§ 4. Pitch.—"The greater the number of consecutive vibrations which fall upon the ear in a second, the shorter the time of each vibration, the higher is the pitch. Hence the pitch of a sound is determined by the length of the wave, a low note having long, a high note short wavelength. We are able to distinguish a whole series of musical sounds of different pitch, from the lowest to the highest audible note."+ In this series each note has its fixed position between two others which are barely distinguishable from it; the one being somewhat higher, and the other somewhat lower. The arrangement is therefore linear, and comparable to the series of greys intervening between white and black. It has been maintained that, as in the greys we can distinguish varying degrees of affinity to white and black respectively, so in the scale of notes of different pitch, two ultimate modes of sensation are involved, corresponding to black and white.* But this view has not been generally accepted.

* Ibid.             +Op. cit., p. 1362.

"Vibrations having a recurrence below about thirty a second are unable to produce a sensation of sound."+ There is a similar limit for high notes. For most persons this is fixed at about 16,000 vibrations a second, though some persons can distinguish tones of 40,000. In music, only a comparatively small portion of these tones are used, beginning with about thirty and ending with about 3,600 vibrations a second.

The power of distinguishing difference of pitch, is very highly developed within a certain range. In tones rising from 100 to 1000 vibrations in a second, practised observers under favourable conditions can discriminate differences of pitch corresponding to differences of one quarter or one fifth of a wavelength. Tones above 4000 or below forty are distinguished from each other with great difficulty. Towards the higher end of the scale, differences of hundreds or even of thousands of vibrations a second may not be recognisable.

*See Mach, Analysis of the Sensations (English trans.), pp. 127, 128. +Foster, op. cit., p. 1363.