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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
<t
CD
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LL_
QQ
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37
PIANO TOUCH AND TONE
a barely audible tone. The threshold of audibility
was set by two observers seated in the usual position
at the key-board, and the numbers here used
represent the average of several judgments made for
each key. Two instruments were tested. Both were
used instruments in fairly good playing condition,
good representatives of the normal conservatory
or student's piano. The following curves are correct
to within one-tenth of an ounce. The weight in
ounces is shown in Fig. i6A and Fig. i6B in
the form of a graph, which presents the variations
more clearly than the figures would. The weight
in ounces is shown on the vertical axis, the
corresponding keys on the horizontal axis. We find
a variation for key-depression between 2-1 ounces
and 4-5 ounces for the one instrument ; 2-3 ounces
and 5-0 ounces for the other instrument. 1 Differences
in point of application : front edge or end of key,
and one inch from the edge, average -4 ounces for the
. first; instrument and -5 for the second instrument.
This means that if, for example, we wish to play the
D major scale, ppp through one octave, ascending,
beginning on D below middle C and touching each
key at its customary point for this scale : D near its
outer edge, E near the black keys, F# at its edge, G at
its edge, etc., in order to secure a dynamically even
scale for these instruments, we should have to distribute
the weight in ounces as follows :
No. i : 2-9 3-2 2-8 2-8 3-0 3-1 2-8 2-6
No. 2 : 3-5 3-4 3-3 2-8 3-4 3-0 3-1 3-0
Almost every key demands a different weight from its
neighbour if the resulting tones are to have the same
1 In a number of instruments the lever-arm of the black keys
is somewhat shorter than that of the white keys, approximately
$| inches and 10 inches respectively. This difference is partly
compensated for through the individual " weighting " of each key
by the piano manufacturer. Otherwise, we should find the dotted
line of figures 16A and 16B well above the solid line.
38
FORCE OF TOUCH
CO
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CD
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39
PIANO TOUCH AND TONE
intensity. Conversely, the same weight used on all
the keys will produce a dynamically uneven scale.
Thus, a weight of 2*9 ounces on the first instrument
will produce no tone whatever on E, A, or B. Again,
a weight of 3-2 ounces will produce the softest
pianissimo on A, a p tone on D, F s , G, and C s , and
almost an mp tone on upper D. Now, these differences,
while clearly audible for intensities ranging from
ppp to p, gradually decrease in audibility as we
increase the dynamic degrees, and in the forte regions,
differences of several tenths of an ounce are not
discerned. 1 Were it not for this fact, it would be
impossible to play a dynamically even scale on any
used instrument. On the other hand, the evenness
of key resistance is doubtless largely responsible
for the technical pleasure derived from playing on
a new, or a newly " voiced " instrument as compared
with a used one.
Thus far we have established values for the least
audible tone only, which, however, is but relatively
seldom used in piano playing. The intermediate
degrees are much more prominent, but, because
they represent subjective generalities, any actual
figures which we deduce can be only very approximate.
Nevertheless, some idea of the great amount of physical
energy expended in the performance of any advanced
piano composition may be gained by a rough
quantitative scaling of the range of the weight of
touch. We have just seen that for the production
of the softest tone, a force varying from 2 to 4 ounces
is required. If we use 3 ounces as an average and
attempt to measure for the same key the force necessary
to produce the various intensities used in music,
1 This is but an application of the famous law of Weber, which
states that for equal positive additions to the sensation we must
make equal relative additions, to the stimulus, or, in other words,
to increase the sensation in arithmetic ratio it is necessary to increase
the stimulus in geometric ratio.
40
FORCE OF TOUCH
remembering, always, that the figures are only rough
approximations, we get ppp = 3 oz. ; pp = 3! oz. ;
p = 4-| oz. ; mp = 6 oz. ; mf = 10 oz. ; /= 17 oz. 4- ;
ff = several pounds to many pounds. These figures
apply to a single key-depression. The increase, as is
seen, does not represent equal force additions from
one dynamic degree to the next. It illustrates,
inaccurately, it is true, but none the less clearly, the
truth of Weber's general law.
Another factor influencing the weight of touch is
the damper, and its controlling device, the damper
pedal. In experiments on the instruments mentioned,
an average difference of -5 ounce for one and
i-o ounce for the other was found between the weight
necessary to produce the least audible tone " senza "
and " con-pedale ". We have a lighter action when
playing with pedal than without, for the resistance
of the damper has been removed when the pedal is
depressed. The drop in the curves of Fig. i6A at the
beginning of the three-lined octave shows where the
dampers in this instrument end.
The measurements thus far made deal with constant
weights. But there is no reason why this weight
cannot vary during key -descent. Even a constant
weight will produce increasing key-speed owing to
the uniformly accelerating effect of gravity. Records
made by constant weights are shown in Fig. 30, b, c,
and d. Now compare them with the records shown
in Fig. $e and /. Two points of difference will be
noticed : the acceleration in the second group is
distinctly greater than in the first group, and it is not
constant. But if uniform weight produced key-speed
such as that shown in Fig. 30, b, c, or d, then e or / can
only be produced by greater weight. And since the
acceleration is greater than that produced by gravity
alone, regardless of the actual weight, we may conclude
that the player adds weight after key -impact in the
41
PIANO TOUCH AND TONE
touches employed in making these particular records.
This phase has been met in various forms in the records
shown in Chapter II.
Besides variations in weight resulting from variations
in pitch, in point of application, in the numerical
value of the force, and in degree of loudness, we have
to consider variations resulting from the direction
of the force. The effect of a force upon a body depends
partly upon the line of application which, as has
been indicated, may vary on the piano through
180 degrees. Since the key-descent is a fixed vertical
motion, the 180 degrees may be divided into two
symmetrical quadrants and the investigation of either
quadrant will suffice. Now, the numerical value of
a force acting at a known angle through a known
distance upon a measurable body is easily calculated,
if we assume the resistance to be a constant. 1 Thus,
we find the forces required for producing tones of equal
intensity by varying the line of application of a vertical
force of 4 ounces to be as follows, the table representing
a sample instance in which the degrees show deviations
from the descending vertical :
o degrees . . 4 ounces.
10 . 4-06
20 . 4-26
30 . 4-62
40 5'22
50 . 6-22
60 . 8-00
70 . 11-69
80 . 23-04
90 . . infinity.
1 Any force acting upon a body may be resolved into two com-
ponents, one of which acts in the direction of the motion of the
body and the other at right angles to this direction. The latter
component does no work and the work done by the former is the
product of its numerical value and the distance through which it
works. This component equals p cos 0, in which p is the original
force, the angle which the direction of p makes with the line of
motion of the body acted upon. The values deduced in Fig. 17e
have been derived from this formula.
FORCE OF TOUCH
A similar instance, using 8 ounces as the force actually
producing tone, is shown in Fig. iyA. A vertical
descent of a force of 8 ounces produces a tone X.
If we strike the key from an angle of 10 degrees,
either from the right or left, a force of 8-13 ounces
is necessary in order to produce the same tone X.
At 30 degrees a force of 9-24 ounces is required. At
60 degrees just double the original vertically acting
force will produce the tone X. The manner in which
this increase takes place is shown for four weights
FIG. 17A.
(3 oz., 4 oz., 8 oz., 12 oz.) in Fig. 173. These curves
show very little increase for the smaller angles or
deviations from the vertical. The increase becomes
much greater for the larger angles. In actual piano
playing a wide range of force direction must be used ;
accordingly, the variations here indicated may help
to explain the selection of certain physiological move-
ments of piano technique in preference to others.
As the mode of touch deviates from the vertical
type, more force is required to produce the same
tonal effect, and since oblique touches are often met
43
PIANO TOUCH AND TONE
oz.
36
34
32
30
29
28
27
26
25
24
23
22
21
20
19
18
17
16
15
14
13
12
II
10
9
8
7
6
5
4
3
2
I
90 80 70 60 50 40 30 20
FIG. 17 B.
IO C
44
FORCE OF TOUCH
with in piano technique, only a part of the energy
expended by the player is transformed into sound.
The further we deviate from the vertical the greater
is the loss in force-effect ; the further we deviate from
non-percussion the greater is the loss in tone-control.
Consequently, the sound produced on the piano
is not in itself a measure of the energy expended.
The numerical value of this energy is always in excess
of the tone produced. It varies, as w$ have seen,
from several ounces to many pounds. (Even a short
and lightly played composition, such as the Chopin
D flat Waltz (Minute Waltz), if we use three ounces
for single tone production and a pp touch throughout,
would demand a minimum expenditure of force
of 235 pounds. Works such as the Liszt B minor
Sonata demand, in a sense, truly a Herculean force ;
a conservative estimate for this sonata would be
25,000 pounds, with work done of 780 foot-pounds?
The weight or force basis for simultaneous Key-
depression now becomes clear. When two keys are
simultaneously depressed it will naturally require
twice as much force as when either key alone is
depressed, for three keys, three times as much, and so
on. This accumulation may be felt by placing a stick
across the entire key-board (white or black keys)
and depressing all the keys at once. Therefore,
chords demand a greater expenditure of energy than
single tones, and the same force applied to a single
key and to a chord will produce a louder tone in the
former case than in the latter. This distribution
of forces is not without some effect upon passages
in piano literature in which double-notes or chords
alternate rapidly with single notes ; for example,
as in the accompaniment of the first theme of Chopin's
B flat minor Sonata, or the accompaniment of the
second theme, first movement, of Beethoven's Sonata
Appassionata. If in such places the single key gets
45
PIANO TOUCH AND TONE
the same force as the two or three keys combined,
the tonal effect naturally will be uneven. In order
to secure an even tonal effect the chords must receive
respectively two or three times the force applied to
the single key. For it is known that the addition
of other tones does not influence the sensation of
loudness. A chord of three or six tones, each tone
played pp, does not seem three or six times as loud
as a single tone played pp. If it did, the production
of a pianissimo ninth or eleventh chord, for example,
would be impossible. Consequently, if a passage such
as those to which we have referred sounds even in
intensity, either the tonal differences resulting from
equal force application are too slight to be heard,
or the force applied varies rapidly between the single
tone and the chord, and thus produces tones of the same
intensity. As we complicate the figure by varying
the number of keys simultaneously depressed, we
complicate the application of forces ; because each
group of keys, numerically different from another
key or group of keys, demands its own force for the
production of a definite tonal intensity. That it
is usually the variation in forces, producing the same
tonal intensity, and not equality of forces producing
unequal tonal intensities, which we find in the actual
execution of such passages, may be seen in the above
figure, in which a represents key-speed for a single
key, &, key-speed for one of a group of keys
played as a chord. Further proof of this force
distribution will be found in Fig. 34 in the chapter
FORCE OF TOUCH
on Hammer-Stroke. There are times, however, when
some intensity fluctuations remain.
The same variation in forces applies to passages
divided between the hands, in which one hand has
simultaneous key-depressions differing in number
from those of the other hand. The " bringing out "
of a melody against an accompaniment, when the
accompaniment is in the form of chords, is influenced
by this distribution of forces, because if each hand
plays with equal force, any one tone of the chord
accompaniment must receive less force than the tone
of the melody. Thus, if the two hands are played
equally strongly, the hand having only one key to
depress will produce a louder tone than the other
hand ; and if we wish to produce the same tonal
effect for both hands, the hand having the greater
number of keys to be depressed must be played with
proportionately greater force.
A similar, though less pronounced, variation exists
for differences between the hands resulting from the
direction of touch and the point of application. If
the right hand plays a series of keys with a vertical
descent, while the left hand plays a series with a very-
oblique touch, equal forces for both hands will not
produce equal tonal intensities. If, in such cases,
equal tonal results for both hands are desired, the hand
using the oblique touch must necessarily receive a
greater force than the other hand.
This balance of forces is further complicated by the
fact that it varies with the dynamic degree. The
weights or forces used for the production of the
dynamic degrees used in music do not increase in an
arithmetical ratio but rather in the manner of a
geometric ratio, as is shown in Fig. 3. For the
softer degrees a relatively slight increase or decrease
in force may alter the balance between melody and
accompaniment, whereas, for the louder dynamic
47
PIANO TOUCH AND TONE
degrees, a greater increment will be necessary to secure
this alteration in balance. Force and tonal effect,
then, do not vary in any constant ratio. We cannot
measure the tonal result by the amount of force
applied until we know the manner of application
of the force.
From these observations it is evident that the best
control, and hence the most accurate tone variation
measured in terms of force-distribution, is secured
by a vertical descent at or near the outer end of the
key in a non-percussive manner. The most difficult
control, naturally, would be a very oblique descent
away from the edge in a percussive manner ; a touch
the physical difficulties of which we learned in Chapter
II. All problems of piano technique, as far as they
influence key-depression, fall at, or somewhere between,
these extremes, and part of their difficulty may be
explained in terms of the physical qualities of the key-
board.
Summarizing, we find that :
Key-action, hence key-resistance in a normal
instrument is not perfectly even or constant. The
variations in the action are small, however, and
have only a slight effect on musical results.
The forces used in piano playing vary from several
ounces to many pounds.
The degree of force and the resultant sound vary
with the point of application, line of application,
duration of application, and numerical value
of the force. The tonal effect is most direct when
produced by a descending, vertical, non-percussive
touch near the end of the key. A fixed ratio exists
between degree of force and intensity of tone only
for the single key and a constant touch, for an increase
in the number of keys or force of touch does not,
of itself, mean a like increase in tonal loudness.
The practical significance and importance of the
FORCE OF TOUCH
contents of this chapter should be neither over-
estimated nor entirely disregarded. We need not
determine whether directing a pupil's attention to
these things will improve his playing, for that, as
a pedagogical problem, is entirely foreign at this
point. We are not concerned here with establishing
the practical value or the effects, in a musical sense,
of these force variations. What we establish is their
existence. Knowing that they exist, to what degree
they exist, and how they vary, we have these facts
to draw upon, if necessary, when explaining the
physiological or psychological aspects of piano playing.
In attempting to reconcile the conflicting opinions
held on the question of the personal element in piano
playing, nothing is too small to be omitted. For,
obviously, an explanation will not be found in gross
differences noticeable to any casual observer. It is
highly probable, however, that it will be found in
fine physical differences which, because of their very
minuteness, have escaped the observer, and which
lie -accordingly, with perfect sincerity, attributes to
indefinable, non-physical elements.
49
CHAPTER IV
TOUCH COMBINATIONS
WHEN, now, we consider the results obtained
for the single key-depression in the light of
practical problems of piano technique, we are not
confronted with any new physical variations; for
the differences between a single key-depression and
the playing of a musical composition, real enough
in practice, are almost entirely physiological and
psychological in nature. Every piano manufacturer
prides himself upon the regularity or smoothness of
his action, an evenness perfected in response to the
urgent demand of the musician for such an action.
Variations from this uniformity are considered defects,
to correct which neither cost nor effort is spared.
The ideal attempted is an action in which each key
is a perfect duplicate of every other key. Con-
sequently, we may formulate as an axiom that what-
ever happens to any one key on the piano can happen
to any other key; or, conversely, nothing can
happen to any one key that cannot happen to any
other key. This perfectly obvious statement is
emphasized here, because if we grant its validity
we are forced to admit the truth of certain important
conclusions in later chapters, which follow as necessary
corollaries.
All devices of piano technique fall into one of two
classes : simultaneous or successive key-depression,
representing, respectively, the harmonic and the
melodic aspects of piano playing. Simultaneous key-
depression may vary in but one way key-speed.
50
TOUCH COMBINATIONS
Successive key-depression may vary in two ways
key-speed and time-interval between key-depressions.
Accordingly, musical variations of simultaneous key-
depression are the result of variations in key-speed ;
musical variations of successive key-depressions are
the result of variations either in key-speed or time-
interval, or in both. These physical quantities, key-
speed and time-interval, may remain constant, they
may change abruptly, or they may vary gradually. For
each phase we have appropriate terms. Thus, "/,"
" p," since they represent tones of constant intensity,
also represent constant key-speed, and a change
from one to the other represents abrupt change in
key-speed. (Of course, we must remember that
the dynamic degrees are not sharply defined areas
of tonal loudness, but are merely convenient divisions
on a continuous scale.) Crescendo and diminuendo
represent gradual variation in key-speed, the former
from slow to fast, the latter from fast to slow.
Andante, Adagio, Allegro, indicate constant time-
intervals ; a change from one of these to another,
or the use of such words as doppio movimento, meno
mosso, indicates abrupt change of time-interval ;
ritard and accelerando indicate gradual variation
in time-interval. Other terms, such as calando,
perdendosi, demand a variation in both intensity
and tempo, hence in both key-speed and time-interval.
Since the terms thus far cited, and many others
belonging to the same classes, are themselves defined
in intensity and tempo, their physical equivalents,
key-speed, and interval between key-release and
key-depression, are practically expressed in the
definition. But there are other pianistic effects and
terms, affecting both the harmonic and the melodic
aspect of piano technique, which are not defined in
terms of intensity and tempo. Such are the various
touches and the terms of style and expression. It
51
PIANO TOUCH AND TONE
is our problem, now, in a very brief survey, to find
the physical equivalents in key-action of such terms,
a detailed account of which demands treatment
from the psychological viewpoint.
The investigation of touches, such as legato, mezzo-
legato, portamento, staccato, requires no experimental
procedure, since the differences can be clearly seen,
by mere observation, to be differences in the ratio
of sound duration to silence duration. Or, expressed
in terms of key-action, they are differences in the time-
interval between a key-release and the next key-
depression. Here, again, we are dealing not with
absolute types of touch, as is often believed, but with
an unbroken series varying in the ratio of silence-
interval to sound-interval, from o for a perfect legato
to i for a theoretically perfect staccatissimo. The
terms used are merely convenient, quite general, and
sliding divisions on this scale. There is no such thing
as the mezzo-legato touch, or the staccato touch,
because the tempo and the character of the passage
fix merely one degree of many. Who, for example,
can locate the exact point where a non-legato becomes
a portamento, or a portamento a mezzo-staccato ?
Let any staccato passage be played in turn in the
following tempi : Adagio, Andante, Moderate,
Allegretto, Presto. Note the many varieties of touch
employed solely to meet the demands of tempo.
Play the passage again as follows : pp, p, f f ff. New
varieties of touch will be employed, this time to meet
the dynamic demands. Moreover, no gaps or clearly
defined lines of demarcation will be found. All
pianistic touches belong to an unbroken, highly
complex series, the elements of which shade impercep-
tibly into each other.
Three other types of producing tones should be
mentioned ; martellato, glissando, and vibrato. The
last-named, though truly not applicable to the piano,
52
TOUCH COMBINATIONS
is included because it has been used by composers
for the piano, for example, by Chopin. Fig. je shows
the characteristic key-descent for martettato. This
touch depends for its effect upon a fairly great key-
speed. Glissando depends for its effect primarily
upon rapidity of tempo. A series of tones played
at a speed of less than 12 per second, ceases to give
the effect of a glissando though played in the glissando
style. The vibrato effect on the piano does not exist
physically, since it depends upon prolonged manipula-
tion of the tone, which we know is impossible on
the piano.
The touch forms used in accentuating a tone of
a chord or in " bringing out " a melody against an
accompaniment (melodia marcato), generally under-
stood as the result of throwing additional weight
behind the melody finger, gain their effect by causing
the melody key to be more rapidly depressed than
the remaining keys.
The physical equivalents of such terms as " con
amore " and " affettuoso " are less easily localized.
These are terms most intimately suggestive of the
" poetic " or " artistic " phase of piano playing.
Yet, if they have any physical effect whatever upon
the playing, and this, after hearing our best performers,
can hardly be doubted, then this effect, too, must be
explained in variations in key-speed and time-interval,
for we have no other physical variable than these two.
For the purpose of determining the normal effect
of various marks of expression, a number of records
of pianists were obtained and measured for variations
in key-speed and time-interval, or, in musical terms,
variations in intensity and tempo. These records
brought to light the interesting fact that for practically
every term such variations did occur. That is, the
effect of every term of expression examined, with
a few exceptions to be mentioned later, could be
53
PIANO TOUCH AND TONE
explained in terms of intensity and tempo. The
following list illustrates in a general way the physical
equivalents of various terms, translated into tonal
qualities :
con abbandono
affettuoso
con amore
appassionato .
con color e
dolce
doloroso
espressivo
giocoso .
lamentoso
mesto
pietoso .
religioso .
scherzando
con tenerezza .
marked variation in both tempo and
dynamics,
marked variation in both tempo and
dynamics,
variations in the slower tempi and
softer dynamic degrees,
marked variations, abrupt and
gradual, in both tempo and
dynamics,
variations in the slower tempi and
softer dynamic degrees,
soft, and in moderate, graceful, or
slow tempo.
no effect other than slow tempo,
variations in both tempo and
dynamics.
rapid tempo and detached tones,
no effect other than slow tempo,
no effect,
no effect,
no effect.
rapid tempo and detached tones,
soft and in slow or moderate tempo.
In other words, except in those cases marked " no
effect ", the attempt to play a phrase or composition
in the manner indicated by the term always resulted
in variation in the intensity and duration of the tones,
two purely physical quantities. For the terms marked
" no effect ", we are obliged to conclude that no
physical variation peculiar to the term exists. At
least, none could be found. That is, so far as effect
on the tone is concerned, it is useless to write
54
TOUCH COMBINATIONS
" religiose *', " pietoso ", " mesto", for a piano passage,
since the key-board cannot be influenced thereby.
The usefulness of such terms must be sought else-
where than in the physical field. The same remark
applies also to numerous other terms not included
in the preceding, necessarily fragmentary, list. On
the other hand, many other terms will show, like
espressivo and affettuoso, variations in either dynamics
or tempo, or perhaps in both.
How do we know, now, that these physical variations
in key-speed and time interval are not merely effects
or accompanying phenomena, instead of causes,
of the poetic elements ? The unqualified answer
is found by playing the same phrases without these
variations in intensity and duration. In experiments
under these conditions, it was impossible to convey
any artistic effect as here understood. [Let the reader
who doubts this attempt to play a Chopin Prelude
or Nocturne, or a Beethoven Sonata strictly with
a metronome and at a uniform intensity throughout.]
It is true that the player uses other devices (psycho-
logical in nature) in addition to these intensity and
duration variations, in order to secure the desired
effect. These are relatively unimportant, however,
and we may safely conclude that all artistic effects
in sound are secured on the piano by variations in
key-speed and in time-interval between successive
key-release and key-depression. This includes, with-
out exception, the most subtle poetic effects.
The {t meaning " of a phrase, its poetical content,
is conveyed to the auditor, not by some individual,
even mysterious, touch of the player, but by
appropriate variations in the speed with which the
latter depresses one or more piano keys. Con-
sequently, the control of key-speed, dynamically
and agogically, becomes of vital importance, since
it is the technical means of securing artistic effects.
55
PIANO TOUCH AND TONE
To what extent, the piano teacher should direct the
pupils 7 attention to key-control itself, is primarily
a pedagogical problem ; the teacher should at least
realize clearly that if the pupil secures the desired
tonal result, it is because he is using appropriate
key-speed, and conversely, that if there are tonal
defects, there is also inappropriate key-speed.
CHAPTER V
THE HAMMER-STROKE
THEORETICAL ANALYSIS
/GENERALLY speaking, whatever motion we
^^ impart to the piano key is transmitted through
the piano action to the hammer. Therefore, if we
analyse key-motion we analyse hammer-motion ;
knowing the one, we can accurately deduce the other.
This is true to a great extent. Two factors, however,
limit this relationship and make a separate investiga-
tion of hammer-stroke necessary. In the first place,
the hammer is not rigidly fixed to the remainder of
the action, and in the second place the point of
escapement is not the point of tone -production. As
a result, the hammer, under certain conditions and
within certain limits, is free to move when the rest
of the action is at rest.
The hammer consists of a head and shank of wood,
formerly mahogany or cedar, and in recent years,
birch and hickory. The head is covered with a thin,
strip of leather, over which several layers of specially
prepared felt of diiferent degrees of compressibility
are fastened, with the most compressible to the outside.
The head is set approximately at right angles to the
shank. The shank is about 5 or 6 inches in length,
and pivots at one end on a horizontal axis somewhat
lower than the level of the strings. When at rest,
the hammer-shank rests upon the hopper, making-
approximately an angle of 20 with the horizontal.
When in this position the upper surface of the head is-
about if or 2 inches below the strings. Since one
end of the shank is fixed, the hammer movement
57
PIANO TOUCH AND TONE
is restricted to an arc of a vertical circle embraced
between the position just described and the position
when the hammer-head surface rests against the strings,
the radius of the circle being the length of the shank.
The hammer cannot be moved in any other direction
or through any greater distance when the action is
in position. This can be readily observed on a working
model. The deductions concerning the constants and
variables in key-movement apply also to hammer-
movement. Since both direction and distance are
fixed, only the speed may vary, and consequently
what differences exist must be differences in speed,
since this is the only variable. Let us assume, for
the present, that the hammer-shank remains in contact
with the hopper throughout its stroke. Then a glance at
Fig. i8A shows that as we depress the key the hammer
must ascend. Since, while the key has traversed
a distance of three-eighths of an inch the hammer
has moved if inches, 1 the hammer evidently moves
about four times as fast as the key. Up to this point
we have a clear illustration of the principle of
the lever, operating in the familiar form of a see-saw.
When such movement takes place, every variation
in key-movement is shown in hammer-movement
magnified four times. All deductions and conclusions
reached in the chapter on key-depression apply also
to hammer-movement, when allowance is made,
of course, for reversal of direction and when the
condition assumed holds true, namely, that the
hammer-shank remains in contact with the hopper.
This phase, then, does not demand separate
experimental investigation. In practice, however,
the above condition is not fulfilled at all points of the
hammer-stroke. It is true that the hammer-shank
cannot get lower than the hopper, but it is not true
1 Owing to the length of the lever arms.
58
THE HAMMER-STROKE
that it cannot be lifted away from the hopper. 1 It
is solely this hammer freedom to which the escapement
mechanism owes its proper functioning. The principle
of the escapement is illustrated in Fig. i8A.
