Re: [tuning] Re: question about 24-tET

>> >> Critical band effects are clearly overwhelming anything like
>> >> the 'magnetism' of "1:1" adding to the concordance of 36:35.
>> >
>> >And what is that 'magnetism' caused by?
>>
>> I thought you just said, harmonic entropy.
>
>Not necessarily. Some or all of it is due to critical band effects.
>
>You're either talking psychoacoustics or numerical theories, both
>of which should, ideally, give the same predictions.

I'm talking what people hear. Both psychoacoustics and numerical
theories had better measure up to it.

>It doesn't make sense for one to overwhelm the other.

I think it makes sense to say that we use two main mechanical
tools to hear: periodicity and place. Depending on the stimulus,
there are probably several different methods of using these
together to do pitch extraction. In some cases you may not get
enough data from either source to hit your normal pitch-extraction
skill. In such a case the source from which most of the needed
information was missing, depending on the method, could be
described as the overwhelming failure.

Alternatively, how do the basilar membrane's resonances look
inside a critical band when stimuli are delivered there? Could
erratic behavior on the membrane ruin the fit of the associated
auditory-nerve periodicites to their templates in the lateral
lemniscus and/or midbrain (thus munging the periodicity
contribution)?

In either case, if harmonic entropy isn't the limiting factor,
improving it may not make a significant perceptual difference.
This might be tested with pairs like 36:35 and 67:65 (and
probably simpler pairs), and in various registrations so that
the peak of critical band dissonance is on either side of the
pair. Just the Plomp & Level sine tones maximum should be
sufficient for harmonic timbres. The test could be extended to
synthetic timbres using the perceptual dissonance peak for the
timbre in question, such that the peak was moved on either side
of the pair.

-Carl

--- In harmonic_entropy@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >> >> Critical band effects are clearly overwhelming anything like
> >> >> the 'magnetism' of "1:1" adding to the concordance of 36:35.
> >> >
> >> >And what is that 'magnetism' caused by?
> >>
> >> I thought you just said, harmonic entropy.
> >
> >Not necessarily. Some or all of it is due to critical band
effects.
> >
> >You're either talking psychoacoustics or numerical theories, both
> >of which should, ideally, give the same predictions.
>
> I'm talking what people hear. Both psychoacoustics and numerical
> theories had better measure up to it.

Right, but it doesn't make sense to say a component of one overwhelms
a component of the other. Otherwise you're implying that the
numerical and psychoacoustical models *together* predict consonance,
which is absurd; it's one or the other way of looking at it, and
ideally it doesn't make a difference.

> >It doesn't make sense for one to overwhelm the other.
>
> I think it makes sense to say that we use two main mechanical
> tools to hear: periodicity and place. Depending on the stimulus,
> there are probably several different methods of using these
> together to do pitch extraction. In some cases you may not get
> enough data from either source to hit your normal pitch-extraction
> skill. In such a case the source from which most of the needed
> information was missing, depending on the method, could be
> described as the overwhelming failure.

Sure -- I have no problem with this. So the thing is, both
periodicity-based and place-based theories predict tolerance (a
component of the *numerical* model), and harmonic entropy doesn't
care which of the theories is correct or how much explains what.

> Alternatively, how do the basilar membrane's resonances look
> inside a critical band when stimuli are delivered there?

They 'beat'.

> Could
> erratic behavior on the membrane ruin the fit of the associated
> auditory-nerve periodicites

Umm . . . if the stimuli inside the critical band are consecutive
harmonics, the beat rate would give the fundamental. Something like
this was part of very early periodicity theories, but unfortunately,
it was soon realized, it did not correctly predict the perceived
fundamental of inharmonic spectra.

> In either case, if harmonic entropy isn't the limiting factor,
> improving it may not make a significant perceptual difference.

Unclear on what you're saying.

> This might be tested with pairs like 36:35 and 67:65 (and
> probably simpler pairs),

Probably . . . what does 36:35 vs. 67:65 test?

