Pitch of sounds with very low fundamental frequency (Arturo Camacho )

Subject: Pitch of sounds with very low fundamental frequency
From:    Arturo Camacho  <acamacho@xxxxxxxx>
Date:    Sat, 3 Feb 2007 07:16:21 -0500

List members, To avoid a confusion between the two threads the discussion has taken, I have changed the subject of the mail. With respect the pitch of sounds with very low fundamental frequency, I think the problem has to do with the definition of pitch. If we use the operational definition of pitch (“A sound has a pitch P measured in Hertz if in a psychoacoustical experiment the sound is matched consistently to a sinusoidal sound of that frequency”) then we cannot hear a pitch lowest than the lowest frequency sinusoid we can hear, because we cannot match it to that sinusoid. However, if instead of a sinusoid we would have used in the definition a signal with a richer spectrum (e.g., one that decays as 1/f), then we may have been able to speak about lower frequency “pitches”. For example, by playing a sequence of three 10-harmonics complex signals with harmonically decaying magnitudes (i.e., 1, 1/2, 1/3,…,1/10) and fundamental frequencies 50, 37.5, and 25 Hz, my musically trained ear can recognize the complex with f0=37.5 Hz as being a fourth below the complex with f0=50 Hz, and the complex with f0=25 Hz as being a fifth below the complex with f0=37.5 Hz, i.e., an octave below the complex with f0=50 Hz. Arturo > Arturo, > > > 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. > > Pierre > > > At 09:23 PM 2/1/2007, you wrote: > >> Pierre, >> >> >> 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? >> >> Arturo >> >> >>> 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://la >>>> bros 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@xxxxxxxx >> Web page: www.cise.ufl.edu/~acamacho >> __________________________________________________ >> > > -- __________________________________________________ Arturo Camacho PhD Student Computer and Information Science and Engineering University of Florida E-mail: acamacho@xxxxxxxx Web page: www.cise.ufl.edu/~acamacho __________________________________________________

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DAn Ellis <dpwe@ee.columbia.edu>
Electrical Engineering Dept., Columbia University