x velocity
squared (-|mv 2 ) .
Potential energy = resisting force x the distance it
is overcome.
If F is mean force and h the distance through which
the body moves, Fh = C + -|mv 2 . Since, in the
piano-action h, C, and m are constants, v, the velocity
of the hammer, can depend only upon F.
xn
CONTENTS
PART I
CHAP. PAGE
I, THE INSTRUMENT .... 3
II. KEY-DEPRESSION .... 14
III. FORCE OF TOUCH 35
IV. TOUCH COMBINATIONS .... 50
V. THE HAMMER-STROKE 57
PART II
INTRODUCTION 89
VI. VIBRATION OF THE STRING ... 91
VII. THE VIBRATION OF THE SOUNDING-BOARD 127
VIII. TONE COMBINATIONS . . . .131
IX. THE NOISE ELEMENT . . . *47
X. THE PROPAGATION OF SOUND . . 160
RESUM 171
BIBLIOGRAPHY 175
INDEX 181
PART I
CHAPTER 1
THE INSTRUMENT
THE ACTION
HPHE action of a grand piano, althougli it varies
-*- in certain details in the product of different
makers, is the same in general principle for all grand
styles of the instrument now in use. This principle is
illustrated in Figures IA and IB. A B is a wooden
block called a key, so pivoted at C that it can move only
in a vertical plane. Beneath each end of the key is
a felt pad (D, E), which limits the descent of either
end. Fastened on the inner arm of the key is a lever,
F, which connects with a second lever, G. This,
with the lever, H (itself a bent lever known as the
hopper), and the lever, I, forms the compound escape-
ment, which will be explained later. The tipper end
of H is cylindrical in shape and covered with leather.
When the key (ivory-covered end) is not depressed,
the upper end of H supports a cylindrical knob on
the arm, J, of the hammer, K, which is pivoted at
L. It is important to note that the only point in
which the hammer (the tone producing body) comes
into contact with the rest of the action before tone
production is in this one point, x, where the end
of H supports J.
When A (the player's end of the key) is
depressed, B rises (principle of the simple lever).
This causes F to push G up, until the point h comes
into contact with M, a stationary (but adjustable)
nut for blocking h, which is the end of the bent lever
H. When F continues to rise, through continued key-
depression, the lever, H, after h touches M, pivots
PIANO TOUCH AND TONE
at this point of contact. This causes the end h' to move
in a direction, roughly speaking, at right angles to
the vertical movement of the hammer-arm J, and
when a given point is reached causes h' to jump or
slide or escape from beneath the hammer-stem. This
point is known as the point of escapement and is
so adjusted as to operate when the surface of the
hammer-head N is about J in. 'from the string,
P. The jerk (under playing conditions) throws the
hammer over the intervening space against the string,
and because of the elasticity of the compressed felt
of which the hammer-head is made, as well as the
FIG. Ic.
elasticity of the steel strings, the hammer is immediately
thrown back. If, in the meantime, the key end, A,
has been permitted to remain in its depressed position,
the hammer is caught by the check, O, and is gradually
released as the end A of the key ascends. If, on the
other hand, we wish to repeat the key-depression,
the escapement mechanism is so adjusted that the
end, h', re-engages the hammer-arm, J, immediately
after it rebounds from the string, whence a second
depression of A will again drive N against the string.
(This is what is meant by the " repeating " action.)
Fig. IB shows the action when the key is depressed
and the hammer about to strike the string. Figs, ic
THE INSTRUMENT
and ID illustrate the principle of the piano-action
very much simplified.
Every student should study the working of the
piano-action on an actual model. This will at once
clear up many misunderstandings as to its operation.
(The action of any piano is easily removed.)
The mechanism here described is a machine. A
machine is a contrivance by means of which force
can be applied to resistance more advantageously
than when it is applied directly to the resistance.
The action of the piano is a machine which enables
us to overcome a resistance at one point (hammer
FIG. ID.
end and strings) by applying a force at another point
(the key end). It employs the principle of the lever
and is a complex leverage system. Since it is obvious
from the diagram (Fig. i) that the distance through
which the hammer end moves is greater than the
distance through which the outer key-end (point
of application of the force) moves, it becomes clear
that the purpose of this machine is to transfer force
into speed.
We have seen under the heading " Physical
Principles " that the fundamental law of mechanical
action may be expressed by the equation f^ =
rs 1 + w. Let rs 1 + w = f 2 s 2 : Then f ^ = ff* or
PIANO TOUCH AND TONE
^i : f 2 : S 2 : s i* That is, two forces vary inversely
as their distances of application. Since, in the piano,
a key-depression of fin. roughly corresponds to a
hammer-movement of if in. the force applied at
A must be four times as great in order to secure
a corresponding force at P. For it must be remembered
that a gain in speed involves a loss in force. No
machine transmits more energy than it receives,
and no practical machine transmits as much. In
other words, there is no machine whose efficiency is
100%. The piano action, then, is a machine which,
roughly speaking, changes force into speed in the ratio
of i to 4, for the distance traversed by the hammer-
head is approximately four times that traversed
by the key end in the same time. It reverses the
direction of application of the forces, the force at the
key end being applied downward, that at the hammer
end, upward. 1
THE STRINGS
When at rest, that is, when the ivory-covered end
of the key is not depressed, the action of the piano
is not connected in any way with the strings (excepting
of course the obvious fact that both are in the same
case). A connexion is made only by throwing the
hammer against the string, which is then set into
vibration.
If I be a length of vibrating string, Y the radius of
the string, d its density, P the stretching weight or
tension, and n the number of vibrations per second,
i r"p~
it is known that n = . \ , in which TT is the
ratio (3-14159) of the circumference to diameter. This
formula expresses four important laws concerning
the transverse vibrations of strings : first, that the
1 The details of the operation of the piano action will be taken
up in subsequent chapters.