> and in various registrations so that
> the peak of critical band dissonance is on either side of the
> pair.

How resolved do you expect this peak to be? And what does this test?

> The test could be extended to
> synthetic timbres using the perceptual dissonance peak for the
> timbre in question, such that the peak was moved on either side
> of the pair.

??Unclear.

>> >> >> Critical band effects are clearly overwhelming anything like
>> >> >> the 'magnetism' of "1:1" adding to the concordance of 36:35.
>> >> >
>> >> >And what is that 'magnetism' caused by?
>> >>
>> >> I thought you just said, harmonic entropy.
>> >
>> >Not necessarily. Some or all of it is due to critical band
>> >effects.

Can you explain how place could cause magnetism?

>> >You're either talking psychoacoustics or numerical theories, both
>> >of which should, ideally, give the same predictions.
>>
>> I'm talking what people hear. Both psychoacoustics and numerical
>> theories had better measure up to it.
>
>Right, but it doesn't make sense to say a component of one overwhelms
>a component of the other. Otherwise you're implying that the
>numerical and psychoacoustical models *together* predict consonance,
>which is absurd;

Place and periodicity together predict consonance. I've lost track
of what you mean by numerical model. If it only modeled periodicity
and "pyschoacoustics" only modeled place, then one could overwhelm
the other in the sense below. If the numerical model is just a general
rule of thumb, then of course "overwhelm" would not be appropriate.
And since the predictions of periodicity and place overlap, any model
of one could be seen as a model of both. But in the case of n*d at
least, I've always seen it as modeling periodicity only, and sans
tolerance. Harmonic entropy I've always justified strictly with
periodicity but including the associated tolerance.

>> I think it makes sense to say that we use two main mechanical
>> tools to hear: periodicity and place. Depending on the stimulus,
>> there are probably several different methods of using these
>> together to do pitch extraction. In some cases you may not get
>> enough data from either source to hit your normal pitch-extraction
>> skill. In such a case the source from which most of the needed
>> information was missing, depending on the method, could be
>> described as the overwhelming failure.
>
>Sure -- I have no problem with this. So the thing is, both
>periodicity-based and place-based theories predict tolerance (a
>component of the *numerical* model), and harmonic entropy doesn't
>care which of the theories is correct or how much explains what.

Ok. Except "tolerance" was originally defined, I thought, as 'the
predictions of harmonic entropy, wherever they disagree with n*d'.
In this case place wouldn't have tolerance. So maybe you can just
speak a little to what you meant by 'place tolerance'. Maybe your
answer to 'place magnetism' atop has already touched on this.

>> Alternatively, how do the basilar membrane's resonances look
>> inside a critical band when stimuli are delivered there?
>
>They 'beat'.

Ok.

>> Could
>> erratic behavior on the membrane ruin the fit of the associated
>> auditory-nerve periodicites
>
>Umm . . . if the stimuli inside the critical band are consecutive
>harmonics, the beat rate would give the fundamental.

Which is a frequency not normally associated with that place on
the membrane. Thus perhaps it is causing the same sort of confusion
as the test tones discussed in the New Scientist article.

>> In either case, if harmonic entropy isn't the limiting factor,
>> improving it may not make a significant perceptual difference.
>
>Unclear on what you're saying.

What if I replaced "harmonic entropy" there with "periodicity"?

You've apparently come to view harmonic entropy as a more general
model? In your original expositions of the idea you presented it
as a model for periodicity, IIRC.

>> This might be tested with pairs like 36:35 and 67:65 (and
>> probably simpler pairs),
>
>Probably . . . what does 36:35 vs. 67:65 test?

Periodicity vs. critical band effects.

>> The test could be extended to
>> synthetic timbres using the perceptual dissonance peak for the
>> timbre in question, such that the peak was moved on either side
>> of the pair.
>
>??Unclear.

You could spectrally morph an additive timbre so that its sensory
dissonance maximum (or local maximum) fell above or below the
larger or smaller interval in the pair (resp.).

