Perception of musical and nonmusical triads

Abstract

Fundamental frequencies of just major triads are in ratios of successive integers 4 to 5 to 6 which produces many coincidences of harmonics. This triad has an unambiguous “fundamental bass” (Rameau and Terhardt. We examined judgments of major (4:5:6) and minor (10:11:12) triads as well as nonmusical triads using ratios of nonsuccessive integers (3:5:7 and 5:7:9) which likewise have coincidences of overtones and unambiguous fundamental bass notes. By using nonmusical triads, we can observe intonation sensitivities apart from biases due to musical experience. We varied the middle note of each triad by −30, −15, +15, and +30 cents thus producing beating harmonics and ambiguous fundamental bass notes. Subjects were presented with pairs of triads and selected (1) the triad that is more “in tune,” (2) the triad they prefer, and (3) the triad that is more smooth. Listeners divided into two distinct groups: one showed an inverted V function, in which ratings are highest for the “just” triads; the other showed an inverted W function in which the triads deviating from just intonation by 15 cents are given the highest ratings.