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Re: Robust method of fundamental frequency estimation.
Richard F. Lyon wrote:
As Kelly Fritz points out, the "stretched" partials of piano notes needs
to be carefully considered. You might want a "fundamental"
approximately consistent with some range of partials, or you might want
to filter those out and look for an actual lowest frequency. Depends on
what you're trying to do.
neither of these things is consistent with the way a piano is tuned. If
I am not mistaken, to accommodate the stretched (due to mass)
quasi-harmonic partials of the low piano strings, those low notes are
tuned such that the lowest partials are low in frequency (relative to
the perceived pitch) and the higher ones are (inspite of that) high.
There has been work on pitch-tracking for piano notes, but f0 is a
slippery concept for something with partials that are so badly mistuned.
If by f0 you mean the frequency of a harmonic tone with which that piano
note would sound "in-tune", then I think there is research that can
point you in the right direction. For classical definitions of f0
though, I am not sure how you would know what to expect for a piano note
any more than you would know what to expect for a gong.
Kelly Fitz, DSP Research Engineer
Starkey Hearing Research Center