-Carl

--- In harmonic_entropy@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >> >> >> Critical band effects are clearly overwhelming anything
like
> >> >> >> the 'magnetism' of "1:1" adding to the concordance of
36:35.
> >> >> >
> >> >> >And what is that 'magnetism' caused by?
> >> >>
> >> >> I thought you just said, harmonic entropy.
> >> >
> >> >Not necessarily. Some or all of it is due to critical band
> >> >effects.
>
> Can you explain how place could cause magnetism?

It does when the timbres consist of harmonic partials. You get local
minima at the simple ratios. See Helmholtz, Plomp/Levelt, Kameoka &
Kuriyagawa, Sethares . . .

> >> >You're either talking psychoacoustics or numerical theories,
both
> >> >of which should, ideally, give the same predictions.
> >>
> >> I'm talking what people hear. Both psychoacoustics and numerical
> >> theories had better measure up to it.
> >
> >Right, but it doesn't make sense to say a component of one
overwhelms
> >a component of the other. Otherwise you're implying that the
> >numerical and psychoacoustical models *together* predict
consonance,
> >which is absurd;
>
> Place and periodicity together predict consonance. I've lost track
> of what you mean by numerical model.

The "COMPLEXITY"-"TOLERANCE"-"SPAN" model.

> And since the predictions of periodicity and place overlap, any
model
> of one could be seen as a model of both. But in the case of n*d at
> least, I've always seen it as modeling periodicity only,

Well that's odd. Take a look at Helmholtz's graphs, which were
all "place"-based. Remember the figure 100/(n*d) associated with
Helmholtz?

> and sans
> tolerance.

Correct.

> Harmonic entropy I've always justified strictly with
> periodicity

That's funny; Bill Sethared made the opposite assumption. It actually
doesn't care which you assume.

> >> I think it makes sense to say that we use two main mechanical
> >> tools to hear: periodicity and place. Depending on the stimulus,
> >> there are probably several different methods of using these
> >> together to do pitch extraction. In some cases you may not get
> >> enough data from either source to hit your normal pitch-
extraction
> >> skill. In such a case the source from which most of the needed
> >> information was missing, depending on the method, could be
> >> described as the overwhelming failure.
> >
> >Sure -- I have no problem with this. So the thing is, both
> >periodicity-based and place-based theories predict tolerance (a
> >component of the *numerical* model), and harmonic entropy doesn't
> >care which of the theories is correct or how much explains what.
>
> Ok. Except "tolerance" was originally defined, I thought, as 'the
> predictions of harmonic entropy, wherever they disagree with n*d'.

No, it's called "tolerance" because it refers to the specific fact
that the strongest consonances each have a certain "tolerance" for
mistuning, thus bringing nearby ratios into their well regardless of
those ratios' complexities.

> >> Alternatively, how do the basilar membrane's resonances look
> >> inside a critical band when stimuli are delivered there?
> >
> >They 'beat'.
>
> Ok.
>
> >> Could
> >> erratic behavior on the membrane ruin the fit of the associated
> >> auditory-nerve periodicites
> >
> >Umm . . . if the stimuli inside the critical band are consecutive
> >harmonics, the beat rate would give the fundamental.
>
> Which is a frequency not normally associated with that place on
> the membrane.

Or with any place on the membrane at all, almost certainly not if the
beating is audible.

> Thus perhaps it is causing the same sort of confusion
> as the test tones discussed in the New Scientist article.

No, for two reasons:

(1) A beat frequency is an *amplitude* modulation; a pitch frequency
is a *pressure* modulation.

(2) The beat frequency almost certainly doesn't have a pitch
frequency "equivalent" which corresponds any place whatsoever on the
basilar membrane.

> >> In either case, if harmonic entropy isn't the limiting factor,
> >> improving it may not make a significant perceptual difference.
> >
> >Unclear on what you're saying.
>
> What if I replaced "harmonic entropy" there with "periodicity"?

The problem is I don't know what you mean by "limiting factor"
and "improving it". Try to restate this more clearly.

