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Re: Robust method of fundamental frequency estimation


When you hear a 30.9-Hz note on your bass, you don't only hear the fundamental (Terhardt's [JASA 1978] "virtual pitch") but also the harmonics and other partials, if any (the "spectral pitch"). If you got rid of the harmonics, what you would hear would be a scratchy sound lacking the tonal quality of the bass' note. What is the most remarkable, and still begging for explanation (which should be difficult to obtain experimentally because it tackles a subjective dimension), is the subjective smoothness of a descending scale played on any of the low-pitched instruments, despite the lack of smoothness when you play only a sinusoid.


At 09:23 PM 2/1/2007, you wrote:

What about the lowest note in a 5-string bass B=30.9 Hz? When I hear a
5-string bass playing this note I am pretty sure I hear that pitch. One
way I could prove it to myself is by playing B one octave above (B=61.8
Hz) and then B=30.9 Hz right after. I am pretty sure I would hear an
interval of an octave between them (I have been musician all my life so I
am pretty confident I know how an octave sounds like). Therefore, I
conclude I can hear a pitch of 30.9.

I guess any bass player would agree with me. Otherwise, why do they bother
paying more for that extra string?


> 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>http://labros
>> a.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.

-- __________________________________________________

Arturo Camacho
PhD Student
Computer and Information Science and Engineering
University of Florida

E-mail: acamacho@xxxxxxxxxxxx
Web page: www.cise.ufl.edu/~acamacho