Re: scales of pitch (at)

Subject: Re: scales of pitch
From:    at <parncuttSOUND.MUSIC.MCGILL.CA>
Date:    Tue, 28 Sep 1993 09:37:54 EDT

A little tutorial on pitch... "Frequency = pitch" is a convenient way of measuring or marking pitch: The pitch of a sound may be measured by the frequency of a pure tone whose pitch is judged to be the same as the pitch of that sound (e.g., Fletcher, 1934; Plomp, 1967, 1976; Terhardt, 1972, 1974; Terhardt et al, 1982). But neither the frequency scale nor its logarithm is generally proportional to perceived pitch. Stevens and Volkman (1940) attempted to create an approximate, proportional scale for the pitch for pure tones of constant loudness. The "mel" scale is related to critical-band rate (Zwicker & Terhardt, 1980) and ERB rate (Moore & Glasberg, 1983), which in turn are related to distance along the basilar membrane (Greenwood, 1961, 1990). The mel scale and its relatives listed above apply only to pure tones, and not (or at least not directly) to music or speech. For complex tones, it is generally safe to assume that pitch is proportional to the logarithm of frequency. This is true over a wider range of frequencies for complex tones than for pure tones. The range over which the JND for the pitch of complex tones is approximately constant is roughly 100 to 5000 Hz (e.g., Henning, 1966; Wier et al., 1977). For a nice overview see Moore (1977). References Fletcher, H. (l934). Loudness, pitch and timbre of musical tones and their relations to the intensity, the frequency and the overtone structure. JASA, 6, 59-69. Greenwood, D.D. (1961). Critical bandwidth and the frequency coordinates of the basilar membrane. Journal of the Acoustical Society of America, 33, 1344-1356. Greenwood, D. (1990). A cochlear frequency-position function for several species -- 29 years later. JASA 87, 2592-2605. Henning, G.B. (1966). Frequency discrimination of random-amplitude tones. JASA, 39, 336-339. Moore, B.C.J., & Glasberg, B.R. 1983. Suggested Formulae for Calculating Auditory-Filter Bandwidths and Excitation Patterns. Journal of the Acoustical Society of America 74: 750-753. Plomp, R. (1967). Pitch of complex tones. Journal of the Acoustical Society of America, 41, 1526-1533. Plomp, R. (1976). Aspects of tone sensation: A psychophysical study. London: Academic. Terhardt, E. (1972). Zur Tonhoehenwahrnehmung von Klaengen. Acustica, 26, 173-199. Terhardt, E. (1974). Pitch, consonance, and harmony. Journal of the Acoustical Society of America, 55, 1061-1069. Terhardt, E., Stoll, G., & Seewann, M. (1982a). Pitch of complex tonal signals according to virtual pitch theory: Tests, examples and predictions. Journal of the Acoustical Society of America, 71, 671-678. Terhardt, E., Stoll, G., & Seewann, M. (1982b). Algorithm for extraction of pitch and pitch salience from complex tonal signals. Journal of the Acoustical Society of America, 71, 679-688. Moore, B.C.J. (1977). An Introduction to the Psychology of Hearing, 3rd edition. Academic, London. Third edition 1989. Stevens, S.S. and J. Volkman. 1940. "The Relation of Pitch to Frequency." American Journal of Psychology 53: 329-353. Wier, C.C., Jesteadt, W., & Green, D.M. (1977). Frequency discrimination as a function of frequency and sensation level. JASA, 61, 178-184. Zwicker, E. and E. Terhardt. 1980. "Analytical Expressions for Critical-Band Rate and Critical Bandwidth as a Function of Frequency." Journal of the Acoustical Society of America, 68, 1523-1525

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