Let A B be a lever, D a pellet resting on, but not
fastened to, the end B. When A is depressed very
slowly, D lifts with B ; and when A strikes its lower
limit, if the movement has been sufficiently slow,
D will remain practically at rest upon B. If the descent
of A takes place more rapidly, then B comes to a
sudden halt, and D, through inertia or momentum,
will tend to continue in its ascending path and will
leave B slightly, and then fall back upon it. If
FIG. ISA.
the descent of A is still more rapid, the distance
through which D is thrown from B will be greater.
Exactly the same thing happens in the piano, in which
A becomes the key end, B the hopper, and D the
hammer.
Press down a piano key very slowly. When it is
near the key-bed, a " jerk " will be felt. This is caused
by the hopper sliding from beneath the hammer-
shank ; in other words, it is the point at which the
hammer " escaped ". If the key-depression has been
sufficiently slow, the movement will not have pro-
duced any tone whatever, for the hammer will not
have touched the string, although the key will have
been depressed its entire distance. As we increase
the speed of key-depression, a point will be reached
at which a tone is just barely produced. When we
1 When the action is removed from the instrument the hammers
may be lifted from or, better, turned on their axes until they pass
beyond the perpendicular, where they will remain if released.
59
PIANO TOUCH AND TONE
continue to increase key-speed beyond this point,
the tone becomes louder. The fact that there can be
complete key-depression and incomplete hammer-
ascent permits a very important conclusion to be
drawn ; namely, that there is no unbroken connexion
between key and string, or tone-production. The
hammer in every case leaves the rest of the action
before it reaches the string* Now the law of the lever
says that for every increase in the distance traversed
by any point in one arm there must be a corresponding
increase in the distance traversed by any point in
the other arm. Since the above experiment shows
that this is not always the case, for example, above
FIG. 18s.
the point of escapement, we cannot apply any laws of
the lever to the hammer-action after the hammer
leaves the escapement. 2
Pass a string beneath the hammer-shank and tie this
so that the striking surface of the hammer-head
rests about -^V of an inch below the piano-string. Now
manipulate the key in any manner whatever, and
notice that nothing affects the hammer. This is
conclusive proof, if further proof were needed, that
there is a part of the hammer stroke during which
we have absolutely no control over the hammer.
1 Again, the observation of a working model will make this
perfectly clear.
2 Certain effects of touch on string, as described in works on
piano -playing, are explained by assuming the action of a piano
to work upon the principle of the lever throughout its course.
This is an incorrect assumption.
60
THE HAMMER-STROKE
Let A be the hammer when at rest. Let B be the
point of escapement and C the point at which the
hammer strikes the string D D'. From A to B
the hammer is under the player's fairly direct control.
Therefore the act of tone-production takes place,
and must take place, between the points A and B.
It is assumed, of course, that the forces acting upon
the hammer from B to C, namely, friction, gravity,
and atmospheric resistance, are constant. Once again,
then, as in key -depression, our problem becomes
the investigation of variations in hammer-speed,
the only variable possessed by the hammer. 1
Now, a body at any one moment of time can have
but one mass, one direction, and one velocity. If
a body begins with a velocity of o and a uniformly
positive acceleration so that at the end of 10 seconds
it has a velocity of 100, its velocity at the fifth second
will be o plus 100 divided by 2 = 5o. 2 Again, if
a second body begins with a velocity of 100 and moves
with uniformly negative acceleration of 10, so that its
velocity at the tenth second is zero, at the fifth second
this, too, will have a velocity of 50. A third body
moving at a constant velocity of 50, will likewise
have a velocity of 50 at the fifth second.
Suppose that the fifth second referred to in the
above theoretical case corresponds to the point of
escapement in the movement of the piano hammer.
Then, at the point of escapement we should have the
hammer travelling at precisely the same velocity,
though this velocity would have been gained differently
for each case. Referring to the physical principle
of the Introduction, we find that in order to change the
velocity of a moving body a force is necessary. We have
1 For reasons, see Chapter on key-depression.
2 Or, applying the formula that the velocity at any moment
equals the product of the acceleration and the units of time
v = V + at, we get v = 10 x 5 = 50.
6l
PIANO TOUCH AND TONE
also seen that from the escapement to the string
we can exert no force upon the hammer. It follows
that we cannot change the velocity of the hammer
after it leaves the escapement, and ignoring the very
slight retardation due to friction, gravity, and resistance
of air, we may conclude that the hammer keeps
this velocity through the distance B C in Fig. i8B
and reaches the string with practically the same
velocity with which it leaves the escapement.
Applying this to the case cited, the first hammer-
stroke starting at o increases to 50 and reaches the
string with a velocity of 50. The second begins
with a velocity of 100, decreases to 50, and also reaches
the string with a velocity of 50. The third begins
with 50, remains at 50, and likewise reaches the string
with velocity of 50. Accordingly, the effect of this
hammer-speed upon the string is precisely the same for
the three cases, although this force has been attained
in a different manner for each case. Since whatever
tonal result we get from the string depends entirely
upon the effect of this force, we can thus produce
the same tonal result in three totally different \\ays.
Moreover, it is evident from the given figures that
the moment we change the velocity at the point of
escapement, we change the tone-producing force.
This means that the only fundamental physical
factor affecting the tone of the piano, so far as this
is caused by the vibrating string, is the velocity at
which the hammer head travels when at the point
of escapement.
Thus far, the examples have dealt only with uniform
acceleration, positive or negative. When the
acceleration is not uniform, which the figures of
key-depression show to be the normal condition
existing in practice, the actual calculation becomes
more complex, but the fundamental principle remains
the same. In such a case, we divide the entire stroke
62
THE HAMMER-STROKE
into unit sectors, and if these are sufficiently small,
we assume each sector to have either a constant
velocity or uniform acceleration. 1
These differences or fluctuations, however, do not
influence tone directly. The sole vital factor is the
velocity at the end of the stroke, not the velocity
or velocities during the stroke. The same body
cannot possess different velocities at the same moment.
Any one hammer, in any one stroke, when leaving
the escapement, is travelling at one and only one
velocity, in one and only one direction, and is capable
of exerting one and only one force. It does not
matter how this force has been attained, gradually
or suddenly, regularly or irregularly ; the quantity
J mv 2 proves that the energy possessed by a moving
body at any one moment is independent of its mode
of generation.
It has been necessary to explain this part in detail,
since many incorrect conclusions concerning the
action of the hammer on the string have been drawn,
even by prominent writers on piano technique. Among
them is the fallacy that if we depress the key gradually
the string is set into motion gradually. This, of
course, assumes that if we begin with little weight
and increase this, thereby increasing hammer-speed,
that this increase continues after escapement. Why
should it continue ? Suppose there were no string
to stop the hammer, nor a pivot to retain it, then
it would always continue to increase in speed, and we
should not only have perpetual motion, but even
perpetually-increasing motion. 2
1 In similar manner, when proving the area of a circle, we assume
the circumference to consist of an infinite number of straight lines
forming the bases of triangles.
2 We certainly have no right to assume that because the distance
(J in.) is so small the physical laws are different for this distance
than for greater distances. It is true that the eye does not perceive
the physical phenomena at this small distance, but it is absurd
to advance that as a proof that these phenomena do not exist.
63
PIANO TOUCH AND TONE
From these facts we draw three primary conclusions :
1. The only variable in hammer movement is speed.
2. The hammer traverses part of its stroke as
a relatively free body, beyond all influence of the
player.
3. The tonal result as produced by the vibrations of
the string depends solely upon the velocity with
which the hammer leaves the escapement.
The Hammer in contact with the String. If, then,
the hammer has sufficient velocity at the point of
escapement, it is thrown across the intervening space
against the string with more or less force. Since the
<outside layer of felt is compressible, this reduces
the audibility of impact to a minimum. The lower
layers yield the necessary elasticity for a rapid rebound
of the hammer.
When the hammer is thrown against the string,
two things occur : the string is displaced upward,
and the felt is compressed. Thus we have both
force effects, a change in shape and a change in volume.
The hammer exerts an upward force on the string,
the string exerts a downward force on the hammer.
!Now, the law of the conservation of energy teaches
-us that energy cannot be destroyed ; it is merely
transferred. Therefore, when the hammer comes
into contact with the string, a transfer of energy from
the former to the latter takes place. It is in the
manner in which this transfer is made that we have
the clue to tone-production on the piano.
To overcome resistance, a force is required. The
string offers resistance to the upward stroke of the
hammer, and, as soon as displacement of the string
-occurs, a transfer of energy, equivalent to a loss of
energy in the hammer, takes place. That is, for each
additional unit of displacement the hammer gives
up a unit of force.
Now, in discussing the first part of the hamrner-
64
THE HAMMER-STROKE
stroke, we found that the velocity of the hammer
cannot increase after escapement, for no new force
can be added, and positive acceleration always means
the action of a force. 1 It is still more obvious that the
velocity of the hammer cannot increase after reaching
the string, because in this case, not only can we not
add any force, but the additional resistance of the
string must be overcome. Therefore, from the moment
of impact, the moment when the hammer touches the
string, a decrease in hammer-speed takes place. Any
increase is a physical impossibility. Hence, any
transfer of energy is negative for the hammer and
positive for the string. This question next presents
Itself : Does the manner of the transfer vary, and if
so, how ? Since we are dealing with a fixed steel
string, we know or can calculate its coefficient of
elasticity. This, for the same string, is a constant
ratio. That is, the resistance offered to the hammer
per unit of time remains the same up to the limit
of elasticity. 2 Thus, two equal initial forces will
always give up their energy in precisely the same
manner. 3 Applied to the piano, this means that when
the hammer reaches the string with a certain velocity,
there can be but one string-response, which is always
the same for every hammer-impact at the given
velocity.
Now, when a greater force acts upon the string,
one of two things may theoretically occur : the greater
force may overcome the same resistance in less time,
or a greater resistance in the same time. The first
assumes that the resistance remains constant, when as
a matter of fact it changes with string-displacement.
Of the two theoretically possible actions of a
1 See Physical Principles.
2 The interesting variations taking place beyond this point
will be treated in the chapter on the vibration of the string.
3 Of course, the irregularities due to the unstable condition
of felt as a striking body are disregarded.
65
PIANO TOUCH AND TONE
greater force, then, we have in our case an increased
resistance, and not a shortened time, with which to
deal. The greater the force the greater the resistance
overcome. Now, since the coefficient of elasticity,
the resistance offered, is a constant ratio, the force
must act through a greater distance, because the ratio
in which the force loses its energy per unit time remains
the same. Therefore, for every increase in hammer-
force we have an increase in string displacement,
or, as it is technically termed, amplitude. Two
unequal hammer-forces cannot produce two tones of
the same intensity ; two equal hammer-forces cannot
produce two tones of unequal intensity. The transfer
of energy from hammer to string takes place as follows :
the greater the hammer-speed, the more rapidly is
energy transferred and the greater is the resistance
overcome. The time required for this transfer,
consequently, varies within certain limits, since it
depends upon the relation of the force of the hammer
to the physical properties, mass, tension, and elasticity
of the string.
The hammer continues on its upward journey,
until its energy has been completely transferred. 1 For
an instant, both hammer and string are at rest at
the upper extremity of their displacement. The
felt of the hammer being depressed, the amount
or length of felt surface actually in contact with the
string depends upon the depth of depression. It
has often been assumed that a good length of contact
surface dampens the high, erroneously called
inharmonic, partials of the string, and that a less
length produces a " harsh " tone. If this were true,
all pp tones, since only a small part of the felt surface
touches the string, would be harsh ; and all tones
1 Not all has been transferred to the string. Part has been lost
in producing noises and in overcoming friction and in compressing
the felt of the hammer.
66
THE HAMMER-STROKE
produced by hammers with well-worn ridges, and
hence long surfaces of contact, would produce
" sympathetic " tones. As a matter of fact, the
reverse is the case. The difference in tonal qualities
is due not to the length of contact surface, but to its
hardness, location, duration of the contact, and to the
cutting-out of partials with nodes at that point.
When hammer and string have reached the upper
extremity of their excursion, the former possesses
zero energy, the latter energy somewhat less than
the initial impact force of the hammer. The string
in turn now exerts a downward force on the hammer ;
the compressed felt, owing to its elasticity, an upward
force on the string. Both forces tend to drive the
hammer down, away from the string. If the key
has been completely depressed and so retained, the
hammer will be caught by the buffer and its energy
dispersed through this, as shown in Fig. i. If the
key, meanwhile, has been completely or partly released,
the hammer is re-engaged by the escapement
mechanism and is ready for a second excursion against
the string should the key again be depressed.
The rising of the dampers simultaneously with
of the depression of the key, as well as the action
the pedals, need not detain us here. These effects
will be studied later.
RECORDS OF HAMMER-STROKE
If, now, we can record the path of the hammer-
head, we have practical and tangible proof of the pre-
ceding theoretical statements and conclusions. Records
of the hammer-stroke may be fairly satisfactorily
obtained by attaching an appropriate stylus to
the hammer-head and passing beneath this, at
a constant speed, a surface of smoked paper. An
ordinary kymograph will not do because of its size
and, secondly, its slow speed. The experiment requires
67
PIANO TOUCH AND TONE
a specially constructed apparatus consisting of one
small vertical cylinder, or preferably several such
cylinders, of such size that the paper passed over them
will present a vertical surface close to the hammer.
By appropriate gearing or belting, a rapid paper
or film-speed may be obtained. Needless to say,
only a section of the piano-action can be used. This
can be made by any piano manufacturer at com-
paratively small cost. The advantage of such an
apparatus is due to the fact that it enables us to record
the hammer-stroke without interfering with tone-
production. Thus the experimenter actually hears
the tone produced and knows whether or not it is
what was desired. Imagine the film passed from left
to right at a constant speed. Then the motion of
a point moving vertically across this film will be
projected upon it, deflected toward the left. If the
point moves rapidly, the line described will be nearly
vertical. If the point moves very slowly, the
line described will be nearly horizontal. Any fluctua-
tion in speed during the stroke will be shown
by curvature toward or away from the perpendi-
cular. This applies to either an ascending or a
descending point. An ascending point beginning
slowly and increasing in speed will describe a
path such as a, Fig. 19. The same point moving
with a constant velocity will describe a path such
as b. A point beginning rapidly and decreasing
68
THE HAMMER-STROKE
2
PIANO TOUCH AND TONE
in speed will describe a line such as c, Fig. 19. When
the film is at rest, a point fastened to the hammer-
head describes the line at d, Fig. ig. 1 In the records
used allowance must be made for this curvature.
That is, a concavity of this amount or less does not
mean increasing speed since the point on the hammer
itself moves in a curve. The records should not be read
for horizontal differences of less than T V inch, which
is equivalent, approximately, to -^ of a second,
since they are not accurate beyond this point. 2 The
additional arc on the records shows the path traversed
by the hammer when the film is at rest ; in other
words, it shows the path which an instantaneous
hammer-stroke would describe. The short horizontal
line shows the point of escapement. The dotted
horizontal line shows the string level. Every record
is shown on a scale slightly less than one-half of
the originals. The great distance, nearly three-
eighths of an inch, against the normal of one-
eighth inch between escapement and string in some
of the records, needs explanation. The escapement
was thus set in order that variations in hammer
speed between escapement and string contact could be
magnified. Many of the observations, of course,
are merely reiterations of those made in the chapter
on key-depression. They are included, however, as
additional proof, and also because they facilitate the
comprehension of the remaining records.
Fig. 20 shows increase in hammer-speed from the
horizontal slow speed, " pp," to the vertical fast speed,
"ff," with intermediate grades. All records of
hammer-stroke are to be read from right to left.
Effect of Muscular Relaxation and Rigidity on
Hammer-Stroke. The effects of relaxation and rigidity
1 This is the arc of the circle whose radius is the length of the
hammer-stem.
8 The piano-action, scientifically considered, is too coarse a
mechanism to permit really fine measurements.
70
THE HAMMER-STROKE
upon hammer-stroke are shown in Fig. 21 and in
Fig. 22. In Fig. 22 we find a slight difference, and
in Fig. 21 a marked difference. In both cases, however,
the hammer-speed produced by a rigid hand and arm
was greater than that produced by a relaxed arm.
FIG. 21.
FIG. 22.
Moreover, when we look at the distance which the
string is displaced (that part of the curve above the
string level) after allowing a little for felt-depression,
we find that the greater hammer-speed has caused
the greater displacement of string, hence louder
tone. Therefore^ generally speaking, rigidity tends
PIANO TOUCH AND TONE
to produce louder tones than relaxation. 1 This is
shown by faster hammer-speed and greater string-
displacement. 2
Effect of Percussive and Non-Percussive Touch on
Hammer-Stroke* Fig. 230 shows the hammer-stroke
resulting from percussive touch, and Fig. 236 that
resulting from a non-percussive touch. Note the
abrupt beginning of the former and the gradual
beginning of the latter. The upper part of the first
curve is practically straight, showing no increase
of speed. In other words, the maximum hammer-
speed is attained before the hammer reaches the
FIG. 23.
escapement. The non-percussive curve, on the other
hand, shows a steady increase up to the point of
escapement. In addition, we find a difference
in intensity, the percussive touch showing the greater
intensity. This verifies those records of key-depression
which illustrate these touch differences.
The key-depression, moreover, showed during its
course a marked irregularity for all percussive touches.
1 Compare with, the corresponding paragraph in the Chapter on
Key-depression. This conclusion involves the assumption that
amplitude of string-displacement is the physical equivalent of
the sensation loud ness.
2 String-displacement will be discussed in detail in Chapter VI.
3 It will be remembered that the one qualitative difference in
key-depression was found to be the result of differences between
percussive and non-percussive touch.
72
THE HAMMER-STROKE
Naturally, we should expect to find a similar
irregularity in the hammer-stroke. Such an irregularity
would result in a hammer-stroke somewhat as follows :
Somewhere in its course would be a momentary
retardation, which would deflect the curve toward
the horizontal. No such deflection, however, was
obtained on any of the many records made, nor could
any be obtained by special attempts to secure such
a stroke. In other words, the retardation which
takes place in key-descent does not take place in
hammer-ascent. And the subsequent increase in
key-speed likewise is not shown in the hammer records.
This difference between key-depression and haramer-
FIG. 24.
stroke can be explained in only one way : that key
and hammer are not in contact at and after the point
when the irregularity in key-depression occurs. This
being so, the important corollary follows : that in
percussive touches the hammer is under control
of the player through only a part of its stroke, the
distance varying with the dynamic degree of
percussion. 1 Whatever motion we wish to impart
to the hammer in percussive touches must therefore
be transmitted before this point where the hammer
leaves the key-action. 2 This phase has other interesting
1 This agrees entirely with the conclusion reached in the Chapter
on Key-depression.
2 Not to be confused with the point of escapement.
73
PIANO TOUCH AND TONE
features. In Fig. 25, 6 and c show, respectively, the
curve resulting from a very light, staccato touch
and the curve resulting from a so-called " surface "
or " shallow " tone. Both are convex almost from
FIG. 25.
the beginning. That is, we have a decrease in velocity.
This means that no appreciable force is acting after
the moment of impact. To prove this, the piano
key was " blocked " l at distances first of J inch
below its surface level and then at -/$ inch. Fig. 26
FIG. 26.
shows the resulting curves, when the key is struck
"/" and "ff". These curves, it will be seen, are
identical with the curves b and c of Fig. 25, a condition
which proves that in percussive touches, the motion
is imparted to the hammer only during the time of
impact and not after. This, of course, necessitates
1 A piece of wood was inserted beneath the key, so that the key
could be depressed only J in. and later $\ in.
74
THE HAMMER-STROKE
very fine muscular adjustment in order to secure
the desired dynamic degree.
Percussive touches are said to produce a " brilliant "
tone ; non-percussive touches, a " sympathetic "
tone. Such differences, when they do exist, are,
as we have seen, in no way due to differences in hammer-
stroke, as is erroneously believed, excepting the fact.
Carved ff/f^er
(ffrtj
Cfose Toucfi
FIG. 27.
FIG. 28.
FIG, 29.
of course, that percussive touches tend to produce
louder tones. It will be shown later that these
differences are due to other factors.
Effect of Hand and Finger Position on Hammer-
Stroke. Figs. 27 and 28 show curves for a bent or
curved and flat or extended finger, respectively,
the latter representing the so-called "clinging"
75
PIANO TOUCH AND TONE
touch. Both curves show differences of intensity
in favour of the curved-finger touches. After extended
practice by the experimenter, this intensity difference
was largely eliminated and the curves of Fig. 29 were
secured. The person making these records admitted,
however, that he " felt " the flat finger touch " louder "
than that of the curved finger, which merely sub-
stantiates the statement that under normal conditions,
a_ Low
6- Mb/> Wrist, perc
FIG. 30.
FIG. 31.
when there is a difference, we tend to play softer with
extended fingers than with curved ones.
Figs. 30 and 31 show curves produced by a high
and a low wrist. As in key-depression, absolutely
no difference was found. Upward or downward
motions of the arm, then, are immaterial, so far as
an influence on the hammer- stroke and hence on the
vibration of the string is concerned. When a particular
76
THE HAMMER-STROKE
.arm or hand movement does produce a particular
effect, this is due to other things than the tone resulting
from the vibration of the string. The same statement
applies to other movements of the arms and hands,
such as rotary motion.
Fig. 32 shows the curves obtained by a percussive
staccato (a touch in which the hand is thrown against
the key and quickly withdrawn) and a non-percussive
{so-called " plucked " staccato), a touch in which the
FIG. 32.
A A tr-
~ 6uncf?ed finders
" **
FIG. 33.
-finger rests against the key and is then quickly
drawn up.
Except for the immediate beginning of the curve,
where the percussive type naturally shows a somewhat
more abrupt beginning than the non-percussive
type, the curves are identical. This identity precludes
.any difference in the tonal result for these two touches,
-so far as this is produced by the string.
Fig- 33 shows a curve made with " bunched "
-.fingers (several fingers for the one key) as musically
77
PIANO TOUCH AND TONE
as the dynamic degree used (sfff) permitted, and a
curve made by using the fist, striking the key a severe
blow. The hammer moves in precisely the same
manner in both cases.
Fig. 34 shows the hammer-speed for a key when
depressed alone, and for the same key when depressed
as a tone of a chord. In Chapter III (Fig. 170) the
fact was mentioned that for simultaneous key-
depression greater force is used in order to keep the
intensity the same. That each key under such
conditions receives the same force is shown in Fig. 34,
in which Figure the two curves are identical.
a. - fr/ad (/.3.5J
'
FIG. 34.
The opinion is sometimes held that it makes a
difference whether, when the damper pedal is depressed,
we play a key staccato or sostenuto. It is said each
produces its own tonal effect. This opinion, evidently,
is based upon the assumption that the shortness of
the one touch and the sustained pressure of the other
is transmitted to the hammer and thence to the
string. Fig. 3^ shows the curves obtained for these
touches. In the records here used there is considerable
intensity difference, the percussive staccato being
louder than the sostenuto. Apart from this difference,.
however, the two curves are alike, inasmuch as they
both show a straight line for the greater part of the
78
THE HAMMER-STROKE
hammer-ascent. We must remember that the parts
of the curve after string contact have no significance.
Consequently, the differences in these touches is without
effect upon hammer-stroke, and hence also upon tonal
result. The explanation of the slight difference
which may exist will be found when we come to discuss
the noise element.
a - pert-staccato
o.~ * sasfenvto
FIG. 35.
FIG. 36.
FIG. 37.
Fig. 36 shows the operation of the repeating
mechanism by means of which the hammer may be
re-engaged and re-driven against the string before
it descends completely. The two tones produced
here were "/" and ' "ff" respectively.
79
PIANO TOUCH AND TONE
Hammer-Stroke and Tone Quality. Figs. 37, 38, 39,
40, and 41 show curves for tones of the various
qualities named with the Figures. Again, we find
a " harsh " tone louder than a "good" tone, since it is
represented by greater hammer-speed; we find
FIG. 38.
FIG. 39.
FIG. 40.
a " shallow " and a " dry " tone weaker than a
" normal " tone. When by additional experimentation
these differences in intensity were corrected, the
difference in so-called "quality" vanished in the
judgment of the subjects originally making the records.
80
THE HAMMER-STROKE
This bears out the findings in the chapter on Key-
depression.
The Hammer-Stroke after Escapement. A study of
the entire series of records showing the hammer-
stroke reveals one important fact concerning the path
after the moment of escapement. In none of the
records do we find concavity, that is, increase of
speed x after the point of escapement. When the line
remains practically straight, we have examples of
approximately constant hammer-speed ; when the
line is convex, that is, bending towards the horizontal
as it ascends, reading from right to left, we have
decreasing hammer-speed. In no case, then, has there
been energy added after escapement, for such an
FIG. 41.
addition would result in an increase of hammer-speed.
A number of instances among the records of key-
depression, however, showed such addition.
Let us now look at that part of the curve above
the string level which represents contact of hammer
and string, bearing in mind, however, that the records
are not sufficiently exact to permit accurate comparison.
We find the greatest hammer-speed at the moment
when the hammer-head comes into contact with the
string. Thereupon there is a decrease in speed.
If the hammer strikes the string with great velocity,
there is a rapid decrease ; if the hammer strikes with
a low velocity the decrease is slower. This is shown
1 It must be 1 remembered that a very slight concavity does not
indicate increase in speed since the actual path of the hammer
is not a straight line, but an arc of a circle, hence concave in itself.
81
PIANO TOUCH AND TONE
by the various degrees of convexity of these arcs
or curves above the line representing the level of the
string. In every case, however, there is convexity,
that^s, decrease in hammer- speed. If there were
increase of speed or even constant speed the curve
would have to bend toward the right. The theoretical
impossibility of this has already been demonstrated.