> You've apparently come to view harmonic entropy as a more general
> model? In your original expositions of the idea you presented it
> as a model for periodicity, IIRC.

That was one possible derivation, but you may recall that I
originally tied it to Terhardt, who was and is a place theorist
through and through.

> >> This might be tested with pairs like 36:35 and 67:65 (and
> >> probably simpler pairs),
> >
> >Probably . . . what does 36:35 vs. 67:65 test?
>
> Periodicity vs. critical band effects.

How so? Both ratios seem roughly the same in both regards. The ratios
are almost certainly too high to evoke periodicity at 1, and the
critical band roughness will be nearly identical for both and for
anything in-between.

> >> The test could be extended to
> >> synthetic timbres using the perceptual dissonance peak for the
> >> timbre in question, such that the peak was moved on either side
> >> of the pair.
> >
> >??Unclear.
>
> You could spectrally morph an additive timbre so that its sensory
> dissonance maximum (or local maximum) fell above or below the
> larger or smaller interval in the pair (resp.).

And what would that tell us?

>>>>>>>>Critical band effects are clearly overwhelming anything
>>>>>>>>like the 'magnetism' of "1:1" adding to the concordance
>>>>>>>>of 36:35.
>>>>>>>
>>>>>>>And what is that 'magnetism' caused by?
>>>>>>
>>>>>>I thought you just said, harmonic entropy.
>>>>>
>>>>>Not necessarily. Some or all of it is due to critical band
>>>>>effects.
>>
>>Can you explain how place could cause magnetism?
>
>It does when the timbres consist of harmonic partials. You get local
>minima at the simple ratios. See Helmholtz, Plomp/Levelt, Kameoka &
>Kuriyagawa, Sethares . . .

Of course. I suppose that could lead to magnetism but I hadn't
thought of it that way before.

>> But in the case of n*d at
>> least, I've always seen it as modeling periodicity only,
>
>Well that's odd. Take a look at Helmholtz's graphs, which were
>all "place"-based. Remember the figure 100/(n*d) associated with
>Helmholtz?

I don't remember that, but of course it should agree with place,
as I said below.

>> >Sure -- I have no problem with this. So the thing is, both
>> >periodicity-based and place-based theories predict tolerance (a
>> >component of the *numerical* model), and harmonic entropy doesn't
>> >care which of the theories is correct or how much explains what.
>>
>> Ok. Except "tolerance" was originally defined, I thought, as 'the
>> predictions of harmonic entropy, wherever they disagree with n*d'.
>
>No, it's called "tolerance" because it refers to the specific fact
>that the strongest consonances each have a certain "tolerance" for
>mistuning, thus bringing nearby ratios into their well regardless of
>those ratios' complexities.

And this differs from what I said how?

>> >> Could
>> >> erratic behavior on the membrane ruin the fit of the associated
>> >> auditory-nerve periodicites
>> >
>> >Umm . . . if the stimuli inside the critical band are consecutive
>> >harmonics, the beat rate would give the fundamental.
>>
>> Which is a frequency not normally associated with that place on
>> the membrane.
>
>Or with any place on the membrane at all, almost certainly not if
>the beating is audible.
>
>> Thus perhaps it is causing the same sort of confusion
>> as the test tones discussed in the New Scientist article.
>
>No, for two reasons:
>
>(1) A beat frequency is an *amplitude* modulation; a pitch frequency
>is a *pressure* modulation.

We're talking about a position (of the membrane) modulation here.

>(2) The beat frequency almost certainly doesn't have a pitch
>frequency "equivalent" which corresponds any place whatsoever on the
>basilar membrane.

Lost me here.

>> >> In either case, if harmonic entropy isn't the limiting factor,
>> >> improving it may not make a significant perceptual difference.
>> >
>> >Unclear on what you're saying.
>>
>> What if I replaced "harmonic entropy" there with "periodicity"?
>
>The problem is I don't know what you mean by "limiting factor"
>and "improving it". Try to restate this more clearly.

