Extension to Stiff Strings

An advantage of the harmonic-comb method, as well as other frequency-domain maximum-likelihood pitch-estimation methods, is that it is easily extended to accommodate stiff strings. For this, the stretch-factor in the spectral-peak center-frequencies can be estimated--the so-called coefficient of inharmonicity, and then the harmonic-comb (or other maximum-likelihood spectral-matching template) can be stretched by the same amount, so that when set to the correct pitch, the template matches the data spectrum more accurately than if harmonicity is assumed.

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written by Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.