Musical fundamental frequency tracking using a pattern

In a recent article [J. C. Brown, "Calculation of a Constant Q Spectral Transform," J. Acoust. Soc. Am. 89, 425-434 ( 1991 ) ], the calculation of a constant Q spectral transform that gives a constant pattern in the log frequency domain for sounds with harmonic frequency components has been described. This property has been utilized in calculating the cross-correlation function of spectra of sounds produced by musical instruments with the ideal pattern, which consists of one's at the positions of harmonic frequency components. Therefore, the position of the best approximation to the "ideal" pattern for the spectra produced by these instruments has been determined, and in so doing the fundamental frequency for that sound has been obtained. Results are presented for scales produced by the piano, flute, and violin as well as for arpeggios played by a wide variety of instruments.