The records furnish the necessary practical substan-
tijition. 1 Consequently, the statement that with
^appropriate touch, e.g. that represented in Fig. 40,
"the string is " gradually pressed " into motion, is
shown to be a complete fallacy. There is not and
cannot be any " unpercussive " attack of the string,
.or " gradual " setting into motion of the string. 1
Above all, it must not be supposed that the gradual
key-depression resulting from the various forms
of " sympathetic " touch is likewise gradually trans-
mitted to the string ; for all this gradual preparation
takes place before the string is touched, and since,
owing to the escapement, it has also ceased before
the string is touched, it might just as well not have
taken place so far as its direct influence on the string
is concerned. This is clearly shown in the records,
several of which have equal hammer velocities at
string level and similar curves above this, regardless
of whether this velocity has been attained gradually
or suddenly. But similarity of that part of the curve
representing contact with the hammer means similarity
of string motion, for when the apexes of two curves
are identical, the string itself, a physical constant,
evidently is set into motion in precisely the same
manner. A study of the records shows this to be
possible regardless of how the escapement velocity
has been attained, for curves totally different at the
beginning have similar apexes : compare Figs, zoe
1 Further proof of this will be found when we treat of the vibration
of the string.
82
THE HAMMER-STROKE
and 256 for example. The quality of string motion
is thus shown to be entirely independent of the manner
of generating the velocity of the hammer, and to be
dependent solely upon the speed with which the
hammer leaves the escapement. This the records
bear out. Wherever the angles made by two curves
at the escapement point are equal, the contact parts
of the curves are practically identical.
Duration of Contact. It is well known that the
vibration of a string depends in part upon the nature
of the stroke. This, in turn, depends upon the length
of time during which the striking body remains in
contact with the string. A body in contact with
the string for only an instant produces one mode of
vibration, and a body in contact for a longer time
produces a different mode of vibration. For that
reason it is advisable to study the given records in
a general way for duration of contact ; i.e. the length of
time during which hammer and string are in contact.
This is represented by the length of horizontal line
at string level included between the two sides of the
curve. The greater this distance, the longer the
contact. We find the shortest distance in the greatest
hammer-speed. The distance increases as the force
of impact (hammer-speed) decreases. Though the
hammer drives the string relatively farther aside in the
former case, the transfer of energy consumes less time
than in the latter case. In other words, in the produc-
tion of loud tones 1 the greater force is transferred
in less time than in the production of weaker tones.
The contact time, then, increases from tones of great
intensity to tones of little intensity 2 ; or, generally
speaking, contact time varies inversely as the intensity,
and the entire variation from fortissimo to pianissimo
1 For vertical string displacement means amplitude, which
means loudness.
* The effect of this relationship on the resulting tone will be
discussed under the vibration of the string.
83
PIANO TOUCH AND TONE
occurs between approximately -^ir and -^r of a second.
Mention of this general tendency must suffice here,
for the records are not sufficiently accurate to permit
detailed calculation, much as this is desired. Nor
would the instability of the felt hammer and piano
action permit this.
The Hammer after Leaving the String. In the tracings
of records here shown the greater part of the downward
or returning stroke of the hammer has been omitted.
There are two reasons for this : first, the descending
stroke has absolutely no influence on tone ; and
secondly, to record it here would in some cases
lengthen the records to several feet. What actually
takes place is this : the hammer when caught by the
check is held about | inch from the string. When the
key is released the hammer falls ; and, owing to the
manner in which it is held by the action, it does not
immediately come to rest, but first describes several
gradually diminishing minor ascents or descents. A
complete record on a small scale is shown in Fig. 42.
Notice that the rebound from the string is considerably
more rapid down to the point where the returning
hammer engages the buffer than for the rest of the
distance. This part is a true rebound, something
very different from the ascent of the piano key.
CONCLUSIONS
The agreement of the records with the theoretical
proof deduced at the beginning of this chapter permits
the following conclusions to be drawn :
1. The only factor directly influencing, or reaponsible
for, the vibration of the piano string is the velocity
with which the hammer leaves the escapement.
2. Regardless of the touch employed, regardless
also of the manner in which the escapement velocity
of the hammer has been attained, there is but one
action of the hammer against the string; namely,
84
XHE HAMMER-STROKE
o
PIANO TOUCH AND TONE
a sharp, percussive action. There is no such thing
as an unpercussive attack of the string.
3. In no case is it possible to increase the hammer-
speed after escapement.
4. In every case there is decrease in hammer-speed
from the moment of string-contact. The greatest
velocity occurs at the moment of impact. Hence
there can be no gradual setting into motion of the
string.
5. For every increase in hammer-speed we have
an increase in the amplitude of string-displacement.
6. The duration of contact between hammer and
string decreases as we increase hammer-speed, or,
what is the same thing, it decreases as we increase
the intensity of the tone.
7. All qualitative differences, such as " harsh ",
"dry", or "singing", are the result of differences
in hammer-speed, and therefore differences in tonal
intensity or loudness.
8. Rigidity and curved finger touches tend in general
to produce greater hammer-speed than relaxation
and flat finger touches. And since greater hammer-
speed is the equivalent of greater tonal intensity,
the former produce louder tones.
9. Normal hammer-action takes place in a period
of time very approximately between -^ and r ^ of
a second for the softest and the loudest tone
respectively. Therefore all tone gradations, as far as
these depend upon intensity, must take place within
these limits.
10. In order to produce the least audible tone,
the hammer must have a velocity of about 5 feet
per second ; for a fortissimo tone, the velocity is
about 40 to 60 feet a second.
86
PART II
INTRODUCTION
TN Part I we sought to analyse the physical mechanism
^ of piano touch and tone; in Part II we shall
seek to analyse the sound produced by this mechanism
from the moment of its generation in the piano to
the impingement of the sound waves upon the ear
of the listener.
When a single piano key is depressed and a tone
produced, the sound heard is generally considered
a simple unity, a " one-ness ". As a matter of fact,
however, this is far from true. The sound is physically
very complex, and with a little training, which
incidentally, is most desirable for the pianist, the ear
can distinguish a number of the elements of this sound
complex. It will be convenient to list these elements
as follows :
L Tonal Elements :
A. Vibration of the String Struck
1. Fundamental tone
2. Partial tones
3. Beats between i and 2
4. Beats among partials
B. Vibration of other Strings
1. Sympathetic resonance
2. Forced resonance
C. Vibrations of the Sounding Board
1. Natural frequencies
2. Forced frequencies
PIANO TOUCH AND TONE
D. Sound Propagation
1. Diffusion
2. Reflection
3. Interference
4. Resonance
II. Noise Elements :
A. Hammer-String percussion
B. Finger-key percussion
C. Action noises
1. Key-bed percussion
2. Friction noises
D. Noise Propagation
1. Diffusion
2. Reflection
f 3. Interference.
Tliis analysis does not exhaust the elements of
variability. Taken as a whole, the piano sound-
complex varies again, as we shaU see, with numerous
other attributes, such as the pitch region or duration,
which are here understood as more or less foreign to
the tone-complex itself. Our problem, therefore,
becomes first a study of the nature of piano sound
and what may be called its internal and external
variability, and, secondly, a study of the effects of
pianistic touch upon this sound-complex and its
physical variations. And since the mechanical forces
are transformed into sound at the contact of hammer
and string, we shall begin with an analysis of the
vibrations of the piano string.
90
CHAPTER VI
VIBRATION OF THE STRING
THEORETICAL ANALYSIS
CTRINGS may be made to vibrate by bowing,
^ as in the case of the violin, by plucking, as in
the case of the harp, or by striking, as in the case of
the piano. The quality of the resulting tone depends
partly upon the mode in which the string is set
into motion. Strings of various material are used
for producing musical sounds, such as the gut strings
of the instruments of the violin family and the harp,
and the metal strings of the piano. The quality of
the resulting tone depends partly upon the material
of the string.
The strings of the piano are made of carefully
prepared steel. They vary in length and thickness,
the shorter and thinner being used for the tones of
the treble region, the longer and thicker for those in
the bass region. In order to reduce the length of
the string necessary for the production of very low
tones, the bass strings are wrapped with thin copper
or steel wire, some once," some twice. This wrapping
makes the string thicker, but at the same time gives
greater flexibility to the string than it would possess
if the steel string itself had the diameter of the wrapped
string. It gives, however, less flexibility than an un-
wrapped string of the same pitch, but necessarily
greater length. When a piano string is stretched
between two points and, either by plucking or
striking it, is made to travel back and forth, that
is, to vibrate, it produces vibrations which, if wide
enough, the ear takes up as a tone.
91
PIANO TOUCH AND TONE
Fortunately, instruments such as the monochord
have enabled us to study and analyse rather minutely
what actually takes place when such a string vibrates.
This study and analysis has led to the formulation
of several fundamental laws :
1. The stretching weight or tension being constant,
the number of vibrations in a second varies inversely
as the length of the string.
2. The number of vibrations per second varies
inversely as the diameter of the string.
3. The number of vibrations per second varies
directly as the square root of the tension.
4. The number of vibrations per second varies
inversely as the square root of the density of the
string.
Moreover, we know that :
1. The duration of a tone depends upon the length
of time during which the vibrations, sufficient to
produce tone, continue to reach the ear.
2. The intensity or loudness of a tone depends
upon the width of the excursions of the string.
3. The height or depth of a tone, its pitch, depends
upon the number of vibrations per second.
4. The quality, timbre, or " colour " of a tone
depends upon the form or shape of the vibrations.
Thus in Fig. 43, which illustrates various types of
vibrations, b represents a shorter sound than a ;
c represents a higher sound than b ; d represents
a louder sound than /; e represents a different tone-
quality from a ; d', a crescendo and diminuendo.
Since we know that the pitch of a tone depends
upon the number of vibrations or waves reaching
the ear per second, in other words, upon the frequency
of the waves, it is evident that a vibrating body,
yielding a curve such as e, Fig. 43, must give forth
more than one tone, for the smaller waves or vibrations
are greater in number per unit of time than the larger
92
VIBRATION OF THE STRING
ones. In such a case we hear what is known as a
complex tone. All tones used in music are complex. 1
We have no musical instrument which when sounded
produces but a single tone, a tone of one pitch. Con-
sequently, we should expect a complex curve to result
whenever the vibrations of the tone-producing bady
of any musical instrument are recorded. It will be
/vvvwx/ww
l \
I AAAAAAAAAAAAAAAAAAA/W
d
-v*y^w\AAA/WV>A/VVXA/V\/W\/WV^^
d 1
FIG. 43.
shown later, as far as the piano is concerned, that this
is invariably true.
The most important law concerning tone quality
is Ohm's law, 2 which states that all varieties of tone
quality, no matter how complex, are analysed into
combinations of simple tones. Later, Fourier 3
1 The tone of a tuning-fork is normally a pure tone. The curve
produced by such an instrument is shown in a of Fig. 43. The tone
is considered musically uninteresting.
2 George Simon Ohm (1787-1854), a German Physicist.
3 Jean Babtiste Fourier (1768-1830), a French Physicist.
93
PIANO TOUCH AND TONE
developed a theorem by means of which any complex
vibration could be analysed into its proper component
simple vibrations. However, because two vibrations
differ in shape, they need not necessarily produce
tones of different quality, since the differences in
their wave form may be merely differences of phase, 1
and it is generally accepted as true that differences
of phase do not affect tone quality.
In Chapter V we traced the operation of producing
a tone on the piano to the point where the hammer
displaces the string. We have to find out now what
happens to the string when so displaced. The string-
is forced upward by the hammer, and a wave runs
along the string from the point displaced to either end.
A
FIG. 44.
Because the tension of the piano string is very high >
this wave progress takes place very rapidly. More-
over, as a result of the softness of the felt hammer
and its graded compressibility, these waves are not
marked. The soft felt displaces the string in the
manner of b, Fig. 44, whereas a sharp, hard point
would displace it as at a. The hammer rebounding
from the string leaves the latter free to vibrate.
It is a well-known fact that a string thus free, vibrates
not only as a whole but also in parts. That is,
a string vibrates as at a, Fig. 45, at the same time
vibrating as at 6, c, d, e, and in yet other ways. But
1 The phase of a wave may be illustrated as follows :
e
from a to b is one phase of the wave, a, b f c, d, e, from b to
another phase, c to d a third, and d to e a fourth.
94
VIBRATION OF THE STRING
each one of these wave lengths produces its own.
tone, because pitch, we learned, depends upon the
length of the string ; b produces the upper octave
of a, c the fifth above b } d the fourth above c, e the
major third above d. For example, if a produces
the C below middle C, b will sound middle C, c will
sound the G above, d the C above the G, e the major
third above the C or two-lined E. 1
47
FIG. 45.
Again, looking at Fig. 44 we see that the greatest
displacement of the piano string at the moment of
impact is at the point of hammer-stroke. But
amplitude means loudness. Therefore, those tones
whose natural width of vibration corresponds to this
point will be loudest at the moment of impact. If
we study Fig. 45 we notice that a point % is moving
through a relatively great distance in a, while it is
1 The presence of these tones may easily be detected by resonators.
95
PIANO TOUCH AND TONE
not moving at all at &, it is moving somewhat at c,
and not at all at d. Years of experimentation
have led the piano manufacturers to select a point
between | and -J- the length of the string l as the point
for the hammer-stroke yielding the most satisfactory
quality of tone-complex for musical purposes. This
point will permit the fundamental, ist, 2nd, 3rd, 4th,
and 5th partials to vibrate. The tones corresponding
to these frequencies are key-note, octave, I2th, double-
octave, major-third above, and octave of the I2th.
The string cannot freely vibrate in sevenths because
the point at i from the end must be at rest, and if the
hammer strikes the string at this point it obviously
cannot be at rest. Higher partials than the 6th are
weak, though they are present in the tone-complex. 2
These partials, however, are not of equal intensity ;
they are not, strictly speaking, the same in number
or intensity for any two strings in the piano ; and they
do not retain either their absolute or their relative
intensities from one moment to the next. But every
piano tone-complex consists of a fundamental and
various upper partials of constantly changing intensities.
The number of these partials and their relative
intensities give the tone-complex its colour or quality.
When the hammer strikes the string with little
force, it is able to overcome but little resistance.
Hence, it displaces the string but slightly ; and, since
loudness of tone depends upon this displacement,
or amplitude of vibrations, we naturally get a soft
or weak tone. Such a tone might be represented
as in Fig. 470. Now, suppose the piano hammer
to strike the string with somewhat greater force.
There will be greater displacement, and, as a result,
1 The distance of the hammer striking-point from the end of the
string is not exactly the same for all strings in any one instrument,
nor for various instruments.
* With sufficiently refined apparatus the presence of as many
as 34 partials has been detected.
VIBRATION OF THE STRING
a louder tone. Let it be represented by Fig. 47^.
A still greater hammer-force will result in still greater
displacement, and the resulting tone may be represented
as in Fig. 47^. Now, it is evident that below a certain
amplitude no tone is audible, since the waves are
too minute to affect the human ear. Otherwise,
there would be no waves too soft for us to hear, which
is, of course, not true. Suppose in our figures that we
represent this point by the line which we shall call
the threshold of audibility (T.A.). 1 What is below
this line is too weak to be heard. Then in Fig. 470
FIG. 47.
we have a tone consisting of a fundamental, ist, and
2nd partial, and a weak 3rd partial ; in & we have a tone
consisting of a fundamental, ist, 2nd, 3rd, and 4th
partials of various intensities ; and in c we have a tone
with all partials present up to and including the gth.
Since the colour or quality of a tone-complex depends
upon the number and relative intensity of the partials
present, we get three tone-complexes of different
quality. From this we can formulate an important
law : that for every difference in intensity there is
a difference in the quality or colour of piano tone-
1 Needless to say, this varies with the individual, pitch, and
distance.
97
PIANO TOUCH AND TONE
complex. The diagrammatic illustrations used are
purely theoretical and do not represent the actual,
more complex relationships as we shall find them
later. The principle, however, is the same. The
vibration of the string is further complicated by the
fact that its own speed varies during the course of
a vibration. The string travels at a maximum speed
when it reaches its point of displacement. Its speed
decreases until it reaches the end of its excursion
in either direction. For a theoretical moment its
velocity at this point is zero. The return excursion
from extremity to centrality of position shows
gradually increasing velocity with a maximum velocity
at the point where the string passes its original position
of rest. Thus, if we project a simple vibration, as
follows :
the string has a maximum velocity at A ; negative
acceleration to B ; zero velocity at B ; positive accelera-
tion to C ; negative acceleration to D ; zero velocity
at D ; and positive acceleration to E. Thereupon
this series repeats itself, each time of course with
diminishing absolute energy, until finally the string
comes to rest. This internal speed variation does
not influence pitch but does influence intensity.
The string travels faster for a loud tone than for a soft
one. It does not make more vibrations per second,
of course, but because it still makes the same number,
and yet has to travel a greater distance (amplitude)
for each vibration, it certainly must move at a greater
velocity. This variation in velocity then must always
occur with a variation in amplitude.
Tension, likewise, has an effect upon tone-quality.
The greater the tension the clearer and longer does
VIBRATION OF THE STRING
the tone tend to be. A low tension reduces the
elasticity of the string and consequently affects the
tendency to vibrate in parts. On the other hand, it
permits the fundamentals and lower parti als to pre-
dominate. The resulting tone is somewhat dull and
heavy. Extremely high tension results in a prepon-
derance of upper, higher, partials, and gives the tone a
metallic colour.
This relationship between intensity and tone-quality
will be better understood if we seek its corollary
in colours. Thus, if we mix yellow and blue, we get
green ; by adding more yellow or more blue we change
the tint of the green. We have a new colour, a change
in quality, obtained not by adding a new element
but merely more of an old element, that is, a change
in quantity or intensity. Precisely the same
phenomenon occurs in piano-tone ; a physical addition
of quantity results in a subjective difference of quality.
Since the resistance which the string offers to the
hammer is the same for each successive hammer-
stroke, and since the physical properties of the hammer
are likewise invariable, 1 it is manifestly impossible
to produce different forms of string-vibration if the
hammer-force remains the same. A study of Fig. 47
will make this clear. If the hammer-strokes are the
same, the string displacement is the same, and
consequently the same number of partials of the same
intensity will result. For if this were not so, the same
force would have to produce various effects upon
a body whose properties remained constant, a state-
ment which contradicts the most fundamental law
of dynamics. In other words, whenever the velocity
with which the hammer reaches the string remains
the same, the form of the resultant string-vibration
remains the same. That is, for any one degree of
i Excepting, of course, the so-called " wear " of the hammer.
99
PIANO TOUCH AND TONE
intensity we can have but one tone quality. In
the piano, two tone-complexes of equal intensity cannot
differ in quality for the same string,
Duration of Tone. These two fundamental laws
of string-vibration, when applied to practical problems
in the piano, become complicated for a number of
reasons. Chief among the latter are the changes
of quality in piano tone-complex occurring from
one moment to the next. It is a well-known fact
that the piano is incapable of sustaining any tone
at a uniform intensity. The tone reaches its loudest
point practically at the moment of impact (the instant
after is really more exact), and then diminishes in
intensity. This variation is accompanied by com-
plexity of tone colour. Not only does the tone-complex
change in intensity, it likewise changes in quality
from each moment to the next, in accordance with
the laws deduced in the preceding paragraph. This
diminution in tone is the result of the transfer of
energy which takes place within the string as a whole,
its internal molecular resistance, the resistance of
its end-pins, and the resistance of the atmosphere. In
terms of the movement of the string, this decrease means
decreasing amplitude of vibration. The vibrations,
scarcely audible at the moment of impact, become
inaudible later on ; those plainly audible become
scarcely audible.
This diminution may vary in speed and also in
quality ; it may be regular or irregular. In other
words, the amplitude of the vibrations may decrease
an equal or unequal amount for each unit of time.
Naturally, any irregularity would tend to complicate
the tone-quality still more. Since the hammer has
left the string before the entire string has been set
into uniform motion, we may expect to find irregular
diminution when we record the vibrations.
Limit of Elasticity. The laws of elasticity teach us
100
VIBRATION OF THE STRING
that the displacement of an elastic body is directly
proportional to the force, within the limits of
elasticity. 1
If a force of I causes a displacement of 2, a force
of 2 will cause a displacement of 4. Applying this
to the piano we have the string displacement varying
directly as the force, as far as the elastic properties
of the strings are concerned. And the physical
properties of the string being constant, they cause
the ratios among the fundamentals and partials to
remain constant. In other words, if the elasticity
of the string alone influenced tone colour, we should
have a series of tone qualities increasing by a constant
ingredient, and not varying by changed relations
within. That is, as we increased the displacement
of the string we should add B to A ; to A and B we
should add C ; to A, B, and C we should add D. But
the relation of A to B in any case would remain the
same. In practice we find no such simple arrange-
ment. Other factors contribute to tone quality
on the piano. They are : the duration of the stroke,
the material of the striking body, and the place struck.
The Duration of the Stroke. As a result of friction,
displacement, inertia, and elasticity of the hammer-
head, the hammer remains in actual contact with the
string for a certain time, which we shall call the
duration of the stroke. The tendency of any body
which rests against a vibrating body is to " damp ",
that is, to destroy the vibrations. Naturally, the
longer this contact lasts the more effectively will
the vibrations be destroyed. The weakest vibrations
are the first to be destroyed ; then follow the stronger
vibrations. A very short contact time permits a
string to vibrate in small as well as larger segments ;
1 The limit of elasticity is the point at which a permanent altera-
tion in molecular structure takes place ; the point at which a
stretched string or a bent stick fails to return to its original shape.
101
PIANO TOUCH AND TONE
a longer contact time destroys these smaller vibrations.
But the vibrations of the small segments produce the
high upper partials, those of the larger segments
produce the lower partials, and that of the whole string
produces the fundamental. Hence, with a very
short duration of stroke we should expect a tone
rich in high upper partials, and with a longer duration
of stroke a tone with fewer upper partials. Helmholtz,
in his Sensations of Tone, has shown that this is
actually so.
By referring back to the records of hammer-stroke
we see that the more rapid the stroke, the shorter
the contact time. Consequently, loud tones (the
equivalent of great hammer-speed) will contain more,
and more intense, upper partials than the soft tones
(the equivalent of slow hammer-speed), because the
duration of stroke is less in the former than in the
latter case. Needless to say, all such variations
in contact time are very small, ranging approximately
between the limits of -ooi and -005 of a second, for
the middle and lower regions ; but this is ample time
to produce tonal differences when we consider that
fraction in relation to the rate of vibration of the
string.
Given the same intensity (force of stroke) for all
strings, each string will have its own contact time in
relation to its vibration time. Suppose the duration
of the stroke to be ^nr second. For a string making
30 v.d. per second, the ratio of contact time to vibration
time, which is the factor determining one phase of
tone-complex quality, will be -%-. For a string of
higher pitch, making, for example, 150 v.d. per second,
the ratio of contact time to vibration time equals
T V, for a string making 500 vibrations the ratio equals
I ; for a string of 1,000 v.d. it equals 2. Which
means that in the region of the contra octave, for the
theoretical force selected, the hammer would remain
102
VIBRATION OF THE STRING
in contact with the string for ^ of one vibration,
in the small octave for fV of one vibration. Near
C 2 it would remain in contact with the string for just
one vibration, and an octave higher the contact time
would equal two vibrations. But we know that
a change in the ratio of duration of stroke to vibration
time results in a change in tone-quality. This may
be seen from the following table, deduced by Helmholtz,
showing the varying intensities of the upper partials
for various intervals of contact time :
t
ft
i A
ft
instantaneous
Partials
near c"
near g f
i below c'
below c'
1
100
100
1 100
100
100
2
99-7
189*4
| 249
285*7
324*7
3
8-9
107'9
242-9
357*0
504*9
4
2*3
17-3
j 118*9
2598
504*9
5
1*2
0*0
| 26'1
108-4
324 '7
6
0*01
0*5
j 1-3
18*8
100*0
7
o-o
0*0
i 0*0
O'O
o-o
The fractions at the head of the columns indicate the ratio of the
hammer-contact time to the string-frequency.
Because of this variation in contact time, the
elasticity of the felt hammers changes for variations
in pitch. We find the more elastic hammers in the
bass region, where the duration of the stroke may be
relatively great and the more rigid hammer surfaces
in the treble region where shortness of duration time,
on account of the high vibration frequency, is essential.
Such differences as these tend, by keeping the ratio of
contact-time to vibration-time an approximate constant
for anv one degree of force, to neutralize the qualitative
tone differences which would otherwise result.
103
PIANO TOUCH AND TONE
The Material of the Striking Body. These qualitative
tonal variations are still further complicated by the
material of the striking body, the felt of the hammer.
This changes in hardness for every change in string
displacement, for as the string is driven aside it
compresses the felt, which in turn becomes harder.
The effect of the compressed felt upon the string, when
the latter is at the end of its displacement, is different
from the effect of the uncompressed felt at the
beginning of string displacement, for the hardness
of the acting surface has been changed. Fig. 44
illustrates what happens when a string is set into
motion by a perfectly hard (steel) hammer and a very
soft one (soft felt or rubber). These are the extremes.
The variations in the hardness of the felt still produce
these same differences in string movement, though,
of course, such differences are much less pronounced.
Now, the resultant tones of longitudinal waves thus
produced are high, being roughly comparable to the
high, partial tones of the transverse vibrations. The
unstability of the felt makes a numerical analysis
of these qualitative differences impossible.
The Striking Pl$ce. The striking place of the
hammer, unlike the factors we have just discussed,
is a constant for any one string, and consequently
no qualitative differences in the tones of that string
can possibly be due to the striking place. However,
its location, to of the length of the string from the
end, affects the "characteristic piano tone-quality"
by eliminating all partials having nodes at this
point. Only a small part of all the clang-tints,
or tonal qualities, which the piano string can give forth
can be obtained on the piano by means of the hammer. 1
Yet, within these relatively narrow limits, there is
1 It is theoretically possible that among the future improvements
upon the piano will be one which permits such a shifting of keyboard
and action that the hammer may strike the strings at different
places. The field of tone colour would be much enlarged thereby.
