Purity Ratings of Tempered Fifths and Major Thirds

Abstract

In this study, the relationship between the degree of tempering of musical intervals and the subjective purity of these intervals was investigated. Subjective purity was determined for fifths and major thirds. The intervals were presented in isolation, that is, they were not given in a musical context. For two simultaneous complex tones the relationship between subjective purity and tempering could be described by exponential functions. These functions were obtained both for ratings on a 10-point equal-interval scale and for subjective distances derived from preference data collected by means of the method of paired comparisons. To verify to what extent subjective purity had been determined by interference of nearby harmonics, the spectral content of the tones was varied. For both the fifths and the major thirds, interference of the various pairs of nearly coinciding harmonics was canceled by deletion of the even harmonics of the higher tone. This deletion resulted in higher purity ratings, the effect being most prominent for the major third. A further reduction of the potential interference between harmonics was still more effective: for simultaneous sinusoidal tones, subjective differences between pure and tempered intervals were much smaller than for complex tones. Purity ratings for simultaneous sinusoids presented at a low sound level were about equal to the ratings for successive tones. The purity ratings were compared with dissonance patterns predicted by models for tonal consonance/dissonance. Only in a few conditions do the patterns predicted by the model of Plomp and Levelt resemble the rating patterns obtained, and the dissonance patterns predicted by the model of Kameoka and Kuriyagawa are at variance with the purity ratings in all conditions. Suggestions for revision of the models are given.

Perception of musical tension in short chord sequences: The influence of harmonic function, sensory dissonance, horizontal motion, and musical training

“…For example, it neglects mutual masking of pure-tone components, the dependency ofthe roughness ofa pair of beating, pure-tone components on their absolute (mean) frequency, and the role of critical bands in the summation of different contributions to overall roughness (for details, see Aures, 1985;Terhardt, 1974a). The model of Hutchinson and Knopoff also assumes that contributions to overall roughness add linearly, an assumption that has been questioned by Kameoka and Kuriyagawa (1969) and Vos (1986). In the present application of the model, however, we are only concerned to compare the roughness ofchords containing a constant number oftones in a similar pitch register.…”

Generality and specificity in the effects of musical expertise on perception and cognition

“…However, we found some (albeit weak) evidence that violinists who started to practice early in life (at 3-4 years) were more likely to choose the just tempered chord as opposed to the slightly sharp chord (see SR.1). While the power to detect this effect was suboptimal (due to the split of the violinist cohort), we tentatively suggest that early training might drive very fine sensitivity to components of harmonic complexes (further to Roberts & Mathews, 1984;Hall & Hess, 1984;Vos, 1986). Such a finding might be explored in future studies comparing the tuning sensitivities of musicians (e.g., violinists) specifically differing in the age of onset of their training (see Steele et al, 2013, for discussion).…”

Calculating Sensory Dissonance: Some Discrepancies Arising from the Models of Kameoka & Kuriyagawa, and Hutchinson & Knopoff

“…Later studies by Greenwood (1961a;1961b) and Glasberg & Moore (1990) still only consider critical bandwidth as a function of frequency, but Vos (1986) acknowledges the importance of SPL in determining the width of critical bands.…”