Yahoo Tuning Groups Ultimate Backup tuning Certainty of "virtual fundamental"?

--- In tuning@y..., J Gill <JGill99@i...> wrote:
>Have you ever considered examples of complicated frequency spectra
>which [as a result of their being composed of several "complex"
>(fundamental sounded together with harmonics of that fundamental)
>tones simultaneously] might (theoretically or demonstrably)
>present a "spectral signature" which a "Fourier-related"
>time/frequency domain transform "mechanism of aural perception"
>may/does find to be "problematic" [in determining *which* location
>(to which) "fundamental" status is to be ascribed]?

The model looks like this: The virtual pitch mechanism gets a
data stream that looks like a real-time FFT (though apparently
the outputs from of a 'center-heavy' bank of progressive notch
filters more accurately models this than the 'top-heavy' FFT,
with equal-width bins).

Now, in my fantasy world, the peaks on this display are tagged
with intensity and arrival time stuff from the two ears (time
is on the y-axis but we imagine that nearly-simultaneous events
at the ears are shown on the display as actually simultaneous,
but tagged with a location marker based on the delay between ears).

Then, a harmonic-series 'mask' is laid over this display. Some
sort of weighting scheme picks the best fit, based on some function
like:

(peaks covered)(energy covered)
--------------------------------------------------
(spatial separation of covered peaks)(fit error)

When a fit is found the peaks it covers are removed, replaced
by the fundamental of the mask. The mask-fit process is then
applied again, recursively, until no fit can be found that
minimizes the function enough. All this is done in real-time,
with all the data (after every iteration) being passed up to
consciousness at once. But we can only pay attention to one or
two things at once -- "categorical perception" collapses this
picture into something more manageable, depending on how
specifically we're trying to focus our attention.

>Or, would you (and/or Terhardt) simply find the *lowest*
>frequency component which occurs in the spectrum (which would not
>appear to *always* be the appropriate selection)?

Don't want to speak for Paul or Terhardt, but I would answer, "no".

>Isn't such a process (of second-guessing the "aural mind") an
>implicitly subjective conceptual exercise, thus prone
>to "falsifiability"???

Do you mean prone to not being falsifiable? The answer to that
question is "no". We're not making any claims that our model
reflects exactly what happens in the human auditory system, we're
just claiming its predictions jive with our experience, and our
experience is falsifiable. If the model predicted that 7:4 was
more concordant than 3:2, we could reject it.

Ironically, the neuroscience part of our story (especially in my
version) is the non-falsifiable part. We just take a glance at
neuroscience and make sure we can hand-wave something together
that sounds reasonable. Non-falsifiable statements aren't
necessarily wrong, though, or even unjustified -- they just aren't
as strong or significant as falsifiable ones.

-Carl

🔗unidala <JGill99@imajis.com>

--- In tuning@y..., "clumma" <carl@l...> wrote:
> --- In tuning@y..., J Gill <JGill99@i...> wrote:

> >Have you ever considered examples of complicated frequency spectra
> >which [as a result of their being composed of several "complex"
> >(fundamental sounded together with harmonics of that fundamental)
> >tones simultaneously] might (theoretically or demonstrably)
> >present a "spectral signature" which a "Fourier-related"
> >time/frequency domain transform "mechanism of aural perception"
> >may/does find to be "problematic" [in determining *which* location
> >(to which) "fundamental" status is to be ascribed]?
>
> The model looks like this: The virtual pitch mechanism gets a
> data stream that looks like a real-time FFT (though apparently
> the outputs from of a 'center-heavy' bank of progressive notch
> filters

JG: Carl, you meant "a 'center-heavy' bank of progressive" BAND-PASS "filters", right? The FFT is not analogous to a bank of "notch" (frequency rejecting, as opposed to frequency passing)filters).

> more accurately models this than the 'top-heavy' FFT,
> with equal-width bins).

JG: Roughly, what kind of reduced filter bandwidths (as the center frequency of those filters increases) are you referring to? What frequency (roughly) would such "bandwidth shrinking" (from an equal-bandwidth system of FFT "bins") begin and/or end?