104
VIBRATION OF THE STRING
still room for rich varieties in quality as a result of
variations in intensity.
Pitch. The quality of a piano tone is further
influenced by pitch. Thus the treble region of the
piano differs in quality from the middle region, and
both of these from the bass region. The explanation
is simple. A short string cannot vibrate in as many
parts as a long string. This means that the strings
in the treble region do not produce as many upper
partials as do lower strings. Greater tension, too,
means less amplitude, and a quicker return of the
ConTre Octave /. //neefQcfoye
a & 6
FIG. 48.
string to its position of rest. Hence the duration of the
tones in the treble region is much less than the duration
of those in the bass region. We have then, not only
initial qualitative differences for every difference of
pitch, but we also have qualitative differences during the
life of a tone which are due to pitch, for the abrupt
diminuendo of a tone gives it a character different from
that of a very slow diminuendo. 1 Representing these
differences diagrammatically we should get for the
bass tone a figure such as a, Fig. 48, for the middle
region one such as b ; for the treble, one such as c.
RECORDS OF STRING- VIBRATION
If these theoretical deductions are true, then, when
we obtain actual records of the vibration of the piano
string we must find :
1 Not a little of the cliaim of certain piano compositions is the
result of the composers' effective application of these pitch
differences of quality.
105
PIANO TOUCH AND TONE
1. A different curve for every difference in intensity.
2. The same curve (excepting phase differences)
for the same degree of intensity.
3. More complex curves for loud tones than for
soft tones.
4. More complex curves for low tones than for high
ones.
5. Changes in the curve during the duration of a tone.
6. Marked differences as we approach the limit
of elasticity.
In order to secure tracings of the movements of
a vibrating piano string, a stylus may be attached
to the string and the vibrations recorded on an
appropriately prepared surface. The stylus in such
a case represents a point of the string. There are,
unfortunately, two important sources of error to
guard against in this method, the creation of false
wavelets by fluctuations in the stylus itself, and the
obliteration of essential characteristics by friction
between the stylus and the recording surface. One
cannot be overcome without increasing the other.
Thus, if we make the stylus more rigid we increase
friction, and if we make it more flexible we increase
its own fluctuations. For this reason it was necessary
to experiment with a number of styli, varying in
material, size, shape, and rigidity.
The curves obtained with a perfectly rigid stylus
naturally cannot contain stylus fluctuations. Some
light at least may be thrown upon the fluctuations of a
flexible stylus by attaching this to a vibrating bo.dy
whose exact mode of vibration is known (such as a
tuning-fork). In spite of these precautions, however,
the records shown in this chapter are not sufficiently
clear or accurate in detail to permit any analysis into
the component partials. Nevertheless, the method
employed satisfied the demands of our problem,
which was merely to show the central tendency of
106
VIBRATION OF THE STRING
variations in intensive and qualitative differences
resulting from pianistic touches, and not the precise
nature of them. Read figures from right to left.
Three strings in different regions of the piano were
used, the " f " below middle C, the " F " an octave
lower, and the contra " F " the lowest F on the key-
board. Two classes of measurements were made,
one showing variations in the duration of the same tone,
the other variations in the vibrations of the string,
PP
P
mp
Jff
FIG. 49.
immediately after hammer-impact, produced by inten-
sive differences and differences of touch. The records
were obtained by passing a piece of smoked glass
over the point of the stylus. The latter was attached
to the string at a point IT of the length of the string
for " f ", M for " F ", and f for " F x ".
Effect of Intensify on Amplitude. The first group
of records, Fig. 49, shows the effect of intensity on
the amplitude of the vibration of the string, which was,
107
PIANO TOUCH AND TONE
in the case here shown, " f " below middle C. As we
increase the intensity of the stroke, the distance
through which the string is displaced increases. In
other w r ords, the amplitude varies directly as the
intensity. The curves of Fig. 50 were made when
the string was repeatedly set into motion by the same
force, and prove the converse of this : that the same
force will always produce the same string displacement.
Whatever differences in intensity are transmitted
by the player to the key and hammer, the hammer
in turn transmits to the string, as the records of
Fig. 49 show. But since amplitude is the physical
basis for the sensation which we call " loudness ",
these differences are only differences in loudness.
FIG. 50.
Effect of Intensity on Quality. Fig. 49 also proves
the statement that for each change in intensity of
tone-complex, there is a change in quality of tone.
The latter, as we know, depends upon the presence
and relative intensities of upper partials. These will
show in little curves or wavelets along the main
curve, which corresponds to the fundamental tone.
In i, 2, 3 of Fig. 49 there is no evidence of irregularities
in the curve, excepting the one distinct one in the
middle. In 4, however, a magnifying glass will show
traces of such irregularities. In 5 they are plainly
visible, and in 6 they alter the contour of the curve.
This gradual increase in the amplitude of these small
108
VIBRATION OF THE STRING
curves means an increase in loudness of the upper
partials. In degrees less than " mf ", for example,
the higher upper partials are too weak to register
with the methods here employed. As we increase
the dynamic degree, the partials become more and
more distinct, adding their own tones to the funda-
mental and hence influencing the quality of the tone-
complex as a whole. A great number of records were
taken, and in no case was it possible to obtain as
complex a curve for the lesser dynamic degrees as
Tone deg/
/ second after
jf 5e co/7 c/^ affer
FIG. 51.
for the greater. For every degree of intensity, then,
we have a corresponding string-vibration which
means a change in tone quality.
Effect of Duration on Vibration. Since the piano
tone cannot be sustained at constant intensities,
intensive and qualitative variations must occur during
the life of a tone. Such variations are shown in
Fig. 51 and Fig. 52, recording respectively small
/ and contra F. First, there is the gradual decrease
in amplitude which means a diminuendo. This
decrease in tone does not occur evenly, for in Fig. 51
109
PIANO TOUCH AND TONE
the amplitude of the curves on the original record
are in inches -n ; -05 ; -02+ ; -02 ; *oi. Since
the time interval between any two successive
records was a constant (2 seconds) we have a much
more rapid decrease of tone immediately after the
beginning than afterwards. In fact, within a fraction
of a second the tone has dropped to within one-half
of its original loudness. Thereupon, it " dies out 3 '
much more gradually.
The qualitative variations occurring during the
life of a tone are shown in the various degrees of
complexity of the curves in Fig. 51 and Fig. 52.
Naturally, the most complex curve is also the loudest.
Just as the partials rise above the threshold of
audibility as we increase the tone, they drop below
this threshold as the tone diminishes, until, when
any tone is scarcely audible, the curve recorded is
a close approximation to a very weak sine curve
a curve free from all upper partials. This proves
that, on the piano, every tone-complex passes through
a series of qualitative changes depending in number
and kind on the initial intensity. For every loud
tone-complex this series will be both longer and richer
in variety than for a weaker tone-complex, since the
former has to pass through a greater number of
intensity gradations before it drops below the threshold
of audibility.
Effect of Pitch on Vibration of String. A comparison
of any curve for the / string, with that for the F
string, using the same intensity degrees, will show
clearly differences due to pitch variation. The
complexity of the curves increases as we pass from
higher to lower pitch. The highest string being
considerably shorter than the others, does not vibrate
as freely in small parts. Hence it produces fewer
upper partials and must be represented by a relatively
smooth curve. The curve for the lowest string,
no
VIBRATION OF THE STRING
on the other hand, shows the presence of numerous
and strong partials. We do not find the same ratio
for both strings between partials and fundamental ;
T0f?e
3 sec. after
8
/6
FIG. 52.
one does not increase in proportion to the other.
As we go from high to low, the intensity of the partial
increases more rapidly than that of the fundamental*
in
PIANO TOUCH AND TONE
This Is not the only effect of pitch on the vibration
of the string. Besides beginning differently, strings
of various frequency " die out " in various ways.
The tonal life of a short string is much less than that
of a long string. 1 This may be seen by comparing
Fig. 51 with 52. The duration of a tone, other things
equal, varies directly with the length of the string.
This may be seen in Fig. 53, which, represents the
3 This explains the absence of dampers for the very high tones.
112
VIBRATION OF THE STRING
approximate curves of duration l for a series of
" ff " tones sounding in four pianos of rather good tonal
quality in rooms with normal reverberation.
The Effect of Muscular Rigidity and Relaxation
on Vibration of String. Since it is generally assumed
among pianists and teachers that " set " muscles
produce a " poorer " tone quality than relaxed muscles,
a
6
FIG. 54.
a
FIG. 55.
records of the vibrations of the string were taken for
both forms of touch. They are reproduced in Fig. 54 and
Fig. 55, one pair for the string " f " and one for " F x ".
Again we notice what was shown in the records of
both key-depression and hammer-stroke, namely, that
1 The duration is the average of a number of judgments made by
an observer seated at the keyboard. There^were no disturbing
noises of any kind.
PIANO TOUCH AND TONE
muscular rigidity tends to produce a louder tone
than does relaxation. This is shown by the amplitude
of the curves, a and a recording the vibrations as
the result of a rigid tone-production, b and b
as the result of a relaxed tone-production. The
amplitudes of the former two curves are greater than
those of the latter two. Hence, the resulting tones
are louder. This difference was not present in all
the records taken, but whenever any qualitative
difference was present it always showed the rigid
tone-complex the louder. 1
Effect of Percussion and Non-Percussion on Vibration
of String. The records for key-depression showed
a decided qualitative difference between percussive
and non-percussive touches. The records for hammer-
stroke showed a slight difference. The records of
vibration of the string show no difference. Fig. 56
shows the vibrations for "1" and "F", obtained by
percussive and non-percussive touches. The two
forms of touch produce precisely the same vibration
form in the string. In the two records for the upper
string, even the intensity is the same. In the records
for the lower string the percussive touch is slightly
louder (greater amplitude) than the non-percussive
touch. This, it will be remembered, agrees with
the tendency mentioned in the chapters on key-
depression and hammer-stroke, namely, that when
there is any intensity difference between these forms
of touch the percussive is louder than the non-
percussive. If additional proof were needed of the
fact that there is no unbroken connexion between
the player's finger and the string, the records for
percussive and non-percussive touch would furnish
1 The cases where no physical difference was found, and in -which.
the subject still held that a difference existed, though the difference
was not noticeable to a trained musician who could not see the
player, can all be explained under the psychological aspect of touch
and tone.
114
VIBRATION OF THE STRING
such proof, because here we have a distinctly
characteristic motion imparted to the piano-key
and no trace of this motion imparted to the string.
Effect of Quality of Touch on String-Vibration.
In order to ascertain whether or not the manner
of touch such as " unsympathetic ", " forced ", or
" surface " touch has any effect on the vibration of
Percussive
/fan-percussive
Tauch
FIG. 56.
the string, a number of records were made for various
forms of touch. Fig. 57 and Fig. 58 show some of
the results obtained. The records were made by
experienced pianists. Fig. 57 shows a curve made
with normal relaxation, the so-called " sympathetic "
touch producing a good " singing " tone. The other
curve was made by " forcing ", producing a " harsh ",
PIANO TOUCH AND TONE
" unsympathetic " tone. When we compare the
curves we find that they are identical in form and
different in intensity. The " forced " tone was
somewhat louder than the " good " tone. Again,
we have a difference in intensity. 1 Fig. 58 shows the
vibration for a full, round tone (made with relaxation)
Tone
/VVVVW
FIG. 57.
FIG. 58.
and that for a tone made by dropping a fairly heavy
(lead) weight on the key. Notice that the curves
are qualitatively identical. Here we have a case
where all that the pianist can possibly do to make
1 The differences between these curves and some of the preceding
ones made on the same string are only differences of phase and do
not affect tone-quality.
116
VIBRATION OF THE STRING
a beautiful tone was done. On the other hand,
we have the most " impersonal " tone production,
a lead weight dropped upon the key. Yet, as far
as the effect on the piano string is concerned, it is the
same for both cases. The experiment was tried
repeatedly, always yielding the same result, a result
obtained also by other variations of touch. In other
words, the greatest possible variations in the manner
in which the player attacked and depressed the key
made not the least variation in the form of the vibration
of the string other than variations in amplitude.
Since tone-quality largely depends upon the form
of this vibration, we may conclude that, aside from
variations in intensity, no difference in quality exists
so far as the vibration of the string is concerned. 1
The difference in phase referred to in the preceding
paragraphs demands a little further explanation.
Fig, 59 shows the curve when the string is struck
a second time immediately after the first time. The
vibrations from the first stroke have scarcely
diminished when a second stroke renews them.
Suppose, now, that the string is just about to ascend
on one of its vibrations when the hammer re-engages
the string. Naturally, since hammer and string
are moving in the same direction, the resultant force
will be the sum of the separate forces. This is what
occurs in a of Fig. 59. The string is about to ascend
as the hammer re-engages it, producing a greater
displacement. In b of the same figure the hammer
chanced to strike the string as the latter was descending,
In such a case the two forces are acting in the opposite
directions, and produce a curve of less amplitude.
On the other hand, the sum of the two equal loops
of curve b equals the sum of the large and small
loop of curve a. The fact that these curves are
1 The effects of touch upon tone-quality are traceable to other
factors.
117
PIANO TOUCH AND TONE
different from each other does not mean that they
produce tones of different quality, because, as Fig. 59
shows, the differences may be due to variations in
phase only. Such differences in phase are easily
discernible. However, although two different curves
may contain the same number and intensity of partials,
any one curve can be composed of but one definite
series of partials. Hence, when two curves are
alike they can produce one tone-complex and one
only. Although Fig. 59 shows that two curves of
different amplitude may yet be tones of equal loudness,
t
FIG. 59.
it also shows that every such increase in amplitude
means a change of form what is added to one wave
must be taken from another. Consequently, when
we have two curves differing in amplitude, and yet
having the same wave form, we know that one tone
is louder than the other, and that both are of the same
quality.
Extreme Vibration of the String. The observations
made in the preceding sections of this chapter are
true for all vibrations of the piano string from
pianissimo to fortissimo. In practice, however, a
string is often struck such a forcible blow that a distinct
change of tone quality suddenly occurs. This degree
118
VIBRATION OF THE STRING
of intensity we might call sffff. (Rachmaninoff,
for example, in his C- minor Prelude, calls for sffff.)
It forms the one exception to the normal string-
vibration. In the experiments with fortissimo tones,
it was repeatedly found very difficult to secure clear
tracings. The form shown in Fig. 60 was usually
obtained. Such a curve can only be produced if
the string vibrates out of its normal vertical plane.
This seems to be what actually happens. Moreover,
it vibrates very regularly in the new plane, which
is parallel to the cross-section of the string, as may
FIG. 60.
f - 4 - j - 1
FIG. 61.
be seen by the regularity with which the " skip "
in the curve of Fig. 60 occurs. In other words, the
manner in which the string is fastened in the piano,
the properties of the string itself, and the manner in
which it is set into motion, combine to set a limit to its
free, vertical displacement. When the string is driven
beyond this, something similar to torsion takes place
and causes it to vibrate in a different manner. No
matter how much additional force we add beyond
fortissimo, we cannot increase the vertical displacement
of the string. This is shown in Fig. 61, which records
119
PIANO TOUCH AND TONE
the amplitude of the vibrations of the strings " i " and
" F " f or the various dynamic degrees indicated. Beyond
ff the amplitude does not increase. When such
extreme vibrations are recorded upon a moving
slide we get the curve of Fig. 62. This is interesting
for two reasons : it shows for " f " below middle C the
same amplitude as the ordinary " ff " curve, but in
addition we find that it no longer retains its former
shape, but begins to approach the form for the lower
strings. 1 That is, high partials become increasingly
FIG. 62.
FIG. 63.
FIG. 64.
prominent, and hence the quality of tone is different.
But this is not all. By counting the number of
" gaps " in the curve of Fig. 60 we find that there
are 6 gaps to 7 parts of the curve proper, which
produced a high (unmusical) partial of its own.
The cross-sectional vibrations, as they may be
called, occur regularly, repeating their path just as
the transverse vibrations. Fig. 63 which shows
3 This proves that these wavelets are not the result of stylus
fluctuations.
120
VIBRATION OF THE STRING
this fact may be better understood by imagining-
the string cut in two, while vibrating, and one end
tracing its motion on the smoked glass. The reader,
in looking at Fig. 63 is looking directly along the
string. The lowest dash (left column, practically
a point) represents the vibration for pp, the dash
above this, the vibration for p. Counting upward
in this manner the next dash corresponds to mf \
the fourth to / ; the fifth to ff ; the sixth and seventh.
to sfff. Up to and including ff, we have normal
increase in amplitude with vertical vibration only.
For sfff the vertical line in the right-hand column
is replaced by an approximate loop. As the left-
hand column of Fig. 63 shows, it was impossible to
obtain this mixed vibration for the low F string,
because this demanded a force which threatened
to break the piano hammer. Fig. 64 gives several
clearer records of the form of the cross-sectional
vibrations for the upper string (" i " below middle C).
As is readily seen, this form closely resembles the
mirrored capital letter P in script.
The details of the foregoing analysis of the vibrations
of the piano string, both moderate and extreme
vibrations, should not be accepted as proved until
further, more extended, and a mechanically more
accurate study of this phage has been made. However,
the records show the one possible condition under
which we can have a change in tone-quality without
a change in amplitude of string vibration. This
dynamic degree (sfff), however, is beyond the range
used for normal purposes, and hence finds very limited
use in artistic piano playing.
Other Modes of String-Vibration. The fact that the
mechanical construction of the piano permits only
a few of the many possible vibration-forms of the
string to be utilized has already been mentioned.
In addition to the types of string-vibration obtained
121
PIANO TOUCH AND TONE
by varying the force of hammer-impact, two other
types are used, namely those corresponding to the
" una corda " pedal, and the harmonic use of the
string. When the una corda pedal is depressed,
the action of a grand piano is shifted laterally so that
a different, naturally softer, part of the felt hammer
surface comes into contact with the string. The
result is a tone of veiled quality similar to the con
sordino tone of the violin group of instruments. This
softness of tone is in part the result of the damping
of the higher partials by the softer felt. Accordingly,
we should expect a somewhat smoother curve for such
a vibration. Figure 65 shows the curve obtained
FIG. 65.
with the una corda pedal on a piano the hammers
of which were sufficiently worn to make the difference
between una corda and ire corde fairly pronounced.
On a new instrument, if the harmonic vibration
of the third string be damped, no difference between
una corda and ire corde is heard because the hardness
of the striking surface of the hammer remains unaltered.
The curve of Fig. 65 is interesting because it shows
the smaller wave in the centre less clearly defined
than that in the records thus far studied. This curve
begins to approach the sine curve more closely, and
hence produces a physically, not musically, somewhat
purer or softer (less rich) tone.
Another type of string- vibration used in the piano
is the harmonic vibration of the string, which is an
example of sympathetic resonance. In this case,
the string vibrates not by being set into motion by
the player, but in response to the vibration of
some other string bearing the proper relationship in
122
VIBRATION OF THE STRING
frequency to it. The third string, where there are
three strings to each tone, when we play una corda,
vibrates harmonically. And when the damper pedal
is used, many strings vibrate harmonically. Fig. 66a
and 6, shows the curve for strings so vibrating, a for
small/, b for contra F. Here we have areally qualitative
variation in tone, an addition of a tonal element which
can only indirectly be traced to intensity. Since,
however, the use of this vibration form depends
upon either the una corda or the damper pedal, it cannot
directly be influenced by the key-board touch of the
player, and hence forms no exception to the general
6
FIG. 66.
rule that the sole variations in tone through touch
are intensive. A possible exception is found when
the player silently depresses certain keys in order
to secure the harmonic vibrations of the corresponding
strings. But these and other similar types of key-
manipulation are special forms which act only as
accessories. The principle remains unaltered.
Sources of Error. Since most of the records here
reproduced were made with a rigid stylus, 1 we may
disregard as a source of error stylus fluctuation.
There remains the possibility that friction has destroyed
1 A stylus so cut that fluctuations In a vertical plane were
practically eliminated. Needless to say, hundreds of trials were
necessary" before the friction was sufficiently reduced.
123
PIANO TOUCH AND TONE
the essential characteristics of the curves. As far
as the deductions made in this chapter are concerned,
this defect may be, in general, ignored. This is true,
in the first place, because the method used was
sufficiently refined to record very soft tones (see
Figs. 5i, 52g) ; and, consequently, any vibrations not
recorded would probably be too weak to reach the ear
and thus to influence quality. In the second place, the
records obtained agree perfectly with the theoretical
deductions and the records of key-depression and
hammer-stroke, which argues for their reliability.
In the third place, several styli of various materials,
rigidity, and shape were used, permitting comparison ;
and again, the same stylus was used in order to keep
fluctuations constant. In the latter case differences
in two curves could hardly be due to fluctuations
of the stylus. Nevertheless, the records obtained
are not accurate in detail, and are meant to show
central tendencies, not absolute values.
Complexity of the Piano Tone. The complexity
of the vibration of a piano string may be observed
with the eye aided by a magnifying glass. If a beam
of bright light be thrown against a part of a piano
string which has been covered with lampblack so
that only a fine horizontal line remains exposed,
a most interesting and quite wonderful play of lines
may be seen when the eye is so placed as to catch
the reflected ray. In addition to the maximum
string displacement, a number of smaller displace-
ments, constantly changing, are seen. Fine lines
seem to run back and forth, some more rapidly than
others, and all within the two apparent edges formed
by the maximum transverse displacement. An
incomplete picture of this phenomenon may be seen
in Figs. 6ja, b, c, d t which shows photographs of one
of the G strings below middle C, in vibration ; a,
immediately after tone-production (ff) ; 6, a little
124
FIG. 67
[face p. 124
VIBRATION OF THE STRING
over a second later, c about 2 J sec. after a ; d about
3Jf sec. after a. In the first picture, the brightest
line is at the top edge and a faint line at the lower
edge. In b, several faint lines are seen between the
extremes, and the brightest line which, in a, was at
the top, has now descended to a point near the middle.
c shows the bright line at the lower edge, d shows
the same line beginning its return upward ; it is just
leaving the lower edge. This motion continues with
modifications until the string comes to rest. In
addition to a bright line there are other, fainter lines
running back and forth in the vertical plane at greater
or less speed, too faint for the photographic method
here adopted to portray.
Needless to say, these movements vary with each
string, and somewhat with each degree of intensity.
The fact that there are lines of various brightness
is also significant, for the brighter the line the longer
has the string remained at rest in its vertical plane.
Since the play of lines is continuous, but does not
repeat itself from moment to moment, it follows
that the character of the vibration of the string also
changes from moment to moment. This is additional
proof of the changing quality of a piano tone. The
records also indicate the irregular diminuendo of the
piano tone ; they show that in a very short time after
its production the amplitude has dropped to about half
of the original. Then it decreases much more slowly.
A number of general observations was made in
order to ascertain the effect, if any, of variations in
touch upon the vibration of the string when observed
in this manner. The results were in accord with
those obtained by the stylus method. In other words,
when the intensity was the same, the mode of string-
vibration, as seen in the line movements referred to,
was also the same.
125
PIANO TOUCH AND TONE
CONCLUSIONS
From the records obtained showing the vibration
of the string, we may conclude that, so far as the
mechanically rather unrefined method of procedure
permits analysis :
1. For every degree of pitch there is a different
quality of tone-complex.
2. For every degree of intensity there is a different
quality of tone-complex.
3. The same degree of intensity always produces
the same quality of tone-complex when measured
in terms of string-vibration.
4. The vibration of the string is independent of
the manner of touch, excepting for variations in
intensity.
5. The duration of tone varies with pitch as well
as with intensity.
6. The quality of a tone-complex changes from
each moment to the next.
7. The mode of vibration of the string changes
radically as we approach the limit of elasticity of
the string.
8. Tone-production with " rigid muscles " produces
greater amplitude of string-vibration than relaxed
tone-production ; hence it produces a louder tone-
complex.
9. Percussive and non-percussive touch normally
produce no difference in string-vibration. When
there is a difference, percussive touch produces the
greater amplitude.
10. When intensity remains constant, the string
vibrates exactly the same for " harsh ", " brittle ",
"full", "good", and "bad" tones. Hence, such
qualitative differences cannot be caused by the
vibration of the piano string.
126
CHAPTER VII
THE VIBRATION OF THE SOUNDING-BOARD
THE vibrations of the piano string are transmitted
through one end of the string to the bridge.
The latter is a block of wood appropriately shaped
to receive the various lengths of strings corresponding
to variations in pitch. It is firmly fastened to the
sounding board and acts as the connecting link between
string and sounding-board. The latter consists of
a series of carefully selected pine boards about J inch
thick. These are firmly joined to make a wooden
plate of the shape and size of the piano case. In
order to keep this plate from " sagging " in the course
of time, it is given a slightly convex form, and is
reinforced by from 8 to 12 strips of wood which are
attached transversely to its lower surface. The sounding-
board is then fastened permanently to the outer
case of the instrument. We have to investigate, there-
fore, a vibrating plate with fixed edges.
Although the complete analysis of vibrating plates
is a very complex and difficult problem, certain
general laws have been definitely proved. These
may be summarized in this statement : the vibration
of a plate varies with its size, shape, thickness, position,
and material, and with the mode of generation.
From this fact, the complexity of the vibrations
of the piano soundboard may readily be imagined.
The latter is of irregular shape, of various thicknesses
(since the bridge and ribs are firm), and must respond
to tones of various pitches. No sounding-board at
present in use fulfils all requirements equally well
The thicker we make the board the more we
127
PIANO TOUCH AND TONE
reduce its displacement, and hence the shorter do we
make the tone-complex. The thinner we make
the board the more we increase its tendency to sag,
.and hence to destroy the quality of the tone-complex.