I already did so, and you said you had no problem with it.

-Carl

--- In harmonic_entropy@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >>>>>>>>Critical band effects are clearly overwhelming anything
> >>>>>>>>like the 'magnetism' of "1:1" adding to the concordance
> >>>>>>>>of 36:35.
> >>>>>>>
> >>>>>>>And what is that 'magnetism' caused by?
> >>>>>>
> >>>>>>I thought you just said, harmonic entropy.
> >>>>>
> >>>>>Not necessarily. Some or all of it is due to critical band
> >>>>>effects.
> >>
> >>Can you explain how place could cause magnetism?
> >
> >It does when the timbres consist of harmonic partials. You get
local
> >minima at the simple ratios. See Helmholtz, Plomp/Levelt, Kameoka
&
> >Kuriyagawa, Sethares . . .
>
> Of course. I suppose that could lead to magnetism but I hadn't
> thought of it that way before.
>
> >> But in the case of n*d at
> >> least, I've always seen it as modeling periodicity only,
> >
> >Well that's odd. Take a look at Helmholtz's graphs, which were
> >all "place"-based. Remember the figure 100/(n*d) associated with
> >Helmholtz?
>
> I don't remember that, but of course it should agree with place,
> as I said below.

Above?

> >> >Sure -- I have no problem with this. So the thing is, both
> >> >periodicity-based and place-based theories predict tolerance (a
> >> >component of the *numerical* model), and harmonic entropy
doesn't
> >> >care which of the theories is correct or how much explains what.
> >>
> >> Ok. Except "tolerance" was originally defined, I thought,
as 'the
> >> predictions of harmonic entropy, wherever they disagree with
n*d'.
> >
> >No, it's called "tolerance" because it refers to the specific fact
> >that the strongest consonances each have a certain "tolerance" for
> >mistuning, thus bringing nearby ratios into their well regardless
of
> >those ratios' complexities.
>
> And this differs from what I said how?

It's very different. It relates to a purely numerical formulation in
which 'COMPLEXITY' is the first criterion. It doesn't relate to
harmonic entropy at all, harmonic entropy could be all wrong,
meaningless, irrelevant to consonance, or completely nonexistent as
far as it's concerned.

> >> >> Could
> >> >> erratic behavior on the membrane ruin the fit of the
associated
> >> >> auditory-nerve periodicites
> >> >
> >> >Umm . . . if the stimuli inside the critical band are
consecutive
> >> >harmonics, the beat rate would give the fundamental.
> >>
> >> Which is a frequency not normally associated with that place on
> >> the membrane.
> >
> >Or with any place on the membrane at all, almost certainly not if
> >the beating is audible.
> >
> >> Thus perhaps it is causing the same sort of confusion
> >> as the test tones discussed in the New Scientist article.
> >
> >No, for two reasons:
> >
> >(1) A beat frequency is an *amplitude* modulation; a pitch
frequency
> >is a *pressure* modulation.
>
> We're talking about a position (of the membrane) modulation here.

Right, but it's a very different kind of modulation at that position.
Why do you think the ear would relate one kind to the other?

> >(2) The beat frequency almost certainly doesn't have a pitch
> >frequency "equivalent" which corresponds any place whatsoever on
the
> >basilar membrane.
>
> Lost me here.

It's too low a frequency!

>> I don't remember that, but of course it should agree with place,
>> as I said below.
>
>Above?

In the original message.

>>>>>>Could erratic behavior on the membrane ruin the fit of the
>>>>>>associated auditory-nerve periodicites
>>>>>
>>>>>Umm . . . if the stimuli inside the critical band are
>>>>>consecutive harmonics, the beat rate would give the fundamental.
>>>>
>>>>Which is a frequency not normally associated with that place on
>>>>the membrane. Thus perhaps it is causing the same sort of
>>>>confusion as the test tones discussed in the New Scientist
>>>>article.
>>>
>>>No, for two reasons:
>>>
>>>(1) A beat frequency is an *amplitude* modulation; a pitch
>>>frequency is a *pressure* modulation.
>>
>>We're talking about a position (of the membrane) modulation here.
>
>Right, but it's a very different kind of modulation at that
>position. Why do you think the ear would relate one kind to
>the other?

