162 



SCIENCE 



[N. S. Vol. XXIX. No. 735 



to investigate the physical cause of these 

 sensations. 



If we investigate how many kinds of 

 sensation the ear can generate, we find 

 that, either because of fundamental or ac- 

 quired distinctions, the ear divides sounds 

 roughly into two main classes, noises and 

 musical tones. Helmholtz's distinction 

 between tone and noise, that one is periodic 

 and the other non-periodic, in the light of 

 recent experiments, seems hardly adequate. 

 Analysis clearly shows that many musicsd 

 tones are non-periodic, at least in the 

 sense intended; and it is equally certain 

 that noises are as nearly periodic as are 

 some tones. In some instances noises are 

 due to a rapidly changing period, causing 

 non-periodicity; but by far the greater 

 number of noises, which are continuous, 

 are merely complex and only apparently 

 irregular; their analysis is difficult or im- 

 possible. The ear, often because of lack 

 of training, or the absence of suitable 

 standards for comparison, or perhaps on 

 account of fatigue, fails to appreciate the 

 relations between certain sounds, and, re- 

 signing its attention, classes the sounds as 

 noises. The study of noises is essential to 

 the understanding of the qualities of 

 musical instruments, and especially of 

 speech ; but their study may well be passed 

 till we more completely understand the 

 nature of the apparently simpler, and 

 much more interesting, musical tones. 

 While actual musical tones may be non- 

 periodic, containing incommensurable par- 

 tial tones, yet it is probable that the com- 

 ponents are individually periodic, and 

 often the entire tone is periodic. "We may 

 proceed with the provisional definition that 

 the sensation of tone is caused by a periodic 

 vibration in the air, and to this we are 

 mainly to confine our attention. 



The ear, further, receives three classes 

 of sensations from tones, and presumably 

 no more. One of these gives rise to the 



characteristic of the tone called pitch; 

 this is easily proven to depend upon a very 

 simple condition, that of mere frequency 

 of vibration. 



The second property of tone is loudness 

 or intensity, which is not so simple as 

 pitch. For tones of the same pitch, it 

 varies mainly as the energy of vibration, 

 and this is a function of the amplitude of 

 vibration, varying approximately as its 

 square; loudness also varies with pitch, 

 approximately as the square of the fre- 

 quency. As regards the loudness of what 

 we hear, very much depends upon the in- 

 dividual ear, and, as Professor Sabine 

 has clearly shown, upon the surrounding 

 objects, walls of rooms, etc. 



The third property of tone is much the 

 most complicated; it is that characteristic 

 of sounds produced from some particular 

 instrument or voice, by which they are 

 distinguished from the sounds of the same 

 loudness and pitch, produced from other 

 instruments or voices. This character- 

 istic is called timbre, clang-tint, klang- 

 farhe, or, best of all, the idea is expressed 

 by the simple English word quality; we 

 shall use the word quality in this specific 

 sense. 



With comparatively little practise any 

 one can acquire the ability to distinguish 

 with great ease any one of a long series of 

 musical instruments, even when they all 

 sound tones of the same loudness and 

 pitch. There is an almost infinite variety 

 of tone quality; not only do different in- 

 struments have characteristic qualities, but 

 different individual instruments of the 

 same family show more delicate shades of 

 tone quality; and even notes of the same 

 pitch can be sounded on a single instru- 

 ment with qualitative variations. The 

 bowed instruments, of the violin family, 

 show this ability in a marked degree. But 

 no musical instrument equals the himian 

 voice in the richness of qualitative va- 



