THE SCIENCE OF MUSICAL SOUNDS
simple ratios, such as 1:2, 1:3, 2:3, etc., the figures are
easily recognized by the eye; and when the ratio is exact,
the figure exactly retraces itself, and because of the per¬
sistence of vision it appears continuous and stationary. If
the ratio of frequencies is not exact, the figure changes,
because of progressive phase difference, and, passing through
a cycle, returns to the original form ; the time for this cyclic
change is that required for one fork to gain or lose one com¬
plete vibration on the exact number corresponding to the
indicated ratio. The application of this method is explained
in connection with the clock-fork.
The Clock-Fork
The most precise determinations of absolute pitch are
those made by Koenig, who investigated the influence of the
resonance box and of temperature on the frequency of a
standard fork. He also determined the frequency of the
forks used by the Conservatory of Music and the Grand
Opera in Paris.15 By combining the clock-fork of Niaudet
with a vibration microscope for observing Lissajous’s fig¬
ures,16 he developed the beautiful instrument shown in Fig.
31. Fig. 31 is reproduced from an autographed photograph
of the original instrument, in the author’s possession, while
the instrument which was exhibited in the lecture is of more
recent construction and is shown in Fig. 32, on page 40.
The apparatus is essentially a pendulum clock in which
the ordinary pendulum is replaced by a tuning fork ; the fork
has a frequency of 64, as scientifically defined; that is, it
makes 128 swings per second, counting both to and fro
movements. The clock has the usual hour, minute, and sec¬
ond hands; but instead of the escapement operating on the
second hand to release it once a second, the gearing of the
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