Moreover, each board has its own natural periods
of vibration, which means that it will respond better
to some pitches than to others. 1 This last-mentioned
phenomenon is illustrated by the curves of Fig. 53,
which show the duration of tones selected at equal
intervals for the entire pitch region. With perfect
construction there should be a steady decrease from
bass to treble. Instead, we have numerous crests
and troughs. Since all tones were struck with the
same force, these differences may be assumed to be
in part the result of differences in resonance. If we
assume the strings to be of uniform variation, the
longest tones will be those most nearly corresponding
to the natural periods of vibration of the sounding
board, the shortest ones those having a frequency
not possessed by the sounding board. Of course,
rsince we are dealing with a case of forced resonance, 2
the sounding board responds in a greater or less degree
to all the tones ; however, the difference within these
limits is often sufficiently pronounced to influence
the quality of the tone-complex. This anyone can
observe by slowly playing "fortissimo" each tone
throughout the pitch region ; some sounds of beautiful
richness will be found, others of duller quality, a
difference, however, that might also result from
-variations in felt or in strings.
The "tone" that we "hear" when listening to
a piano is not that produced by the vibration of the
string, but that produced through the vibrating
string by the vibrations of the sounding-board plus
the phenomena discussed in Chapter X. Hence,
1 This is the result of resonance, which, is explained in Chapter X.
2 For explanation see Chapter X.
128
2
VIBRATION OF THE SOUNDING-BOARD
a survey of the vibrations of the sounding-board is
necessary. On the other hand, we may dispense
with an experimental procedure, since, regardless
of the process of reinforcement and selection which
the tone undergoes at the hands of the sounding-board,
these variations are beyond alteration by the touch
of the player, and it is the effect of touch upon tone
with which we are primarily concerned.
The sounding-board can add no new vibrations
to those which it receives from the strings. It merely
transmits them to a larger surface of air. Tone
production, so far as it may be influenced by the
touch of the player, ends with the nature of the
vibration of the string.
The vibration of the sounding-board is limited by
its fixed edges. Within these limits, however, as
we have indicated, there is variety of response. On
the other hand, the relation of the vibrations of a given
sounding-board to tones of the same pitch, produced
on the same instrument, is a constant. It does not
respond differently to the same tone. This definiteness
of response explains why we attribute to the string the
sound which we hear. As a matter of fact, the tone
produced by the vibrations of the string alone, as
may be observed on the monochord, has very little
similarity, indeed, to the piano tone heard when
reinforced by the sounding-board.
Not all parts of the sounding-board vibrate with the
same degree of freedom. Generally speaking, the
points of least vibration are those near the fixed
edges, those of greatest vibration near the relatively
free centre of the board. This scale, however, is
further complicated by variations in thickness ; for
instance, such points as the application of the bridges
and the ribs. And since the bridge is firmly fixed
throughout its length to the sounding-board, the
vibrations which it transmits are not transmitted
129
PIANO TOUCH AND TONE
through one point only, but through all points,
although not equally through all points. For each
string vibration we have the complex vibration of
the entire sounding-board. This in turn varies
for tones of various pitches and intensities, but remains
constant, on the other hand, for any one tone, enabling
us to grade the tone as desired. A certain force
produces a certain effect.
The vibrations which the sounding-board transmits
to the adjoining air are, therefore, exceedingly complex.
The air next to various parts of the sounding-board
is not set into vibration in precisely the same manner
for all parts of the board. This complexity would,
perhaps, influence the tone quality were it not for
the equalizing effect of certain phenomena treated
in Chapter X.
130
CHAPTER VIII
TONE COMBINATIONS
T TP to the present point our inquiry has dealt almost
^ entirely with the single tone. This apparent
restriction was advisable for two reasons : the single
tone is fundamental ; and every physical attribute
of any combination of tones can be traced to some
attribute of the single tone. Analysis will make
this clear.
The condition of tone-combination most closely
approximating single tone-production is the successive
sounding of two tones with a greater or less interval
of silence between. Physically speaking, this is
merely a repetition of the process which accompanies
the production of a single tone at a greater or less
duration, higher or lower pitch, or at a greater
or less intensity. No new physical qualities are
introduced. The same condition prevails when the
second tone begins just as the first tone ends. These
two examples, the second of which is diagrainniatically
illustrated in A, Fig. 68, illustrate non-legato and legato,
neither of which contains any physical element that '
is not present to the same extent, and in the same
form, as in the single tone.
As soon as two such tones overlap, the second
beginning before the first ends, we touch upon an
inexhaustible field of tone-colour. Even for the same
two tones a different combination results from each
variation in the degree of overlap, because the piano
tone is never constant, but changes its contour from
each moment to the next. 1 This variation may be
1 See Chapter VI, pp. 124 1
PIANO TOUCH AND TONE
seen in Pig. 68 6,0,0. The differences in the heavily
shaded portions show the differences in the co-existing
tones or tone-complex.
The overlap is not the same for differences in pitch,
because the duration of a tone (hence its rate of decay)
varies ior every variation in pitch.
FIG. 68.
In other words, two pairs oi tones of equal intensity
and equidistant apart (in duration) ,but indifferent pitch
regions, will not result in the same colour combination,
because theamounts oi co-existent tone -will differ. Two
132
TONE COMBINATIONS
tones in the great octave, for instance, will overlap
when played forte, if the second is sounded a quarter-
minute after the first. In the fourth-lined octave
two tones played forte at an interval of five seconds
will not overlap. In the former case we have co-
existing tone, in the latter, we have not. These
differences are shown in Fig. 69 A, B, C.
FIG. 69.
When the time-interval between the two tones
becomes zero, we have perfect overlap, or the condition
resulting when two tones axe struck simultaneously.
Again our resources of tone colour are greatly enriched,
since a new colour is produced with the slightest
variation of intensity in either tone, or in
both tones, apart from all the varieties of pitch
changes which we have discussed. Tones struck
simultaneously illustrate the condition known as
harmony, as opposed to melody. Harmony in a
physical sense, therefore, is nothing more than simul-
taneous melody ; and melody is merely successive
harmony. Qualitative differences in co-existent tones
resulting from intensive variations are shown in
Fig. 70.
133
PIANO TOUCH AND TONE
Now, since a single tone on the piano may vary
in intensity, pitch, or duration, but in no other funda-
mental way a fact proved both positively and
negatively in the preceding chapters it follows that
any other tone taken separately, cannot vary in any
other way ; for all the keys and strings of the piano
operate on the same principle. It is known that we
do not play a group of keys in the same manner
as we play a single key. But it is entirely wrong
to assume that this difference introduces physical
elements not present when a single key is depressed.
We cannot in any way alter the mechanism of the
FIG. 70.
piano by touch. The attributes of the individual
key remain constant ; what we change is the relation-
ship of the attributes of one key and the resulting
tone, to those of a second or third key and tone.
And the only physical qualities here present
are pitch, duration, and intensity. Therefore, what-
ever variation of tone-combination exists, whether
it is purely qualitative or not, must be produced by
variations in one or more of these three fundamental
attributes, to which every device of piano technique
may be reduced. All dynamic variations, including
134
TONE COMBINATIONS
the artistic " bringing out " of a melody against
an accompaniment, are variations in tone intensity.
All rhythmic variations, including the finest shades
of rabato, are variations in duration (time-interval).
In practice any one form seldom appears separately,
the three types of variation intensity, duration,
and pitch generally occurring concomitantly.
As we increase the number of tones sounded, we
complicate and refine the colours, but we do not add
any new fundamental element. Three tones are
produced precisely in the same manner as two, four as
three, so far as the physical aspect of touch or tone is
concerned.
There are, however, certain physical phenomena
beyond the direct influence of the player, the result
of combinations of tones, which cannot be said to
exist for the single tone. 1 These are beats, summa-
tional tones, and differential tones. When two tones
whose frequencies are nearly equal sound simul-
taneously, certain fluctuations or pulsations of
intensity are produced. This is a primary condition
similar to the secondary condition of beats discussed
under reflection in Chapter X. When these beats
occur at a slow rate, they are heard separately ;
when, however, they become so rapid that the ear
cannot separate them, they give the sound a dis-
agreeable roughness. When they increase still
further in number, they produce the musical effect
known as dissonance. Also, when two tones are
produced simultaneously, they create tones other than
their own. The pitch of one of these tones is the
difference between the frequencies of the two con-
stituent tones, and the tone is known as a " difference
1 In the last analysis they are present also in the single tone,
for, musically speaking, there is no single tone. Every musical
tone is complex, and the fundamental and partials contain in
miniature the phenomena here referred to.
135
PIANO TOUCH AND TONE
tone " ; the pitch of the other, the " summational "
or " combinational " tone, is the sum of the frequencies
of the two constituent tones. Both beats and these
additional tones contribute their share to the quality
of the tone-complex. But it must be remembered
that these new tonal elements are themselves possessed
of only the three attributes, pitch, duration, and
intensity, and that the intensity of beats and additional
tones depends upon the intensity of each of the con-
stituent tones. Any change in tone-quality of any
combination of tones is the result of a change in tone-
quality of one or more of the constituent tones, which,
in turn, is the result of variations of intensity, pitch,
or duration.
The variety of tone combinations is further enriched
by the use of the pedal. 1 The damper pedal enables
us, first, to prolong a tone or tones which we could
not prolong by holding the keys with the fingers,
and, secondly, to add other tones to the tone-complex
than those corresponding to the keys struck with the
fingers. In a physical sense, and in sound, the
prolongation of a tone by means of the pedal is iden-
tical with the prolongation by key-depression. The
difference is purely a technical matter, and need not
detain us here. The other effect, that of colour,
is distinctly a physical addition. It is a conspicuous
and beautiful example of free resonance. 2 Thus,
when the pedal is depressed, and a string is made
to vibrate, other strings, twice, three-times, four-
times, one-half, one-third, one-fourth, etc., as long,
also begin to vibrate " sympathetically ". The
" sympathetic " vibrations of a string one-half as
long as the string struck are shown in Fig. 66a.
1 The sustenuto pedal has the same prolongation effect in principle
as the damper pedal, but only possesses the colour effects of the
latter to a small degree.
* Contrast this with the forced resonance of the sounding-board.
136
TONE COMBINATIONS
Naturally, each one of these added tones enriches
the original tone, so that a tone-complex of great
beauty results. But here again the strength of these
" harmonics ", as they are called, depends upon the
intensity of the original tone or tones, and since the
relative intensity of the partials is fixed for any one
instrument, and is entirely beyond control of the
player, except in intensity, all pedal effects of colour
are entirely the result of intensive differences of touch.
Even the differences noticed when the moment of
pedal depression is either retarded or advanced
may be traced to intensive differences. A pedal
depressed early in the life of a tone produces rich
" harmonic " colour, because the intensity of the
original tone is great. A pedal depressed late in the
life of a tone produces less effect because the original
tone is itself weak.
The extent and variety of these tonal additions
through the use of the damper pedal are realized
when we remember that this pedal device causes
from two to ten or more tones to sound when a single
key is depressed, and that each one of these tones
can vary as did the single tone which we have
discussed. Moreover, pedal-action is dependent upon
pitch, intensity, and duration for its effect ; close
and dispersed harmony, chords, and arpeggios, soft
and loud tones, produce each its own effect. Not
only that, the tones which the damper pedal adds
have not all the same duration or intensity. Con-
sequently, their rate and manner of decay will vary,
adding yet other elements to the variability of the
tone-complex.
The beauty and richness, as well as the variety
of pedal effect are readily demonstrable. A few
examples which any one can observe for himself,
will give a glimpse into this field of tone colour.
Silently depress the key corresponding to Contra C
137
PIANO TOUCH AND TONE
and hold it. Play an arpeggio of the C major triad,
ascending and descending once or twice, through
two or three octaves, forte. Release the pedal
immediately. The single string (Contra C) will now
sound the major triad.
Silently depress all of the white keys in the contra
octave. Play, as before, a C major arpeggio. Release
the pedal immediately. A very beautiful, ethereal
tone-complex will be heard from the low octave,
the keys of which are still held.
The damper pedal may even produce melodic
effects. The closing measures of MacDowelTs " To
a Wild Rose " are these :
FIG. 71.
If the damper pedal be taken as the F* is played
and be then released at the beginning of the next
measure, the ear hears the F ft apparently descend
into the E, resolving the dissonant seventh chord
into the major triad a subjective, not physical,
melodic resolution made entirely with the pedal.
These examples will suffice to show the qualitative
tone possibilities of the damper pedal.
A study of the use of the pedal emphasizes again
the importance of intensity gradations. To lay down
the general law that the pedal must not be held through
a change of harmony is wrong. Whether or not the
138
TONE COMBINATIONS
effect will be musical, will depend, among other things,
upon the absolute and relative intensities of the
component tones of the tone-complex. The subtle
pedal effects which lend the art of some of our pianists
such a charm, are secured less, perhaps, by variations
in the length of pedal depression than by appropriate
variations in the intensities of the tones during pedal
depression. The effect, for example, of the accompani-
ment of Chopin's " Berceuse ", is not primarily due to
a pedal held throughout each figure, but to the intensity,
at which the notes of this figure are played. If
the tones are soft enough, and then the pedal be held,
a beautiful veil will be thrown over the composition.
Not that duration of pedal is unimportant ; we
find this point discussed at length in all treatises
on the pedal, yet we seldom find the important
bearing of tonal intensity upon the use of the pedal
emphasized. Pedal effects, then, do not introduce
any difficulties into our analysis, since pedal effects, too,
are seen to be the result of variations in the pitch,
duration, and intensity of the tones themselves, these
being, finally, the three basic elements that determine
all laws of pedaling.
The effect of the una corda pedal upon tone colour
is different. This pedal shifts the entire action l
sidewise so that a comparatively unused part of the
felt hammer strikes only two of the three strings
for each tone. Two effects result. The softer felt
tends to dampen the partial vibrations of the string,
thus softening the tone-quality 2 ; and the third string,
since it is tuned in unison with the others, vibrates
harmonically as a result of sympathetic resonance
and adds its tone to the other, A combination of
such tones obeys precisely the same laws as tones
1 Of course a grand piano is meant. On an upright piano the
pedal action works on a different principle.
* Also, in part, on account of variations in the noise element.
139
PIANO TOUCH AND TONE
produced without pedal. We have merely altered
the basic tone-complex. The variations which this
may undergo must be produced in the same manner
in which the variations of the basic tone of three
strings was produced, for the key and hammer action,
once the soft pedal has been depressed, are constants.
The effect of the una corda pedal on a new
instrument is never so pronounced as that on a used
instrument ; because, in the former, all parts of the
felt hammer possess the same degree of elasticity.
Therefore, we do not alter the striking material as we
do in the case of the used hammer.
Tones, then, can be differently combined only by
varying pitch, duration, or intensity. There is no
further physical variant either for simple combination
or for the most subtle dynamic, rhythmic, or " poetic "
shading. This conclusion applies as well to a
Beethoven Sonata as to a few tones, for physically
speaking, a Beethoven Sonata is but a combination
of many single tones, of definite pitches, durations,
and degrees of intensity.
The question may be asked : "If this be true,
why do we differentiate between the playing of a
mechanical player-piano and that of an artist ? "
The answer is that the player-piano has not yet
reproduced accurately all the physical sound elements
which constitute the piano sound-complex, and on
the other hand has added sounds of its own, such
as the " whirr " of the motor and roll. If the playing
of the artist is to be accurately reproduced, impact
noises, among other things, and not merely the tonal
elements must be reproduced. The fact that player-
pianos have not yet solved the problem entirely
is not an evidence of some subtle influence which
defies recording, but merely an indication of mechanical
imperfection which, so far as physical elements are
concerned, may eventually be overcome. For it is
140
TONE COMBINATIONS
entirely wrong to suppose that the physical variations
alone are too coarse to explain the artistic side of
piano playing. They may be coarse, but in the hands
of the artist they may be, in fact, they actually are,
extremely fine. We need only consider the analysis
of the sound-complex on page 89 to see what great
variety of combinations of elements are possible for
the single tone. And when this tone itself is but
a small part of a musical phrase, the possible com-
binations are greatly multiplied. In order better
to realize this richness of purely physical variety,
let us select at random, a comparatively simple
example : two measures from the E minor Nocturne
of Chopin.
FIG. 72.
The passage may be played with the following
variations :
Dynamic :
R.H. Accentuation of the highest notes, the middle
or the lowest, as melody.
Accentuation of two tone lines at the same time
as contrasting melodies.
Crescendo and diminuendo in any one or more
melodies.
L.H. Throughout ppp, pp, or p.
Accentuation of the upper B first measure, O*
second measure, as a sort of bell effect.
141
PIANO TOUCH AND TONE
Accentuation of the descending diatonic figure
as secondary melodic fragment.
Accentuation of the lowest E.
Agogic :
Delay upon almost any beat or sub-beat in the
first measure.
Delay upon several points, such as the first beat,
the second, for the introduction of the G#, and the
first beat of measure two, for chord emphasis and
melodic distribution of the grace-notes.
Pedal:
With or without the una corda pedal, using the
damper pedal in any of the methods indicated in
the figure.
Even if we use only one of the variables enumerated,
keeping the remaining ones constant, we produce
a specific tone-complex for each separate variation.
Moreover, the degree to which the player introduces
these variations, whether the accentuation or retarda-
tion be slight or pronounced, again produces an
entire series of tone -complex gradations. Here,
then, in two measures alone, variations in intensity
and duration readily permit more than a score of
possible executions, none of which will overstep the
bounds of musical propriety, and each of which
contains some element of artistic shading.
If we approach the problem from the other side,
that of actual records made by prominent pianists,
we shall find further evidence in support of the assump-
tion that the artistic or poetic phases of piano playing,
so far as they affect our ear, are due entirely to varia-
tions in intensity and duration. In each record
of artistic playing we find these variations. The
following tables and graphs illustrate some differences
in duration. Table i represents the first two measures
of Chopin's Nocturne in G major, Op. 39, No. 2,
the notation of which is shown in Fig. 73A. The
142
TONE COMBINATIONS
figures of this and of the succeeding tables were
deduced as follows : that time-interval occurring
most frequently for the note-value most often used
(in this case the eighth-note), was selected as the
standard time-value for that note-value. Then
the percentile deviation of all the other notes from
this value was calculated. The left-hand column
shows the values as written by the composer, the right-
hand column the deviations as played.
And ant i no
sempre legato
TABLE I.
right hand. left hand.
FIG. 73A.
TABLE II.
MELODY right hand.
TABLE III.
'40
40
"20
20
20
*175
20
20
20
25
1-20
1'35
40
50
20
20
20
15
20
20
20
20
45
50
45
35
45
40
45
*45
45
45
45
35
45
45
45
40
45
45
45
50
45
40
*45
45
32
38
32
33
48
'48
16
19
16
16
16
15
16
20
16
25
48
42
note
rest
note
rest
note
rest
aote
rest
note
rest
aote
rest
note
5
5
5
45
5
5
'5
45
5
5
'5
40
5
65
*5
40
5
-90
5
15
5
90
5
50
5
1-50
143
PIANO TOUCH AND TONE
The considerable amount of deviation is seen more
clearly if we array the figures in the form of a graph,
such as the following, Figs. 736 and c, in which the
dotted line represents the note values as written,
FIG. 73B.
FIG. 73c.
and the solid line their value as actually played by
the particular artist making this record. The spaces
between the lines show the amount of deviation.
Table II represents the melody tones of the first few
144
TONE COMBINATIONS
measures of the slow movement of Beethoven's Ci Sonata
Pathetique", Op. 13, Fig. 74. The standard time
unit adopted is the most frequently found value for
the sixteenth note of the accompaniment. When
,,j i
FIG. 73D.
Adagio cantabile
'
FIG. 74.
* Andante
FIG. 75.
thus measured the record gives the percentile array
shown in Table II. This deviation is also shown for
Fig. 75. Even in this relatively simple and uniform
145
PIANO TOUCH AND TONE
passage we find such deviations. Thus Table III
shows the results when we analyse the first measure
(uppermost note) of Mendelssohn's " Rondo Cap-
riccioso ".
Many more records could be quoted. Those selected
are typical instances, made by the best-known artists,
and do not represent extreme cases. They suffice
to show that in each instance there is variation from
the printed score. At once the objection will be
made that just because such records record only
the physical elements of the pianist's art, and not the
" personal " element, we are able to distinguish
between the playing of an artist and the reproduction
of his playing by a player-piano. This objection
has been answered elsewhere. Moreover, be that
as it may, what we establish here is that every artist
does so deviate from the printed score, and what is
more, no two artists deviate in the same way ; that is,
these deviations are " personal " through and through ;
the artist is directly reflected in deviations in intensity
and duration. Finally, experiment has shown also
that when these dynamic and temporal deviations
are eliminated, the " poetic " or expressive character
of the performance is lost entirely. All of which
points to a scale of intensity and duration, that is,
to a purely physical basis, for artistic effects on the
piano.
And when, finally, the problem of artistic shading
is adequately investigated, the poetry of the pianist's
art, as is indicated in the records described here
and in preceding chapters, so far as poetry is trans-
mitted by sound, will be found in just these fine
gradations of intensity and duration, not in the manner
in which fingers and hands are used, nor in any psychic
element mysteriously transmitted through the key
to the tone.
146
CHAPTER IX
THE NOISE ELEMENT
INASMUCH as we do not find In music a theoretically
*- pure tone-complex, that is, one produced without
noise, the analysis of the noise element becomes
a necessary part of our inquiry. In wind instruments
the noise element is present in the hissing of the
air, in bowed instruments in the scraping or scratching
of the bow, in percussive instruments in the percussion
or impact of one part of the instrument against
another. It results from non-periodic vibrations.
In order to establish the influence of the noise element
upon piano-sound, as produced in normal playing,
it is necessary to separate the noise element from the
tonal element. This can be done by damping the
entire set of strings with numerous small sandbags,
felt, and weights. The damping must be continued
until all indications of pitch vanish. 1 This procedure
was followed in the experiments here described-
Later on, as the various noises were investigated,
each one of these was isolated in its turn by appropriate
manipulation of the parts of the piano-action. No
attempt was made to eliminate the vibration of the
sounding-board or the reverberation, since both factors
are present in normal playing.
If we exclude the unstable noises, such as sympathetic
resonance, etc., outside of the instrument, which are
largely due to local conditions, and instead, consider
those noises present in great or small degree when
1 A good test is to play a chromatic scale / or ff throughout
the compass of the instrument. If all pitch elements have been
eliminated, an observer will not be able to tell whether an ascending
or a descending figure has been played.
147
PIANO TOUCH AND TONE
any piano is played under any conditions, we may
conveniently divide these noises into four parts :
A. The impact of the finger upon the key (absent
in all non-percussive touches).
B. The impact of hammer against string.
C. The impact of key against key-bed.
D. Friction noises of the action, including the
impact of the rebounding hammer.
The most important of the four noise elements,
is the impact of the hammer against the string. The
piano manufacturers have reduced this noise to
a minimum by the use of felt of appropriate com-
pressibility and elasticity. The noise of impact,
however, has not been entirely eliminated, by any
means, a fact which appropriate damping of the
strings vividly illustrates. This noise is one of the
results of the transfer of energy taking place when
the hammer sets the string into motion. Since
the object of the hammer is to transmit this energy
to the string, and not to produce noise, the noise-
impact, physically speaking, represents so much
wasted work. A part of the energy possessed by
the hammer-head at the moment of impact is lost
in producing this noise. The string itself, then,
has slightly less energy transmitted to it for tone-
production than the hammer originally possessed.
This same principle applies to the other noises as
well. Wherever noise is produced in the transfer
of energy, a corresponding consuming of energy must
occur.
The character of the hammer-impact noise may
be described as a dull thud. It is readily audible,
when isolated, throughout the dynamic range from
" pp " to " ff ". Its intensity, and therefore audibility,
varies with the dynamic degree ; it is weakest when
a soft tone is produced. Generally speaking, for
a normal ear, under normal conditions, it is audible
148
THE NOISE ELEMENT
for a pp degree only close to the instrument, audible,
let us say, to the player ; for the degrees p and mp,
it can be heard anywhere in the classroom ; while
for forte and fortissimo, it is audible throughout
a medium-sized recital hall. Naturally, then, the
loudness of the noise increases with the loudness of
tone, when tone is produced. Two tones of different
intensities are therefore accompanied by noises of
different intensity, or, in other words, for every
degree of tone a fixed degree of noise is present. This,
of course, excludes the exceptional condition due to
permanent alterations in the felt hammer-surface
resulting from extended use.
The noise of hammer-impact occurs simultaneously
with the beginning of tone. It is very brief ; and
FIG. 76.
after the very instant of sound-creation, the tonal
element continues unaccompanied by the impact
noise. Since no tone on the piano can be produced
without this noise, since, moreover, the intensity of
the noise varies directly with the intensity of the
tone, and finally, since for all degrees of normal playing
the noise is audible, it follows that the quality of the
sound-complex of the piano is partly due to the impact
noise and is not purely tonal, as is generally beEeved*
The effect of this noise on tone may be diagram-
matically iEustrated by Fig. 76, in which the shaded
portion represents the noise element, the unshaded
portion the tonal element.
Next in importance is the noise of finger-impact,
the result of the finger striking the key-surface. It
PIANO TOUCH AND TONE
depends upon the touch employed. Apart from the
fact that in non-percussive touches this noise is entirely
absent, the variations in percussive touch enable
us to increase or decrease this impact noise. There
is a direct relation between the manner of touch and
the intensity of finger-impact. 1 Thus the impact
noise produced by a rigid hand and arm is louder
than that produced by a relaxed arm, though the
actual arm-speed be the same. That is, if the speed
of arm-descent is approximately the same, the relaxed
tone-production will be accompanied by less impact-
noise than the rigid tone-production. As far as
finger-speed itself is concerned, this varies directly
with the impact noise. Now in the chapter on hammer-
movement we learned that a soft tone could be
produced by striking the key a sharp blow, necessitating
a key-descent of only ^ inch. Of course, the blow
must have considerable force in such a case, and as
a result, we get a decided impact noise. But this
yields only a small amount of tone, and it is well
known that noise is an undesirable element, which
tends to impoverish " good " tone quality. 2 Con-
sequently, the sound produced above will be musically
unsatisfactory. But the so-called surface or slapped
tone is produced in just this manner, which explains
the disagreeable quality of tones of this category,
including " shallow ", " depthless ", and other tones
of like kind.
