Psychophysical Comparison of Just Tuning with Equal Temperament in Sequences of Individual Tones

Abstract

The alleged merits of “just” musical scales are frequently recommended to designers and manufacturers of keyboard musical instruments employing the equally tempered scale. Consequently it is a matter of practical interest to determine the conditions under which the two types of scales are discriminable. Two experiments were performed investigating one facet of the question: discriminability of melodic sequences. First an ABX test was given to 20 listeners, using prerecorded ascending diatonic scales of each type. Two widely different timbres were used, one flutelike and the other spectrally complex. Only three subjects gave results significantly different from chance. A second experiment employed scales deviating from equal temperament in a manner similar to the just scale, but varying in amount from −6 to −30 cents on the third, sixth and seventh steps (mi, la and ti). These were compared to equally tempered scales by both ABX and AX procedures. Results showed that the maximum difference between the just and equally tempered scales (16 cents) lies just below the “ABX threshold,” but above the “AX threshold,” for most of these relatively well-trained observers. It is significant that music students used here (admittedly well conditioned to equal temperament) said that when they were certain of a discrimination, it was because one of the scales contained tones which were “too flat.”