Complex tones with log-spaced partials
Elizabeth A. Cohen, Earl D. Schubert · The Journal of the Acoustical Society of America · 1980
The importance of ratio in the chromatic scale and in the perception of musical intervals, coupled with the evidence that the cochlear transmission line exhibits logarithmic frequency spacing suggests that logarithmically spaced partials could produce exciting new musical materials. Tones with log-spaced partials were generated such that the complex tone has the same number of partials per octave as the regular harmonic series. Partial structure is of the form f1 = 2(n+m/2n)f1, with n = octave above f1 (=0, 1, 2 …); m = 0, 1, 2 … 2n − 1. In such log-spaced tones, all neighboring partials within any octave above the fundamental have the same frequency ratio. Since tones with log-spaced partials do not time lock readily, having no least common divisor, it should be difficult to separate the voices in multipart composition compared to chords composed of conventional tones. Subjects were required to identify standard intervals and were tested on hearing separate voices of simple musical phrases.