HAEMOxYY IN MUSIC. 69 



octave. By taking 8 and 12 holes, -which give numbers of 

 vibrations in the ratio of 2 to 3, we have the concord of a 

 perfect fifth. Similarly 12 and 16 or 9 and 12 give fourths, 

 12 and 15 give a major third, and so on. 



The upper box is furnished with a contrivance for slightly 

 sharpening or flattening the tones which it produces. This box 

 is movable upon an axis, and connected with a toothed wheel, 

 which is worked by the driver attached to the handle d. By 

 turning the handle slowly while one of the series of holes in the 

 upper box is in use, the tone will be sharper or flatter, according 

 as the box moves in the opposite direction to the disc, or in the 

 same direction as the disc. When the motion is in the opposite 

 direction, the holes meet those of the disc a little sooner than 

 they otherwise would, the time of vibration of the tone is 

 shortened, and the tone becomes sharper. The contrary ensues 

 in the other case. 



Now, on blowing through 8 holes below and 16 above, we 

 have a perfect octave, as long as the upper box is still ; but 

 when it is in motion, the pitch of the upper tone is slightly 

 altered, and the octave becomes false. 



On blowing through 12 holes above and 18 below, the result 

 is a perfect fifth as long as the upper box is at rest, but if it 

 moves the concord is perceptibly injured. 



These experiments with the siren show us, therefore : — 



1. That a series of puffs following one another with sufficient 

 rapidity, produce a musical tone. 



2. That the more rapidly they follow one another, the sharper 

 is the tone. 



3. That when the ratio of the number of vibrations is exactly 

 1 to 2, the result is a perfect octave ; when it is 2 to 3, a 

 perfect fifth ; when it is 3 to 4, a pure fourth, and so on. The 

 slightest alteration in these ratios destroys the purity of the 

 concord- 



You will perceive, from what has been hitherto ad- 

 duced, that the human ear is affected by vibrations of the 

 air, within certain degrees of rapidity — viz. from about 

 20 to about 32,000 in a second — and that the sensation 

 of musical tone arises from this affection. 



