What is the octave of a harmonically rich note?
Roy D. Patterson, Robert Milroy, Michael Allerhand · Contemporary Music Review · 1993
A sound composed of the harmonics of 131 Hz produces the note C3 with abuzzy timbre if the components have equal amplitude and are in cosine phase. Notes with the same tone chroma and a tone height between C3 and C4 can be produced by 1) attenuating the lower harmonics of the sound, 2) attenuating the odd harmonics, or 3) shifting the phase of the odd harmonics. The effects of the manipulations were measured in an octave experiment: a note was chosen at random and used to play a brief melody on the notes around C; the octave varied from C1 to C6 and the listeners judged the octave of each melody on a scale from C0 to C7. The results show that waves with the same period can lead to average octave judgements that differ consistently by more than half an octave, and that a substantial component of many timbre differences (e.g. that between a piano and a harpsichord) is actually a tone-height difference. The effects of manipulations 2) and 3) are difficult to explain with traditional hearing theories because the manipulations do not affect the centre of gravity of the spectrum of the sound. The effects can be explained by the “spiral” model of pitch (Patterson, 1987) because the spokes of the multi-channel spiral contain both a spectral dimension (within circuits) and a temporal dimension (across circuits). It appears that octave judgements are closely related to the position of the centre of gravity of activity on the main spoke of the spiral.