Subject: Re: critical bands and dissonance From: David Huron - Conrad Grebel <dhuron(at)WATSERV1.UWATERLOO.CA> Date: Thu, 29 Jul 1999 13:53:23 -0400
Regarding Marc Leman and Bill Sethares question about critical bands and sensory dissonance, let me offer the following mini-history. The story begins with the work of Harvey Fletcher who linked the frequency-place coordinates of the Bekesy cochlear map to experimental data from frequency discrimination and masking experiments (Fletcher, 1953; pp. 168-175). Fletcher showed that there is a close correspondence between distances along the basilar membrane and regions of masking. In pursuing this research, Fletcher defined a hypothetical entity dubbed the "critical band" to denote frequency-domain regions of roughly equivalent or proportional behavior (Fletcher, 1940). Subsequent research by Zwicker and others established critical bandwidths as an empirical rather than hypothetical construct. Most notably, Zwicker, Flottorp, and Stevens (1957) showed that distance along the basilar membrane accounts for changes in cumulative loudness as a function of the overall frequency spread of several tones or a band of noise (see also Scharf, 1961). Greenwood (1961b, 1990) extended Fletcher's work by comparing psychoacoustic measures of critical bandwidth with the frequency-place coordinates of the Bekesy-Skarstein cochlear map. Greenwood showed that there is a linear relationship, with one critical bandwidth being roughly equivalent to the distance of 1.0 millimeter on the basilar membrane Greenwood (1961b) went on to suggest that tonotopic effects might also account for the perception of sensory dissonance. Greenwood tested this hypothesis by comparing perceptual data collected by Mayer (1894) against the critical bandwidth/cochlear map. Mayer had collected experimental data where listeners were instructed to identify the smallest possible interval free of roughness or dissonance. This interval is not constant with respect to log frequency -- as implied in traditional music theory. Greenwood showed that Mayer's data correspond almost precisely with changes of critical bandwidth with respect to frequency. Plomp and Levelt (1965) extended Greenwood's work linking the perception of sensory dissonance ("tonal consonance") to the critical band -- and hence to the mechanics of the basilar membrane. Plomp and Levelt estimated that pure tones produce maximum sensory dissonance when they are separated by about 25% of a critical bandwidth. However, their estiamte was based on a critical bandwidth that is now considered to be excessively large, especially below about 500 Hz. Greenwood (1991) has estimated that maximum dissonance arises when pure tones are separated by about 40% of a critical bandwidth. Regretably, the music perception community has overlooked the seminal work of Donald Greenwood and has misattributed the origin of the tonal-consonance/critical-band hypothesis to Drs. Plomp and Levelt (see Greenwood, 1961b; especially pp.1351-1352). In addition, the auditory community in general overlooked Greenwood's accurate early characterization of the size of the critical band. After the passage of three decades, the revised ERB function (Glasberg and Moore, 1990) was virtually identical to Greenwood's 1961 equation -- as acknowledged by Glasberg and Moore. A good survey of the relation of consonance and critical bandwidth to cochlear resolution can be found in Greenwood (1991). Subsequent work by my students has drawn attention to physiological correlates of sensory dissonance (Simpson, 1994) and errors in sensory dissonance formulae proposed by Kameoka and Kuriyagawa and Hutchinson and Knopoff (Mashinter, 1995). Work on sensory dissonance is continuing in my Ohio State lab. An up-to-date bibliography can be found at http://www.music-cog.ohio-state.edu/Music829B/bibliography.html David Huron ----------------------------------------- References Glasberg, B. R., & Moore, B. C. J. (1990). Derivation of auditory filter shapes from notched noise data. Hearing Research, 47, 103-138. Greenwood, D. D. (1961a). Auditory masking and the critical band. Journal of the Acoustical Society of America, 33 (4), 484-502. Greenwood, D. D. (1961b). Critical bandwidth and the frequency coordinates of the basilar membrane. Journal of the Acoustical Society of America, 33 (4), 1344-1356. Greenwood, D. D. (1990). A cochlear frequency-position function for several species -- 29 years later. Journal of the Acoustical Society of America, 87 (6), 2592-2605. Greenwood, D. D. (1991). Critical bandwidth and consonance in relation to cochlear frequency-position coordinates. Hearing Research, 54 (2), 164-208. Mashinter, K. (1995). Discrepancies in theories of sensory dissonance arising from the models of Kameoka & Kuriyagawa and Hutchinson & Knopoff. Bachelor of Applied Mathematics thesis, University of Waterloo. Plomp, R., & Levelt, W. J. M. (1965). Tonal consonance and critical bandwidth. Journal of the Acoustical Society of America, 37, 548-560. Plomp, R., & Steeneken, H. J. M. (1968). Interference between two simple tones. Journal of the Acoustical Society of America, 43, 883-884. Simpson, J. (1994). Cochlear modeling of sensory dissonance and chord roots. Master of Applied Science thesis, University of Waterloo.