# Re: Robust method of fundamental frequency estimation

From the perceptual point of view, a 27.5-Hz fundamental frequency is not heard as pitch. The \$64K question is: how come we react to that lowest piano key's vibrations as if they were truly conveying pitch on the same dimension as, say, the key 2 octaves higher does? Yes, Dan is probably right claiming that a double bass' lowest note evokes a more purely-pitch pitch than the same note on the piano, but that E has a frequency 1.5 times higher than the lowest A on the piano. (NB: concert Boesendorfers descend down to the F below...)

Pierre

At 07:59 PM 1/31/2007, Dan Ellis wrote:

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.