Music Trade Review

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TECHNICAL^SUPPIY DEPARTMENT
William BraidWhiteXecfimcalEditor
The Rationale of the Striking Distance
in Drawing the Scale for the Piano
A Vital Problem of Which It Is Necessary There Should Be a Clear and Accurate Understand-
ing on the Part of the Draftsman—Young's Law and Its Application to the Piano Scale
—Striking the String at One-eighth of Its Speaking Length—The Effects Produced
N the course of the article which came be-
fore this one in the scale drafting series, I
managed to make a silly mistake, which is
herewith amended with regrets. On page 29 of the
issue of September 4, in talking about string
length, I said (top of first column) that unison
No. 86 will have a length of 2.15 inches on the
system of scaling adopted. This should have
been 2.22 inches, as doubtless more than one
reader has by now found out for himself.
As showing how such errors will sometimes
occur and even persist for a long time, it may
be interesting to point out that some time ago I
prepared an elaborate table giving lengths from
C7 at 2 inches, on the 1: 1.875 octave ratio, to-
gether with the logarithm of the length and log-
arithm also of the length squared, in order to
facilitate the labor of scale calculation, which is
a good deal of a tedious job when everything
has to be worked out in detail each time.
Throughout the greater extent of the scale the
lengths run on the same ratio from C7, what-
ever be the length of the piano.
In making this table I misread the logarithm
for unison No. 86 and consequently miscalcu-
lated the length. I have since gone over the
whole list, and checked it up, but have found
no further mistakes.
Rationale of Striking Distance
We have now reached the important and in-
deed vital question of striking distance. It is
very necessary that there should be a clear un-
derstanding as to the reasons for choosing one
rather than another contact point for the meet-
ing of hammer and wire, more especially be-
cause there is a great deal of misinformation
afloat on the subject.
Piano makers have been experimenting, as a
matter of course, ever since pianos became com-
mercially important, with every possible kind
of construction which has presented any faint
hope of improvement in tonal quality or quan-
tity. A good deal of the effort has indeed been
wasted, largely because the piano makers have
been very loath to call in the aid of men
skilled in the analysis of sound. Nevertheless,
the many poorly made or unsoundly based ex-
periments have, in due course, destroyed them-
selves, whilst those which have had sound foun-
dation have survived and, in most cases, have
been worked into the body of general practice.
Among these none has been of greater im-
portance than the long series devoted to find-
ing the best points on the string for the con-
tact of the hammer.
The late A. J. Hipkins, than whom no greater
authority on the history and development of
the piano ever lived, has stated (in a letter
to the late A. J. Ellis, the translator of Helm-
holtz, printed in one of the appendices to that
monumental work) that extant harpsichords,
spinets and virginals show no sign of calculated
striking points. It appears that the points of
contact varied in different instruments and
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regions of their scales from one-half to one-
seventh of the speaking length of the strings.
There does not appear to have been any sys-
tem at all, nor any knowledge of the control
over tone quality which is the result of proper
choice of these points. In fact, it appears that
John Broadwood the first, more than one hun-
dred years ago, at or near the close of his long
career, was the first to attempt to put this
question upon a sound basis, if indeed he was
not also the first to perceive its practical im-
portance. He called in the ablest physicists of
the day to help him in deciding upon string
lengths, tensions and striking points. The prin-
cipal results of their experiments have come
down to us in some of the now generally ac-
cepted methods of construction Among these
is the practice of scaling the striking points at
from one-seventh to one-ninth of the speaking
lengths. The choice of these positions was
largely animated.it may be guessed, by the pub-
lication of Young's law. This rule announces
that when a string is struck at a node the par-
tial tones originating at that node are blotted
out.
