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Pitch of sounds with very low fundamental frequency



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@xxxxxxxxxxxx
>> Web page: www.cise.ufl.edu/~acamacho
>> __________________________________________________
>>
>
>


-- 
__________________________________________________

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

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