P.S.E.追跡法による主観的倍音の測定と位相効果

抄録

Subjective harmaonics are generally interpreted to be caused by the nonlinearity of ears, and seem to have great effects on timbre or tone quality. Wegel and Lane assumed that the intensity of a subjective harmonic could be known by introducing a mistund tone of a slightly different frequency and determing the intensity giving the most pronounced beat sensation. Although this so-called 'Best Beat Method' has been adopted for measuring the intensity of subjective harmonics by many researchers^&lt1), 3), 5), 6)&gt, some objections have been raised against the above-mentioned interpretation^&lt3), 10)&gt. In this paper a P. S. E. Tracing Method developed by the authors is introduced, and the results of experiments are discussed on the sound pressure level and phase of subjective harmonics, monaural phase effect on timble, the phase rule, and a subjective pure tone synthesis. Both soud pressure level and phase of subjective harmonics were measured simultaneously, by adopting the P. S. E. Tracing Method based on successive pair comparisons. This method is characterized by exploring tones consisting of two reciprocal assisiting tones A_&ltnB&gt(Basic phase) and A_&ltnR&gt(Rsversed phase), and a mistuned the M_n. The frequency of assisting tones is the same as that of the subjective harmonic, while the frequency of M_n is slighily different. The mistuned tone is merely introduced to make beats, which intensify observer's sensitivity in adjusting P. S. E. Theoretical considerations are carried out in Fig. 1 under the assumption that the vector addition law holds good in adding external harmonics (assisting tones) to the subjective harmonics. Fig. 2 gives a block diagram of the equipment. A_&ltnB&gt and A_&ltnR&gt are alternately transferred by an electronic switch with a time sequence shown in Fig. 3. The results of experiments are tabulated in tables 2 and 3. Experimental vector loci obtained by this method are shown in Fig. 4, 5 and 6. The agreement of the experimental loci with ones determined theoretically is satisfactory, showing the appropriateness of the assumption. In Fig. 7. comparisons between the results by the Best Beat Method and by the P. S. E. Tracing Method are depicted. The conclusions reached are as follows: (1) The subjective harmonics measured by the new method were approximately 20 dB lower than those by the Best Beat Method. The second subjective harmonic of a fundamental (440 cps. 80 dB SPL), for example, was 46 dB SPL eqe. with a sine phase angle of 262°, while it was 63 dB SPL according to Fletcher. (2) The vector addition law holds good in adding external harmonics to subjective harmonics. (3) The M. P. E. (Monaural Phase Effect) depends largely on subjective harmonics. (4) By adjusting the intensity and phase of external harmonics, observers can hear subjective pure tones. (5) The above-mentioned suggest a hypothesis that the M. P. E. shows itself eventually in the form of a change in amplitude of harmonics due to interactions with subjective harmonics. The phase rule seems to be less reliable with nonlinear actual ears.