I'm saying it *wouldn't*. But how is it different?

>>>(2) The beat frequency almost certainly doesn't have a pitch
>>>frequency "equivalent" which corresponds any place whatsoever on
>>>the basilar membrane.
>>
>> Lost me here.
>
>It's too low a frequency!

Yes.

-Carl

--- In harmonic_entropy@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >> I don't remember that, but of course it should agree with place,
> >> as I said below.
> >
> >Above?
>
> In the original message.
>
> >>>>>>Could erratic behavior on the membrane ruin the fit of the
> >>>>>>associated auditory-nerve periodicites
> >>>>>
> >>>>>Umm . . . if the stimuli inside the critical band are
> >>>>>consecutive harmonics, the beat rate would give the
fundamental.
> >>>>
> >>>>Which is a frequency not normally associated with that place on
> >>>>the membrane. Thus perhaps it is causing the same sort of
> >>>>confusion as the test tones discussed in the New Scientist
> >>>>article.
> >>>
> >>>No, for two reasons:
> >>>
> >>>(1) A beat frequency is an *amplitude* modulation; a pitch
> >>>frequency is a *pressure* modulation.
> >>
> >>We're talking about a position (of the membrane) modulation here.
> >
> >Right, but it's a very different kind of modulation at that
> >position. Why do you think the ear would relate one kind to
> >the other?
>
> I'm saying it *wouldn't*. But how is it different?

The pressure modulation is the thing that itself gets modulated in an
amplitude modulation. Amplitude modulation takes the amount of
pressure modulation and varies it periodically between zero and some
maximum value.

>>>>>>>>>Could erratic behavior on the membrane ruin the fit of the
>>>>>>>>>associated auditory-nerve periodicites
>>>>>>>
>>>>>>>Umm . . . if the stimuli inside the critical band are
>>>>>>>consecutive harmonics, the beat rate would give the
>>>>>>>fundamental.
>>>>>>
>>>>>>Which is a frequency not normally associated with that place on
>>>>>>the membrane. Thus perhaps it is causing the same sort of
>>>>>>confusion as the test tones discussed in the New Scientist
>>>>>>article.
>>>>>
>>>>>No, for two reasons:
>>>>>
>>>>>(1) A beat frequency is an *amplitude* modulation; a pitch
>>>>>frequency is a *pressure* modulation.
>>>>
>>>>We're talking about a position (of the membrane) modulation here.
>>>
>>>Right, but it's a very different kind of modulation at that
>>>position. Why do you think the ear would relate one kind to
>>>the other?
>>
>> I'm saying it *wouldn't*. But how is it different?
>
>The pressure modulation is the thing that itself gets modulated in
>an amplitude modulation. Amplitude modulation takes the amount of
>pressure modulation and varies it periodically between zero and some
>maximum value.

Yes, I understand AM. When you earlier said "they beat", I was
assuming you meant something like 'a spectral analysis of the motion
of the membrane reveals only a single low frequency'. The other
frequencies are still present. Ok, so I can't immediately gloss
a reason why place could overwhelm periodicity, but since periodicity
detection is applied to the output of the cochlea's spectral
decomposition, I wouldn't be a bit surprised if it was munged by
critical band effects. IIRC, the hair cells sit in units which are
apparently more finely resolved than the critical band. Anyway, you
get cross-activation for any true frequency, and the DSP approach is
to use assume a Gaussian distribution over the units' activity,
centered on the true frequency. I wonder what the introduction of
AM would do to that...

If we assume that "periodicity buzz" really is caused by periodicity
and roughness by critical band effects, my experience tells me that
the two can coexist up to a point, beyond which roughness only
remains.

