The effect of fundamental frequency on the discriminability between pure and tempered fifths and major thirds

Abstract

Thresholds were determined for discrimination between pure and tempered musical intervals (DTs) consisting of simultaneous complex tones. Tempered intervals are characterized by small frequency differences between those harmonics that coincide in pure intervals, Interference of these nearly coinciding harmonics gives rise to the perception of beats. Two parameters of beats were varied independently: (l) beat frequency and (2) depth of level variation (temporal envelope) as a measure of DT. DTs were determined for musical fifths and major thirds at a tone duration of 0.5 sec, The geometric mean of the fundamental frequency of the tones was varied in octave steps from 92.5 to 740 Hz, The beat frequency of the intervals was varied within a range of 2 to 64 Hz. The major result of our experiment was that, for a frequency range comprising 3 to 4 octaves, DTs do not depend on the frequency of the fundamentals, provided that the DTs are ordered according to beat frequency, When tempering (T) is expressed in cents and only those conditions are considered in which the degree of T corresponds to that found in the relevant tuning systems, it can be concluded that perceptual differences between tempered and pure fifths are increasingly irrelevant for tones lower than about middle C (262 Hz). Tempered major thirds, even those in a compromise tuning system such as that proposed by Silbermann (T=6 cents), can be discriminated from pure major thirds for all fundamental frequencies that are relevant in musical composition. © 1985 Psychonomic Society, Inc.