Abstract
The octave, a relation between two tones whose fundamental frequencies stand in the ratio 2:1, is a foundation of tonal musics worldwide: notes separated by an octave are considered harmonically equivalent, and melodies are often sung or played in parallel octaves yet are considered identical melodies. Why do octaves sound the same? I hypothesize that our perceived similarity of octave-related tones derives from other properties of the octave interval -- namely spectral fusion, sensitivity to interval tuning, and generalization of response to the common fundamental -- which are qualitatively similar to properties of larger intervals in the harmonic series. Consequently, double-octaves (ratio 4:1) should have less similarity (in the above sense) than twelfths (ratio 3:1) have; the octave equivalence present in music is the result of a learned transitivity applied to the natural perceptual similarity. I further hypothesize a mechanism for these properties in which neural circuits in the brainstem inferior colliculus detect coincident firing of neurons tuned to harmonics of a fundamental to compute the periodicity pitch; occasional skipped firings lead to excitation of subharmonically tuned neurons, causing a note to sound like its subharmonic octave. Psychoacoustics experiments to measure musical and nonmusical humansU tuning sensitivity, generalization, and spectral fusion of twelfths and double-octaves should serve to evaluate the first hypothesis. Animals trained to respond to one note generalize this response to other notes (Blackwell and Schlosberg 1943); raising these animals in artificial acoustic environments may alter the patterns of generalization and thus provide a test for learning of octaves. Direct extracellular recording from the brainstem of animals could provide evidence for the proposed neural mechanism of harmonic equivalence.
Complete research proposal, in PDF format.