Terhardt, E. (1979). Calculating virtual pitch. Hear. Res. 1, 155-182

A procedure for the schematic and automatic extraction of "fundamental pitch" from complex tonal signals, such as voiced speech and music, has been developed. While the aurally relevant "fundamental" of a complex signal cannot be defined in purely mathematical terms, an existent model of virtual-pitch perception turns out to provide a suitable basis. The procedure comprises the formation of determinant spectral pitches (which correspond to the frequencies of certain signal components), and the deduction of virtual pitch (or "fundamental frequency") from those spectral pitches. The latter deduction is accomplished by a principle of subharmonic matching, for whose realization a simple, universal and efficient algorithm was found. While the calculation may be confined to the determination of "nominal" virtual pitch, certain typical auditory phenomena, such as the influence of SPL, partial masking and interval stretch, may be accounted for as well, in which case 'true' virtual pitch is obtained. The procedure operates on the frequencies and amplitudes of the signal's spectral components, is suitable for implementation on readily available programmable calculators and other arithmetic computers, and may be used in real-time "fundamental-pitch" extraction as well. The procedure's performance and its applicability to the research and engineering of auditory communication are illustrated by some examples.