60 ON THE PHYSIOLOGICAL CAUSES OF 



second. This gives us the once-accented c' of our musical scale [that 

 is, ' middle c,' written on the leger line between the bass and treble 

 staves]. But on opening the series of 16 holes instead, we have twice 

 as many, or 16 times 33, that is, 528 vibrations in a second. We 

 hear exactly the octave above the first </, that is, the twice-accented 

 c'' [or c on the third space of the treble staff]. By opening both the 

 series of 8 and 16 holes at once, we have both c' and c" at once, and 

 can convince ourselves that we have the absolutely pure concord of 

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

 tions 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 sharpen- 

 ing 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 natter, 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 vibra- 

 tion 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 ic 

 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 adduced, 



