Acoustics & Sound For Musicians - Online Book

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

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	VI. § 73.] VARIETY OF RESULTANT WAVE-FORMS. 147
	number of partial-tones, and can assign to them any degrees of intensity and phase-difference that we choose, it is manifest that we may produce by their combination an endless series of different resultant wave-forms. On the other hand, it is not evident that, even out of this rich abundance of materials, we could build up every form of wave which could possibly be assigned. The French mathematician Fourier has, however, demonstrated that there is no form of wave which (unless itself simple) cannot be compounded out of a number of simple waves whose lengths1 are inversely as the numbers 1, 2, 3, 1 Arranged in diminishing order. 10—2