倍音の非調和性と楽音の自然性との関係

抄録

So far, the tone quality of electronic musical instruments have been considered as "artificial" and "unfamiliar", when compared with those of natural musical instruments, and it has been expected that there is an essential difference between them. The primary reason for such a difference is the fact that the electronic musical instruments today are manufactured considering only physical properties such as spectral structure of sound, attack time and so on, but overlooking the other physical properties of general musical tones as shown in Fig. 1. Here, the authors carried out two sets of psycho-acoustical experiments to explain the difference in tone quality more concretely, through the introduction of the concept "naturalness" of musical tone. The purpose of the first experiment is to propose a definition of the concept of "naturalness". As shown in Table 2, several kinds of tones representing timbres of string, wind, and reed families were selected. Fifteen subjects rated the tones on each of scales by the category method. From the matrix of rating scores for each timbre, the correlation matrices were calculated and analyzed by the principal axis method. The axis corresponding to the naturalness was explained by two or three psychological rating scales. These psychological rating scales suggest the existence of similar structure in the concept of naturalness for the three timbres. In the second experiment, the influence of "inharmonicity" of partial tones on the tone quality of musical tones was studied, applying concept of naturalness defined in the first experiment. The sound stimulus was synthesized by a sound synthesizer. This device has oscillators for four sounds of 349, 392, 440 and 466Hz and the frequency of the partial tones of each sound can be modulated up to the 15th independently at 6 steps (21, 14, 7, 0, -7, -14 cent). In the first part of the experiment, about 100 sounds of various kinds, whose frequency structurs are illustrated in Table 3 for each of the four timbres, were prepared by this device. Then psychological difference in tone quality between the sound whose partial tones are all in harmonic relations to the fundamental tone, and the sound whose partial tones are in inharmonic relations, is scaled. According to the variance analysis, the degree of effective partial tones, whose inharmonicity contributes to the psychological difference in tone quality was determined. Referring to the results of variance analysis, an experimental formula for the psychological difference R in tone quality in terms of physical variables was derived as follows. R=αΣKn|log(fn/fsn)|, where fn: frequency of the nth degree non-integral partial tone of fundamental tone, fsn: frequency of the nth degree integral partial tone of fundamental tone, Kn: weight coefficient of the nth degree partial tone. Fig. 8 through 11 give the diagrams showing the correlation between the experimental and theoretical values for each timbre. We can deduce the aspects of psychological variation in tone quality from the physical variables, when the partial tone is modified in an inharmonic relation. Fig. 12 shows the relation between the naturalness and the sound with inharmonic partial tones. On this basis, we can infer that an adequate amount of inharmonicity in the partial tones increases the naturalness, while an excessive inharmonicity reduces the naturalness, maximun naturalness being obtained for R at about 10 for each timbre.