THE INSTRUMENT
number of vibrations per second varies inversely
as the length, if the tension be constant ; secondly,
that the number of vibrations per second varies
inversely as the diameter of the string ; thirdly,
that the number of vibrations per second varies
directly as the square root of the tension ; fourthly,
that the number of vibrations per second varies
inversely as the square root of its density.
These relationships explain the process of selection
used in the strings of a piano. In the treble region
we find the thin, short strings, hence a high frequency,
pitch, or rate of vibration. As the pitch becomes
lower, the strings may become either longer or thicker,
or both. Generally speaking, a one-foot length of
vibrating string is found in the region of C 2 . In
the bass region the thickness of the strings is increased
by wrapping the steel string once or twice transversely
with thin steel or copper wire. Steel is used for all
string-cores because of its elasticity, which permits
greater freedom of vibration than other metals. It is,
moreover, not immaterial whether we increase length
or thickness, since, assuming the pitch to be the same,
greater length permits more freedom of partial vibra-
tions, which influence tone quality. In other words,
a long, thin string produces 'a better musical tone
than a short, thick string. 1
When a piano is tuned, that is, when the pitch
of the strings is altered or corrected, this result is
obtained solely by a change in tension. 2
Since the hammer strikes the string from below,
it causes an upward displacement, in consequence
of which the string vibrates in a vertical plane. 3
1 This partly explains the beauty oi tone in a concert grand
as compared with other grands.
2 It is interesting to note that pianos are built to withstand
a combined tension of all the strings on a grand piano when tuned
to proper pitch of over 50,000 Ib. or 25 tons.
3 Certain exceptions will be noted later.
PIANO TOUCH AND TONE
The number of strings used varies with the pitch.
In the treble region when, because of the high tension
and shortness, the tone would be weak, three strings
to each tone are used. In the region of large C, two
strings suffice, and in the lowest register, one string.
Not all strings are stretched in the same direction. 1
THE SOUNDING-BOARD
Every musical instrument may be divided into
two parts : a tone-producing mechanism, that part
in or by which vibrations are created or produced,
and a tone-controlling mechanism, that part in or
by which the tone is moulded, shaped, or intensified
before being transmitted to the surrounding
atmosphere. The piano is no exception. What we
hear when a string in the piano is struck is not due
chiefly to the vibration of the string but to the resulting
vibration of the sounding-board. This is a resonator,
a large, thin, slightly convex and carefully constructed
sheet of wood, covering practically the entire inner
case of the instrument beneath the strings. It is
in direct and permanent contact with the supports
at the end of the strings, and is joined to the outer
case of the instrument, though otherwise free to
vibrate.
The vibrations of the string are transferred to
the sounding-board which, through its size, intensifies
them by setting into motion a much greater volume
of air.
A resonator does not create tones. It can reproduce
only what the generator transmits. Moreover, partly
on account of its own natural periods of frequency,
it may not reproduce with equal accuracy all the
vibrations which the generator transmits. Thus, what
we hear in the piano, as in all musical instruments,
1 The experiment of using four strings has been made, but it is
said without the desired result of enriching the tone quality.
THE INSTRUMENT
is due as much to the resonator as to the body originally
producing the vibrations.
Two kinds of resonators are in use. One responds
only to a single frequency or its harmonic partials,
as does the Helmholtz spherical resonator ; the other
responds to tones of various pitches, and combinations
of them, as does the body of a violin or the sounding-
board of a piano. The duration of a tone, that length
of time during which vibrations, through inertia,
continue after the initial force is no longer applied,
depends upon the speed with which the energy of
these vibrations is absorbed by the resonator. That
often misused expression, " singing " tone, when
applied to the piano, is due to the above-mentioned
phenomenon. That is, the tone-quality of an instru-
ment is largely dependent upon the resonance relation-
ship existing between generator and resonator. 1
The action of the sounding-board of the piano is
not due to sympathetic resonance. The fundamental
condition of sympathetic resonance equality in the
natural frequencies of the two vibrating bodies is
not present in the piano. The sounding-board does
not vibrate because the air waves proceeding from
the strings fall upon its surface, but because it is
joined to the string through the bridge at one end
and thus receives the vibrations directly. If one
of two tuning forks of the same frequency be sounded,
the other will also vibrate without any other medium
of transmission than the air. That is a case of
sympathetic vibration. If a tuning-fork be sounded
and held in the air its tone is scarcely audible. If
1 Future improvements in the piano will doubtless include
improvements in the sounding board. At present there are three
difficulties : if the board is too thick it loses the necessary elasticity,
producing a short tone ; if too thin it warps or loses its tension
and necessary strength. Lastly, the fastening to the case prevents
great freedom of vibration. Some of these difficulties have been
overcome in modern grands.
PIANO TOUCH AND TONE
placed firmly upon a table, the tone becomes distinctly
audible, since the vibrations are communicated to
the table, which, acting in turn as a resonator, reinforces
them. This is a case of forced vibration, and it is this
type of resonance that we find in the piano. 1
THE PEDALS
There are three kinds of piano pedals in general
use : the damper pedal (popularly, though inaccurately,
termed loud pedal), the wna cor da pedal (known as
the soft pedal), and the sostenuto pedal. The first,
when depressed, keeps the dampers lifted from the
strings, all of which are consequently free to vibrate
until their energy is spent or a release of the pedal
brings the dampers down upon the strings again.
The una corda pedal shifts the entire action of the piano
sidewise so that the surface of the hammer, instead
of striking three or two strings, strikes two or one.
The sustenuto pedal keeps any damper or dampers
raised which happen to be raised when the pedal is
depressed.
The pedals of the piano have two primary functions :
to sustain tone and to colour tone. Since the first
purpose was devised as a means of enlarging the field
of activity of the fingers, this has no influence on the
single tone, the central object of the present
investigation. 2
The effect on tone-complex quality is due to the
phenomenon of sympathetic resonance, in consequence
of which vibrations are set up in other strings than the
string which has been struck. Although this certainly
affects the quality of the tone-complex, its influence
1 In a violin the sound heard is not due chiefly to the vibrating
string nor to the transfer of these vibrations over the intervening
-air space to the belly of the instrument. It is due to trans-
mission by means of the bridge which, owing to the tension of the
strings, is firmly pressed upon the belly.
