Pitch and timbre discrimination at wave-to-spike transition in the cochlea

Abstract

A new definition of musical pitch is proposed. A Finite-Difference Time Domain (FDTM) model of the cochlea is used to calculate spike trains caused by tone complexes and by a recorded classical guitar tone. All harmonic tone complexes, musical notes, show a narrow-band Interspike Interval (ISI) pattern at the respective fundamental frequency of the tone complex. Still this fundamental frequency is not only present at the bark band holding the respective best frequency of this fundamental frequency, but rather at all bark bands driven by the tone complex partials. This is caused by drop-outs in the basically regular, periodic spike train in the respective bands. These drop-outs are caused by the energy distribution in the wave form, where time spans of low energy are not able to drive spikes. The presence of the fundamental periodicity in all bark bands can be interpreted as pitch. Contrary to pitch, timbre is represented as a wide distribution of different ISIs over bark bands. The definition of pitch is shown to also works with residue pitches. The spike drop-outs in times of low energy of the wave form also cause undertones, integer multiple subdivisions in periodicity, but in no case overtones can appear. This might explain the musical minor scale, which was proposed to be caused by undertones already in 1880 by Hugo Riemann, still until now without knowledge about any physical realization of such undertones.