Bauhaus-Universität Weimar

The science of musical sounds
Miller, Dayton Clarence
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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