2 Some of the sustenuto effects will be discussed in later chapters.
10
THE INSTRUMENT
is entirely beyond the effect of the touch as here
understood, and for that reason will not be treated in
the comprehensive manner which it otherwise deserves.
THE WREST-PLANK
The plank or block which carries the tuning pins is
called the wrest-plank. It is made of wood in the older
makes of instruments, and *of metal, with holes for
containing wooden plugs, in the modern makes. The
tuning pins, which are threaded to ensure a firmer
grip, are driven into these plugs. The wrest-plank
is firmly fastened to the frame and case of the piano.
Through it no vibrations are intended to be conveyed.
Consequently, absolute rigidity, which ensures the
maintenance of the string-tension, is a desideratum.
THE BRIDGES
There are two bridges in the piano : the wrest-plank
bridge, and the sounding-board or belly-bridge. The
former, sometimes called the pressure-bar, regulates
the various string levels necessitated by over-stringing ;
the latter accommodates the various string lengths
at the vibrating end. The sounding-board bridge
is important because it transmits the vibrations
of the strings to the sounding-board. The exact
position of the belly-bridge varies somewhat with
the various instruments. It is generally divided into
two or three sections, one for each group of strings,
according to the manner in which they are overspun
or overstrung. In certain pianos the position of
the belly-bridge is further determined by the length
of string on the far side of the bridge. A position
is chosen so that this length bears a desired ratio
to the freely vibrating portion on the other side of
the bridge, in consequence of which it vibrates
harmonically. This is known as the " Duplex " or
" Aliquot " scale. Another type of aliquot scale is
II
PIANO TOUCH AND TONE
found in those instruments carrying an extra string:
stretched above the usual ones and parallel to them.
The wrest-plank bridge determines the point at
which the vibrating length of string begins. It is
used in any of several forms : a blunt edge above
or below the strings, a metal nut, or a hole for each
string.
Overstringing is that process adopted in order to
accommodate the various lengths of the strings to
the size and shape of the instrument. It permits
the lower, longer strings to be stretched above and
diagonally across the higher strings. When this
occurs once, the instrument is said to be single-over-
strung ; when done twice, it is double-overstrung.
The plane of the hammer in these cases is always
kept parallel to the string.
THE FRAME AND THE CASE
The modern piano dates from the time of introduc-
tion of metal into its construction. This took place
about 1820. Between 1770 and 1820 the complete,,
all-wood grand piano was perfected. Originally, the
metal frame was conceived to overcome difficulties
of tuning strings of various metals which were
influenced differently by the same change in
temperature. Whatever form the metal frame has
now assumed, it consists essentially of a great or small
number of iron bars set at various angles. The iron
frames are situated at the sides of and immediately
above the strings. The introduction of metal into
piano construction has influenced tone because of the
greater elasticity of metal as compared with wood.
Below the strings and sounding-board we find the
wooden frame, consisting of a series of horizontal
heavy wooden bars placed at various angles. They
mutually reinforce each other and also reinforce
the harp-shaped case. This is either solid wood
12
THE INSTRUMENT
(mahogany, oak, or black walnut) or in the more
recent makes layers, sometimes more than twenty, of
maple and oak. The advantage of the layer-process
*r is supposed to be an increase in resonance effect.
~ The entire object in selecting a case and framing
^ is to secure a proper ratio of elasticity and rigidity,
enough of the former to permit freedom of trans-
mission of the vibrations, and enough of the latter
(TJ to ensure stability against the enormous tension of
n the strings. Generally speaking, the use of metal
tends to give the tone brilliance, and the use of wood
tends to give it "softness" and "depth". We
should therefore expect a combination of metal and
wood to produce the best results. Too much or all
metal would produce a metallic, clangy tone, too
much wood, a dull, thick, and " plump " tone.
C*^ All variations in the tone of the piano may roughly
"" be divided into two classes : those resulting from
Q differences in the make of the instrument, and those
resulting from variation in the manipulation of key-
board and pedal. Variations of the first class account
lor variations in the tone of instruments of various
makes. It is not our purpose, here, to trace the source
ffj or the effect of these variations, since they bear no
- direct relationship to the effect upon tone by the
*0 touch of the player. The tonal variations analysed
(Pin subsequent chapters are all variations in class
*-"two, that is, differences in tonal effects occurring
* within the tonal range of any one instrument.
CHAPTER II
KEY-DEPRESSION
THEORETICAL ANALYSIS
HPHE action of the piano is operated by the hands
-^ and arms of the player. The nature of these bodily
movements, their variability and usefulness, on the
psychological side, do not concern us here. We have
to investigate only their effect upon the action,
and through this, upon the sound-complex of the
piano. Such an investigation should begin at the
point where the player comes into contact with
the playing mechanism, in this case the key-end of the
action. And the first question becomes : What are
the effects of the various forms and gradations of
pianistic touch upon the movement of the piano key ?
In accordance with the method of procedure out-
lined in the introduction we shall first examine the
theoretically possible effects of touch on the key
mechanism, and then consider a number of original
records in the light of the theoretical possibilities.
The piano key (the part visible to the player
represents less than one-half of the entire key or
lever) is a piece of wood about a foot and a half long
and seven-eighths of an inch wide. It pivots on a
point midway from either end, which makes it a lever
of the first kind, that is, one in which the fulcrum
is between the power and the resistance. The vertical
pin at the fulcrum, with an additional vertical pin
at the outer key end, prevents the lever from moving
in any plane except a vertical one. Moreover, the
felt key pads beneath each end of the key limit the
vertical distance through which the key may move
KEY-DEPRESSION
to approximately three-eighths of an inch at its
extremity. We have, then, a mechanism capable-
of being moved at its extremities through a vertical
arc of three-eighths of an inch and immovable in
any other way.