-Carl

--- In harmonic_entropy@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >>>>>>>>>Could erratic behavior on the membrane ruin the fit of the
> >>>>>>>>>associated auditory-nerve periodicites
> >>>>>>>
> >>>>>>>Umm . . . if the stimuli inside the critical band are
> >>>>>>>consecutive harmonics, the beat rate would give the
> >>>>>>>fundamental.
> >>>>>>
> >>>>>>Which is a frequency not normally associated with that place
on
> >>>>>>the membrane. Thus perhaps it is causing the same sort of
> >>>>>>confusion as the test tones discussed in the New Scientist
> >>>>>>article.
> >>>>>
> >>>>>No, for two reasons:
> >>>>>
> >>>>>(1) A beat frequency is an *amplitude* modulation; a pitch
> >>>>>frequency is a *pressure* modulation.
> >>>>
> >>>>We're talking about a position (of the membrane) modulation
here.
> >>>
> >>>Right, but it's a very different kind of modulation at that
> >>>position. Why do you think the ear would relate one kind to
> >>>the other?
> >>
> >> I'm saying it *wouldn't*. But how is it different?
> >
> >The pressure modulation is the thing that itself gets modulated in
> >an amplitude modulation. Amplitude modulation takes the amount of
> >pressure modulation and varies it periodically between zero and
some
> >maximum value.
>
> Yes, I understand AM. When you earlier said "they beat", I was
> assuming you meant something like 'a spectral analysis of the motion
> of the membrane reveals only a single low frequency'.

No, like with all beating, there is *no* spectral energy at the beat
frequency itself. Rather, if the analysis has a short enough time
window, it will show the spectral energy at the higher (pressure
modulation) frequency grow and shrink in time. If the analysis has a
longer time window, it will simply show both of the nearby higher
frequencies.

> but since periodicity
> detection is applied to the output of the cochlea's spectral
> decomposition, I wouldn't be a bit surprised if it was munged by
> critical band effects.

Why would it be? Look at Cariani's paper again.

> If we assume that "periodicity buzz" really is caused by periodicity

Not necessarily -- it's the "buzz" due to a periodic waveform, which
could be explained with coinciding combinational tones or coinciding
beat frequencies, for example.

> and roughness by critical band effects, my experience tells me that
> the two can coexist up to a point, beyond which roughness only
> remains.

Hmm . . . can you elaborate on this please?

>> >The pressure modulation is the thing that itself gets modulated in
>> >an amplitude modulation. Amplitude modulation takes the amount of
>> >pressure modulation and varies it periodically between zero and
>> >some maximum value.
>>
>> Yes, I understand AM. When you earlier said "they beat", I was
>> assuming you meant something like 'a spectral analysis of the motion
>> of the membrane reveals only a single low frequency'.
>
>No, like with all beating, there is *no* spectral energy at the beat
>frequency itself. Rather, if the analysis has a short enough time
>window, it will show the spectral energy at the higher (pressure
>modulation) frequency grow and shrink in time. If the analysis has a
>longer time window, it will simply show both of the nearby higher
>frequencies.

I guess I've never understood how beating is AM. Of course I've
heard, when mistuning piano strings, the amplitude of an audible
frequency being modulated at the beat frequency. But in this case
I'm thinking of displacement of a point on a membrane over time,
which is driven by the composite of two audible frequencies a few
hertz apart. If you draw a picture like in the JI Primer, you
can show that this composite wave is indeed a displacement at the
difference frequency.

>> but since periodicity
>> detection is applied to the output of the cochlea's spectral
>> decomposition, I wouldn't be a bit surprised if it was munged by
>> critical band effects.
>
>Why would it be? Look at Cariani's paper again.

Which one?

I'm currently thrashing through...

http://lumma.org/stuff/MissingPitchTemplates.zip

...did you refer me to it?

>> If we assume that "periodicity buzz" really is caused by periodicity
>
>Not necessarily -- it's the "buzz" due to a periodic waveform, which
>could be explained with coinciding combinational tones or coinciding
>beat frequencies, for example.

