Critical bandwidth and consonance: Their operational definitions in relation to cochlear nonlinearity and combination tones

Abstract

A recent paper (Greenwood, 1990) reviewed cochlear coordinates in several species in relation to empirical frequency-position functions (Greenwood, 1961b, 1974b), one of which well fits the Békésy-Skarstein human cochlear map (Békésy, 1960; Kringlebotn et al, 1979). This increased the independence of the human function from the psychoacoustic data originally used to construct it and encouraged a second assessment of the relations of similar psychoacoustically significant bandwidths to distance and position on the cochlear map. The companion paper (Greenwood, 1991, this issue), found that, among such bandwidths, ‘classical’ critical bandwidth, and also ‘consonant interval’, estimates in man correspond to equal distances to a closer extent than generally recognized, and over large parts of the frequency range they conform also to an exponential function of distance, as do most of the ERB estimates. This correspondence to almost constant and similar distances facilitates, and forms a part of, an explanation of the operational definitions of critical bandwidth in different experiments. The present account recapitulates the basic explanation of critical bandwidth and consonance offered in Greenwood (1971, 1972b, 1973b, 1974b) and Greenwood et al. (1976): by adding schematic details to the earlier account of critical bandwidth measurements in pure tone masking (the masker-notch interval), two-tone masking, narrow-band masking, and two-tone dissonance-consonance judgments and by outlining its applicability to AM and Quasi-FM detection and to two-band (nominally notched-noise) masking experiments. The measured bandwidths derive from approximately uniform dimensions of traveling wave envelopes in the peak region and from the effects of the resulting spatial pattern of nonlinear interference among primary components. In this account, critical bandwidth in man corresponds to a distance of about 1 or 1.25 mm, depending upon the direction the interval projects from the stimulus frequency to which it is referenced. It is identified with the apical segment of the traveling wave displacement envelope, which in guinea pig and squirrel monkey appears to be about 2/3rds and 3/4ths of a millimeter, respectively and would be about 1.25 mm in man if these distances were scaled (Greenwood, 1962) among these three species (Greenwood, 1974b, 1977a). When reflected also in the basal direction, the upper end of the frequency interval, at a 1.065 mm distance, makes a total two-critical-band distance, which corresponds with the region of nonlinear input-output functions that extends in both directions from the envelope peak and hence also with the frequency-dispersive region of accelerated phase accumulation (Greenwood, 1974b, 1977a). Thus the critical bandwidths measured in these experiments reflect a common pattern of nonlinear effects around the peak of the displacement envelope and are co-determined (a) by combination tones that elicit the relevant and apically distributed neural effects determining the criterial experimental outcomes (Greenwood, 1971, 1972b,c) and (b) by an asymmetrical gain control jointly controlled by the primary stimulus components (Greenwood, 1986a,b,c; Greenwood, 1988), which imposes a relative disadvantage on the higher primaries (of a pair or set), a ‘suppressive’ effect (Greenwood and Goldberg, 1970; Greenwood, 1971), which (a) strongly and negatively affects their direct detectability when they serve as the ‘signals’ on which the experimenter may be focussed but on which the system is not, and (b) gives to combination tones a more important role generally.