CONSONANCE THEORY .2. CONSONANCE OF COMPLEX TONES AND ITS CALCULATION METHOD

A theory for calculating subjective dissonance of static complex tones has been established. The theory proposes a dissonance perception model that assumes that the mutual interactions between two components constitute an essential additive unit contributing to the dissonance. The model introduces a new concept of “dissonance intensity” in a certain process of dissonance perception and extends the “power law” to the dissonance sensation, which is not clearly related to a certain physical value. Practical calculation procedures are described according to the experimental results of dyads in Part I. Theoretical calculation for various kinds of complex tones showed good agreements with psychological experiments. An application to chords of synthesized harmonic complex tones predicted great dependence of consonance characteristics on the harmonic structures, which are not taken into account in the conventional theory of harmony. It became clear that the fifth (2:3) is not always a consonant interval. A chord of two tones that consists of only odd harmonics, for example, shows much worse consonance at the fifth (2:3) than at the major sixth (3:5) or some other frequency ratios. This was proved true by psychological experiments carried out in an other institute (Sensory Inspection Committee in the Japan Union of Scientists and Engineers) with a different method of scaling. Thus, the fact warns against making a mistake in appling the conventional theory of harmony to synthetic musical tones that can take variety in the harmonic structure. The theory next explains difference in quality reduction of reproduced sounds through a nonlinear audio instrument by the physical characteristics of input sources, and it provides a measure of evaluating nonlinear distortion. © 1969, Acoustical Society of America. All rights reserved.