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X. § 117.] SMOOTHNESS OF EFFECT. 217
Assuming, for the moment, that such a property does in fact exist, the ear, if called on to arrange the consonant intervals in the order of their pleasantness, might very well bring out a different arrangement from that adopted by physical science on grounds of smoothness alone. AEsthetic considerations come in here with the same right to be heard that mechanical considerations possess within their own domain.
117. Now unquestionably the ear's order of merit is not the same as the mechanical order. It places Thirds and Sixths first, then the Fourth and Fifth, and the Octave last of all. The constant recurrence of Thirds and Sixths in two-part Music, compared with the infrequent employment of the remaining concords, leaves no doubt on this point. In fact these intervals have a peculiar charm about them, not possessed by the Fourth or Fifth to anything like the same extent, and by the Octave not at all.
The thin effect of the Octave undoubtedly depends on the fact that every partial-tone of the higher of two clangs forming that interval coincides exactly with a partial-tone of the lower clang. Thus no new sound is introduced by the higher clang ; the quality of that previously heard is merely modified by the alteration of relative intensity among its constituent partial-tones. Major and