> Now, in my fantasy world, the peaks on this display are tagged
> with intensity and arrival time stuff from the two ears (time
> is on the y-axis but we imagine that nearly-simultaneous events
> at the ears are shown on the display as actually simultaneous,
> but tagged with a location marker based on the delay between ears).
>
> Then, a harmonic-series 'mask' is laid over this display. Some
> sort of weighting scheme picks the best fit, based on some function
> like:
>
> (peaks covered)(energy covered)
> --------------------------------------------------
> (spatial separation of covered peaks)(fit error)

JG: So the phrase "spatial separation of covered peaks" above refers to a "mechanism" which extracts the (possibly non-uniform) distance in frequency between what is somehow determined to be the frequencies of the "predominate amplitude maxima" of the frequency spectrum present?

BTW: There is a transform called the "cepstrum" which attempts to extract such information (it is equal to the "inverse" Fourier transform of the *logarithm* of the values of an original "forward" Fourier transform, and as a result of the processes' second ("inverse") Fourier transform, represents "time-domain" result function. It was (I believe) developed in order to attempt to accurately time the "echo return time" of sonar/radar echos which return highly dispersed in the time domain (as a result of the transmission medium having non-equal "group delay"), as well as possibly returning attenuated relative to other (non-removable) forms of noise which exist within the receive bandwidth of interest. It has been utilized in audio analysis (as well), in order to attempt to extract information regarding any (possibly present) predominant "fundamental frequency" which (may) exist within a spectrum including the contribution of signal sources whose spectra contain "harmonic energy" of some fundamental (which is not apparent from visual inspection of the composite waveform in either the time or the frequency domains).

> When a fit is found the peaks it covers are removed, replaced
> by the fundamental of the mask. The mask-fit process is then
> applied again, recursively, until no fit can be found that
> minimizes the function enough. All this is done in real-time,

JG: Wow! Try building *that* out of (any) electronic components!!!

> with all the data (after every iteration) being passed up to
> consciousness at once.

JG: Such would imply a "sampling" process occuring within the larger process. If one assumes that the repetition rate at which such would occur *must* (by Nyquist's sampling criterion) be less than 1/2 of the period of 20 KHZ (which is 50 microseconds)in order to avoid the horrible sounds we hear when we digitize an analog waveform with an inadequately low sampling frequency, that means that such an "upload" to the "conciousness" would have to occur every 25 microseconds. From the (limited) reading which I have done on the rates at which individual neurons can operate, it would seem that many, many, (parallel pathwayed) neurons would have to be involved for this to be so. Perhaps there is a neurologist (or a biochemist) reading this who might enlighten us as to the electro-chemical "bandwidths" of CNS neurons?

> But we can only pay attention to one or
> two things at once -- "categorical perception" collapses this
> picture into something more manageable, depending on how
> specifically we're trying to focus our attention.

JG: But, it seems, that phenomena alone does not a hypothesis make...
>
> >Or, would you (and/or Terhardt) simply find the *lowest*
> >frequency component which occurs in the spectrum (which would not
> >appear to *always* be the appropriate selection)?
>
> Don't want to speak for Paul or Terhardt, but I would answer, "no".

JG: Sounds reasonable to me. One (it seems) could easily fashion numerous complicated frequency spectrums (even ones that contain *no* non-harmonic energy, at all) where it would (appear to) be very hard for either a mathematician, an oscilloscope, a spectrum analyzer, or even a "cepstrum analyzer" (as previously described) to "resolve" a single and indisputable "fundamental frequency/period" from the veritable "forest" of (never fully resolvable) spectral lines existing at integer multiples of the *various* fundamental frequency components which would be and are present in "complex" composite musical signals.
>
> >Isn't such a process (of second-guessing the "aural mind") an
> >implicitly subjective conceptual exercise, thus prone
> >to "falsifiability"???
>
> Do you mean prone to not being falsifiable?

JG: No, I mean "falsifiable" (in the sense of averements of fact in general which could be deduced from other "assumptions" which can be shown to be implicitly subjective, and/or inaccurate, and/or unknowable).

> The answer to that
> question is "no". We're not making any claims that our model
> reflects exactly what happens in the human auditory system, we're
> just claiming its predictions jive with our experience

JG: How do you differentiate "jive with our experience" from "exactly what happens" when you (might be) utilizing their agreement in order to confirm a hypothesis? If a model "works" it would be the best thing that one has... Regardless of the specific (neural) mechanics involved *inside* the "black-box" mechanism between the "sound pressure level waves" and "our experience", you appear to desire to state that "our experience [jibes]" with the "sounds", and to state that such a correlation between these two is a direct result of the specific hypothesis which you are proposing be true.

