Music Trade Review

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DEPARTMENT
TECHNICALANDSUPPLY
William Bra\dWhite,7ecAmcalEditor
Bass String Lengths and the Problem
of Compensation for Shortened Lengths
A Continuation of the Series of Articles on Piano Scale Drafting—The Bass Layout and the
Basis of Calculation!—"Settling" of Keybeds and Some Other Interesting Ques-
tions From a Portland, Ore., Tuner—A Question of Pitch
I N the issue of September 18 we had arrived
*• at an understanding as to the striking dis-
tances to be used in our scale. We have now
worked out the slopes of the strings, the ten-
sion level, used in the' treble, the lengths and
the striking distances. It now remains to dis-
cuss the bass string lengths and the question of
loading applied to these strings for the purpose
of compensating the shortened lengths.
Difficulties of Bass Scaling
, Everybody knows that the bass section is the
most troublesome of all from a tonal stand-
point, especially in small instruments. The worst
feature of the very small grand, if and when
it is unscientifically designed, is naturally to be
found in this section. Nor can we wonder at
this, for in truth it is no more possible to dis-
cover an absolute rule applicable to every case
than it is to square the circle by Euclidean
methods. The designer here is in an impossible
position. He is confronted by interdependent
factors, no one of which can be altered without
proportionately altering some or all of the
others. If he alters the value of any one of
them in obedience to some imperious physical
necessity, he is almost certain to find that the
others refuse to accept the proportionate altera-
tions required of them in consequence of the
first alteration. Thus, he must cut down his
lengths, but can he proportionately load the
shortened strings so as to maintain his tension
level without enormously increasing the stiffness
of the resulting strings, and so obtaining vibra-
tional forms too much like those which come
from rods or bars? It is evident that the short-
ening cannot go on indefinitely and it is the duty
of the designer to make such compromises as
will give the best possible results within the
lengths which the size of the piano he is de-
signing allows him to lay out.
It is possible to say in advance, and with a
very close approach to accuracy, just what can
be done in the way of bass lengths, simply from
consideration of the size of the piano. For the
purposes of the present discussion I shall in-
clude as part of the bass those notes of the
treble of which the strings have to be shortened
on account of the close approach of the bridge
to edge of the case. Taking as a good practical
rule that one should not allow the lower row of
bridge pins anywhere to, lie closer than six
inches from the outer edge of the inside rim of
the case, we may see that in a five-foot-two-
inch piano no bass string can very well be
much longer than forty-three inches. In a re-
cent five-foot two-inch grand of my design the
highest (in pitch) bass string is 40.1875 inches
and the lowest 43.0625 inches long. The bridge
is straight and the lengths from unison to uni-
son increase continuously by .125 inch. In this
same scale, the shortening on the treble side be-
gins at unison No. 34, where the strings are
made .625 inch shorter than the calculated length
from C 7—two inches. Union No. 33 is 34.56
Piano Technicians School
Courses in Piano Tuning, Regulating and Repairing.
(Upright, Grand,, Playor and Reproducing Pianos.)
Professional Tuners have taken our courses to
broaden the scope of their work. Write for Catalog R.
The T. M. C. A. of Philadelphia, 1421 Arch Street
inches instead of 35.67, No. 32 is 35.375 instead
of 37.97, No. 31 is 35.9375 instead of 39.60, No. 30
is 36.125 instead of 41.73 and No. 29 is 36.3125
instead of 43.98. These last two are scaled with
wound strings, two to a unison, and the bass
section begins with No. 28.
It can readily be seen that the problem now is
to adjust the loading, whether this be on the
treble or on the bass side of the crossing. The
principle is the same in both cases. Let us see
how it worked out in the case I have been quot-
ing.
Treble Loading
The lengths are worked out in the already
quoted octave ratio of 1: 1.875 and with a chosen
tension level averaging 160 pounds the treble
loadings work out in the following manner:
Unison No.
