The psychology of sound / by Henry J. Watt.

  • Henry J. Watt
Date:
1917
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Licence: In copyright

Credit: The psychology of sound / by Henry J. Watt. Source: Wellcome Collection.

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    cannot be expressed exactly with the names used in our musical scales. If we played this series of tones on a musical instrument, the physical rates of vibrations which would theoretically correspond to the pre¬ dominant pitches of each would be respectively, n being the rate of vibration of c: n, 2n, 3n, in, 5n, 6n, In, 8n, 9n, 10%, 11 n, 12n, etc. That is to say, they are all simple multiples of n. This can readily be shown with the monochord upon which the presence of components in an apparently simple tone is often demonstrated. The tones of the above series can be obtained by plucking the string when it has been stopped with a fine brush at a half, a third, a quarter, etc., of its length. Or the stopping brush may be applied to these points of the string after it has been plucked, thus isolating the physical component, if it is present. It is a familiar fact that the rate of vibration of a string is inversely proportional to its length. We thus obtain a simple rule for the components of the pitch of tones: they are one or any of a series related to the physical rate of vibration or to the pitch of the lowest predominant component in the following manner. Rate of vibration: n, 2n, 3n, in, 5n, Qn, 7n, 8n, 9n, 10n, 11 n, 12n. Corresponding relative pitch: c, c', g', c2, e2, g2, < , c3, d3, e3, >/3, g3.... Thus the pitch of any suspected component may easily be calculated. Component pitches may be known as partial pitches, the lowest and predominant partial being the fundamental partial, and the others the upper partials. As confusion is liable to arise if the upper partials be numbered without inclusion of the fundamental, it is usual to include the latter in the numbering as the first partial. Partials are then numbered according to their numeral in the n series above. The even partials are c' (2w), c2 (in), g2 (Qn), etc.: the uneven are n (c), 3n (g'), 5n (e2), etc. Helmholtz, whose work on this subject is authoritative, summarised the results of his researches in a few general rules showing the usual components of the pitches of various instruments and the relation between these sets of components and the musical character of the sounds. These rules are as follows: 1. Tones of simple pitch, like those of tuning forks with resonance chambers and those of wide stopped organ pipes, sound very soft and pleasant, free from all roughness, but wanting in power, and dull at low pitches. 2. Tones containing the lower partial pitches up to about the sixth in moderate prominence are produced by the pianoforte, open organ pipes, and by the human voice and the French horn in medium strength. 2 w. p. s.
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