This unsatisfactory quality is due, not to any
peculiarity of touch, key-action, or tone itself, but to the
unaesthetic ratio of noise to tone ; too much of the
former, and too little of the latter. That this is
generally true was amply verified by experiment.
Every " slapped " key-depression showed a maximum
1 See Fig. 32, Chapter IV.
2 Otherwise we should not have the painstaking effort of piano
manufacturers to eliminate noise, by cushioning every joint and
buffer.
150
THE NOISE ELEMENT
noise and negative hammer-acceleration, and every
negative hammer-acceleration, when percussive touch
was employed, resulted in a " slapped " tone effect.
A tone of the same intensity, measured accurately
by key- and hammer-speed, but produced with a non-
percussive touch, lacked this disagreeable quality
entirely.
Another factor which influences finger-impact, is
the nature of the striking body, the finger-tip. Every
experienced teacher has noticed that certain fingers,
well rounded and padded ones, produce an acceptable
tone more readily than pointed, tapering fingers.
It is quite true that other factors l influence the tone
control in such cases ; nevertheless, there is also a
slight difference in the impact-noise, which is louder
for the tapering, softer for the padded fingers. 2 Of
course, such differences will often vanish with good
training and altered use of the finger.
The finger-impact noise is the first sound made in
playing the piano. It occurs before the beginning
of tone, and for this reason remains audible in every
case of percussive touch. The difference in impact
noises explains why a normal ear can readily distinguish
percussive from non-percussive touches, when the
keyboard is not in view. The former is heard as
a double sound, the latter as a single sound. The
character of this noise is that of a light snap. It
differs in quality from the hammer-impact noise,
and is perhaps the most influential and characteristic,
though not necessarily the loudest of all the noises.
It may be diagrammatically shown in connexion with
the tonal element as in Fig. 77, in which the shaded
portion represents the finger-impact noise, and the
unshaded portion, the tonal element.
1 Circulation and nerve sensitivity, for example.
2 The noise made by the finger nail striking the key surface is
not included, since this manifestly, is always to be avoided.
151
PIANO TOUCH AND TONE
The finger-impact noise explains several " tonal "
qualities which are attributed to certain forms of
touch. Thus, the familiar " plucked " staccato used
by a number of well-known pianists for certain effects
is a non-percussive touch. 1 Naturally, this will
produce a different sound from the usual hand-staccato,
in which the hand is thrown against the key and
immediately withdrawn, since the finger impact-noise
is absent in one and present in the other. Some
differences between the sounds produced by a high
and a low wrist, by rigidity and relaxation, may also
be explained by the presence in varying degrees,
or the absence of, finger-impact noise. It is important
FIG. 77.
to note that practically all forms of touch used
for the production of " good ", " sympathetic ",
" beautiful", or " singing " tone, are forms of touch in
which either no finger-impact noise at all, or a minimum
of such noise is present. And in most cases where
disagreeable "tones*' are produced, the -finger-impact
noise is well marked. Moreover, when the form of
touch is retained but the impact-noise reversed, 2 the
" good " tones become less agreeable, the disagreeable
tones more agreeable. The explanation, then, of
a number of supposed qualitative differences in tone
is to be found, not in the tone, but partly in the
accompanying noise production of the finger when it
strikes the key.
1 The fingers touch the keys before playing and the hand is then
jerked back.
1 Impact-noise added to those forms of tonch ordinarily not
possessing it, and eliminated from the forms ordinarily possessing it.
152
THE NOISE ELEMENT
A third noise element is that resulting from the
impact of the key upon the key-bed. As a rule,
an increase in finger-impact noise results in an increase
in key-bed impact noise. 1 In point of intensity the
latter is less than the former, and may be disregarded
for dynamic degrees less than mf. Even above this
degree its effect upon the sound-complex normaEy
is slight. This is due not alone to the quality of the
noise itself, which in this respect closely resembles
the noise- of hammer-impact, but also to the fact
that the noise occurs simultaneously with hammer-
impact noise and tone-production, and is consequently
difficult to distinguish as a separate noise element.
The various forms of touch have no effect upon this
noise apart from intensive differences, and extensive
experimentation leads to the conclusion that although
the noise varies slightly with key-speed, these variations
contribute only to a very small extent, if at all, to
the so-called tone-colour. Nevertheless, the key-
pad may be used to illustrate the effect of the noise
element on the tonal qualities in general. If the felt
pad beneath a key be removed and a wooden disc
of proper size and thickness substituted, we obviously
have not altered anything about the action or tone
itself. The tone so far as touch and string-vibration
are concerned can still be produced as before. How-
ever, under this condition it is quite impossible to
produce a musically satisfactory tone, because we
have altered the ratio of noise to tone too much.
If tone-complex quality were independent of the
noise element, and purely tonal, we should still be
able to produce a " good " tone when we increase
the noise as indicated. The quality of the tone-
complex that we get is poor, and may be described
as dull or thick. This is but additional proof of the
1 There are certain exceptions.
153
PIANO TOUCH AND TONE
well-marked influence of the noise element on tonal
qualities, for in the experiment as made we have
increased the noise element only, and any difference in
the sound-complex is therefore due to this change,
when touch and intensity remain constant.
The final group of noises consists of friction noises
and the thud of the rebounding hammer and inner
key-arm. A popular belief exists that chords played
staccato with the pedal held sound differently (some
say shorter) than the same chords played sostenuto
with the pedal. Now, if the conclusions reached
in the first part of this book are true, it is manifestly
impossible for this difference to be due in any way
to the vibration of the string. The only remaining
influence would be the noise element. If we depress
eight or ten keys, without causing the tones to sound,
hold them for a moment, and then release them,
there will be an audible rattle or scraping, due to
the friction of parts of the action and the impact
of the rebounding hammer and the returning key.
This noise, of course, is also present when tone is
produced, though in such a case it is obscured by
the tone. In sostenuto touches, on the other hand,
this noise is largely absent, since the keys are held
depressed. Although there is, then, a difference
in noise elements between staccato and sostenuto
touches, this difference is insufficient to warrant
the conclusion that when keyboard and player are
not visible, the two touches can still be discriminated.
After much testing it was found that these touches
cannot safely be discriminated by sound, 1 unless
the listener is very close to the instrument. In such
1 When the damper pedal is not used, the impact of the falling
damper should be added to the noise accompanying the cessation
of tone. While this has no physical influence" on'preceding tone, it
may have on succeeding tone. This noise may be heard by lifting
several dampers from the strings with the fingers and then releasing
them.
154
THE NOISE ELEMENT
a case the presence and absence of the noise element
is the deciding factor.
The emphasis here placed upon the noise element
in piano playing may appear to be exaggerated, for
under normal conditions of tone-production the
average pianist and listener are seldom aware of the
presence of noise. The observations made apply
to a single key. Naturally, this noise element occurs
with every key-depression, and increases when several
keys are depressed simultaneously. The amount of
noise present in the performance of a composition
such as the March Militaire of Schubert-Tausig,
a Chopin Polonaise, or a Liszt Rhapsody, is surprising
to all who hear it for the first time. In such cases
the compositions can be recognized in an adjoining
room separated from the piano by a solid wall. This
recognition is due to the rhythm, it is true, but suppose
a similar test with appropriate compositions to be
made on a violin whose tonal element had been
eliminated. Recognition would obviously be
impossible, for not only would the noise be less but
it would scarcely be intermittent. This proves the
influence of noise on the rhythmic force of piano
playing, and also demonstrates how well the piano,
compared with string instruments, is adapted to
predominantly rhythmic music. It explains, for
example, why a march played on the piano is
much more effective, as a march, than the same
composition played by a string orchestra, unless
in the latter case the orchestration contains special
rhythmic effects, such as pizzicaii.
Naturally the amount of noise varies with the style
of composition played. If we place the works
mentioned at one end of the scale, such compositions
as Chopin's Berceuse would come at the opposite
end. Thus, throughout the range of practical piano
playing we have noise audibly present. We cannot
155
PIANO TOUCH AND TONE
ignore the influence of this factor, though it is undesir-
able. The less so, since when we change the noise,
we change in part the " tonal quality ", as popularly
understood. Within certain limits, these changes
can be definitely forecast. This is ample proof that
the noise element plays a measurable part in the
formation of piano " tone " and the adoption of
piano touch. 1 The inter-relation between the various
noise elements may be represented as in Fig. 78,
which represents, in a very general way, a staccato,
FIG. 78.
percussive touch, played "/" : A, finger-impact
noise ; B, hammer-impact ; C, key-bed percussion ;
D, thud of returning action ; E, friction noises.
The dotted line represents the beginning and the
duration of tone. The audibility of the individual
noises varies with the touch. Thus, for example,
in staccato, D follows B and C so closely that it is not
separately distinguished. If the key returns slowly,
1 Needless to say, these influences vary with different instruments,
with the distance of the listener from the instrument, and with the
usage of the instrument. Use tends to increase the noise element
in all instruments, and " overhauling " a used instrument means
little more than reducing the noise element again.
156
THE NOISE ELEMENT
D is largely eliminated. In non-percussive touches
A is absent. In " slapped " effects A is high and
B low, altitude representing intensity.
Practically all the important noise influences act
only at tone-beginning, since at the moment when
the action comes to rest, action-noises cease. This
leads to the question as to whether those words with
which we are accustomed to qualify piano-sound,
such as " harsh ", " brittle ", etc., apply to the
beginning of the sound-complex or to the tone-complex
at any moment of its duration. If the above deduc-
tions on the effect of the noise element be true, then
that part of the sound-complex after sound-production
must be free from all noise influences ; and if, on the
other hand, the qualitative differences apply only
to the beginning of the tone, this is a further indication,
though not proof, that the noise elements are
responsible for these differences.
It can easily be shown that most qualitative terms
apply to tone-beginning only. By plugging the
meatus of the ear (with fingers or appropriate wax
form) and arranging a convenient signal, immediately
after tone-production, at which the plugs may be
quickly removed, it will be found that these qualitative
differences vanish and the tones heard can be dis-
criminated only in point of intensity. 1
TONAL-NOISES
The separate treatment of the tonal and noise
elements was necessary for a clear presentation of
the questions involved. Not all noises, however,
which play a part in music are as readily distinguished
from tones as those which we have just discussed.
In the chapter on touch combinations we learned
that the piamstic touches are not sharply defined
types, but shade into one another. We find a similar
1 Care must be taken to control reverberation properly.
157
PIANO TOUCH AND TONE
condition existing with regard to tone and noise.
The explanation that the former is caused "by regular
and the latter by irregular vibrations is true but not
absolutely defined. For it is often difficult to say
where regularity stops and irregularity begins, or in
sensorial terms, where tone stops and noise begins.
If we depress a piano key in a low octave we hear
a relatively rich (that is, clear-cut) tone. If we strike
three adjacent keys, the dissonance increases and
makes a clear recognition of the constituent tones
more difficult. If, now, we depress an entire octave
of adjacent keys, or better, two or three octaves*
the normal ear certainly hears a sound closely
approximating a noise. Where has the transition
occurred ? Or we might proceed from the other
end. With the damper pedal depressed, nib two
pieces of sand-paper together, clap, cough, or make
some other noise near the instrument. A number
of strings will immediately begin to vibrate sympatheti-
cally, showing that the tones whose frequencies
correspond to those of the various strings thus
vibrating, were all present in the noise made. And
if we had a sufficiently great number of pitches,
we could reproduce many noises by compounding
the component tones.
By cutting a number of small sticks of appropriate
wood, (walnut, rosewood, or box) to the proper length
or thickness, the phenomena of the tonal noises may
be still better heard. A series of such sticks when
dropped in a bunch will produce the customary
noise of impinging wooden sticks, a noise in which
the ear detects no tone, or at best very little. If these
same sticks are then dropped one by one, each gives,
forth a tone. Of course, this tone is not so pure as the
tones produced on our musical instruments, but it
is none the less heard as a tone, and if the pieces of
wood have been cut to produce the tones of a scaie >a
158
THE NOISE ELEMENT
a clearly defined melody can be played by dropping
them in an appropriate order. (The earlier types
of the musical instrument known as the xylophone
had, and some modern forms still have, wooden slabs
for tone-production.)
Thus we see that noise shades gradually into tone
or vice versa. In every piano tone-complex a certain
noise element (other than those noise elements which
we have been studying) is present. It varies in degree
with the number of tones, their pitch, and their
intensity. These tonal-noises, as they may be called,
are important, for tone and noise are our two most
fundamental aesthetic concepts in music.
Reviewing briefly the deductions made in this
chapter, we find that :
1. A number of " tonal qualities " are partly the
result of noise qualities.
2. " Good/' " sympathetic," or " beautiful " tone,
means, in part, a sound- complex with a maximum
of tonal elements and a minimum of noise elements.
Conversely, " poor/' " shallow/' or " dry " tone,
means a minimum of tonal elements and a maximum
of noise elements.
3. The most marked differences in sound-complexes
occur at the beginning of sound.
4. The elimination or reduction of the noise element
is one of the reasons for the adoption and rejection
of certain forms of touch.
5. The most characteristic difference in touch,
when measured in terms of the noise element, is that
between percussive and non-percussive touch.
6. Generally speaking, rigidit}?" tends to produce
more noise than relaxation.
7. The noise element is one of the chief vitalizing
factors for rhythmic force in piano playing.
8. For degrees less than p, noise is of little effect
on tone colour. Above this point, its importance
increases with the dynamic degree.
159
CHAPTER X
THE PROPAGATION OF SOUND
HPHE vibrations which the sounding-board receives
-*- from the string, altered by it, are given off to the
surrounding air. We have now to trace the progress
of these waves from the time when they leave the
instrument to the time when they reach the ear of
the listener. Do they reach the ear in the same manner
in which they leave the piano, or do they undergo
change in their passage from the piano to the listener ?
Among well-known phenomena of sound are those
of diffusion, reflection, interference, and resonance.
Diffusion is the spreading out of the sound wave
as it moves out from its source. If we imagine a
sound produced in a perfectly homogenous medium,
this spreading out will take the form of a smooth
spherical wave. 1 Naturally, there must be an increase
in area as the wave moves from the source an increase
as the square of the radius of the sphere. Moreover,
since the wave is not energized anew, it decreases
in intensity as it increases in area, and we have,
as our first law of diffusion : the intensity of the sound
varies inversely as the square of the distance of the
sounding body from the ear. The general tendency
of sound to decrease in loudness as we recede from
the source of sound is a universally known phenomenon.
The second law of diffusion that the intensity of
the sound depends upon the density of the medium
traversed does not bear upon our problem, since
1 A similar phenomenon, occurring, however, in only one plane,
may be observed by dropping a pebble into a quiet body of water,
whereupon concentric, widening, circular waves will recede from
the point of impact.
160
THE PROPAGATION OF SOUND
musical tones are here considered as produced in
closed auditoriums, where variations in atmospheric
density and motion (direction of the wind) are relatively
negligible factors.
Reflection is the changing of the direction of waves,
and occurs whenever sonorous waves meet a fixed
obstacle. The reflection always takes place according
to the law that the angles of incidence are equal
to the angles of reflection. If the reflecting surface
be plane, waves diverging from any centre in front of
it are reflected as from a theoretical centre
symmetrically situated behind it. If the reflecting
surface is complex, that is, is made up of a number
of plane surfaces, each one of these reflects the waves
as a separate plane surface. Curved surfaces may be
considered as made up of an infinite number of plane
surfaces, and, as such, are obedient to the law
referred to.
The most familiar instance of reflected sound
is the echo. We have an echo whenever the duration of
the original sound is short enough, and the distances
between source, reflecting surface, and observer, are
great enough, to separate the original sound from its
reflection (echo) by a great or small interval of silence.
If, now, a second reflecting surface be placed opposite
and parallel to the first, and the sound be produced
between them, it ^111 be reflected back and forth,
and will give rise to what is known as multiple echo.
Multiple echo may also be produced by the reflection
of the original wave from objects at various distances
from the source. One form of this latter kind of
echo deserves attention, since indirectly it has
significance for our problem. If we use an electric
spark as the sound producing body, and place a
number of parallel reflecting surfaces at regularly
increasing distances from it (a long staircase answers
the purpose), the multiple reflection gives the original
161
PIANO TOUCH AND TONE
electric snap (a noise) distinct tonal qualities, and
thus changes the nature of the sound heard. In
musical auditoria, however, clearly defined echo
plays an insignificant part, because the dimensions
of the halls are not sufficiently simple or great.
A second condition resulting from the reflection
of sound waves is known as interference. Since
the reflected waves traverse the same medium as the
unreflected waves, 1 but in different directions, there
must be interference. A remarkable attribute of this
interference is that it does not affect the actual
propagation of either or any set of waves. The
interference does affect, however, the physical qualities
of any one wave at the point of interference. When
two systems of waves traverse the same medium,
the actual motions of each particle of the matter
is the resultant of the motion due to each separate
system. When these component motions occur in
the same direction, the resulting motion equals their
sum ; when the directions are opposite, the resulting
motion equals their difference. Thus, if a returning
wave of condensation coincides with an outgoing
wave of condensation, their energies are added ;
and we have an augmentation of the intensity of
the sound. If, on the other hand, a wave of con-
densation coincides with a wave of rarefaction, their
energies are subtracted ; and we have a diminution
of the intensity of the sound. " An ear stationed
at the point of interference would in the first case
hear a loud sound ; in the second case, a weak one.
In fact, if perfect reflection were practically possible,
interference could just double the intensity or reduce
it to silence. Such extreme variations are not met
with in practice, but we do meet many degrees of
variation between the extremes. When a number
1 No tone produced in music produces but a single wave. Even
the shortest staccatissimo sends out a train of waves.
l62
THE PROPAGATION OF SOUND
of these fluctuations in intensity occur, they produce
what are known as " beats ". When, in turn, these
beats occur in sufficiently rapid succession x to become
inaudible as separate fluctuations, they lend a peculiar
character of roughness to the sound, which has a
decided effect upon its quality.
A third condition produced by reflection, and one
which directly concerns us here, is reverberation.
Reverberation is the result of multiple echo and
irregular reflection. Primarily, it is the result of
the overlapping of one series of echoes or interference
with other series.
It may best be expressed as confused propagation
of residual sound. The complexity of reverberation
is realized when we consider that each surface of
each obstacle is constantly reflecting any living
sound, and that these reflections vary with the shape,
size, and material of the reflecting bodies. This
complexity is so great that if a sound be maintained
constant for five or six seconds in an ordinary haJl
the reflections in this time will have occurred in every
conceivable manner, causing the sound to be fairly
homogeneously distributed throughout the hall. For
very short tones, this diffusion of residual sound
remains incomplete. Moreover, since tones of various
pitches have waves of various lengths, each wave
length will produce a series of reverberation phenomena
peculiar to its own pitch.
Resonance is that condition which results when
the waves from one vibrating body meet another
body whose natural period of vibration is equal to
that of the first body, or stands in some simple
numerical ratio to it. The second body will then begin
to vibrate " sympathetically ". The various types
of reflection which have been mentioned do not increase
the actual amount of sound generated. Resonance,
1 Over 16 to 20 per second.
163
PIANO TOUCH AND TONE
on the other hand, alters the total amount of sound
in the space of the auditorium, and always results
in an actual increase in sound. If a second body
vibrates through resonance, it will continue to vibrate
after the first body has come to rest. Such sympathetic
or free resonance may occur with noises as well as with
tones. Every musician has had the experience of
trying to locate often in vain the rattling of some
article in the room which invariably responds to
a certain tone.
It has been necessary to devote attention to the
phenomena of diffusion, reflection, and resonance,
because their effect upon the so-called quality of
piano-tone-complex is very generally underestimated.
Not an inconsiderable part of the attributes which
we assign to the tone itself before, or as it leaves
the instrument, is in reality due to the changes which
the tone undergoes after leaving the instrument and
before reaching the ear. The influence of diffusion
may conveniently be grouped into three classes :
super-normal diffusion, resulting in a weakening of
desirable tonal elements ; normal diffusion, resulting
in a musically appropriate duration of the sound ;
and sub-normal diffusion, resulting in an intensifica-
tion of the undesirable elements of the sound-complex.
We have super-normal diffusion and a corresponding
decrease in tonal beauty when a tone is produced
in the open air or a very large auditorium ; we have
normal diffusion and a corresponding beauty of tone
when the tone is produced in a hall of so-called good
accoustic properties ; and we have sub-normal diffusion
when the ear is placed close to the instrument, a point
at which the impact and action noises, and the weak
high partials, impoverish the musical tone quality. 1
1 In chamber music concerts the mistake is sometimes made
of seating the audience too close to the players. The unavoidable
scraping noises of the instruments considerably lessen the beauty
of the tone-complex in such a case.
164
THE PROPAGATION OF SOUND
The most important change, however, which the sound
undergoes after leaving the instrument is due to
reflection, and of the three classes of reflection, to
reverberation. In analyzing the effects of reverbera-
tion upon tone-quality, we are here less concerned
with the component reflections than with the duration
of the phenomena and its rate of decay. Assuming, for
the sake of analysis, the same sound to be produced in
three rooms, one with prolonged reverberation, one with-
out reverberation, and one with normal reverberation,
what are the physical changes which the normal tones
undergo ? l In Chapter IX we learned that the
piano sound-complex consists, in brief, of a number of
noise elements of short duration and tonal elements of
long and short duration. In a room with prolonged
reverberation each of these elements is prolonged
well beyond the moment when the original source
ceases to give forth sound. Thus, a momentary
snap, such as an electric spark, would continue to
re-echo for as long, perhaps, as several seconds. The
noise elements and so-called inharmonic high partials
of a sound-complex are likewise prolonged. But we
have seen that our musical ear strives to eliminate
both noises and very high partials on account of their
undesirable effect on beauty of tone-quality. There-
fore, when we have super-normal reverberation,
we intensify, by prolongation, the undesirable sound
elements, and hence impoverish the musical value
of the sound. In a room without reverberation we
have the opposite extreme. All sound ceases as soon
as the original source ceases to vibrate, since there is
no reflection. The only waves are those coining
directly from the vibrating source. The result of such
a condition is to give us, first of all, a clear picture
1 Extensive observations were made under these three conditions.
However, since the method of approach to the problem was largely
psychological, the resnlts must be described under the psychological
aspect of tone, and only a few general remarks are included, here.
165
PIANO TOUCH AND TONE
of the sound as it actually leaves the instrument. 1
The noise elements have practically no duration,
and the length of the tonal attributes is equal to
their length of vibration-time. The result is that we
increase the purity of the tone, for by reducing the
time for which the musically undesirable elements
of the sound-complex sound, we practically eliminate
them. It follows that if our concept of a musically
beautiful tone demanded only physical purity, a tone
produced without reverberation would be such a tone.
As a matter of fact, this is not the case. Our musical
ear demands other attributes than purity of tone.
Tone-production under conditions of normal
reverberation is modified to an extent which experience
has shown to be musically desirable. The physical
basis of such a condition is a moderate prolongation
of both noise and tone in such proportion that their
duration permits them to influence the sound-complex,
and yet not to cause a " blurring " by too much
overlapping. This is the condition which exists in
halls with good acoustic properties.
When the reflection of sound is controlled, either
by chance acoustical properties of the hall or by
deliberate adjustment for experimental purposes,
some interesting effects occur. The phenomenon of
the whispering galleries is a familiar example of
the great variation in intensity of sound at various
points, ranging from points of silence to points of
fairly great maximum intensity. Practically every
hall, theoretically speaking, is an imperfect whispering
gallery, and hence has its regions of minimum, medium,
and maximum intensities.
Reflection also affects pitch. It is possible to change
the apparent pitch of a complex tone as much as an
1 All physical measurements of piano sound, if we attempt to
measure it irrespective of reflection, must be made in a room from,
which reverberation has been eliminated.
166
THE PROPAGATION OF SOUND
octave by slightly altering the position of the listener
when reflection is properly controlled. This change
of pitch is in reality a change of quality. It is the
result of certain resonance effects of the hall. Thus,
if the listener stands at a point which is the focal
point of reflected waves whose length equals that of
the octave of the fundamental tone, this octave
becomes proportionately louder and the fundamental
proportionately weaker, and if the difference in
intensity (the scheme of reflection) is sufficiently
pronounced, we actually hear a change of pitch.
This incomplete survey of the propagation of sound
will suffice to show that any or all of the tonal
attributes : pitch, intensity, duration, and quality,
may be, and actually are, altered considerably after
the original sound waves leave the instrument. For
purposes of musical analysis it is useless to photograph
these changes, since they vary with each hall, with
the size of the hall, its shape, materials, and furnishings
(including the audience), and likewise with different
points in the same hall. In view of these facts, we
should proceed very carefully when assigning certain
tone-qualities to the touch of the player or to the
original tone-complex. In many cases these tone-
qualities are produced not by the player or directly
by the instrument, but by the propagation of the
sound through the auditorium.
If, after the analysis in the foregoing chapters,
we still wish to define a so-called " good " tone in
physical terms, we should be obliged to say : a tone-
complex of a fundamental and partials, about four to
seven. The fundamental shoxild be loudest, the
partials diminishing in intensity as we recede from
the fundamental. Neither fundamental nor partials
should be too strong or too weak. The entire tone-
complex should be of sufficient duration to be dearly
audible as an agogic extension. Moreover, a really
167
PIANO TOUCH AND TONE
" good " tone would include the absence of all noise
elements. It will be seen at once that a tone-complex
such as that we have just described can find but very
limited use in piano playing. We can, however,
look upon such a tone-complex as the purely physical
ideal. But because this ideal is never really reached
in practice, many authors and teachers maintain
that we should demand of the pupil, not the production
of a good tone, but the production of a suitable tone.
The pupil should ask : is it adapted to the particular
passage ? Does it harmonize with its tonal environ-
ment ? Certainly from the interpretive side this
viewpoint is to be preferred.
