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MAY
15
Mtrsic TiiAt)E REVIEW
17, 19i9
OurTECHNICAL DEPARTMENT
CONDUCTED BY WILLIAM BRAID WHITE
FUNDAMENTAL ELEMENTS OF PIANO TONE
Written for Piano Makers, Technicians and Tuners by William Braid White—Third Article
In the last'article I made a rather painstaking
explanation of the physical phenomena involved
in the propagation of a perfectly simple sound-
wave. Of course, in view of what was said be-
fore this explanation, the reader will at once
understand that I have described the propaga-
tion of a mathematically simple sound only. I
mean by this a sound produced by the perfect
pendulum vibration of a mathematically uniform
and constant body. Such bodies, making such
forms of perfectly simple vibration at a constant
rate, or at any rate at all, are very rare, and,
in fact, purely speaking, cannot be said to exist.
The nearest approach to them will be found in
the tuning fork, especially in the magnificent
electrically-driven instruments which are used
in physical laboratories.
But we have to deal with the sounds of every
day and, even in the piano, with sound-producers
which are not, and cannot be, of mathematically
exact construction. Moreover, the sound-pro-
ducers of the piano—its strings—are not, and by
their nature cannot be (as we shall see later),
capable of producing wholly perfect and simple
forms of vibration. Indeed, we shall find that
the strings of the piano perform extremely com-
plex forms of vibration, and give rise to sounds
equally complex, although their complexity does
not appear until we try to study them in order
to discover means for their improvement.
It is therefore important to keep in mind the
fact that the physical explanation of a sound-
wave given in the last article refers to the
simplest possible form of vibration producing
the simplest possible form of sound: that is
to say, sound uniform, constant and unitary.
Nevertheless, let it be also remembered that
all sounds, no matter how complex, can be re-
duced and, in fact, are composed of various
simple vibrations of the type already described.
These simple forms of vibration or sound-
waves are the raw material, as it were, of all
the saunds of daily life.
During his investigations into the phenomena
of heat, which he discovered to be a mode of
motion, like sound, the great French mathema-
tician and physicist, Fourier, made the impor-
tant discovery that any complex curve can be
analyzed into a series of simple curves which
bear to each other certain definite mathematical
relations. Now, mathematically, we can accu-
rately represent a motion like that of a vibrat-
ing tuning fork in the shape of a curve, and
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This formerly was the tuning department of the New
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since the path of such a curve can be traced
by knowing that it travels according to certain
mathematical ratios between angles formed at
perpendiculars drawn from its base line it fol-
lows that we can represent the path of any
curve in a mathematical expression. Fourier
did this in the form of an equation, following
the method originally laid down by Descartes
one hundred and fifty years earlier. Thus he
was able to show that a mathematical expression
covering the most complex path of a complex
curve can be analyzed into a series of simple
expressions, each representing the perfectly
uniform path of the simple type of curve already
described, a simple curve of sines, as it is called.
Such simple curves differ from each other only
in length and amplitude (width).
The raw material, then, of sound is the sim-
ple vibration form, producing some simple tun-
ing fork tone. All sounds, whether we call
them tones or mere noises, are more or less
complex congeries of these.
Noise and Tone
The vastly greater number of the sounds we
hear are to be classified as noises. Without
being able always to furnish an explanation of
the difference between the two kinds of sound,
we are always able to recognize a musical tone
as against a noise. What is the prime quality
in a musical tone which we recognize at once
and by the recognition of which we at once
identify the sound as musical and not as noise?
Evidently it is, in the musical tone, the ele-
ment of continuity and persistence. The mu-
sical tone is recognized as continuous and per-
sistent, as the constant result of a constant
force, whatever its nature may be. On the con-
trary, the noise is recognized because its prin-
cipal characteristic is its discontinuity, and
what we may call "raggedness." It is evidently
the result of many smaller sounds clashing and
jairing together as if thrown in a heap without
any question of fitting the one into the other.
The tone, then, is'characteristically continuous
and constant, the noise discontinuous and arbi-
trary.
Within the bounds of this definition, of
course, a multitude of classifications may be
made. There are noises which just hover on
the verge of continuity; that is to say, which
are almost musical tones. ,So, too, there are
tones which just escape degeneration into mere
noise. The definition holds good, nevertheless,
and within the very widest limits, it is proper to
say that noises and tones can always be distin-
guished.
What has been said of noise, of course, does
TUNERS
not in the least alter the previous definition of
simple sounds. A noise is a congeries of sim-
ple sounds so mixed as to clash against each
other and produce discontinuity of effect. A
tone is a congeries of simple sounds preserving
continuity and constancy.
Measuring Simple Tones
Any musical tone may be distinguished by
three properties. We may consider its relative
loudness. We may judge its gravity or acute-
ness (its highness or lowness). Or we may
distinguish its "quality." All tones can be
measured by these three standards. We can
tell more or less accurately how loud a tone
is. We can judge by various methods or by
mere practice of the ear its position in the scale
ol" tones, which we call its pitch. We can like-
wise distinguish sounds of the same pitch from
each other by their "tone-color" or quality,
meaning the peculiar individuality possessed by
the tones produced from individual human
voices, musical instruments or other tone-pro-
ducing apparatus. Thus, to take a simple ex-
ample, the quality of a tone produced upon the
piano is quite easily distinguished from the
tone of the same pitch and even the same loud-
ness produced on the violin, the harp, or the
cornet.
Loudness
We have no trouble at all in recognizing a
noise as louder or as less loud than another, nor
have we any greater difficulty in perceiving sim-
ilar differences in musical tones. As we con-
tinue to improve our faculties of perception by
practice we find that we can distinguish ever
more delicate distinctions between one degree of
loudness and another. But what is the physical
cause of loudness?
Obviously the loudness of a sound must de-
pend upon the violence of the disturbance which
is created in the surrounding atmosphere by
the original vibrating body. In a word, the
wider the swing of the vibrations the more
violent will be the alternate reciprocal motions
of the surrounding air, and consequently the
more violent will be the aerial disturbance. As
the wave of propagated sound expands con-
centrically through the circumambient air, it
gradually loses its original force through the
gradual increase in frictional resistance of the
air particles till by degrees the entire vibra-
tion of the sounding body itself is brought to
a close through the same cause, or else the
propagated wave, even though the body keeps
up its original strength of vibration, comes tb
an end at a distance from the body simply
through the accumulation of frictional resist-
ance to its further motion.
*
Technically, the width of swing of a vibrating
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(Continued on page 16)
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