Intonation preferences for major thirds with non-beating ensemble sounds

The frequency ratios, or intervals, of the twelve-tone scale can be mathematically dejned in several slightly diferent ways, each of which may be more or less appropriate in different musical contexts. For maximum mobility in musical key, instruments of our time withfied tuning are typically tuned in equal temperament, except for performances of early music or avant-garde contemporary music. Some contend that pure intonation, being free of beats, is more natural, and would be preferred in instruments with variable tuning. The sound of choirs is such that beats are very unlikely to serve as cues for intonation. Choral performers have access to variable tuning, yet have not been shown to prefer pure intonation. The diference between alternative intonation schemes is largest for the major third interval. Choral directors and other musically expert subjects were asked to adjust to their preference the intonation of 20 major third intervals in synthetic ensemble sounds. The preferred size of the major third was 395.4 cents, with intrasubject averages ranging from 388 to 407 cents.