On account of the smallness of the ratio of this-
arc to the length of the lever arm (9 inches) the^arc
may, for practical purposes, be considered a straight
line. 1 No matter how we hold our hands, how gently
or harshly we stroke or strike the key, no matter
how relaxed or rigid our arms are, how curved or
flat our fingers, we can do nothing else to the key
than move it three-eighths of an inch or less vertically
downward. 2 This limit is absolutely fixed by the
unyielding wooden action, a glance at which will
dispel any doubt as to the possibility of other
movements.
Since the key when played upon becomes a moving
body, the laws governing moving bodies also apply
to the key. The three fundamental properties of
a moving body, as we have seen, are mass, direction,
and speed. For any one key the mass is fixed ;
the direction for all keys is fixed ; the only variable
remaining is speed. Consequently, any differences
of effect of touch upon key -movement must be
differences in speed. There is no other variable.
From the fundamental law of mechanical action,
we know that in addition to the force the distance
through which the force acts influences the work
done. The piano key gives as a maximum distance
slightly less than three-eighths of an inch. 3 Whatever
1 Defective action, such as a slight lateral motion due to the
wear on the felt packing, need not be considered, since this represents,
an individual, abnormal, and musically undesirable condition ;
hence it is of no value for general deductions.
2 A perfectly obvious fact. Yet what wonderful tonal effects,
are ascribed to differences in key " manipulation ? "
3 Whatever effect we wish to transmit to the hammer must be-
transmitted to the key before this reaches the end of its downward
15
PIANO TOUCH AND TONE
force is transmitted to the key must, in order to be of
any musical value, be transmitted within this distance.
It may require as little of the distance as is desired,
but it cannot require more. Again, any difference
in degree of force or its mode of application must
show itself in the speed of key-depression, for in the
equation F = ma, F, the force, cannot vary without
similar variation in a, the acceleration, since m,
the mass of the key or action, is a constant.
Concerning variations in key-speed, a number of
possibilities present themselves. The speed of key-
descent may be slow or fast, constant or positively
or negatively accelerated, or it may be a combination
of these factors. We have, then, a definite indication
of the effect of touch on key-movement, namely,
speed. If we can record the variations in key-speed,
we can record all the differences of the effect of touch
on key-movement ; for when there is no difference
in key -speed there is no difference in touch so far
as effect on the key is concerned.
Conversely, any variation in touch which does not
influence or in some way change key-speed is useless
when evaluated in terms of the result on the action.
RECORDS OF KEY-DEPRESSION
It is possible to record the variations in key-speed in
several ways. One that is clear, and that at the same
time permits detailed reading of the records without
additional measurement, is to fix a piece of smoked
glass 1 to the side of the key and record upon this
the tracings of a tuning-fork whose frequency is known.
As the key is depressed, this will yield the sine curve.
movement. The reason for this will appear from a study of Fig. IB.
The hammer leaves its escapement before the key is fully depressed.
_ Consequently, what the key does below this point does not affect
the hammer in any way. This will be more fully explained when
we discuss the hammer-stroke.
1 A microscopic slide serves the purpose very well.
16
KEY-DEPRESSION
The slightest variation in speed will show a variation
in wave length (in this case vertical distance from
crest to crest or trough to trough). A horizontal
line indicates no motion ; an increase in wave length
means an increase in speed. Thus, in Fig. 2, reading
from top to bottom, a means slow and constant
velocity ; b, fast and constant velocity ; c, positive
acceleration (from slow to fast) ; d, negative accelera-
tion (from fast to slow) ; e, an initial speed, then
a decrease, then an increase. The records, Fig. 3
to Fig. 15, were made with a 256 v.d. fork. Each
wave length (the vertical distance between two such
points as / and g, Fig. 2) represent -^TT of a second.
FIG. 3.
Since F = ma, and m is a constant, an increase
in F will result in an increase in a. If we apply a
greater force to the key we will get greater key-speed.
17
PIANO TOUCH AND TONE
Fig. 3 shows the key -movement when initiated by
various weights. Thus, a is the movement made by
the key when a weight of 3 \ oz. is applied ; 6, 4 oz. ;
c, 5 oz. ; d, 8 oz. ; e, approximately i Ib. ; and /,
considerably more. The curves show a gradual
increase of key-speed from a to /. The relationship
is also shown in Fig. 4, in which a is a tone produced
with the finger ; 6, with the hand ; and c and d with
the arm. As we increase the weight of the playing
body (force) we increase key-speed. Therefore, key-
speed varies directly with the force. But in making
these records the tones produced by the key-speeds
also varied directly with the increase in weight.
That is, a yielded a tone of approximately^ intensity ;
6, a tone of p intensity ; c, mp intensity ; d, mf
intensity ; e, f intensity ; and /, ff intensity. 1
d cd a
FIG. 4.
It follows that an increase in key-speed means
an increase in dynamic tone value ; the faster the
key is depressed, the louder is the resulting tone. 2
The Effect of Muscular Relaxation and Rigidity
on Key-Depression. If a relaxed tone-production
(meaning the bodily movements made in key-attack)
affects the key differently from a rigid tone-production,
these differences must reveal themselves in variations
in key-speed, since there can be no other variation.
Fig. 4 shows the key-depression made for tones made
with a rigid wrist and arm, a = pp ; b = p ; c = / ;
1 This variation can be seen in the remaining figures as well.
2 Certain partial exceptions will be explained as they are met.
18
KEY-DEPRESSION
and d = ff> Fig. 5 shows the key-depression for tones
made with normal pianistic, relaxation, a = pp ;
b = p ; c = / ; and d =ff. [In spite of repeated
trials, fff could not be obtained for relaxed production,
and this shows that the dynamic range of tone-
production with rigidity embraces wider limits than
that of relaxation.] Both Fig. 4 and Fig. 5 represent
non-percussive touches ; that is, in both cases the finger
touched the key-surface before any movement for
tone-production was made. In both figures we
get the speed increase with the dynamic increase
mentioned in Fig. 3. Comparing Fig. 4 with Fig. 5
we note that in each paired instance, pp with pp ;
1
I
d c 6 a
FIG. 5.
