| Abstrakt: |
According to Helmholtz's classic description, aural harmonics and combination tones arise from the same nonlinear process (i.e., x = a0 + a1p + a2p2 + ... + anpn). This polynomial nonlinearity hypothesis predicts identical growth rates for difference tones and aural harmonics of equal order as well as independence from any frequency effects. To further evaluate its validity, estimates of second and third aural harmonics of 1000 Hz (f1) have been obtained from six normal-hearing listeners. Coefficients of the power series were computed and used to predict amplitudes of certain combination tones. Experimentally obtained estimates of the quadratic sum (fh + f1;fh/f1 = 1.2), the cubic sum (2f1 + fh;fh/f1 = 1.2 and 2fh + f1;fh/f1 = 1.6), and cubic difference tones (2fh - f1;fh/f1 = 1.6) compared well with predicted values. The exception is 2fh - f1, an inaudible cubic difference tone which was consistently about 25 dB above the other comparative distortion products. Growth rates of all distortion products including 2fh - f1 were consistent with the hypothesis. Frequency effects such as reliable amplitude differences for 2f1 + fh as fh changed from 1200 Hz to 1600 Hz were not found. Agreement between aural harmonic and combination tone amplitudes, accelerated growth rates of higher-order subjective tones, and lack of frequency dependence support the classic hypothesis of subjective tone generation. The discrepancy in the absolute amplitude of 2fn - f1 remains to be explained. [ABSTRACT FROM AUTHOR] |
