Chap. XXXI I. ] MUSIC A L INTER VALS. 427 



to produce the given sound. Then -y^ = the wave 

 length in feet=il0'9 feet. "With a higher temper- 

 ature the wave length would increase. 



With such an instrument it is easily shown that 

 there are vibrations occurring too slowly, i.e. too few 

 of them in a second of time, to be perceived by the 

 ear as a continuous sound. Helmholtz fixed this 

 lower limit at sixteen vibrations per second. W 7 ith 

 fewer than sixteen vibrations per second, the ear has 

 no power to fuse them together to produce the 

 sensation of a musical tone. If the disc could be 

 rotated swiftly enough, the same instrument might 

 also show that there are vibrations occurring too 

 swiftly to be perceived by the ear. The upper limit 

 has been fixed by Helmholtz at 38,000 vibrations per 

 second. The highest musical sound capable of being 

 perceived by the human ear is produced by 38,000 

 vibrations per second. There are, of course, many 

 people who cannot hear at all sounds of this pitch. 

 The resemblance to the case of light is here interesting. 

 Just as there are vibrations, fewer than those pro- 

 ducing the red of the spectrum, which are not visible 

 to our eyes, and which have yet been shown to 

 possess very great heating properties, and as there are 

 vibrations faster than those producing the spectral 

 violet, which are invisible to our eyes, and are yet of 

 great chemical activity, so there are vibrations of 



O V ' 



another kind fewer than 16 per second, and more 

 than 38,000 per second, of which, however, the ear 

 has no cognisance, so far as the perception of musical 

 sound is concerned. 



Intervals. Pitch of sound the siren proves to 

 be due to number of vibrations per second of time. 

 But the siren, as modified by Helmholtz, can render 

 still other service. Helmholtz devised what is called 

 the DOUBLE SIREN. The lid of the air chamber is 

 perforated by four series of holes arranged in four 



