SOUND AND MUSIC 85 



invented for the purpose of numbering them. One is 

 called Savart's wheel. In it there is a larger wheel 

 driving a smaller, which is toothed. A piece of card- 

 board or strip of metal is so set as to touch the teeth as 

 they go round. When the wheel is made to go slowly, 

 clicks are heard. As the rapidity increases, the sound- 

 ing rises to a continuous and harmonious blow. Knowing 

 the number of teeth and of the revolutions in a second, 

 the number of blows, and consequently of vibrations, is 

 determined. In the siren a quick succession of puffs of 

 air produces a musical sound. There is in it a wheel 

 driving a circular disc, with holes at regular intervals, 

 and a bellows which throws air on it as it rotates. As 

 the rotation proceeds, the air is intercepted and passes 

 through alternately, and when the motion is sufficiently 

 rapid, and puffs sufficiently numerous, a note is produced. 

 When an instrument or voice is sounding a note, it is 

 only necessary to set one of these instruments in motion 

 with a velocity which yields the same note in order to 

 find the number of vibrations in it. In this manner the 

 number of vibrations of certain insects' wings is found. 

 In one case there are 12,000 in a second. 



Tuning-forks yielding certain notes can thus have the 

 number of their waves determined, as that they are 256, 

 320, 384, and 512 per second. The octave of every 

 note is found by doubling the number of vibrations. A 

 note of a hundred waves has for its first, second, third, 

 fourth, and fifth octaves, 200, 400, 800, 1600, 3200. 

 The lowest number, according to Helmholtz, which can 

 make an impression on the human ear is 1 6 ; the highest 

 38,000. This represents a range of more than eleven 

 octaves. The practical range is, however, from 40 to 

 4000, or seven octaves, thus equalling the number of 

 colours. And as in the case of colours the sensations 