/ with /, etc., there is practical identity. 1 Many
records, duplicates of Fig. 4 and Fig. 5, were made,
all yielding the same general result. This means
that when intensity is controlled or equal there is
absolutely no difference between key-movement
initiated with a rigid arm and key-movement initiated
with a relaxed arm. 2
In addition to these, a number of records was made
in which the normal kinsesthetic feeling 3 of the player
1 This was only secured after extended practice in controlling
the intensity. Without this practice the average individual
produces a louder tone with rigidity than with relaxation. In
fact, a shade of this difference is noticeable between Figs. 4 and 5.
2 For those who still doubt this statement it is hoped the
following chapters offer sufficient additional proof.
3 The feeling present in the usual playing of a composition.
PIANO TOUCH AND TONE
was the sole regulator of intensity. Fig. 6 is an
example of such a record. Omitting for the time
being the peculiar irregularity, which will be explained
later, we notice upon comparing Fig. 6 (rigid) with
Fig. 7 (relaxed) that in each case the speed is less when
relaxed tone-production is used than when a rigid
tone-production is used. As a result the tone produced
with relaxation under normal (uncontrolled) conditions
is weaker than the tone produced by rigidity.
ed c d a
FIG. 6.
e d c 6 a
FIG. 7.
The Effect of Percussive and Non-Percussive Touch
on Key -Depression. Since practical piano playing
often precludes placing the finger upon the key before
starting its depression, it is necessary to differentiate
between percussive and non-percussive touches. A
percussive touch is one in which the moving finger
strikes the key-surface ; a non-percussive touch
demands that a finger rest on the surface of the key
before descent. 1 Fig. 6 was made with a rigid arm
1 Needless to say, this classification is not always clearly defined,
since one class shades into the other. A very slowly moving
finger, or one moving through a very small distance, may belong
to either class, its assignment depending largely upon the subjective
mood of the player.
20
KEY-DEPRESSION
and wrist, an example of the percussive touch.
Compare this with Fig. 4, which was also made with
rigid arm and wrist but with a non-percussive touch.
The various intensities are the same for the two
figures. In the case of the non-percussive touch
we notice a gradual increase in key-speed from top
to bottom. There is practically uniform, positive
acceleration. In Fig. 6, on the other hand, there
is a well-marked irregularity. Interpreting the curve,
we find that the key begins its descent with a sudden
jerk. 1 Thereupon, its speed decreases and again
increases. This gives us an interesting insight into
the nature of percussive touch. The finger striking
the key rebounds slightly from it, or, what is the
same thing, sends the key off. The finger then
re-engages the key in its continued motion downward
and " follows it up " to the key-bed. This " folio wing-
up " differs from the usual key-depression, as we shall
see later. Figs. 6 and 7, a, 6, c, d, e, show, in addition,
how the distance, through which the initial impact
sends the key down, increases as we increase the force
of the impact ; in pp, the key is thrown through
a negligible distance ; in sfff, it is thrown practically
its entire distance of descent, for the dense, apparently
blurred, portion of the curve, that momentary retarda-
tion after the impact (shown in Fig. 7 by the
small arrows), moves further down for each increase
in force. A number of deductions may be drawn
from this. Since the key, for that part of the
stroke above the dense portion, is not in actual
contact with the finger, we naturally have no control
over it during this distance. Consequently, what-
ever speed we wish to communicate to the key
will have to be transmitted either at the moment
1 Sudden, as compared to the curve of Fig. 4, for it takes time
in all cases to set into motion a body at rest.
21
PIANO TOUCH AND TONE
of impact or after the finger regains the key. The
first is a matter of a moment only ; the latter, consider-
ably shorter (for all degrees louder than mp) than the
usual depth of key-descent. Since, then, we have less
space in which to guide the key (consequently also
less time), key-control with percussive touch is more
difficult than with non-percussive touch. In the latter
the finger " weighs " the key down throughout its
descent, thus enabling us to gauge the resistance
more accurately. The non-percussive touch, then,
permits finer control of key-movement than the
percussive. In the percussive touches the move-
ment must be communicated to the key almost
instantaneously, the word " instantaneously " being
used in its usual sense. A comparison of Fig. 5 and
Fig. 7 illustrates the same difference. This pair
is similar to the preceding pair, Figs. 4 and 6, except
that the former, Figs. 5 and 7, represent relaxed tone-
production, and the latter, Figs. 4 and 6, rigid tone-
production. When these records are studied for
dynamic differences, the percussive touches show
greater key-speed than the non-percussive touches, 1 for
in Figs. 6 and 7 the wave lengths are in the aggregate
greater than in Figs. 4 and 5. Further, more clearly
defined differences may be seen by comparing Fig. 13
with Fig. 14. We have, then, as the physical reason
for the adoption of certain forms of touches, the setting
into motion of the action with a minimum of jar or
percussion and a maximum of kinassthetic control.
In percussive touches there is no gradual addition
of weight. Key-control, in those instances, depends
entirely upon the speed with which the finger reaches
the key. This means that the psychological factors
1 This, of course, does not mean that the order cannot be reversed.
It merely means, that, other things equal, we normally tend to
play louder when using percussive touches than when using non-
percussive touches.
22
KEY-DEPRESSION
involved in percussive and non-percussive touches
are different. 1
Effect of Finger and Wrist Position on Key-
Depression. Finger position we shall divide into
the two most common forms : curved or bent finger,
and flat or straight finger. The curved finger strikes
the key with its nail joint vertical. The straight
or flat finger has its nail joint almost horizontal.
Fig. 8 shows the curves for flat and curved fingers.
