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33
The Music Trade Review
AUGUST 21, 1926
The Technical and Supply Department—(Continued from page 32)
sating truly for shortened lengths by changes unisons in each octave, meanwhile preserving
on the other factors. Good damping and well constant the unit mass, or, in other words, by Fire Hazards in the
placed tuning pins are essential and I think that using the same size of wire throughout the
Wood-Working Factory
it is worth making every possible practical sac- scale. Why then do we not do this, especially
rifice to get them. It will be found, I think,
when we get into the details of this matter
that 1 am sacrificing nothing that cannot be
thrown overboard safely.
It is not essentially important at this stage
but we may ask whether the bass bridge
should be straight or curved. Personally I al-
ways use a straight bridge because it is more
convenient for a calculated set of bass strings
such as I shall shortly explain.
Incidentally, it is as well to remind the reader
that among the bass string-lines the first ten
or so represent single unisons and the re-
mainder an imaginary line drawn precisely half
way between the two doubles.
Problem of String Dimensions
It is now time to consider the question of
string lengths. The first point which comes
up for discussion and settlement deals with
the proportioning of lengths. Tensions and
weights will also come into the picture but we
must settle the length matter first. We must
settle it first because it is really fundamental.
The musical scale we use, and which naturally
forms the foundation of all musical instruments
of fixed tones, is based on the equal tempera-
ment. True, it retains names and notations
which belong to the age of diatonic music en-
livened only by an occasional accidental sharp
or flat. The seven white and five black keys
of the pianoforte's keyboard still bear witness
to this epoch, which nevertheless is no longer a
reality, in fact no longer has the slightest claim
to recognition. The equal temperament is the
basis of modern musical art and practice.
Now the equal temperament is the division
of the octave into twelve equal parts. We
know that the ratio in sound of an octave space
is 1:2, so that the exact octave to the musi-
cal sound emitted by a body vibrating at
100 v. p. s. will be given by another body vibrat-
ing at 200 v. p. s. On the other hand it is also
an established rule that, if unit mass remains
constant, that is if mass is directly propor-
tional to length, and if other factors remain
also constant, the number of vibrations executed
by a string must be inversely proportional to
the string's length. So that if, for instance,
a string forty-four inches long gives out 100
v. p. s., a string twenty-two inches long must
give out 200 v. p. s., other factors, as said be-
fore, remaining constant.
..,.„
Why Ratios Are Changed
Plainly then if there were no more to it than
this we should scale our lengths by doubling at
every octave or, what is the same, increasing
the length from semitone to semitone by multi-
plying by the factor 12-2, there being twelve
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as thereby we might easily maintain an equality
of tension?
String Lengths
Simply because doubling length means
doubling weight and halving stiffness, or con-
versely doubling flexibility, while at the same
time it means that the lengths of the bass
strings would be unmanagable. A length of
more than twenty-two feet for unison number
1 would be one consequence. We must there-
fore do several things. We must modify the
octave ratio so as to bring the string lengths
within manageable compass, and simultaneously
increase their diameter so as to maintain stiff-
ness without enormous artificial changes of ten-
sion which would have to be produced by spe-
cial straining devices. Moreover we must b«
content to see the low bass strings compara-
tively very much shorter than they ought to be
and very much heavier; which in turn will com-
pel us to cross these strings over the others
in order to obtain with better resonance and
the longest possible length within the size of the
instrument.
Is there then any mathematical, physical or
other way of pulling together all these oppos-
ing factors so as to obtain strings of the
proper size and weight without spoiling tone
and doing other damage? It is necessary to
build on the equal temperament one way or an-
other. Since we cannot double our lengths at
each octave, what can we do that will not send
us astray? This is a very important question,
which I shall discuss at some length in the
next article.
Correspondence
is solicited and should be addressed to William
Braid White, 5149 Agatite avenue, Chicago.
This Problem Takes Prominent Place in Re-
cent Conference in Washington Under the
Auspices of the Labor Department
The fire hazard entailed in woodworking-
plants through the presence of large quan-
tities of sawdust, which becomes a highly in-
flammable gas, when mixed with air, has long
been recognized by industrial executives and
engineers. Attention was recently centered on
the economic and personal dangers resulting
from sawdust explosions as a result of one of
these catastrophes in a prominent phonograph
manufacturing plant in the East. It is not
strange therefore to find that the subject of
dust explosions was given a prominent place in
a recent conference on accident prevention
given in Washington under the auspices of the
U. S. Department of Labor.
The fact that many large piano factories arf>
equipped with effective blower and suction ap-
paratus for removing sawdust to an incinerator
or other receptacle does not remove the fire
hazard, according to the latest authorities. The
danger of electric sparks from a blower motor
or even spontaneous combustion in certain cases
is ever present as a menace to the plant's wel-
fare. David J. Price, of the Bureau of Chemistr
of the Department of Agriculture, gave a most
instructive talk on the subject at the Washing-
ton conference, which was in part as follows:
"When it is realized that at least 28,000 in-
dustrial establishments in the United States are
subject to the hazard of dust explosions and
dust fires, the importance of prevention can be
more fully appreciated. These plants employ
approximately 1,324,322 persons and manufac-
ture products of an annual value in excess of
$10,000,000,000. At least 281 explosions of this
character have been reported to the Department
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