Re: Robust method of fundamental frequency estimation

[Dan Ellis <dpwe@xxxxxxxxxxxxxxx>]

I've always wondered why playing a bass line on the bottom octaves
of the piano can almost never serve the same sonic role as playing
the same bass line on a stand-up (acoustic) bass or electric bass guitar
(I'm talking about a popular music and jazz context here).

I don't know the answer, but I took the FFT of the lowest note of the piano
from the MUMS grand piano samples; it's at:

  http://labrosa.ee.columbia.edu/~dpwe/tmp/mumsPianoA0.jpg

Obviously this depends on recording setup etc., but there's no discernable
energy at the fundamental, and almost none at the second harmonic.  It's
only at the 3rd harmonic (82.5 Hz nominal) and above that you really start to
get energy.  I would bet a double bass has better representation of lower
harmonics.

The plot also shows in green the expected locations of harmonics of 27.5 Hz.
The piano harmonics aren't all that close, and over this range it doesn't look
like a simple stretching either - seems like a much more complex pattern of
per-harmonic deviations, both above and below.

  DAn.