Music Trade Review

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THE
12
MUSIC TRADE REVIEW
OiuTTECHNlCAL DEPARTMENT
CONDUCTED BY WILLIAM BRAID WHITE.
THE SECRETjOFJHE SCALE.
(Continued.)
Last week, in concluding the first article with
the above title, I remarked that in the next instal-
ment we must consider the scaling of the bass
strings. But before it is possible to do that we
shall have to consider one other factor in string
dimensioning; the factor of tension.
When we stretch a string of a given length and
proceed to extract sounds from it through the
process of striking with a hammer, we are imme-
diately brought face to face with the element of
tension. In the last article I was obliged to call
attention to this factor in discussing the rule for
octave and semitone proportions. At the time,
however, I did no more than mention the matter,
leaving its details for the present occasion.
The tension of a stretched string varies, for the
same force, with the length and density. The more
the length is increased and the greater the weight
becomes the less effective is a given stretching
force. Other things being equal, a string gives
out a better sound when its tension approaches
to its elastic limit. Hence, it has been found fiy
piano makers that, allowing for the necessary size
limits of a piano, and remembering that the octave
and semitone proportions already given are based
upon a C7 of about 2 inches in length, the average
tension should be 150 pounds per string.
Now, if the piano scale be carefully gone over
and the length of each string taken, from the
table of lengths which will have been prepared in
advance of the draughting by the use of the pro-
portions given last week, and if then the average
tension of 150 pounds be considered as right, by a
very simple formula the weight of each string may
be had. This formula is as follows:
675,000 T
M =
V a L
or in other words, the weight (M) is found by
multiplying the square of the number of vibrations
of the string (V) by the length in inches, and di-
viding this product into the product of the tension
(T) by 675,000.
This will give the weight in grains, if now we
compare this weight by that of each number of
music wire, as may be done from a table supplied
by the maker of the wire, it follows that we can
choose the wire nearest in weight to the theoreti-
cal weight as developed by the calculation. Thus
we shall be saved the mistake of making our grad-
uation of wire depend upon chance. Moreover,
by this process of calculation it will be found that
it is much easier to equalize the strains throughout
the scale.
Now, when we approach the bass strings, we
have to consider that the factors hitherto fixed
must be changed and that there must be a general
realignment all round. Tn the bass, we must be-
gin by disregarding the length dimension. In many
pianos this dimension cannot be carried out in
ideal proportion below G2, so that the lowest of
the strings above the actual bass overstring por-
tion must also be shortened. But the principles
about to be enunciated will apply also to these.
Inasmuch as the length factor has to be dis-
turbed in the bass string scaling, and since the
element of pitch is fixed and cannot be disturbed,
it follows that, after the new length basis has been
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Piano, Player-Piano, Pipe and Reed Organ Toning and Re-
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This formerly was the tuning department of the New Eng-
land Conservatory of Music, and Oliver C. Faust was head
of that department for 20 years previous to its discontinu-
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Courses in mathematical piano scale construction and
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Pupils have daily practise in Checkering & Sons' factory.
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determined, which plainly is a matter for the size
of the piano to settle, the factors of tension and
weight alone remain. But it is equally obvious
that we cannot profitably meddle with the tension,
since to do so would be to destroy the symmetry
of the strain sheet of the scale. So it remains that
we can do no more than use the formula given
above, and from this calculate the necessary weight
which each string is to have.
We shall, therefore, begin by scaling the strings
as long as possible and adjusting the figures for
the tension and for the pitch. Then we may ob-
tain the weight as above. When reduced, this
weight will give us the weight in grains per inch
and this may then be compounded according to the
size of core wire and wrapping wire determined
upon.
By knowing the respective weights in
grains per inch of all the possible core wires and
wrapping wires, we Can easily see what weight
will result from the use of any given core with
any given wrapping. The combination that best
agrees with our figures is the combination to be
used.
Now, I would point out that the matter of pitch,
which may have appeared puzzling to some, is
very simple indeed. A table showing the pitch
of every note, from any given standard, may easily
be constructed. Supposing that the international
pitch is chosen, giving C 3 = 258.05 vibrations per
second. Then it is very simple to multiply by oc-
tsves until we reach the pitch of the highest note,
C 7 = 4,138.44. Starting from this pitch, we may
now proceed to obtain the pitch of each and every
one of the remaining notes, by the obvious proc-
ess of dividing at each semitone by the factor
1.059, which is the twelfth root of the octave fac-
tor for pitch = 2. Thus, if C 7 = 4,138.44, B flat
6, which is one semitone below, is found by divid-
ing 4,138.44 by 1.059. The quotient is the required
pitch. When this quotient again is divided by
1.059, the result is the pitch of B (i. And the proc-
ess may be repeated to the end.