The intensity was kept approximately constant at
mf. a represents flat finger, percussive touch ; 6
represents curved finger, percussive touch ; c, curved
finger, non-percussive touch ; and d, flat finger,
non-percussive touch. The greatest difference is again
found in the percussive and the non-percussive
elements, as is shown by the dark line below the
top in a and 6, but not in c or d. Careful inspection,
however, shows also a slight intensity difference
in favour of the curved finger. This difference would
be too slight to have any practical value if it occurred
only occasionally. We find it present, however,
in every case of a number of similar records taken,
such as a, and 6 of Fig. 12. Apart from this slight
difference of key-speed there is no difference in key-
movement when initiated by flat or curved finger,"
1 Since it is only the physical aspect which concerns us here,
it will suffice to mention only the fundamental psychological
difference. In non-percussive touches key resistance is a sensation,
in percussive touches it is essentially an image.
23
PIANO TOUCH AND TONE
provided both are percussive or both non-percussive
touches.
Wrist position we shall divide into high-wrist
and low-wrist. In the former case, the wrist is held
well above the key-level and descends when the key
is depressed. In the latter case, the wrist is held
below the key-level, and with a " snap " movement
ascends, the fingers at the same time descending.
Fig. 9 shows the curves thus obtained. Intensity
was controlled approximately at /. In this figure,
a represents low-wrist, non-percussive touch ; &,
high -wrist, non- percussive touch ; c, low -wrist,
percussive touch ; d, high-wrist, percussive touch.
Note again the well-defined difference between
of c d a
FIG. 9.
percussive and non-percussive touches, shown by the
presence of the dark line in c and d and its absence in
the non-percussive touches a and 6. For all practical
purposes no difference in key-movement, whether
initiated by high or low wrist, exists, the curves for
both cases being practically identical. True, there is
an occasional slight difference in key-speed, but since
this was found to vary, sometimes in favour of the
high-wrist touch and sometimes in favour of the low-
wrist touch, it cannot be considered a differentiating
quantity in the sense here understood.
Key-Depression and Tone-Quality. Have we a right
to speak of a single piano tone as " good " or " bad ? " 1
1 In the final chapter an attempt will be made to define a standard
" good *' tone in terms of physical quantities.
24
KEY-DEPRESSION
In the last analysis, perhaps not ; for the so-called.
quality which we assign to a single tone is almost
invariably the result of a combination, either simul-
taneously or successively, of this with other tones.
Nevertheless, although the terms " good " and " bad '"
are primarily of subjective value only, the long list
of adjectives with which we describe even single-
tones, words the meanings of which are readily under-
stood by many piano teachers, proves the existence
of objective qualities which give rise to these descriptive-
terms. Thus, we know and distinguish on the piano,.
among many other tone-complexes, the following :
harsh, brilliant, mellow, full, singing, round, shrill,,
dry, metallic, steely, brittle, shallow, poor, ringing,
clear, velvety, bell-like, jarring, and strident. Since-
1 1
e d c 6 a
FIG. 10.
the majority of these tone-complexes have a fairly
distinct meaning to the teacher, their investigation
becomes a necessary phase of our problem, especially
because the creation of these various tone-qualities-
is generally attributed directly to the quality of touch
employed. The following records were all made
by experienced pianists and teachers who were asked,,
after producing a tone, whether it had the desired.
quality harsh, shallow, or some other quality. Many
repetitions were sometimes found necessary before the
desired tone-quality was satisfactorily produced,
and it should be stated that most teachers found
the production of ^ a specific quality difficult for
a single tone. This is, in itself, a proof that this*
25
PIANO TOUCH AND TONE
tone-quality, generally attributed to a single tone,
is due largely to a combination of tones. The
descriptive terms were selected by the teachers making
the record, and the mode of tone production, that is,
the touch employed, was left entirely to the teacher.
The records represent the following : Fig. 10, a, good
tone ; b, dry tone ; c, dry tone ; d, thumped (ugly)
tone. Fig. n, a, good tone ; b, forced tone ; c,
depthless tone. Fig. 12, a, shallow tone ; 6, good
tone ; c, forced tone ; d, good tone ; e, " harsh "
(ugly) tone ; /, full tone.
c c/
a
FIG. 11.
f e of c d a
FIG. 12.
A study of these records brings to light the
interesting fact that for every difference in quality
we have a difference in key-speed. Thus, we find
that forced, harsh, ugly, and thumped tones mean
great key-speed ; good, sing'ng, and full tones mean
moderate key-speed ; shallow and dry tones mean
slow key-speed. But Fig. 3 showed that with every
increase of key-speed we have an increase in the
dynamic value of the resulting tone. Therefore, all
these supposedly qualitative differences as applied
to the single tone are merely differences in intensity.
26
KEY-DEPRESSION
Moreover, we find that the most satisfactory tone
is one of medium loudness, the unsatisfactory qualities
being at either end of the dynamic range.
Why the ear so often accepts these differences as
purely qualitative instead of quantitative will be
explained in the chapter on the vibration of the string.
Effect of the Playing Unit upon Key-Depression.
Although in actual piano playing we do not entirely
isolate any part of the arm, nevertheless, various
members are used more or less independently. Thus,
for example, in true hand-staccato, it is largely the
weight of the hand that depresses the key. In
C c b a
FIG. 13.
d c d a
FIG. 14.
cantabile passages the weight of the entire arm is
used. The effect of the use of various parts of the
arm, and of the arm as a whole, are shown in Figs. 13
and 14. The former represents non-percussive touches,
the latter, percussive touches. In both figures,
a shows the key-speed for the finger as the playing
unit, 6 for the hand, c of Fig. 13 and c of Fig. 14 for the
forearm, and d of Fig. 14 for the whole arm. Both
figures show the increase in key-speed as we increase
the weight of the playing unit. This is, of course,
27
PIANO TOUCH AND TONE
the result of the increase in force which an increase
in weight produces. In the percussive touches this
increase is clearly shown by the various positions
of the heavy portions of the curve, the points,
representing, in a and b at least, a momentary cessation
of aU key-movement. (Note also the marked
differences in key-movement when initiated by
a percussive as against a non-percussive touch, and
the considerably greater key-speed for the percussive
than the non-percussive touch.)
