短時間スペクトル分析法の自然楽器音への適用

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Investigations of musical instrument tone are classified into three categories, (1) mechanical study of the musical instrument and generation of tone, (2) analysis of acoustical wave generated by musical instrument, and (3) study of the correlation between acoustical wave and human sense of hearing. In the first part, are reviewed briefly the results of the latest digital processing of musical instruments. Then, the physical features of musical instruments are reported for the first time which are derived from the author's short-time spectral analysis. In a previous paper, prior to the experimental analysis, mathematical considerations were made with regard to the analytical error when DFT was applied to the musical instrument tone. Here, a new analytical method with examples are presented with regard to the "inharmonicity" of musical instrument tone, which could not be dealt with by the method proposed earlier. Eleven kinds of musical instruments are used -violin, viola, cello, flute, clarinet, oboe, bassoon, trumpet, trombone, guitar and piano. To save the space, only representative notes of analytical results for these instruments are shown (Figs. 1〜14). In these figures, the ordinate shows the amplitude of each harmonics in a linear scale, and numerical figures and alphabet signs show each harmonics. The changes of fundamental frequency are shown by a percentage scale using P or %. It is an outstanding feature that string tones of violin, viola and cello have long attack transient time, in general. The amplitude of each harmonics presents complicated behavior in a pseudo-steady state and especially so in case vibrato is applied to violin and cello. It is also a characteristic feature that flute and clarinet show the attack transient as S-form. The attack transient time of the two instruments are relatively long of the order of 100 msec, while their decay times are of the order of 200 msec. The attack transient time of bassoon and oboe are very short of the order of 20 msec. The pitch variation of bassoon is very easily recognized. Change of pitch of -2% at the attack transient and that of +2% at the decay part are recognized, when the steady state part is regarded as 0% change. In case of oboe, the vibrato and the amplitude variation of each harmonics are regular in the steady state part, and the pitch variation is synchronized with the change of amplitude. When the instruments are normally played at a given dynamic marking, mf, the attack transient time of trumpet tone A_4 is very short, while that of trombone tone A_3 is considerably long. The attack transient time of piano and guitar are very short. And, the max. spectral density lies in the region of max. amplitude. With regard to decay, the low order harmonics show gradual exponential function, while the high order harmonics show more fast decay. As for the analysis of inharmonicity, in order to improve the resolving power of frequency, DFT analysis was applied to the sum of zero of three times that of data window and the waveform which is A/D converted at sampling frequency, in which the fundamental frequency of musical instrument tone is pitch synchronized with data window. Fig. 17 shows the peak value of each spectrum obtained by this method approximated by quadratic function, and accurate amplitude and frequency are calculated. The inharmonicity of grand piano tone can be calculated by the frequency of each harmonics obtained as stated above, and in the actual measurement, constant B is 0. 00008 at note A_2.
社団法人日本音響学会の論文
1977-06-01

短時間スペクトル分析法の自然楽器音への適用

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