Thresholds for discrimination between pure and tempered intervals: the relevance of nearly coinciding harmonics

Thresholds for discrimination between pure and tempered musical intervals consisting of simultaneous complex tones (fundamental frequencies f1 and f2) were investigated. For these tones the main clue for the discrimination of pure intervals (f1:f2 = p:q; p and q small integers) from moderately tempered intervals (f1:f2 approximately p:q) is absence versus presence of beats. The strength of the beats (level difference between envelope maximum and minimum or level-variation depth D) was manipulated by introduction of differences in level (delta L) between the two tones. In each of three experiments the discrimination thresholds (DTs) were determined for 13 intervals with different values for p and/or q. Experiment 1 showed that there is a simple relation between frequency-ratio complexity and discriminability: DTs gradually increased (smaller values of delta L) with increasing p + q. Experiment 2, in which tones with harmonics of equal amplitude were used, indicated that level of the interfering harmonics was not responsible for the relation between DT and p + q. Yet, Experiment 3, in which the spectral content of the tones was varied, clearly showed that for all intervals DT had been determined by the interference between nearly coinciding harmonics. Detailed analysis of the results revealed that the relation between DT and ratio complexity might have been the result of masking.