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VI. § 73.] SIMPLE AND RESULTANT WA VE-FORMS. 145
among the systems of simple vibrations to which the constituent partial-tones are due. Accordingly, we may expect to find that not one single ivave-form, but many such forms, correspond to a sound of given quality and pitch.
In Figs. 48, 49, 50, the associated wave-form corresponding to our clang of two partial-tones (p. 140) is constructed for three degrees of phase-difference. The simple constituent waves are shown in thin, the result of their composition in full lines. In each case two complete wave-lengths of the latter are exhibited.
Figs. 51 and 52 present two wave-forms drawn, in the same way, for a clang of constant pitch and quality containing the partial-tones 1, 2 and 3.
The dissimilarity of form, and therefore of corresponding particle-vibration, is in both sets of figures very marked.
73. It has been shown that, by mere alteration of phase, a very great variety of resultant wave-forms can be obtained from two sets of simple waves of given lengths and amplitudes. Each one of these forms will give rise to a cycle of others, if we allow the relative amplitudes of the constituent systems to be changed, while keeping the difference of phase constant. If, therefore, we have at our disposal the systems of simple waves corresponding to an unlimited T. 10