Quantification of the hierarchy of tonal functions within a diatonic context

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

Isomorphism of Pitch and Time

An ongoing debate regarding the perception of pitch and time is whether information on the two dimensions is processed independently or interactively. To study this, we tested whether listeners prefer sequences in which tonally stable tones coincide with rhythmically stable tones. Our study builds on a noted isomorphism between pitch intervals in the diatonic scale and tone durations in the standard rhythm originating in Ghana. This isomorphism is shown in a) the maximally even structure of 2212221 and b) the cyclic nature with seven possible starting points. To better understand pitch-time relationship, we conducted two experiments. In Experiment 1, we created seven scales based on the diatonic pattern and seven rhythms based on the standard pattern by shifting the starting pitch interval or tone duration. To measure the perceived tonal stability of tones in the scales, in Experiment 1a each scale was followed by a probe tone and listeners judged how well the tone fit into the scale. To measure the perceived rhythmic stability of tones in the rhythms, in Experiment 1b each position of the sequences was accented dynamically and listeners judged how well the accent fit into the rhythm. These ratings were then used in analyzing the results of Experiment 2 that used all 49 pairs combining the 7 scales and 7 rhythms in Experiment 1. Participants rated a) how well the rhythm fits the scale for each pair and b) familiarity and well-formedness of each scale and rhythm. Results show that probe ratings from Experiment 1 predict judgments in Experiment 2. Specifically, scale/rhythm pairs received higher ratings when tonal and rhythmic hierarchies correlated more strongly with each other. In addition, we found a familiarity bias toward the major scale. After accounting for this bias, results remain significant, suggesting that information from the two individual dimensions interact perceptually