Acoustics & Sound For Musicians - Online Book

The Theory Of Sound Which Constitutes The Physical Basis Of The Art Of Music.

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94                       THEORY OF QUALITY                IV. :7
tone is capable of but two degrees of loudness. Re­presenting one of these by f and the other by p, we
mental tone is sounded forte, and the two overtones piano. The different cases which present themselves are the following:
rapidly as we take more partial-tones together. Thus a clang of four tones will produce 15 sounds of different quality; one of five tones 31; one of six tones 63, by variations of intensity only. Alto­gether we could form, with six partial-tones, each susceptible of only two different degrees of intensity, upwards of four hundred clangs of distinct quality, all having the same fundamental tone. The suppo­sition above made utterly understates, however, the possible variety of quality dependent only on changes of relative intensity. A very slight increase or dimi­nution of loudness, on the part of a single constituent tone, is enough to produce a sensible change of qua­lity in the clang. We should be still far below the mark if we allowed each partial-tone four different degrees of intensity, though even this supposition would bring us more than eight thousand separate
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