SENSE OF HEARING LAWS OF PROPAGATION OF SOUND. 781 



tions required to produce an appreciable musical sound, in persons endowed 

 with an acute sense of hearing, may vary from 8 for the lowest, to 36,500 

 for the highest, note. From some observations of Dr. Wollastou, it seems 

 probable that the ears of different individuals are differently constituted in 

 this respect ; some not being able to hear very acute tones produced by 

 Insects, or even Birds, which are distinctly audible to others. Again, the 

 sound resulting from 16 impulses per second is not, as has been usually sup- 

 posed, the lowest appreciable note ; on the contrary, M. Savart has succeeded 

 in rendering tones distinguishable, though they can scarcely be termed musi- 

 cal, which are produced by only 7 or 8 impulses in a second ; and continuous 

 sounds of a still deeper tone could be heard, if the individual pulses were 

 sufficiently prolonged. In regard, however, to the precise time during which 

 a sonorous impression remains upon the ear, it is difficult to procure exact 

 information, since it departs more gradually than do visual impressions from 

 the eye. This is certain, however, that it is much longer than the interval 

 between the successive pulses in the production of tones; since it was found 

 by M. Savart, that one or even several teeth might be removed from the 

 toothed wheel, without a perceptible break in its sound, showing that, when 

 the tone was once established, the impression of it remained during an inter- 

 mission of some length. 



640. A very recondite investigation into the theory of Acoustics, and 

 especially into the conditions on which the distinct qualities of musical tones 

 depend, has recently been undertaken by Helmholtz. 1 It is possible, he 

 observes, to produce sounds consisting of only a single primary or fanda- 

 mental note; the fundamental note of a sonorous body being the lowest tone 

 which it yields when the whole of it is in vibration together ; but in by far 

 the greater number of instances, sounds however produced, and whether 

 musical in their character or not, are compounded of the fundamental note 

 and a number of secondary, collateral or harmonic notes ; and the peculiar 

 quality or timbre of particular instruments appears to be determined by a 

 variation in the mode of grouping of the secondary sounds. Each such 

 group Helmholtz designates a " sound color." In a series of experiments 

 upon the vowel sounds, a, e, i, o, and u, he has remarked that we distinguish 

 them from one another 2 by the harmonic sounds which accompany the chief 

 or fundamental note, and he endeavors to render this evident by the follow- 

 ing experiments. He terms the fundamental note the first (1), whilst the 

 harmonics (2, 3, 4, 5, 6, etc.) are notes produced by two, three, four, five, or 

 six times the number of vibrations of the fundamental note. Thus, taking 

 the middle C of the piano as the fundamental note, the harmonics will be 

 C. 2 (octave) G, C 3 (double octave) E 3 G 3 , etc. Now if the vowel a be sung 

 2 34 56 



close to a piano with the damper up, not only will the wire corresponding 

 to the fundamental note be thrown into vibration, but also the wires corre- 

 sponding to the 3d and 5th harmonics, or those vibrating three times and 

 five times as often as the fundamental note, and also more feebly the 2d, 

 4th, and 7th harmonic notes. When the vowel o is sung, the 3d harmonic 

 note vibrates somewhat more weakly than when a is sung ; the 2d and 5th 

 harmonics very weakly. With u the fundamental note vibrates almost 

 alone ; the third harmonic very feebly. With e the 2d harmonic wire is 



the double Bass with 41 J vibrations, the highest the d T of the Piccolo flute with 4752 

 vibrations (Tyndall). 



1 Die Lehre von den Ton-empfindungen als physiologische Grundlage fiir die 

 Theorie der Musik, Braunschweig. 1862. 



2 It must be borne in mind that the German pronunciation of the vowels is here 

 implied. 