Young's Law
Now we already know that a string always
subdivides itself when it is struck, after it has
begun with its whole length vibration. We also
know that the first eight of the resulting partial
tones are concordant to the fundamental sound
of the string, with perhaps the single exception
of the seventh, which may or may not be re-
garded as discordant. One the other hand, the
higher partials, from the ninth upward, are
mainly discordant, save the tenth, twelfth, six-
teenth and twentieth. It is therefore obvious,
if Young's law be correct, that if we wish to
blot out, say, the ninth partial, we must strike
the string on the ninth node, that is to say, at
exactly one-ninth of its length. And so on. In
spite of the rule, however, piano makers con-
tinued to come more and more generally to the
use of one-eighth of the string's length for the
middle, bass and alto regions of the instru-
ment. It was evident that the rule did not al-
ways work, perhaps because, as we know,
Young had experimented with thin wires struck
with sharp pointed steel hammers, whereas the
piano string is relatively stiff, thick and heavy,
William Braid White
Associate, American Society of Mechanical
Engineers; Chairman, Wood Industries
Division, A. S. M. E.; Member, American
Physical Society; Member, National Piano
Technicians' Association.
Consulting Engineer to
the Piano Industry
Tonally and Mechanically Correct Scales
Tonal and Technical Surveys of Product
Tonal Betterment Work in Factories
References
to manufacturers of unquestioned
position in Industry
For particulars, address
209 South State Street, CHICAGO
39
and is struck by means of a soft and relatively
blunt-headed mass of felt. At any rate, the
translator of Helmholtz, A. J. Ellis, determined
to make trial of the facts, and, with the assist-
ance and aid of A. J. Hipkins, tested carefully
the partial tone emergence from strings on
Broadwood grands, selecting strings in the
region of the one-eighth striking distance. The
results of the experiments showed beyond a
doubt that when a string is struck at one-eighth
of its length the eighth partial is not destroyed.
In other words, when one strikes a string
at one-eighth of its speaking length, the first
eight partials are all present, with their multi-
ples. Now the first eight partials, with the
single exception of the seventh, are all elements
in what is called the common chord major of
the fundamental. Thus, in the case of any C, the
partials respectively are C an octave above, G
above that, C again, E above that, G again, B
flat and C, the third octave. The E, G and C
are all parts of a much-extended common chord
major. Even although they are very feeble in
their intensity as compared with the original
fundamental C, their coloring effect is definite;
and definitely tends towards mellowing and
making what we call, for a want of better terms,
"full" and "round" tone. If the seventh partial,
B flat, were very strong, the effect upon the
tone quality would be in the opposite direction.
Effect on Treble
Since it is well known that we obtain good
ringing power from the short strings of the
high treble only by steadily pushing the strik-
ing point of the hammers (which themselves arc
more acutely pointed and harder as the scale
goes up) upwards towards the extreme treble
from about an octave above middle C, and since
evidently this sharpening and hardening of the
sound can only be the effect of richer partial
tone segmentation, it should seem that the effect
of striking a string upon a node should rather
be to stimulate the production of the particu-
lar partial tone, with its multiples, which has its
origin at that point. At least, it is sure that
when we want to get the higher dissonant
partials into the sound in order to make it
more brilliant, we push upwards the striking
point. Further evidence in support of the be-
lief as to the effect of striking at a node upon
partial tones is to be found in the fact that the
highly rigid short treble strings do not with
ease form partial tones, since it is difficult for
them to maintain discontinuities, or points of
minimum motion (nodes) between the vibrating
segments. The stimulating effect of the higher
striking points is thus made quite evident.
Analysis of every kind of piano tone that
has been popular from the earliest days shows
that the best makers long since became certain
that the best possible quality in the regions
from an octave above middle C downwards to
the extreme bass is to be obtained by a mix-
ture of eight partial tones in the complex, these
being a strong fundamental, a strong second
partial, a strong third partial, a weak fourth,
a weak fifth, a strong seventh and a weak
eighth. Most of the grand pianos I have had
occasion to test, including concert grands by
the very best makers, show something much
like this arrangement. I know of more than
one instrument the middle strings of which
(Continued on page 40)
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