Music Trade Review

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PRACTICAL PIANO TUNING
By ALEXANDER HART
Formerly with Steinway & Sons Tuning Department, Instructor in
Piano Tuning, Teachers College, Columbia University, N. Y.
Registered Member of the
National Association of Piano Tuners
Notes of Interest on Tuning
T
HE principal intervals employed
by the tuner are unison—octave
— fifth —fourth—third—minor third—
minor sixth. The procedure is as fol-
lows: unison 1/1, octave 2/1, fifth 3/2,
fourth 4/3, third 5/4, minor third 6/5,
minor sixth 8/5.
5IX
is also true of harmony). The ear de-
mands smoothness, with mathematical
ratios, as I will try to show with a little
musical arithmetic.
Again look at C.I, Fig. 6, "in a new
light, mathematical ratios." C.I, Fig. 6,
vibrates about 130 times per second, but
6-f
A
FIG-I
CD
C
One important item to note is the
value of a musical interval does not de-
pend upon the absolute pitch of its com-
ponents.
The interval between two tones whose
frequencies are 60 and 120 is an octave.
The interval between two tones whose
frequencies are 256 and 512 is also an
octave.
A musical interval depends only up-
on the ratio of the frequencies of the
tones which bound it, and is independ-
ent of absolute pitch.
Undoubtedly tuners try to hear the
difference between the octave, fifth and
fourth, because there are no other inter-
vals perfect within the octave, since all
the others are related to it.
Let' us pause a moment and quote
from a master mind on musical mathe-
matics, an authority on tuning chimes
and his treatise on "The Fundamental
in Tone Production".
I am of the opinion that the average
ear does not understand nor care any-
thing about musical intervals where the
question of partials is involved (this
28
to make our example very simple, we
will imagine that C.I, Fig. 6, vibrates
100 times a second instead of 130. Now
if C.I, Fig. 6, vibrates 100 times per
second, C.2, one octave higher, accord-
ing to musical mathematics, will vibrate
200 times per second. This interval of
one octave is represented by the ratio
2/1, which means that while C.I is vi-
brating once, C.2 vibrates twice—or 100
and 200 vibrations per second, respec-
tively.
From C.2, to G.3—an interval of a
fifth, which is represented by the ratio
3/2 which means that while C.2 is vi-
brating twice, G.3 vibrates three times,
or 200 and 300 vibrations per second
respectively.
G.3 and C.4, an interval of a fourth,
which is represented by the ratio 4/3
which means that while G.3 is vibrating
three times, C.4 vibrates four times, or
300 and 400 times per second respec-
tively.
C.4 and E.5, an interval of a major
third which is represented by the ratio
5/4 which means that while C.4 is vi-
brating four times, E.5 vibrates five
times, or 400 and 500 vibrations per
second respectively.
E.5 and G.6, an interval of a minor
third, which is represented by the ratio
6/5 which means that while E.5 is vi-
brating five times, G.6 vibrates six
times, or 500 and 600 vibrations per
second respectively.
My idea of presenting Figure 6 to the
thoughtful musician who loves his art
and wishes to go deeper into the funda-
mental principles of the science of tone
building, is to show Figure 6 in a new
light, "Ratios." You will observe that
the Octave, Fifth, Fourth, Third and
Minor Third are all 100 vibrations
apart, or 100 vibrations between each
interval. This is the mathematical pre-
cision demanded by the ear in tone
building.
The octave does not mean any more to
the ear than does the minor third or
any other interval of figure 6. That is,
the ear does not distinguish intervals,
the ear distinguishes ratios, inasmuch
as the intervals are all the same distance
apart. On account of the faster vibra-
tion of each tone of the ascending scale,
each tone of Figure 6 vibrates 100 times
faster than the next one beneath it, mak-
ing an equal 100 vibrations between
each interval.
If the partials are all 100 vibrations
apart and the volume of tone in each
partial is in proportion to one another,
then the ear hears smoothness, evenness,
fullness, beauty—the ideal tone. Have
I not placed in your hands the proper
clue by which much of the perplexity
surrounding the mystery of tone qual-
ity may be cleared up?
One of the main problems that con-
front the student is hearing steady
chords that sound well in an key. To
do this without getting .too involved
with beats from the start, we can ap-
proach this method from another stand-
point, i.e., (1) by tuning two octaves in
perfect intonation, (2) by tuning the
thirds in relation to the fourths, fifths
and octaves, and (3) by relating the
THE MUSIC TRADE REVIEW, APRIL, 1952