In order to verify the fundamental variations
shown in the results obtained for the vibration of
the piano string, a few photographs were made, for
which an improved form of vibrating reflector, invented
by Preston Edwards, was used. This consists
essentially of a small mirror mounted on a tuned
rod and placed before the mouth of a resonator.
The torsional vibration resulting serves the purpose
of greatly magnifying the vibration, so that a beam
of light, when reflected from the vibrating mirror,
makes a considerable excursion, the amplitude of
which may be further increased by increasing the
distance of the recording surface from the mirror.
When properly adjusted, this device is very sensitive,
and will show minute variations in intensity.
Since the resonator used vibrated only for one
pitch, the photographs are not pictures of the complete
piano-sound, which, as we have seen, is a highly
complex thing. The pictures show the variations
for one pitch, which in these cases was the fundamental.
All the illustrations were made under constant con-
ditions, so that the secondary phenomena discussed
in this chapter could not influence the variations.
The light bands in the pictures represent the path
168
3
THE PROPAGATION OF SOUND
traversed by the reflected ray of light. Horizontal
distances are equivalent to amplitude of vibration,
hence loudness of tone. The brighter the streak of
light, the longer has the ray of light remained at rest
in that particular point. Accordingly, a perfect
diminuendo should show a band of light growing
steadily dimmer as we recede from the central point
in either direction. On the other hand, the irregular
diminuendo property of the piano tone should show
strips of brightness upon a paler background. Such
a difference is at the same time proof that the vibrator
used did not contribute vibrations of its own to those
of the air. Fig, 79 shows the picture of a moderately
loud tuning-fork tone allowed to diminish freely.
Fig. 80 shows the same for a piano tone. The absence
of irregularity in the former, and the streaks seen
in the latter, show the marked difference in the nature
of the two tones used. In Fig. 80 three levels are seen
at which a stead}^ diminuendo was broken. And the
most marked of these, indicated by the bright central
portion, is less than half of the original intensity, and
was reached immediately after tone-beginning. Fig.
8ia shows the reflection for a curved finger touch,
Fig. 816 that for a tone of the .same intensity (as
nearly as the subject could control intensity) made
with a flat finger. A very small difference in intensity,
in favour of the curved finger tone, is noticeable.
Accordingly, the curved finger produced the louder
tone. A similar distribution is shown in Fig. 82,
where a represents a tone made with a rigid arm, and
6, a tone made with a relaxed arm. The wider displace-
ment in a indicates a louder tone for rigidity than for
relaxation.
Besides agreeing with the conclusions drawn in
the other chapters, these figures, since they are based
on a more sensitive method of procedure than that used
for the string-vibration, show that where differences
169
PIANO TOUCH AND TONE
are so small that they are ordinarily not clearly noticed,
they may yet exist and influence our judgments.
For the ear is itself a very sensitive instrument.
Thus, a tuning-fork, vibrating on an ordinary resonator
with an amplitude of vibration considerably less
than one twelve-hundredth of an inch, nevertheless
produces a readily audible tone. Hence, in recording
sound waves, we need not expect always to find
wide differences, but must remember that a very
minute difference may be sufficient to account for
our reaction.
Moreover, the concha and the external meatus of
the ear themselves form a resonator as a result of
which the loudness of pitches of appropriate frequencies
is materially reinforced. This may be strikingly shown
by placing the cupped hand immediately behind the
ear while tones in the high treble region of the piano
are sounded at moderate intensity. The loudness is
then often increased to a more or less painful degree.
One of the many theories explaining the so-called
characteristic qualities of the .various tonalities is
based upon this natural resonance property of the ear.
170
RESUME
What we actually do, then, when playing the piano,
is to produce sounds of various pitch, intensity,
and duration. Nothing more. Certain forms of touch
are effective only because they enable us to secure
a proper relationship among these variables. The
quality of a sound on the piano depends upon
its intensity; any one degree of intensity produces
but one quality, and no two degrees of intensity can
produce exactly the same quality. If A plays
<{ poetically " and B does not, then, as far as the single
tone is concerned, A plays sounds of different intensity
from those of B ; and if B could play sounds of the
same intensity as A, B would play just as poetically
as A.
What we imagine we do and hear is a different
question, the answer to which awaits the outcome
of an experimental investigation of the physiological
and the psychological aspects of the problem. The
division into the physical and the non-physical is
necessary for an explanation of the conflicting theories
and opinions. Whether or not piano pedagogy can
profit by thus differentiating between the constant
elements, those physical attributes which vary
according to constant physical laws, irrespective
of the individual, and those psychological attributes
which vary with the individual, is not our question
here. But it is safe to say that in any pedagogy the
distinction between cause and effect is an important
one. A certain hand- or finger-motion is often taught
because it produces a certain tonal quality, and in
'actual practice we find that other types of touch can
produce the same tonal quality. Relaxation is taught
171
PIANO TOUCH AND TONE
for its effect upon physical piano-tone, but rigidity
can produce the same tone. A certain finger-stroke
produces a certain tone, not because that stroke is
correct and all other strokes are incorrect, but because
the finger reaches the key with an appropriate force.
A relaxed arm produces a certain tone, not because
the arm is relaxed (for the action of the piano cannot
be affected by a muscular condition), but because
the arm condition permits better control of force.
This explains the various modes of using arms and
fingers adopted by the concert artists for producing
the same tonal quality.
If tone-quality depended directly upon type of arm
or finger movement, then one arm and hand position
for all pupils would be essential. If, on the other hand,
it depends upon the force of stroke, arm and hand
positions may be varied in order to secure appropriate
force, thus taking into consideration the not incon-
siderable differences in anatomical formation.
Again, if good tone-quality resulted directly and
entirely from relaxation, then relaxation would be the
sine qua non of piano playing. As a result, we should
find it impossible to play, musically effectively, a very
great portion of piano literature. For all piano
playing demands some degree of rigidity, and, in many
cases, a great degree of rigidity.
In the data secured in this analysis we have the
concrete material which, in one form or another,
is at the bottom of every art. And since sensation
is the first link in the complex chain of neural response,
and depends entirely upon the concrete objective
material of the physical world, an analysis of this
physical element is a logical and necessary beginning.
Without the wooden keyboard and the metal strings
there could be no pianism, either artistic or inartistic.
Such an analysis, moreover, gives us a clue to the
answer of the question : How do these physical variants
172
RESUME
produce the emotional response in the auditor ?
In the first place, variations in pitch, intensity, and
duration, as we have seen, cover a wide range and
involve very fine gradations ; and in the second place,
there is no reason why these variations cannot suffice
for the production of the psychological reactions.
The popular conception that they are too coarse
or not sufficiently subtle is based upon ignorance
of the true complexity and great variety of physical
piano-sound and of the sensitivity of the ear.
Is all piano playing, then, merely a variation in the
physical attributes of tone ? Yes and no. So far as
auditory stimulation is concerned, yes. So far as
total stimulation is concerned, no. Every pianistic
effect existing for audition, including the most subtle
shades of emotion, can fully be explained in terms
of the physical attributes. And when these fail to
explain all the effects, this does not establish the
presence and operation of other mysterious, super-
psychological stimuli ; it means, merely, that piano
playing as an art is not entirely auditory in character,
but appeals also to other sense departments. Chief
among these are the kinassthetic and the visual
senses, which, in the music appreciation of to-day,
are of very decided importance.
173
BIBLIOGRAPHY
TN the following list of references no attempt has been
*- made toward exhaustiveness. Enough works have
been listed, however, to furnish ample proof for any
statement in the text not verified by the experiments
themselves. Needless to say, any investigation of
to-day owes much to the investigators who have already
blazed a path, and conclusions similar to _ those drawn
in the foregoing pages will be found in many of the
following works.
Any book on general physics will contain the
essentials of mechanics and sound. For more detailed
treatment the reader is referred to the works listed
under the separate heads. The omission of all books
on piano touch and technique is the result of the
attempt to exclude any psychological phases of the
subject, and the chapters in such works devoted to the
piano-action aie more reliably duplicated in the books
on piano-manufacture that are included here.
GENERAL ACOUSTICS AND SOUND
AMES, JOSEPH S. Textbook of General Physics. New York :
American Book Co., 1904. A fine, concise and
authoritative textbook.
WINKELMANN, A. Handbuch der Physik. Leipzig, 1909.
The second volume is devoted to acoustics, treated
both theoretically and experimentally, and contains
a comprehensive subject-index.
POYNTING and THOMSON. Sound. London : Griffin and
Co., 1899. One of the best modern textbooks.
RALEIGH, LORD. Theory of Sound. Two volumes. London,
1896. A very complete mathematical treatment,
containing also summaries of the experimental phases.
HELMHOLTZ, HERMANN VON. Vorlesungen uber die
mathemathischen Principien der Akustik. Leipzig,
1898. A mathematical analysis.
174
BIBLIOGRAPHY
BARTON, E. H. Text-book of Sound. London, 1908.
TYNDALL, JOHN. Sound. New York : Appleton and Co.,
1882. A standard work containing descriptions of many
experiments on sound phenomena.
SCRIPTURE, E. W. Experimental Phonetics. Washington:
D.C., 1906. Interesting analysis of speech by means of
the phonograph.
POLLAK, HANS W. Phonetische Untersiichungen.
KOENIG, R. Quelques Experiences d'Acoustique. Paris,
1882.
BARNES, C. L. Practical Acoustics. London : Macmillan
and Co., 1909. An experimental investigation of
various sound phenomena.
CATCHPOOL, EDMUND. A Text-book of Sound. London :
W. B. Clive, 1894.
HARRIS, T. F. Handbook of Acoustics. London: Curwen
and Sons, 1910.
STONE, W. H. Elementary Lessons on Sound. London :
Macmillan and Co., 1895.
BATTELL, JOSEPH. Sound. New York, 1910.
KALAHNE, ALFRED. Grundzuge der Mathematisch-
phvsikalischen Akustik. Leipzig : B. G. Teubner, 1910.
KLIMPERT, R. Lehrbuch der Akustik, 1904-1907. The
fourth volume is devoted to Architectural Acoustics.
MECHANICS
TAIT. Properties of Matter. Edinburgh, 1885. A useful
textbook.
ROBINSON, S. W. The Principles of Mechanics. London :
Chapman and Hall, Ltd., 1910. A systematic, com-
prehensive treatise ; substance of class lectures.
POYNTING and THOMSON. Properties of matter. London,
1902. An advanced work, useful for reference.
MAURER, EDW. R. Technical Mechanics. London :
Chapman and Hall, Ltd., 1903.
MARTIN, Louis A., JUN. Text-books on Mechanics. New
York : John Wiley and Sons, 1910.
CREW, HENRY. The Principles of Mechanics. London and
New York : Longmans, Green and Co., 1908.
BARTON, E. H. Analytical Mechanics. London : Longmans >
Green and Co., 1911.
GARNETT, W. Elementary Dynamics, 1882.
175
BIBLIOGRAPHY
ACOUSTICS OF Music
HELMHOLTZ, HERMANN VON. On the Sensations of Tone.
London : Longmans, Green and Co. The pioneer
and epoch-making work. Ably translated and
annotated by Alexander Ellis.
MILLER, DAYTON C. The Science of Musical Sounds. New
York : Macmillan and Co., 1916. A general, modern,
experimental, and descriptive treatise by one of the
leading authorities on sound. Based largely upon
years of painstaking experimental work with special
apparatus. Contains a valuable bibliography.
BROADHOUSE, JOHN. Musical Acoustics. London :
W. Reeves, 1881. An adequate general treatment,
often referred to as the " Student's Helmholtz ".
HAMILTON, CLARENCE. Sound and its Relation to Music.
Boston : Oliver Ditson Co., 1910. A practical hand-
book, written in the clear and systematic style
characteristic of this author.
MEERENS, CHARLES. Acoustiq^te Musicale.
RIEMANN, HUGO. Handbuch der Akustik, 1915.
TACCHINARDI, ALBERTO. Acustica Musicale. Milano:
U. Hoepli, 1912.
TAYLOR, SEDLEY. Sound and Music. London : Macmillan
and Co., 1873. The physical basis of musical sounds and
of harmony, treated from a non-mathematical stand-
point.
BUCK, PERCY C. Acoustics for Musicians. Oxford :
Clarendon Press, 1918.
GUILLEMIN, AUGUSTE. Les premiers elements de I'acoustique
musicale. Paris : F. Alcan, 1904.
WOOD, ALEXANDER. The Physical Basis of Music. New
York : G. P. Putnam, 1913.
SCHAFER, KARL L. Musikalische Akustik. Leipzig : G. J.
Goschen, 1902.
MAYRHOFER, ROBERT. Der Kunstklang.
ZAHM, J. A. Sound and Music. Chicago, 1920. A very
readable general discussion.
STARKE, HERMANN. Physikalische Musiklehre. Leipzig :
Quelle und Meyer, 1908. An investigation into the
nature and formation of instrumental and vocal tone.
GRIESBACH, JOHN H. Analysis of Musical Sounds. 1867.
BLASERNA, PIETRO. The Theory of Sound in its Relation to
Music. New York : D. Applet on and Co., 1876. A
176
BIBLIOGRAPHY
translation from the standard Italian work, appearing
as vol. xxii of the International Science Series.
THE PIANOFORTE
BLUTHNER und GRETSCHEL. Lehrbuch des Pianofortebaites*
1872.
BLUTHNER, JULIUS F. Lehrbuch des Pianofortebaues
in seiner Geschichte, Theorie, and Technik. 1886.
Reprinted and revised, 1921. Leipzig : B. F. Voigt.
An authoritative analysis by one of the foremost
manufacturers in Europe, based upon a manufacturing
experience with more than seventy-five thousand
instruments,
HIPKINS, A. J. Description and History of the Pianoforte.
London : Novello, Ewer and Co., 1896. Part I is
a detailed description of the modern instrument by
the author of similar articles in Grove's Dictionary and
in the Encyclopaedia Brittanica.
RIEMANN, LUDWIG. Das Wesen des Klavierklangs und
seine Beziehung zum Anschlag. Leipzig : Breitkopf
und Hartel, 1911. The most thorough and detailed
non-experimental analysis ; diagrammatically richly
illustrated. Treats all phases of piano-tone and its
combinations, and their relationship to touch.
WHITE, WILLIAM B. Theory and Practice of Pianoforte
Building. New York, 1906.
WESSELL, NICKEL, and GROSS. Illustrated Catalogue of
Pianoforte actions. 1893. A catalogue by the manu-
facturers of many actions in use to-day.
STEINWAY AND SONS/ A brief History and Explanation of
the Steinway System in Pianofortes. New York :
Stein way and Sons, 1895. A paper by one of the
foremost piano manufacturers.
PONSICCHI. II Pianoforte, sua origine e sviluppo, 1876.
CESI, B. Storia del Pianoforte. 1903.
STRAUCH BROS. The Manufacture of Pianoforte Action.
New York : Strauch Bros., 1895.
GEPPERT, WILLIAM. Piano Quality. New York, 1911.
HANSING, SIEGFRIED. Das Pianoforte in seinen akustischen
Anlagen. 19X)9.
WING, FRANK L. The Book of Complete Information about
Pianos. New York : Wing and Son, 1897.
SPILLANE, DANIEL. History of the American Pianoforte.
HASLICK, PAUL N. Pianos, their construction, tuning, and
repair. London : Cassell and Co., 1905.
177
BIBLIOGRAPHY
ROSENKRANTZ, I. The Piano. Chicago : The Tunella Co.,
1902.
NORTON, EDW. Q. Construction, Tuning, and Care of the
Piano. Boston : Oliver Ditson Co., 1887.
WHITE, WILLIAM B. Modern Piano Tuning and Allied
Arts. New York : E. L. Bill, 1917.
SMITH, BUCHNALL. Wire, its Manufacture and Use.
London, 1892.
HANSING, 0. Das Pianoforte. 1910.
DREIER, THOMAS. Sheep's Wool and Paderewski. A
description of the manufacture of felt by the American
Felt Co. for piano hammers.
OTHER INSTRUMENTS
RAMAN, CHANDRASEKHARA. On the Mechanical Theory of
the Vibration of Bowed Strings.
RITZ, JOSEPH. Untersuchungen uber die Zusammensetzung
der Klange der Streichinstrumente. Mlinchen : G. Franz,,
1883.
GILTAY, J. W. Bow Instruments : their Form and con-
struction. London : W. Reeves. 1923.
DEAGAN, JOHN C Fundamentals in Tone-Production.
Chicago, 1916. A mathematical treatment of good
and bad qualities of musical tones.
LOCHER, CARL. Die Orgelregister und ihre Klangfarben.
Bern: E. Baumgart, 1912.
PLASSIARD, JOSEPH A. Des Cordes harmoniques en general,
et specialement de celles des instruments a archet. 1879.
SMITH, HERMANN. The making of sound in the Organ and
in the Orchestra. New York : C. Scribner's Sons, 1911.
An analysis of sound propagation.
ARCHITECTURAL ACOUSTICS
SABINE, WALLACE C. Collected Papers on Acoustics.
Harvard University Press, 1922. A series of
miscellaneous papers by a leading authority on this
subject.
WATSON, F. R. " Correction of Echoes and Reverberation.
Bulletin of University of Illinois, No. 87. A paper
dealing with an experimental investigation of the
acoustics of the University Auditorium.
WATSON, F. R. " Acoustic Properties of Auditoriums/'
Bulletin of the University of Illinois, No. 73, 1914.
Engineering Experiment Station. The paper contains
a bibliography of the subject.
178
BIBLIOGRAPHY
WATSON, F. R. " Sound Proof Partitions." Bulletin of
University of Illinois, No. 127, 1922. Engineering
Station.
KELLY, EUGENE H. Architectural Acoustics. Buffalo, N.Y. :
Bensler and Wesley, 1898.
SMITH, T. R. Acoustics in relation to Architecture and
Building. 186 ?
SWAN, M. Architectural Acoustics. Johns Manville Co
1921.
EICHHORN, A. Der akustische Massstab fur Project-
bearbeitungen grosser Innenraume. 1899.
STURMHOFEL. Die Akustik des Baumeisters. 1898.
LACHEZ. Acoustique et optiqite des salles de reunions. 1879.
FANARO. L'acustica applicata. 1882.
WHITMAN, F. P. " Acoustic Properties of Auditoriums."
Science, xxxviii, p. 707, 1913 ; Science, xlii, p. 191, 1915.
ANGERER, E. " Experimentelle Beitrage zur Ausbreitung
des Schalls in der freien Atmosphare." Annalen der
Physik, Ixvi, p. 293, 1921.
BARUS, C. " Acoustic Topography in a Room/' Proc.
Natl. Acad. of Sciences, viii, 1922.
FOLEY, A. L. " A photographic study of Sound Pulses
between Curved Walls." Physical Review, xx, p. 505,
1922.
HENRY, JOSEPH. "On Acoustics applied to Public
Buildings." Annual Report Smithsonian Institution,
Wash., D.C. 1857.
PERIODICAL LITERATURE
ENGEL, GUSTAV E. Uber den Begriff der Klangfarbe.
HaUe, C. PfeSer, 1886.
WEBSTER, A. G. " Absolute Measurement of Sound."
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KAUFMANN, W. " Uber die Bewegung geschlagener
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LLOYD AND AGNEW. " Phase and Tone-quality/ 5 Bulletin
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STEINMETZ, C. P. " Harmonic Analysis." Engineering
Mathematics, New York, 1915.
RUNGE, C. " Harmonische Analyse." Zeitschrift fur
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GROVER, F. W, " Harmonic Analysis." Bulletin Bureau
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179
BIBLIOGRAPHY
THOMPSON, S. P. " Harmonic Analysis." Proc. Physical
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MILLER, D. C. " Material and Tone-quality/' Science,
xxix, p. 161, 1909.
KRIEGAR-MENZEL, OTTO. Uber die Bewegung gestrichener
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EDWARDS, PRESTON H. " A Method for the qualitative
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No. 1, 1911.
WEBSTER, A. G. " Loudness of Sound/' Physical Review,
xvi, p. 248, 1903.
DAVIS, H. N. " Vibration of Violin Strings." Proc. Amer.
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HEWLETT, C. W. " Analysis of Complex Sound-waves."
Physical Review, xxxv, p. 359, 1912.
RANKINE, A. 0. "On recording and reproducing sounds by
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KARCHER, J. C. " A Method for the Measurement of
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REDDIE, L. N. " The Gramophone and the Mechanical
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WOOD, R. W. "The Photography of Sound-waves."
Nature, vol. Ixii, 1900.
JONES, L. A. " On the Theory of Tone-reproduction, with
a graphic method for the solution of the problem/'
Journ. Franklin Institute, Philadelphia, Pa., cxc,
p. 39, 1920.
FERGUSON, DONALD N. " The ' Secret ' of the Pianist's
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ORTMANN, 0. " The Sensorial Basis of Music Appreciation."
Journ. Comparative Psychology, vol. ii, No. 3, 1922.
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180
INDEX
iccelerando, defined in terms of
time-interval, 51
Acceleration, affected by variable
weight, 41 ; effect on key-de-
pression, 17, 21 ; forms of, 62 ff. ;
effect on hammer-stroke, 62 ;
in string-vibration, 98.
accents, dynamic, see Dynamic
degrees
Accompaniment, 142
Acoustics, 164, 166 ; bibliography,
175 ; of music, bibliography,
177 ; see also Propagation of
sound ; see also Architectural
Acoustics
Vction, of piano, description of, 3 ;
illustration of, 2, 4 ; irregularities
in, 38 ; not a fixed unit, 6, 31,
59, 114-15; purpose of, 6;
"weighting" of, 38
Adagio, defined in terms of time-
interval, 51
Aesthetic values, 167, 171 ff. ; see
also Poetic values ; Tone-quali-
ties ; Touch-forms
Affettuoso, 54
\gogic relationship, effect on tone
combinations, 133 ; effect of
variations in, 142 ; see also
Duration
Air, see Melody
Aliquot scale, 11
Allegro, defined in terms of time-
interval, 51
Amplitude, as determinant of loud-
ness, 95 ; as determined by
intensity, 107 1 ; as element of
string- vibration, 93, 108
Anatomical differences, 172
Andante, defined in terms of time-
interval, 51
Angle of force -incidence, 42 ff.
Appassionato, 54
Application, point of, as deter-
minant of force, 38 ; on key-lever,
39
Appreciation of music, not solely
auditory, 173 ; see also Poetic
values, Tone-qualities
Arc of circle, as hammer-path, 60
Architectural Acoustics, 160 ff. ;
works on, 179 ; see also Propaga-
tion of sound
Arm, effect on hammer- stroke, 79,
81 ; effect on key-depression, 18,
27 ; see also Playing-unit ; Re-
laxation; Rigidity
-Arpeggio, 138
Artistic playing, see Poetic values
Ascent of key, see Key-ascent
Atmospheric conditions, 161
Attack of key, see Touch-forms
Attenuation of waves, 147, 162
Audibility, determinants of, 97 ;
threshold of, 97, 110 ; variations
in, 97, 160 ff.
"Bad "tone, 79, 159
Balance, between melody and
accompaniment, 47
Balanced action, 3fL, 32
Bass region and tone-quality, 35,
39, 102, 105, 110; see also
Treble region
Beats, 135, 163
"Beautiful" tone, 152, 159
Beethoven, "Senate Pathetique,"
145
" Bell-like " tone, 25
Belly-bridge, 11
Bibliography, 175-81
Bowed instruments, 179
Bravura, see Brilliant
Bridge, description of, 11, 127
" Brilliant " tone, 25, 75
" Brittle " tone, 25
Buildings, acoustics of ; see Archi-
tectural Acoustics
Bunched fingers, 77
Calando, defined in terms of key-
movement, 51
CantaUh, 80
Case, of piano, 12
Check, for piano-hammer, 4
Chopin, " Berceuse," 139 ; E Minor
Nocturne, 141 ; G Major Noc-
turne, 142
181
INDEX
Chord, more resistance than single
tone, 45, 78
Chord-work, effect on force of touch,
45 f., 78
" Clangy " tone, 13
"Clear" tone, 25
Close touch, 75 ; see also Non-
percussive touch
Coefficient of Elasticity, 66
Co-existing tone, effect on tone-
quality, 132 f . ; intensity effects
on quality of, 133-4 ; see also
Tone combinations
Colours, compared with tone-
quality, 99
Combinational tones, 135
Complex lever, 5
Complex- vibrations, 93, 95 if.
Complexity of tone ; see Tone, com-
plexity of
Components of forces, 42
Compositions analysed, 143 ff.
Compression of felt hammer, 104
Conclusions, on force of touch, 48 ;
on hammer-stroke, 84 ; on key-
depression, 33 ; on noise-element,
159 ; on string- vibration, 126
Con abbandono, 54
Con amove, 54
Con calore, 54
Con tenerezza, 54
Condensation, wave of, 162
Conservation of energy, law of, 64
Consonance, see Harmony
Contact of, finger and key, 18 ff. ;
hammer and string, 64, 101 ff. ;
key and hammer, 57 ff .
Contact-time, see Stroke, duration
of
Continuity of piano-action, 6, 31 , 59,
114
Control, of force-distribution, 48 ;
of hammer-stroke, 74 ; of key-
depression, 20 ff.