The ever-present "Achilles' heel" in all this (I believe) is that there is *no way* to ever bring the subjective listening experiences of any two people (and probably of even the same person, at a different time, in a different "mood", and in a different "listening context) under the cloak of "objectively determined agreement"...

Therefore, my speculations (I'll speak for myself :), no matter how fond I may become of them (and I have been a "sinner" myself, in my time), and no matter how nuch they may *seem* to be "so right", can never be abvanced to the level of a "non-falsifiable" hypothesis.

> and our
> experience is falsifiable.

JG: I would agree (and I would group all of my and everyone else's speculations on these fascinating, but problematic subjects of the "aural mind" in the same category, that is - "falsifiable").

> If the model predicted that 7:4 was
> more concordant than 3:2, we could reject it.

JG: Great, but this (alone) shows our "adaptivity", and does not speak to the "provability" of hypothesis arising out of our speculations in these subjects of the "aural mind".

> Ironically, the neuroscience part of our story (especially in my
> version) is the non-falsifiable part.

JG: I get the impression that we are each using the term "falsifiablity" to mean a very different (and, it appears diametrically opposed) thing?!? Please advise as to this...

> We just take a glance at
> neuroscience and make sure we can hand-wave something together
> that sounds reasonable.

JG: Well then, who needs "neuroscience" at all! Why not "biorhythms", or "astrology", or "divine providence", or "your brand of toothpaste"? For all we (would then) know, any of these are (it seems) similarly qualified to be considered as a qualifying factor!?!

> Non-falsifiable statements aren't
> necessarily wrong,

JG: Would not a "non-falsifiable statement" (hypothesis, or averement)in fact, be an actual candidate *for* the status of a "truism"?

> though, or even unjustified -- they just aren't
> as strong or significant as falsifiable ones.

JG: Carl, our definitions of the phrase "non-falsifiable statement" must (certainly) be exactly 180 degrees out of phase here! Please advise me as to how I have misunderstood the concept (a possibility)!

Sincerely, J Gill :)

🔗paulerlich <paul@stretch-music.com>

🔗clumma <carl@lumma.org>

>>The model looks like this: The virtual pitch mechanism gets a
>>data stream that looks like a real-time FFT (though apparently
>>the outputs from of a 'center-heavy' bank of progressive notch
>>filters
>
>JG: Carl, you meant "a 'center-heavy' bank of progressive" BAND-
>PASS "filters", right? The FFT is not analogous to a bank of
>"notch" (frequency rejecting, as opposed to frequency passing)
>filters).

You can make a notch filter with a pair of band-pass filters, I
think. I'm not sure it really matters here, in the loose
description I'm attempting.

>>more accurately models this than the 'top-heavy' FFT,
>>with equal-width bins).
>
>JG: Roughly, what kind of reduced filter bandwidths (as the center
>frequency of those filters increases) are you referring to? What
>frequency (roughly) would such "bandwidth shrinking" (from an equal-
>bandwidth system of FFT "bins") begin and/or end?

I don't know that much about it. I drew that comment from work
being done by a private company in San Jose called ANC. Right
now, that work is secret. When they get their patents, I'll be
able to tell you more.

>>Then, a harmonic-series 'mask' is laid over this display. Some
>>sort of weighting scheme picks the best fit, based on some
>>function like:
>>
>> (peaks covered)(energy covered)
>> --------------------------------------------------
>> (spatial separation of covered peaks)(fit error)
>
>JG: So the phrase "spatial separation of covered peaks" above
>refers to a "mechanism" which extracts the (possibly non-uniform)
>distance in frequency between what is somehow determined to be
>the frequencies of the "predominate amplitude maxima" of the
>frequency spectrum present?

Not sure what you're asking. That variable is just a penalty
for grouping frequency peaks that probably come from different
sources into the same harmonic series (and thus, the same
virtual fundamental). As far as I know, "probably come from
different sources" means some sort of intensity and timing
difference between the ears. I don't know about a 'possibly
non-uniform frequency distance'.

>BTW: There is a transform called the "cepstrum" which attempts
>to extract such information
//

Thanks! I've clipped that; I'll look into it.

>> When a fit is found the peaks it covers are removed, replaced
>> by the fundamental of the mask. The mask-fit process is then
>> applied again, recursively, until no fit can be found that
>> minimizes the function enough. All this is done in real-time,
>
>JG: Wow! Try building *that* out of (any) electronic components!!!