In order to do this work expeditiously, 1 recom-
mend the use of a table of logarithms, which are
immensely useful in simplifying arithmetical com-
putation.
Now, from all that has been said above, it must
appear that the scaling of the strings of a piano is
not by any means a matter of inspiration, but is
altogether one of perspiration, since hard work
based on the rules I have given is all that one
needs for drawing out a string plan quite cor-
rectly. Any one who will follow the course I have
here set forth will get a string plan as nearly ideal
as is possible in practical conditions. The limits
imposed, by these practical conditions are the arbi-
trary grading of the wire sizes and the space limi-
tations of the piano. And I once more assert that
if every piano were re-calculated according to these
figures, the result would be a general improvement.
There is one more point connected with the scal-
ing of pianos to which I may now draw attention.
I refer to the calculation for shrinkage. As we
all know, iron shrinks while cooling from a molten
to a solid state. It is therefore evident that we
must pay attention to this matter of shrinkage, es-
pecially as any change whatever in the proportions
of the frame dimensions will affect all the string
dimensions also. Hence, in order to calculate the
plate dimensions rightly, it is necessary to lay out
a second plan for the latter, after the string plan
has been set down on paper, and in this second
plan to make all dimensions of the plate larger
than is actually correct, by the amount of the es-
timated shrinkage. This shrinkage amounts to
about %-inch in 1 foot and the iron plate design
must therefore be enlarged in this proportion
throughout.
There is still another point of great importance
which cannot be neglected in these remarks. The
hammers strike the strings at points predetermined
according to the tone-quality requirements of the
scale. It should be understood that a piano string
never vibrates simply as a whole, but invariably
vibrates, simultaneously with its whole length vi-
bration, in a series of segments, each of which
bears some definite arithmetical ratio of length to
the whole, so that the tone produced by each sep-
arate segmental vibration bears some definite pitch
ratio to that of the whole length. Thus we have
the so-called partial tones which, according to
their number, prominence and intensity, govern
the quality of tone emitted by the string.
The
pitch of the string, then, is determined by the
strong vibration of the whole length, while the
tone quality is controlled by the weaker vibrations
of the segments. This being the case, it is ob-
vious that one of the desires of the piano de-
signer will be to control the procession of partial
tones generated by each string. One of the most
powerful weapons to this end is provided by
changing the position of the hammer with refer-
ence to the string. If the hammer were to strike,
for example, exactly in the middle of the string,
it would immediately damp off one-half of the
string vibration, so that immediately after the
whole length had sounded, the second partial tone,
produced by the vibration of one-half of the string,
would sound out by itself. This partial would be
pitched at the octave above the fundamental tone.
Now the partial tones are produced by the vibra-
tion of the 1 /4, %, y±, YB, Va, and succeeding frac-
tions of the whole length and, therefore, since the
placing of a blow at the exact point where one of
these begins has the effect of damping off the cor-
responding tone and all tones produced by seg-
ments above it, it is obvious that as we alter the
place of the hammer blow we alter the tone
quality.
Now it is also a fact well known to acousticians,
and to piano makers also, that the tone quality of
a string becomes more and more metallic and
brilliant as the number of the upper dissonant par-
and Up-
ight piano plates
in one quality only
— the highest.
A small portion
of steel in the plate
metal insures
strength.
Polk's Piano Trade School
Piano,
14th YEAR
Player-Piano and Organ Tuning,
Repairing and Regulating.
Jobn Davenport Co.
Most thoroughly equipped Piano Trade School in
U. S. Private instruction; Factory experience if de-
sired. Students assisted. Dinlomas awarded. School
entire year. Endorsed by leading piano manufacturers
and dealers. Free catalogue.
C. C. POLK
Box 293, Valparaiso, Ind.
Stamford, Conn.
C5TMUSM£0 1MB
The Tuners' Magazine
NORTHWESTERN OHIO SCHOOL
A Monthly Journal, Devoted to the Joint Interests of
the Manufacturers and Tuners of
Musical Instruments.
SWMNER L. BALES, Editor and Proprietor
N o . 1 San Rafael, Cincinnati, Ohio
Iasmtf the Flrat el* the Hearth.
Tarns. %\jm per Year.
OF
PIANO TUNING
Catalog
D. 0. BETZ, Dir., Ada, 0.