Variations in Force during Key-Depression. It is
interesting to know whether the force with which
we depress a key in playing remains constant (allowing
of course, for the accelerating effect of gravity) after
key-descent begins or changes during key-depression.
If we secure a picture of key-depression resulting from
a constant weight standing or dropped upon the key,
and compare this record with that made by the hand
or arm, we have an index of this force variation.
Since the resistance to be overcome (weight and
friction of the inner half of the piano-action) remains
a constant, a weight acting upon the outer key-end
throughout the three-eighths of an inch of key-depression
will not show uniform key-speed, but positive accelera-
tion, as a result of the action of gravity. For the
weight, in a very general way, at least, may be con-
sidered a falling body, and, if we ignore the> action-
resistance, will show an increase in speed characteristic
of falling bodies. This acceleration from one unit of
time to the next will show in a gradual increase in the
wave length of the curves here secured. A greater
increase than this normal acceleration will naturally
mean added weight, and a less increase will mean sub-
tracted weight. Fig. 3, a, b, c, d, shows key-depression
when initiated by weights. When we compare these
records with any record made by the player for the
softer dynamic degrees, such as a and 6 of Figs. 4 and 5,
28
KEY-DEPRESSION
we notice that the curves are practically identical,
only the slightest intensity difference being noticeable.
Whether the descent is initiated by hand or by a
mechanical weight does not affect the increase in
key-speed. As we proceed to the louder dynamic
degrees, mf and /, however, c and d of Figs. 4
and 5, although beginning no faster than c and b of
Fig. 3 respectively, show a considerably greater key-
speed as the key approaches the end of its descent. That
is, there is greater acceleration for the former than
for the latter. Since F = ma, this added accelera-
tion results from weight added after the key has
started its descent. For all degrees of intensity,
excepting the very soft ones, when we play with
a non-percussive touch, we do not use the entire
force desired at the beginning of key-depression,
but add more and more weight as the key descends.
In other words, we set the key into motion gradually.
In percussive touches, since no such increase in the
curves is noticeable, the key is not regulated throughout
its descent but only at the moment of impact. Such
records throw interesting light upon the problem
of key-control, the chief tonal problem of artistic
piano playing. They indicate, as we have mentioned
before, that the so-called f( clinging " or " sympathetic "
touch (which is nothing else than a non-percussive
touch) enables us, not per se to produce a better
tone, but by permitting more accurate key-control,
enables us to secure just the appropriate key-speed,
and through this, the appropriate tone-intensity.
Many other records dealing with miscellaneous
minor phases of touch were made. Among them the
martellato touch, the strisciando of the finger and
the " slapped " touch. Tones were produced by
various articles dropped upon the key, knuckles and
fist were used. In all cases where the records showed
no differences in key -speed, no differences in tonal
29
PIANO TOUCH AND TONE
quality were heard. In addition, the ascent of the
key, usually termed rebound, was recorded. This
concerns us only so far as it influences tone. Although
key-ascent does not influence the production of tone >
it does influence cessation of tone, since the damper
cannot fall back upon the string until the key ascends.
This key-ascent may be retarded to any extent
desired by the player, but cannot be advanced or
increased in speed except for a very slight increase
resulting from pressure upon the key -bed. This
is due to the elasticity of the felt pad. Other than
this there is nothing elastic about the upward or
return motion of the key. The word elasticity
(applied to the key and not to the finger) is a misnomer.
Even the word rebound is somewhat misleading,
since it does not accurately express what takes place.
The key does not return as a rubber ball rebounds,
from the ground, but solely because it is the lighter
arm of a lever. In other words, excepting of course
when the pressure upon the key -bed adds a very
slight element of elasticity, the return of the key
does not take place because upward forces act at its,
outer end, but because downward forces act on its,
inner end. This may be conclusively proved with
a model action. If we raise all the parts from the
key, leaving this free, it will at once tilt and remain,
with the outer end (ivory or player's end) depressed.
If we lift this with our fingers and let it drop back
there will be no rebound, or at the best only a very
slight one.
What actually takes place when a key is depressed
and then returns to its original position may be seen
by the following diagram. Let A B be a lever in
which the force acting downward on B is greater
than that on A. I B 7^ A The
player depresses A by adding a force greater than B.
30
KEY-DEPRESSION
This causes A to descend, B to ascend. Now, suppose
that the moment A reaches its lower limit the player
removes the added force. Then B again outweighs A
and causes the lever to return to its original position.
The same return would take place if A were held
depressed any length of time and then released. Hence,
we cannot speak of a rebound in the sense in which
the hammer rebounds from the string.
The ascent of the key is further influenced, though
again only slightly, by the speed of the rebounding
hammer which exerts a diagonally downward force
on its catch or buffer and hence on the inner key-
arm. When the key, on its ascent, reaches the
starting-point, its momentum carries it slightly
beyond, whereupon it returns again and gradually
comes to rest. That is, the key does not make a single
depression and ascent, but one pronounced movement
of this kind and one or two lesser ones. These latter,
of course, have no influence whatever on the tone
since this has been dampened when they take place.
They are evidence that the piano-action is not a firmly
connected unity. None the less, because it is often
believed that certain modes of key-release influence
tone by varying the manner (speed ?) with which
the damper falls back upon the string, a number of
records were secured for various types of key-release.
These are shown in Fig. 15. They should be read
upwards : a, shows the curve when the finger is
lifted perpendicularly from the key ; 6, when the finger
31
PIANO TOUCH AND TONE
is pulled away from the edge ; c and d, the same for
.a piece of metal ; e, for the finger after considerable
pressure upon the key-bed. The curves for a, b, c, d,
-.show a very slight increase in key- ascent to the middle,
then a slight decrease again. This is natural. Gravity
is responsible for the slight increase, and the resistance
of parts of the action which are re-engaged as the key
.approaches the upper end of its ascent is responsible
for the slight decrease.