You'd be surprised. The ANC cochlea modeling algorithm runs in
real time on a Pentium III laptop under Windows 2000.

>> with all the data (after every iteration) being passed up to
>> consciousness at once.
>
>JG: Such would imply a "sampling" process occuring within the
>larger process.

I'm not so sure.

>>But we can only pay attention to one or two things at once --
>>"categorical perception" collapses this picture into something
>>more manageable, depending on how specifically we're trying to
>>focus our attention.
>
>JG: But, it seems, that phenomena alone does not a hypothesis
>make...

That's for sure!

>>>Or, would you (and/or Terhardt) simply find the *lowest*
>>>frequency component which occurs in the spectrum (which would not
>>>appear to *always* be the appropriate selection)?
>>
>>Don't want to speak for Paul or Terhardt, but I would answer, "no".
>
>JG: Sounds reasonable to me. One (it seems) could easily fashion
>numerous complicated frequency spectrums (even ones that contain
>*no* non-harmonic energy, at all) where it would (appear to) be
>very hard for either a mathematician, an oscilloscope, a spectrum
>analyzer, or even a "cepstrum analyzer" (as previously described)
>to "resolve" a single and indisputable "fundamental
>frequency/period" from the veritable "forest" of (never fully
>resolvable) spectral lines existing at integer multiples of the
>*various* fundamental frequency components which would be and are
>present in "complex" composite musical signals.

You bet! Plenty of noises in every-day life -- even some
percussion instruments -- for which this is so. White
noise is the quintescential example.

> JG: How do you differentiate "jive with our experience"
> from "exactly what happens" when you (might be) utilizing their
> agreement in order to confirm a hypothesis? If a model "works"
> it would be the best thing that one has... Regardless of the
> specific (neural) mechanics involved *inside* the "black-box"
> mechanism between the "sound pressure level waves" and "our
> experience", you appear to desire to state that "our experience
> [jibes]" with the "sounds", and to state that such a correlation
> between these two is a direct result of the specific hypothesis
> which you are proposing be true.

Right. It's a black box, we don't care what's inside, because
we don't have any way of knowing until the field of neuroscience
gets better. All we can do is hand-wave and try to keep abreast
of the latest news.

Look at it this way: we're looking to work with musical sounds
on paper. So, we cook up a way to manipulate ratios and such,
on paper, that reflects what people say they hear. Simple stuff,
and not necessarily un-scientific.

>Therefore, my speculations (I'll speak for myself :), no matter
>how fond I may become of them (and I have been a "sinner" myself,
>in my time), and no matter how nuch they may *seem* to be "so
>right", can never be abvanced to the level of a "non-falsifiable"
>hypothesis.

I'm still not sure I get your use of "falsifiable" and "non-
falsifiable". Where I'm from, non-falsifiable means weak,
falsifiable means strong.

I'm not sure how you could show that some psychoacoustic
prediction refers to an unknowable phenomenon. In certain
formal systems, you can prove that certain statements will
never appear as axioms, but...

>> If the model predicted that 7:4 was
>> more concordant than 3:2, we could reject it.
>
> JG: Great, but this (alone) shows our "adaptivity", and does
> not speak to the "provability" of hypothesis arising out of
> our speculations in these subjects of the "aural mind".

I doubt provability exists for physical systems. All you can
do is show that one theory works better than another. If you
can show this, the theories are said to be falsifiable. If
not, they are non-falsifiable, and some would argue, non-
scientific.

>> We just take a glance at
>> neuroscience and make sure we can hand-wave something together
>> that sounds reasonable.
>
> JG: Well then, who needs "neuroscience" at all! Why
> not "biorhythms", or "astrology", or "divine providence", or
> "your brand of toothpaste"? For all we (would then) know, any
> of these are (it seems) similarly qualified to be considered
> as a qualifying factor!?!

We pick neuroscience because it provides a better theory of
hearing than biorhythms or toothpaste. _It_ isn't unscientific,
it's our application of music theory to neuroscience that's
unscientific. But it beats a scientific application of music
theory to toothpaste!

-Carl

Certainty of "virtual fundamental"?

🔗J Gill <JGill99@imajis.com>

🔗clumma <carl@lumma.org>

🔗unidala <JGill99@imajis.com>

🔗paulerlich <paul@stretch-music.com>

🔗paulerlich <paul@stretch-music.com>

🔗clumma <carl@lumma.org>

🔗unidala <JGill99@imajis.com>