Length
88
84
80
76
72
66
02
58
52
46
40
36
34
32
2.0
Wire No.
13
13'/S
2.46
3.04
3.75
4.625
6.332
7.808
9.625
13.190
18.050
24.750
30.480
33.125
35.375
Tension
in Pound:
14
141/2
15
15/2
16
16^
17
17 li
18
18J4
19
20
154
157
161
163
164
164
166
168
165
163
160
160
159
15t-:
This led as far as the two unisons which 1 de-
cided to treat with wound strings. It was evi-
dent that the drop in tension would be unbear-
ably great unless wire of No. 21 and No. 22
sizes were used for these two unisons respec-
tively, but prudence forbade this, since wire
of this thickness is not capable of giving a suit-
able vibrational form at such short lengths.
But the table shows the nature of the problem
to be solved in these bass strings, for it illus-
trates how loading may be done with some
approach to accuracy by taking a given tension
level as one's base and working to this as near-
ly as may be possible.
Bass Layout
When we come to the bass layout we pro-
ceed just as I have above hinted, by obtaining
the best length possible without bringing the
lower row of bridge pins closer at any point
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
40
than six inches to the outer edge of the inside
rim. If now the bass bridge is run straight
across between the points indicated when the
first and last strings have been drawn in pencil
lines, the remaining lines can be set in, and it
will then be found that the increase of length
from string to string is substantially regular,
whereby we shall be able to calculate the load-
ing for each string much more accurately than
otherwise would be possible.
Basis of Calculation
For all wound strings, whether on the bass or
on the treble side of the crossing, it is possible
to calculate only upon one basis. We must
choose a proper tension level and then calculate
the required weight of string to give the re-
quired pitch at that tension. Knowing then the
length of each string, we may calculate the re-
quired combination of core and covering to give
that weight, or the nearest possible approach to
it. It will be found that the bass strings can-
not be scaled on so low a tension as will suit
the treble strings, and this mainly because of
the need to maintain adequate stiffness. With
a tension level of 160 pounds in the treble
it will be necessary to take for the bass not
less than 175 or 180. With the latter level
chosen, at any rate, one can be sure of fairly
meeting both the tension and the stiffness re-
quirements. It is in the skillful management
of this part of the scale that the art of the de-
signer shows itself to best advantage. The
great artists have here always especially shone.
We shall take up this question in the next
article of the present series.
"Settling" of Keybeds, etc.
E. U. Will, of Portland, Ore., writes:
"A point I have not seen discussed yet is the
'setting' of pianos after they have left the.
factory. The end action brackets in many up-
rights, for instance, are often found not to be
resting on the bolts after a short time. Why
is this? Does the keybed warp upwards?
And in such cases, is it best to lower the center
bolts or to raise the end bolts?
"I find that less regulating is needed when
the end bolts are raised to meet the brackets.
"2. How would you measure a piano after it
has been built to get the correct striking points
of the hammers? This might answer the former
question.
"3. How do you proceed to replace hammer
stems when working in private houses? I mean,
especially, how does one manage to get the
proper angle for the slanted hammers? I use
two twist drills of different sizes. First I use
a drill one size smaller than the proper one
and pointed much sharper than is usual. I
clean out the original hole with the proper size
of drill and in that way I hardly ever fail to
get the stem and hammer in line with the other
hammers.
"4. While you are discussing piano tone it
would be opportune to mention the texture of
the dampers. Almost any kind of a new
damper will function, but a good many
dampers, after some use, will develop packed
or shrunk felt and will give a distinct twang
upon being released. In order to overcome
this on used pianos, I carry a lady's hat pin
with the point slightly bent, with which I can
reach in and soften the felt without taking out
the action (this refers to upright pianos). Tn
Tuners
and Repairers
Our new illustrated catalogue of Piano and
Player Hardware Felts and Tools is now
ready. If you haven't received your copy
please let us know.
OTTO R. TREFZ, JR.
2110 Fail-mount Ave.
Phila., Pa.