The dimensions of tonal experience: A nonmetric multidimensional scaling approach

Abstract

Subjects were required in each trial to directly compare two pairs of tones and indicate which pair of tones had the greater subjective difference or dissimilarity. Eleven tones differing in both intensity and frequency were employed. Subjects made binary comparisons among the 65 tone pairs which can be formed from the set of 11 tones. These paired comparisons of tonal intervals were used to determine a two-dimensional Euclidean representation for tonal experience. Loudness and pitch appeared as orthogonal dimensions in this representation. However, a 46-deg rotation of loudness and pitch axes produced axes which could be identified as volume and density. This relationship suggested that volume and density were simple functions of pitch and loudness. Volume and density predictions based on this two-dimensional representa· tion were shown to provide a good account of the data from three experiments on volume and density.While pure tones can be specified physically in terms of their frequency and intensity, it has been suggested (see Stevens, 1934) that it might take as many as four psychological dimensions (pitch, loudness, volume, and density) to represent them experientially, This creates a curious situation in which there appear to bemore psychological dimensions than there are physical attributes. Normally this does not create a problem, since these psychological attributes are usually studied independently of one another. However, the dimensionality of tonal experience must be considered in any kind of perceptual judgment that may involve more than one of these psychological dimensions. This is clearly the case when one considers judgments of tonal dissimilarity.If two pure tones differing in both frequency and intensity are presented sequentially, a subjective impression of tonal dissimilarity or difference results. In theory, the magnitude of this dissimilarity should be some joint function of the difference between these two tones along one or more of the relevant psychological dimensions. A dimensional analysis of this sort suggests a geometrical representation for tonal experience with loudness, pitch, volume, and density as dimensions in a tonal space. The dimensionality of this space could be as high as four if all four dimensions turned out to be mutually orthogonal. A pure tone would be represented as a point in this four-dimensional space, with its location determined by its loudness, pitch, volume, and den- sity values. We would also expect that the distance between any two points in this space would reflect tonal dissimilarity.However, there are suggestions in the literature that these four dimensions are not linearly independent. Stevens, Guirao, and Slawson (1965) demonstrated a systematic relationship between magnitude estimates of the volumes, densities, and loudness of narrow-band noises. They found that the loudness estimates were roughly the product of the density and volume estimates. If this systematic relationship were to characterize any arbitrary selection of pure tones, it would indi...

On cross-modal similarity: The perceptual structure of pitch, loudness, and brightness.

“…Thin solid lines connect constant frequencies as LL increases from left to right; thin dashed lines connect constant LLs as frequency increases from bottom to top. This straightforward two-dimensional structure agrees well with multidimensional scaling solutions obtained with tones alone (Carvellas & Schneider, 1972;Marks, 1985;Schneider & Bissett, 1981).…”

“…A goal of spatial representation is to express similarity relations among percepts, in that some measure of distance between the spatial locations of two perceptual experiences expresses the degree of their dissimilarity. In auditory space, simple sounds, such as pure tones, may be represented as points in a plane defined by the two roughly orthogonal dimensions of pitch and loudness (e.g., Schneider & Bissett, 1981); in visual space, colored lights may be represented as points defined by the three dimensions of brightness, redness/greenness, and blueness/ yellowness (so a two-dimensional plane of red/green and blue/ yellow gives variations in hue along concentric circles and variations in saturation along radii emanating from the center, e.g., Indow & Kanazawa, 1960).…”

“…Possibly relevant to this issue is the multidimensional analysis of perceived tonal similarity. Schneider and Bissett (1981) identified the putative attribute of auditory density as lying on an axis halfway between pitch and loudness in a two-dimensional, Euclidean auditory space. In some sense, then, auditory density may be said to “contain” pitch and loudness.…”

Root‐tip cutting and uniconazole treatment improve the colonization rate of Tuber indicum on Pinus armandii seedlings in the greenhouse

“…Alpha Diversity (species richness, Chao1), ACE (http://www.mothur.org/wiki/Ace), Simpson and Shannon indexes, and beta diversity were calculated with qiime (version 1.7.0). The differences in bacterial community compositions between the samples were visualized by nonmetric multidimensional scaling (NMDS) analysis (Schneider and Bissett, ) using r software.…”

Optimal presentation orders for the method of paired comparisons

“…Recent studies using paired comparisons have investigated topics as diverse as satisfaction with health care (Sutherland, Lockwood, Minkin, Tritchler, Till & Llewellyn-Thomas, 1989), sexual relationships in the context of Aids (Stockdale, Dockrell & Wells, 1989), children's moral development (Matsumoto, Haan, Yabrove, Theodorou & Carney, 1986), children's causal beliefs (Lee & Lee, 1983), facial expressions (Mueser, Grau, Sussman & Rosen, 1984), tonal experience (Schneider & Bissett, 1981), speech perception (Sawusch & Jusczyk, 1981), the feeling of knowing (Nelson & Narens, 1980), and narcotics preferences of multiple drug abusers (Harford, 1978).…”