Cords, see Strings
Covering wire, 7, 91
Crescendo, defined in terms of
key-speed, 51 ; see also Dynamic
relation
Cross-sectional vibrations, 1191
Curved fingers, 23, 169 ; effect on
hammer-stroke, 75 ; effect on
key-depression, 23 ; effect on
tone, 169 ; see also Flat fingers
Cushioned fingers, 151
Damper, effect on weight of touch,
41
Damper pedal, 10 ; effect on force
of touch, 41 ; effect on hammer-
stroke, 78 ; effect on staccato,
78 ; effect on tone, 139
Damping of string- vibration, 101,
147
Decrescendo, see Diminuendo
Density, as determining vibration-
form, 92
Depression of piano key, 14-34
" Depthless " tone, 26, 150
Descent of hammer, see Hammer-
stroke, after leaving string
Diameter of string, as determining
vibration-form, 92
Diatonic scale, 38
Difference-tones, 135
Diffusion, effect on tone-quality,
164 ; laws of, 160 ; types of, 164
Diminuendo, characteristic of
string- vibration, 100, 109 ; de-
fined in terms of key-speed, 51 ;
in terms of key-movement, 51 ;
irregularities of, in piano tone,
110, 125, 169 ; see also Dynamic
relation
Direction of force, effect on accen-
tuation of parts, 47; effect on
force of touch, 42
Displacement of string, see String-
vibration; Amplitude
Dissonance, physical basis of, 135
Distortion of waves, 160
Dolce, 54
Doloroso, 54
Doppio movimento, defined in terms
of time-interval, 51
Double-overstrung, 12
" Dry " tone, 26, 80, 159
Duplex scale, 11 ; see also Aliquot
scale
Duration of contact, between finger
and key, 21 f. ; between hammer
and string, 83 f. ; between key
and hammer, 73 f.
Duration of force-application, 48
Duration of stroke, see Stroke,
duration of
Duration of tone, 112 ; determined
by pitch, 105, 112, 133; effect
on musical value of tone, 167 ;
effect on string-vibration, 100,
109 ; nature of, 92
182
INDEX
Dynamic degrees, effect on touch-
forms, 52 ; in hammer-stroke,
69 ; in key-depression, 19 ; in
noise-elements, 148 ; in string-
amplitude, 119 if. ; in string-
vibration, 107 ; shown in key-
speed, 29
Dynamic relationship, effect on
string-displacement, 119; effect
of variations in, 142 ; see also
Intensity
Dynamics, in terms of hammer-
speed, 70 ; in terms of key-
movement, 51
Ear, resonance of, 170 ; sensitivity
of, 170, 173
Echo, 161
Elasticity, coefficient of, 66 ; of
hammer, varies with pitch, 103 ;
of key-action, 30 ; of metal
construction, 12 ; of touch, 30 ff.
End of tone, see Tone-end, Key-
ascent, Key-release
Energy, conservation of, 64 ; trans-
fer of, from hammer to string,
62 f., 66
Error, sources of, 123
Escapement, as determining
hammer-speed, 615 ; as freeing
the hammer, 59 ; description of,
4 ; diagram of, 59 ; hammer-
stroke after, 81
Espressivo, 54
" Even " touch, see Touch-forms
Expression, miscellaneous terms of,
54 ; see also Poetic values
Extreme vibrations, 118
Eye, as determinant of musical
value, 173
/, see Dynamic degree^
Falling-body, 28
Feeling, see Poetic values
Felt, changes in, during string-
contact, 64, 104 ; effect on tone,
66, 139 ; varies with pitch, 103
ff, see Dynamic degrees
Finger, effect on key-depression,
18, 27 ; see also Finger-position
Finger-impact, as determinant of
tone-quality, 152 ; determined
by finger-tip, 151 ; noise of, 149 1 ;
time of, 151 ; see also Percussive
touch
Finger-position, curved finger, 23,
75, 169 ; effect on hammer-
stroke, 75 ; effect on key-de-
pression, 23 ; flat finger, 23, 75,
169
Finger-stroke, effect on hammer-
stroke, 75 ; effect on key-de-
pression, 23, 27 ; effect on
string- vibration, 169 ; effect on
tone, 171
Finger-tip, as determinant of noise,
151
Fist, 77
Fixed movement of action, 3, 15
Flat finger, effect on hammer-
stroke, 75 ; effect on key-de-
pression, 23 ; effect on tone/169 ;
see also Curved finger
Flexibility of string, 91
Foot-pounds, 45
Force of touch, 35, 49 ; affected by
damper pedal, 41 ; conclusions
of chapter on, 48 ; dependence
on direction, 42, 47 ; dependence
on number of keys, 45 ; deter-
mined by pitch, 35 ; determined
by point of application, 39 ;
divided between the hands, 47 ;
effect on simultaneous key-de-
pression, 45 ; illustrations of, 37,
39 ; irregularities in, 38 ; quan-
titative measurements of, 37 ff. ;
variations in, 36 ; variations
during key-descent, 28, 41 ;
varies with dynamic degree, 47
"Forced "tone, 26, 115
Forced vibrations, see Resonance,
forced
Forces, action at hammer-string
contact, 66 ; action of, 42
Fore-arm stroke, effect on key-
depression, 27
Forms of extreme vibration, 118
Formula, for kinetic energy, 63 ;
for string-vibrations, 6; for
velocity. 61
Forte, see Dynamic degrees
Forte pedal, see Damper pedal
Fortissimo, see Dynamic degrees
Forzando, see Dynamic degrees
Fourier's Theorem, 94
Frame, kind of wood used, 13 ;
metal, 12 ; wooden, 12
Frequency, 92; effect on beats,
135 ; in relation to contact-
time, 102
183
INDEX
Friction-noises, description of, 148,
154
" Full " tone, 26
Fundamental tone, 92 ff., 167
fz, see Dynamic degrees
Generator, see Fundamental
Giocoso, 54
Glissando, 52
" Good " tone, 26, 150, 152, 159,
167 ; affected by noise, 150, 153 ;
effect on hammer-stroke, 80 ;
effect on string- vibration, 116
Grand piano, 3
Halls, acoustics of, 160ff.; see also
Architectural acoustics
Hammer, of piano, as a free body,
57, 60, 73, 82 ; changes in, during
string-contact, 104 ; changes with
use, 140 ; conclusions on move-
ment of, 64 ; description of, 57 ;
effect of movement on tone, 66 ;
form determined by pitch, 103 ,
independence at escapement 59 ;
in contact with string, 64 ; move-
ment of, 58 ; speed as sole
variant, 61 ; variations in gener-
ating speed, 61-3
Hammer-impact, description of,
148 ; noise of, 148 ; point of, 96 ;
time of, 149
Hammer-speed, relation to key-
speed, 6 ; sole variant in hammer-
movement, 61
Hammer-stroke, after escapement,
81 ; after leaving string, 84 ;
conclusions on, 84 ; effect of
relaxation on, 71 ; effect of
rigidity on, 71 ; effect on tone-
quality, 80 ; effect of weight on,
69, 70 ; independent of key-
stroke, 73 ; method of recording,
67-68; records of, 67-82; see
also Stroke, of hammer
Hand -posit ion, effect on hammer-
stroke, 75 ; effect on key-
depression, 18, 27
Hand -staccato, 152 ; effect on
noise-complex, 156
Hand-stroke, effect on key-depres-
sion, 27
Harmonic vibration, 122, 137, 139
Harmonics, see Partials
Harmony, physical basis of, 51,
133
" Harsh " tone, 26, 80, 115, 116
Helmholtz, table of contact -time,
103
High wrist, see Wrist position
Hopper, 4, 59 ff.
Illustration, of compositions, 142-5;
of force of touch, 37, 39 ;
of hammer-stroke, 67-85 ; of
key -depression, 16-31 ; of noise-
elements, 147-59 ; of piano-
action, 3, 4 ; of player-piano
records, 142-5 ; of sound from
string, 169 ; of string- vibration,
105-23 ; of vibrating string, 95,
96
Imagination, as factor in tone-
reaction, 171 ; see also Poetic
values
Impact-noises, 148 ff. ; of finger-
key, 151; of key-bed, 153
Impersonal tone-production, 117
Incidence, angle of, 161 ; of force-
angle, 42-3
Inertia, of string- vibration, 9
Intensification of sound, by ear-
resonance, 170
Intensity, as determined by per-
cussiveness, 114 ; as determined
by relaxation and rigidity, 20, 71,
114; as determined by sound
propagation, 162 ; as determined
by finger-position, 169 ; as de-
termined by string-speed, 98 ;
effect on amplitude of string-
vibration, 107, 117 ; effect
on harmonics, 137 ; effect on
noise-elements, 149 ff. ; effect on
partials, 102 ; effect on sounding-
board, 130
Intensity of tone, as determinant of
pedal effects, 139 ; as determin-
ant of quality, 26, 80, 97, 108,
110, 116, 136, 138 ; depends on,
92 ; determined by finger-posi-
tion, 76, 169 ; determined by
hammer-force, 96 ; effect on
simultaneous tones, 133-4; varia-
tions in, 100
Interference, 160, 162
Interference of sound-waves, 162
Interpretation, see Poetic values
Interval, of pitch, see Touch-com-
binations ; of time, see Touch-
combinations ; physical rela-
184
INDEX
tionship of, 96 ; see also String-
vibration
" Jarring " tone, 25
Jerk of key, 21 ; see Escapement
Key, of piano, ascent of, 32 ; as
falling body, 28 ; as moving
body, 15 ; as simple lever, 30,
36 ; description of, 14 ; move-
ment of, 14
Key-ascent, 30 ; illustrations of,
31 ; independent of descent, 32 ;
noise of, 154
Key-bed impact, as determinant of
tone-quality, 153 ; description of ,
153
Key-board, see Action ; Key ;
Lever
Key-control, as determinant of
" artistic " playing, 56 ; as de-
terminant of touch-form, 22 ;
depends upon touch-form, 29 ;
how best secured, 48
Key-depression, 14-34 ; conclu-
sions of chapter on, 33 ; de-
termined by key-speed, 16 ;
effect of percussion on, 20, 29 ;
effect of pressure on, 32 ; effect
of relaxation on, 18 ; effect of
rigidity on, 18 ; effect on weight
on, 18 ; effect on tone-quality,
24, 26 ; limitations of, 15 ;
method of recording, 16 ; records,
of, 16 ff., simultaneous and suc-
cessive, 51 ; variations in force
during, 28 ; variations in speed
of, 16
Key-pressure, effect on key-move-
ment, 32
Key-speed, as sole variant in key-
movement, 16ff., 50; deter-
mined by part of arm used, 27 ;
determined by percussiveness,
22 ; determined by relaxation or
rigidity, 18; variations in, 16-17
Kinesthesis, as aid in reaction, 173
Lamentoso, 54
Layer process, in piano-case, 13
Least audible tone, numerical
values for, 38
Legato, physical basis of, 131 132
Length, of hammer-stroke, 58 ;
of key-depression, 14 ff. ; of
string, 6, 92, 110; see also
Duration, Time-interval
Lever, laws of, 14, 60
Limit of Elasticity, 100
Line of force-application, 36
Loops, see Node
Loud pedal, see Damper pedal
Low wrist, see Wrist-position
MacDowell, "To a Wild Rose," 138
Martellato touch, 21, 52, 77, 119
Mass, 61
Maximum force-effect, vertical, 43
Mechanical action, laws of, 5
Mechanics, bibliography of works
on, 176
Mechanics of piano-action, 4
" Mellow " tone, 25
Melody, accentuation of, 47, 53 ;
dependence on successive key-
depression, 51 ; physical basis
of, 133 ;
Membrane, laws of vibrating, 127 ;
see also Sounding-board.
Mendelssohn, Rondo Capriccioso,
146
Meno mosso, defined in terms of
time-interval, 51
Mesto, 54
Metal, in piano construction, 12
" Metallic " tone, 25
Mezzo-forte, see Dynamic degrees
Mezzo-legato, 52
Mezzo-piano, s& Dynamic degrees
Mezzo-staccato, 52
mf, see Dynamic degrees
Motion, of hammer, 57 ff. ; o
piano-key, 14 ff, ; of sounding
board, 127 ff. ; of sound waves
160 ff.; of string, 9l E.
Movement, used in playing, o
hammer, 57 ff. ; of key, 14 ff.
of string, 105 ff. ; see also Touc)
forms
Moving body, laws of, 15
mp, see Dynamic degrees
Multiple Echo, 161, 163
Muscles, see Relaxation an<
Rigidity
Muscular sense, 173
Musical tone, as free from nois<
150; not a pure tone, 93,166
Musical touch, see Poetic values
Node, 67, 104
Noise, nature of, compared wit
tone, 158
185
INDEX
Noise-complex, 156, 165 f.
Noise-element, 147-159; affected
by percussiveness, 150 ; analysis
of, "90 ; classification of, 148 ;
depends on style of composition,
155 ; effect on tone-quality, 152 ;
general effects of, on sound-
complex, 159 ; illustration of,
156 ; integral part of sound-
complex, 140, 147 ; marked
effect on tone, 155 ; method of
separation from tone, 147 ; of
finger-impact, 151 ; of hammer-
impact, 148 1 ; of key-bed im-
pact, 153 ; time of, in relation
to tone, 157 ; tonal-noises, 157
Non-legato, 131
Non-percussive touch, 19 ; absence
of noise-element in, 150 ; as
determinant of key-control, 22 ;
control of, 22, 74; effect on
hammer-stroke, 72, 74-5, 77;
effect on key-depression, 22-4,
28, 29 ; effect on string- vibration,
114; free from impact -noise, 151;
nature of, 21 ; never transmitted
to string, 82
Normal tone, 75, 80, 81
Notation, deviations from, 143 ff.
Note, see Tone
Ohm's Law, 93
Overlapping of tone, 131 ff.
Overstringing, 12
Overtones, dynamic relations of,
97 ; effect of touch on, 97 ff. ;
see Partials ; see Fundamental
p, see Dynamic degrees
Padded fingers, effect on tone-
complex, 151
Partials, affected by pedal, 137 ;
as determined by pitch, 105, 110 ;
description of, 96 ; effect on
string-vibration, 101, 109, 111,
122 ; production of, 95 ; table of
intensities, 103
Pedals, 10 ; damper, 10 ; una
corda, 10 ; sostenuto, 10 ; func-
tion of, 10 ; effect determined by
intensity, 137, 139; effect on
string-vibration, 122 ; effect on
tone-combination, 136, 138,
142 ; effect on tone-complex, 10 ;
resonance effects of, 10
Percussive touch, control of, 21 ;
nature of, 20, 21 ; effect on
impact-noise, 151 ; effect on
intensity, 22 ; effect on hammer-
stroke, 72, 74-5, 77 ; effect on
key-depression, 20, 22-4, 28, 29 ;
effect on string- vibration, 114
Perdendosi, defined in terms of key-
movement, 51
Period of vibration, see Frequency
Periodical Literature on sound and
on piano, 180
Phase, effect on quality, 94, 117 f. ;
explanation of, 94
Photograph, of amplitude of sound
waves, 169; of piano-action, 3, 4 ;
of vibrating-string, 124
Pianissimo, see Dynamic degrees
Piano, see Dynamic degrees.
Piano, construction of, 3 ff. ;
essentially a rhythmic instru-
ment, 155 ; sound-complex of,
89
Piano -action, see Action of piano
Pianoforte, works on construction,
tuning, tone, etc., 178
Piano pedal, see Una corda pedal
Piano -tone, characteristic quality
of, 104 ; complexity of, 124 ;
determined by construction, 3 ff.,
15, 64, 96 ff. ; determined by
hammer-stroke, 80 ; determined
by intensity, 107, 117; deter-
mined by key-depression, 24, 26 ;
determined by noise-element, 152 ;
determined by string- vibration,
92 ff. ; instability of, 100, 102,
131 ; see also Tone-quality
Piano touch, see Touch-forms
Pietoso, 54
Pitch, depends on frequency, 92 ;
effect on force of touch, 35,
37, 39, 42 ; effect on simultaneous
tones, 132 ; effect on sounding-
board, 130 ; effect on string-
vibration, 110; effect on tone-
quality, 105
Plane of incidence, see Angle of
incidence
Plate, vibrating, 127
Player-piano, 140, 142, 146 ; records
of, 142
Playing-unit, see Finger, Hand,
Wrist, Arm
Pleasant tone-quality, physical
basis of, 167
186
INDEX
" Plump " tone, 13
Poetic values, as determined by
intensity, 135 ; as determined by
intensity and duration, 140,
142 ff. ; as determined by key-
speed, 55 ; as determined by
pedal, 139 ; as determined by
string-vibration, 115 ft. ; fine-
ness of, 141 ; in tone-combina-
tions, 135 ; not purely auditory,
173 ; physical basis of, 142, 171 ;
terms of, 53
Point of application, of force, 40 f.
"Poor " tone, 25, 113
Portamento, 52 ; see also Relaxation ;
" Good " tone
Portato, see Portamento
pp, see Dynamic degrees
Pressure, effect on key-ascent, 32 ;
after key-descent, 32 f. ; see
also Weight-touch
Propagation of sound, 160-70 ;
effect on tone-quality, 164 ;
general effect of, 167; not
affected by interference, 162
Properties of moving bodies, 15
Pure tone, 93, 166
Quality of Tone, see Tone-quality ;
see Intensity
Rachmaninoff, C# minor Prelude,
119
Rarefaction, wave of, 162
Records, of compositions, 142-5 ;
of hammer-stroke, 67-85 ; of
key-depression, 16-31 ; of player-
piano records, 143-5 ; of string-
vibration, 105-23
Reflection, 160, 161 ; laws of, 161 ;
effect on intensity, 162 ; effect
on pitch, 166
Reflector, 168
Relaxation, effect on control, 172 ;
effect on hammer-stroke, 71 ;
effect on intensity, 169; effect
on key-depression, 18, 20 ; effect
on noise-element, 150 ; effect on
string- vibration, 113, 115 ; effect
on tone, 20, 172
Religioso, 54
Repeating action, see Repetition
mechanism
Repetition mechanism, 4, 79
Resonance, 160 ; forced, 10, 128 ;
of ear, 170 ; sympathetic, 9, 122,
136, 163
Resonator, 8, 9
Retardation, in key-descent, 20 ;
absent in hammer-stroke, 73
Reverberation, 163, 165 ; effect on
sound-quality. 165
Rhythm, as variations in duration,
135 ; affected by noise-element,
155
Rigidity, as influencing intensity,
114; effect on hammer-stroke,
71 ; effect on intensity, 169 ;
effect on key-depression, 18, 20 ;
effect on noise-element, 150 ;
effect on string- vibration, 113,
115 ; effect on tone, 20, 172
" Ringing " tone, 25
Ritardando, defined in terms of
time-interval, 51
" Round " tone, 25
Rubato, as variations in duration,
135
Scales, unevenness in key-action,
38
Scherzando, 54
" Set " Muscles, 113
$/, see Dynamic degrees.
sffff, 119 ; see also Dynamic degrees
Sforzando, see sf, sff, sffff] see also
Dynamic degrees
"Shallow" tone, 26, 75, 81, 150,
159
" Shrill " tone, 25
Silent key-depression, 137 ; effect
on tone, 138
Simple vibrations, 93, 95
Simultaneous tones, 131 if. ; effect
on noise-element, 155 ; effect
on tone-quality, 131 ff.
Sine curve, 16, 122
"Singing" tone, 26, 115, 152; see
also " Good " tone
Single-overstrung, 12
"Slapped" tone, 150, 157; see
also " Shallow *' tone
Sostenuto 78, 154
Sostenuto pedal, 10
" Soulful " tone, see Poetic values
Sound, bibliography of works on,
175 ; propagation of, 160
Sound-complex, analysis of, 89 1
Sounding-board, description of, 8,
127 ff. ; effect on tone, 128 f. ;
improvements in, 9; laws of
vibration of, 127 ; rocking of, 33
187
INDEX
Sources of error, see Error, sources
of
Speed, sole variable in key-move-
ment, 15 ; sole variable in
hammer-movement, 61
Spun -string, 7
Staccato, effect on hammer-stroke,
74 ; effect on noise-element, 152,
154 ; non-percussive staccato,
77 ; percussive-staccato, 77
" Steely " tone, 25
" Strident " tone, 25
Striking-body, effect on noise-
element, 151
Striking-place, 96, 104
String, description of, 7, 91 ;
displacement by hammer, 94 ;
forms of vibration of, 94, 95, 98 ;
illustration of vibration of, 95,
96 ; laws of vibration of, 6, 92 ;
material of, 7, 91 ; never set into
vibration gradually, 82 ; not
in permanent contact with action,
6 ; tension of, 7, 92
String- vibration, affected by
duration, 100, 125 ; affected by
relaxation and rigidity, 113;
analysis of, 94 ; complexity of,
120 1, 124 ; conclusions on, 126 ;
determined solely by hammer-
velocity, 65, 83 ; effect of dura-
tion on, 109 ; effect of intensity
on, 107, 120, 125; effect of
pitch on, 110 ; extreme form of,
118 ff. ; method of observing,
125 ; methods of producing, 91 ;
method of recording, 106 ; mis-
cellaneous forms of, 121 ; records
of 105-23 ; variations in dura-
tion of, 110, 112, 125; various
forms of producing, 91
Stroke, of hammer, duration
of, 101, 102 ; effect on tone-
quality, 102 ; relation to string-
frequency, 102 f . ; see also
Hammer-stroke
Style, miscellaneous terms of, 52 ff.
Stylus, used for recording vibra-
tions, 106, 123 ; forms of, 106
Successive tones, 131 ff.
Summational-tones, 136
"Surface" tone, 115, 150; see
also " Shallow " tone ; " Depth-
less " tone
Sympathetic Resonance, see Re-
sonance, sympathetic
Sympathetic tone, 25, 115, 116,
152, 159
Tapering fingers, effect on tone-
complex, 151
Tempo, in terms of key-movement,
51; effect on pedaling, 139;
effect on tone-combinations,
131 ff . ; effect on touch-forms,
52
Tension, asdeterminantof vibration-
form, 92 ; effect on pitch, 7 ;
effect on quality, 98
Thickness of string, see Diameter
Threshold of Audibility, 40, 97, 110
"Thumped "tone, 26
Time-interval, as determinant of
successive key-depression, 51 ;
variations in, 51
Tonal-noises, 157
Tone, analysed in terms of string-
vibration, 92 ff. ; complexity
of, 89, 124 ; definition of "good"
and" bad ", 25, 167; dependence
on hammer-movement, 66; de-
pendence on instrument, 13 ;
dependence on player, 13 ; vari-
ations in complexity of, 141,
137 ; various qualities, 25 ; see
also Tone-complex, Tone-quality
Tone-beginning, as determinant of
quality, 157
Tone-colour, see Tone-quality
Tone combinations, 131 ff. ;
comparison with single tone, 131,
134, 140
Tone-Complex, affected by pedal,
10 ; analysis of, 89, 96 ff. ;
determined by intensity, 100 ;
determined by metal construc-
tion, 13 ; in terms of string-
vibration, 124 f. ; present in
all musical instruments, 93 ;
variations in, 100, 124, 142
Tone-end, determined by key-
release, 32
Tone-production, impossible beyond
escapement-point, 61 ; see also
Touch-forms
Tone-qualities, 13, 24, 29, 34, 53,
74-5, 115, 150, 152, 157
Tone-quality, as determined by
"beat-tones", 136; as deter-
mined by co-existing tones, 132 ;
as determined by combination
of key-movements, 51, 55 ;
188
INDEX
as determined by duration of
string-vibration, 100, 110; as
determined by duration of
stroke, 83, 102 ; as determined
by hammer-stroke, 80, 99 ; as
determined by intensity, 80 , 96 ff. ,
108 ; as determined by key-
speed, 25, 26 ; as determined by
material of striking-body, 104 ;
as determined by multiplicity of
tones, 132 ; as determined by
noise-element, 150-153 ; as
determined by partials, 96 ff.,
102 ; as determined by per-
cussiveness, 114; as determined
by pitch, 105, 128, 167; as
determined by simultaneous
tones, 133-4 ; as determined by
sound - propagation, 164 ; as
determined by sounding-board,
1291; as determined by striking-
place, 104 ; as determined by
string, 91, 92 ; as determined by
string- vibration, 113, 115; as
determined by vibration-form,
92; effect of metal on, 13;
effect of pedals on, 136 ff. ; how
best secured, 48 ; independent of
amplitude, 123 ; independent
of phase, 94 ; physical basis of,
136
Tone-succession, 132 ff.
Torsion, 119
Touch combinations,50 ff.; similarity
to single key, 50
Touch-forms, affected by dynamics,
52 ; affected by tempo, 52 ;
based on control, 22, 29, 171 ;
determined by force, 35 ff. ;
determined by noise-element, 156 ;
effect on string- vibration, 115;
purpose of, 22, 171
Transfer of energy, from hammer
to string, 66
Transverse vibrations, 6, 92 ff.
Treble region and tone-quality, 35,
39, 102, 105, 110 ; see also Bass
region
Tune, see Melody
Tuning, 7
Tuning-fork, quality of tone of, 93,
169; records of, 16
Una cor da, 10 ; effect on string-
vibration, 122 f. ; effect on
tone-combination, 139, 142
" Uneven " touch, see Touch-forms
Unpercussive touch, see Non-
percussive touch
Unpleasant tone-quality, physical
basis of, 167
" Unsympathetic " tone, 115,116
Use of piano, variations with, 140
Velocity, independent of manner of
attainment, 61 ; of hammer, sole
determinant of tone, 62 ; of key,
sole determinant of tone, 24
" Velvety " tone, 25
Vertical force, 43
Vibration-forms, see String-vibra-
tion
Vibration of string, see String-
vibration ; of sounding-board,
see Sounding-board, vibration of
Vibrato touch, effect on key-move-
ment, 32 1
Vibrator, 168
Vision, as aid in reaction, 173
Voicing, 40
Volume, of tone ; see Tone-quality,
Intensity, Pitch
Waves, of sound, 160 ff. ; change
in direction of, 161
Weber's Law, 40 ; effect on tone
intensities, 41
Weight-touch, addition after key-
impact, 42 ; effect on hammer-
stroke, 71, 75, 79, 80; effect
on key-depression, 20, 26 ; effect
on noise-element, 152 ; effect on
string- vibration, 116
Whispering galleries, 166
Wood, in piano construction, 12
Work, measure of, 45
Wrapped strings, 91 ; see Spun-
string ; Over-stringing
Wrest-plank, 11 1
Wrist-position, effect on hammer-
stroke, 76 ; effect on key-
depression, 23
Printed in Great Britain by Stephen Austin & Sons, Ltd., Hertford.
