Roberts L A, Mathews M V
J Acoust Soc Am. 1984 Mar;75(3):952-9. doi: 10.1121/1.390560.
We studied listeners' intonation sensitivity to traditional (major and minor) and nontraditional chords. The nontraditional chords have frequency ratios of 3:5:7 and 5:7:9 and, like the major chord, have coincident upper partials and unambiguous fundamental basses. The center tone only of each of these four triads was varied from its just (integer ratio) value by -30, -15, 0, +15, and +30 cents. Each tone had ten partials whose amplitudes decreased with frequency relative to the fundamental (9 dB per octave). Subjects judged which chord (or chordal sequence) of a pair was more in tune, smooth and/or pleasant. Listeners' intonation sensitivity curves exhibited regular patterns for both traditional and nontraditional chords. However, our subjects divided into two groups: One group preferred chords in just intonation and their preferences decreased monotonically as the intonation deviated from just intonation; the other group preferred intonations that deviated from just intonation by +/- 15 cents.
我们研究了听众对传统（大三和弦和小三和弦）和非传统和弦的语调敏感度。非传统和弦的频率比为3:5:7和5:7:9，并且与大三和弦一样，具有重合的高音部分和明确的基础低音。这四个三和弦中每个的中心音仅从其纯律（整数比）值变化-30、-15、0、+15和+30音分。每个音有十个泛音，其幅度相对于基音随频率降低（每倍频程9分贝）。受试者判断一对和弦（或和弦序列）中哪一个更和谐、流畅和/或悦耳。听众的语调敏感度曲线在传统和弦和非传统和弦上都呈现出规律模式。然而，我们的受试者分为两组：一组更喜欢纯律中的和弦，并且随着语调偏离纯律，他们的偏好单调下降；另一组更喜欢偏离纯律+/-15音分的语调。