Notice the width ( in.) of the blurred tops. This
is caused by the fact that the key does not immediately
-come to rest when it reaches its top level, but through
the slight elasticity of the felt pads and the " balanced "
form of the action is bounced back and forth through
a short distance. This also applies to the piano-
hammer. The more rapid key-ascent shown in e
of Fig. 15 results from the upward force which the
compressed key-bed pad exerts upon the key. The
-extent of this compression is shown by the lower
beginning of e as compared with a, b, c, or d.
The differences in key-speed found in these and other
records are all so slight as to have no practical effect
-upon the cessation of tone. It is true that we -can
retard the ascent of the key and thereby permit
the damper to fall back very gradually upon the
string. This mode of key-release gives tone-cessation
.a curious " fuzzy " character, which, because of its
-unmusical quality, is seldom desirable. The important
fact is that, no matter how we release the key, we
cannot increase the speed of its ascent. Regardless
of touch, the key returns in but one fixed way as
soon as the finger leaves it.
Influence of Key-Pressure and Movement after Key-
.Defiression. This includes the effect of lateral rocking
to and fro, the so-called "kneading" or " vibrato "
, and all other motions made after the key has reached
*its key-bed. Since the key, once it is depressed, is no
32
KEY-DEPRESSION
longer in contact with the string, any further motion
of the key cannot influence the string. The idea
that such motions set up air disturbances of their
own which affect the ear is entirely fallacious, since
these would have to occur, at the very least, 18 times
per second to have any pitch value, and in the second
place would have to occur with absolute regularity.
The one physically possible effect of all such motions
on tone is that they rock the entire instrument, hence
also the sounding-board. The practical significance
of this theoretical possibility will be treated in a later
chapter. 1 Here we have to ascertain only the effect
of such movements on the key. Of such effects there
is none, since all we do is to press the key more
firmly against the key-bed, and when employing
a lateral movement, we merely help to " loosen "
the action and to hasten the day when it will find
its way to the factory for repair.
The records reproduced in this chapter are but a few
of many that were made. They were selected because
they embrace all the differences found. Tested from
all angles, and in many practical and even impractical
ways, no record was obtained which does not agree
with one or more of those here reproduced.
CONCLUSIONS
From the results of the above experiments we may
conclude the following :
1. Differences in touch, so far as they affect the
vibration of the string, always involve differences
in speed of key-descent.
2. Considered with reference to their effect on key-
descent, there are but two touches, percussive and non-
percussive. These represent qualitative differences
in key-movement. All other touch classification
1 tc The Vibration of the Sounding-Board. "
33
PIANO TOUCH AND TONE
or nomenclature represents merely quantitative
differences in key-speed.
3. Non-percussive touch permits easier and finer
key-control than percussive touch.
4. All differences in tonal quality are due to
differences in intensity, with the exceptions noted in
later chapters.
5. Such words as shallow, harsh, forced, dry, and
others of this nature, are merely descriptive of the
intensity of the tone.
6. Under normal conditions, rigidity tends to
produce greater key-speed (hence louder tone) than
relaxation.
7. Under normal conditions, curved finger touches
tend to produce slightly louder tones than flat finger
touches, though this difference is not always present.
8. The dynamic range of tone-production through
relaxation is less than the dynamic range of tone-
production through rigidity. Hence, if that portion
of the latter which is not contained in the former,
is required for a special effect in a composition, rigidity
is necessary.
34
CHAPTER III
FORCE OF TOUCH
17" EY-DEPRESSION results from the action of a
"- force upon the key. Chapter II dealt with the
variations of this key-movement, produced by varia-
tions in touch and tone. This, primarily, had
a qualitative end in view, though the conclusions
mainly show quantitative variations. In the present
chapter we shall seek to determine some numerical
values for the forces of touch. Needless to say,
the limits of key-resistance set by various instruments
are by no means fixed, and consequently the values
herein deduced are representative of individual
instruments, and not of pianos in general. The absolute
values give a fair approximation for other instruments ;
the relative values result from certain general principles
functioning for all pianos.
The present quantitative evaluation of touch
was originally prompted by a young pupil possessing
a rather refined sense of kinaesthetic discrimination,
who complained of the added resistance which the
keys in the bass region offered to her then weak fingers.
This added weight is due to the larger size of both
hammer and damper in the bass region as compared
with the treble. The complaint led to a desire to
ascertain, in a general way, the extent of these
variations.
The effect of a force upon a material body depends
upon three things : its numerical value, its direction,
and its point of application. The numerical value
of the force acting upon the piano key varies between
zero and the limit set by the physiological capability
35
PIANO TOUCH AND TONE
of the player ; the direction of the force may be any
line in a tri-dimensional space, between the horizontal
and the descending vertical ; the point of application
is limited by the length of key seen on the key-board,
about six inches. If the line of action and point
of application be constant the effect on key-depression
will vary directly with the force. If force and point
of application be constant the effect will vary with
the direction. Practical piano playing demands that
the key be struck from various angles ; in other
words, it demands various lines of application of
force. The effect is greatest when the force acts
in a line with key-descent, which on the piano is
vertically downward. The effect decreases as the
line of application deviates from this vertical, because
to change the direction of a moving body, a force
is required. 1 Finally, if the line of application and
the numerical value of the force remain constant,
key-depression will vary with the point of applica-
tion. The further the point of application is from
the fulcrum the greater is the effect of the force.
The key lever measures about ten inches from the end
of the key to the fulcrum. About six inches is visible
as the key-board, and all variations in the application
of touch naturally fall within this 6-inch distance.
The following measurements have for their object
the quantitative evaluation of vertical forces acting
at different points of the key lever. A metal cup,
of appropriate size, was placed upon the key. Its
weight was regulated by pouring small shot into it,
and the key was released by removing a point lightly
pressed against the outer surface, which ensured
a fairly constant mode of release. The amount of
shot was adjusted until the release of the key produced
1 Thus, when the direction of the hand is changed by key-
depressions (the key has only one line of movement) energy is con-
sumed in making this change.
36
FORCE OF TOUCH
CD
