Bauhaus-Universität Weimar

The science of musical sounds
Miller, Dayton Clarence
till any required accuracy has been obtained; for instance, 
if the cyclic change occurs in 10 seconds, the error of tuning 
is 1/10 vibration per second. 
The clock-fork is provided with a mirror on the side of 
one prong so that it may be used to produce Lissajous’s 
figures by the light-ray method or to record the vibrations 
directly on a photographic film. 
Pitch Limits 
The range of pitch for the human voice in singing is from 
60 for a low bass voice to about 1300 for a very high soprano. 
Fig. 34. Organ pipe over 32 feet long giving 16 vibrations per second. 
The piano has a range of pitch from 27.2 to 4138.4. The pipe 
organ usually has 16 for the lowest pitch and 4138 for the 
highest ; an organ pipe giving 16 vibrations per second, Fig. 
34, is nominally 32 feet long, though its actual length is 
somewhat greater ; there are a few organs in the world hav¬ 
ing pipes 64 feet long which give only 8 vibrations per 
second, but such a sound is hardly to be classed as a musical 
tone; the frequency 4138 is given by a pipe 1% inches long. 
Neither speech nor music makes direct use of all the 
sounds which the ear can hear. Helmholtz considered 32 
vibrations per second as the lowest limit for a musical sound, 
that is, one which gives the sensation of a continuous tone ; 
yet the piano descends to 27 and the organ to 16 or even to 8 
vibrations per second. The tuning fork shown in Fig. 35 


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