PREDICTING MUSICAL PITCH FROM COMPONENT FREQUENCY RATIOS

A computer algorithm has been developed for music applications that automatically estimates pitch from any small number of frequencies, not necessarily of equal amplitude. Low-integer ratios are sought for each pair of frequencies. If an actual frequency-pair ratio closely approximates a low-integer ratio, the matching integers of this latter “ideal harmonic ratio” are accepted as possible harmonic numbers of the two actual frequencies in the tone. Hence, by comparing components to each other we can infer their likely harmonic numbers; if this is done successfully, then estimating the fundamental becomes a straightforward task. Therefore, the efficacy of the method lies in the cumulative effect of several component pair evaluations, all substantiating consistent harmonic assignments to the participating components. The method has proven to be useful in extracting pitch from spectral peaks taken from natural musical sounds, and it closely approximates some results of earlier experimental measurements of pitch perception. The method operates well with no fundamental present and for nonsuccessive partials (as well as inharmonic partials), and it is “phase insensitive.” Prior knowledge regarding the source of the signal (e.g., the musical instrument being played) is not required. © 1979, American Association of Physics Teachers. All rights reserved.