Isomorphism of Pitch and Time

Abstract

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.