Quantification of the hierarchy of tonal functions within a diatonic context

Abstract

Listeners rated test tones falling in the octave range from middle to high C according to how well each completed a diatonic C major scale played in an adjacent octave just before the final test tone. Ratings were well explained in terms of three factors. The factors were distance in pitch height from the context tones, octave equivalence, and the following hierarchy of tonal functions: tonic tone, other tones of the major triad chord, other tones of the diatonic scale, and the nondiatonic tones. In these ratings, pitch height was more prominent for less musical listeners or with less musical (sinusoidal) tones, whereas octave equivalence and the tonal hierarchy prevailed for musical listeners, especially with harmonically richer tones. Ratings for quarter tones interpolated halfway between the halftone steps of the standard chromatic scale were approximately the averages of ratings for adjacent chromatic tones, suggesting failure to discriminate tones at this fine level of division. The study of perceived pitch and of the perceived relations between tones differing in pitch has generally been approached from one of two quite different traditions: the psychoacoustic and the musical. The psychoacoustic approach has typically focused on simple, physically specifiable properties of tones isolated from any musical context— properties of frequency, separation in log frequency, or simplicity of integer ratios of frequencies. The results of such studies have provided some precise information about how the ear responds to isolated tones or tones in random sequences. We believe that they have been less informative with regard to how the listener perceives tones in organized musical sequences. Music theory suggests that the perception of such sequences may rely on the listener's sensitivity to different and structurally richer principles associated with tonal and diatonic organization. Such principles are useful in explaining the cognitive phenomena of reference point, motion, tension, and resolution that underlie the dynamic force of virtually all tonal music. They have, however, been subjected to relatively little systematic laboratory investigation or quantitative formulation