That might explain why it seems more intense for higher-limit
intervals than 5-limit ones?

>> and roughness by critical band effects, my experience tells me that
>> the two can coexist up to a point, beyond which roughness only
>> remains.
>
>Hmm . . . can you elaborate on this please?

I imagine one could, with harmonic complex tones, play a 7:4 and
then introduce a third tone that beats with either the 7 or 4, to
the point where the original interval is indistinguishable.

-Carl

--- In harmonic_entropy@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >> >The pressure modulation is the thing that itself gets modulated
in
> >> >an amplitude modulation. Amplitude modulation takes the amount
of
> >> >pressure modulation and varies it periodically between zero and
> >> >some maximum value.
> >>
> >> Yes, I understand AM. When you earlier said "they beat", I was
> >> assuming you meant something like 'a spectral analysis of the
motion
> >> of the membrane reveals only a single low frequency'.
> >
> >No, like with all beating, there is *no* spectral energy at the
beat
> >frequency itself. Rather, if the analysis has a short enough time
> >window, it will show the spectral energy at the higher (pressure
> >modulation) frequency grow and shrink in time. If the analysis has
a
> >longer time window, it will simply show both of the nearby higher
> >frequencies.
>
> I guess I've never understood how beating is AM. Of course I've
> heard, when mistuning piano strings, the amplitude of an audible
> frequency being modulated at the beat frequency.

So you do understand it!

> But in this case
> I'm thinking of displacement of a point on a membrane over time,
> which is driven by the composite of two audible frequencies a few
> hertz apart. If you draw a picture like in the JI Primer, you
> can show that this composite wave is indeed a displacement at the
> difference frequency.

Here's a picture -- this what you want?

/tuning-math/files/Paul/walter.jpg

There is no component of displacement at the difference frequency, as
the average displacement remains the same during all phases of the
difference frequency's cycle.

> >> but since periodicity
> >> detection is applied to the output of the cochlea's spectral
> >> decomposition, I wouldn't be a bit surprised if it was munged by
> >> critical band effects.
> >
> >Why would it be? Look at Cariani's paper again.
>
> Which one?

Temporal coding of tonal information . . .

> I'm currently thrashing through...
>
> http://lumma.org/stuff/MissingPitchTemplates.zip
>
> ...did you refer me to it?

No; interestingly it uses "periodicity" where others use "place", to
mean the same thing (e.g., Goldstein's theory).

> >> If we assume that "periodicity buzz" really is caused by
periodicity
> >
> >Not necessarily -- it's the "buzz" due to a periodic waveform,
which
> >could be explained with coinciding combinational tones or
coinciding
> >beat frequencies, for example.
>
> That might explain why it seems more intense for higher-limit
> intervals than 5-limit ones?

Yes, you need those low-frequency roughness effects.

> >> and roughness by critical band effects, my experience tells me
that
> >> the two can coexist up to a point, beyond which roughness only
> >> remains.
> >
> >Hmm . . . can you elaborate on this please?
>
> I imagine one could, with harmonic complex tones, play a 7:4 and
> then introduce a third tone that beats with either the 7 or 4, to
> the point where the original interval is indistinguishable.

Indistinguishable? You mean like a 1:1?

>> But in this case
>> I'm thinking of displacement of a point on a membrane over time,
>> which is driven by the composite of two audible frequencies a few
>> hertz apart. If you draw a picture like in the JI Primer, you
>> can show that this composite wave is indeed a displacement at the
>> difference frequency.
>
>Here's a picture -- this what you want?
>
>/tuning-math/files/Paul/walter.jpg

Duh, duh, duh. I was thinking of phase offset, not frequency
offset!!

>> >> but since periodicity
>> >> detection is applied to the output of the cochlea's spectral
>> >> decomposition, I wouldn't be a bit surprised if it was munged
>> >> by critical band effects.
>> >
>> >Why would it be? Look at Cariani's paper again.
>>
>> Which one?
>
>Temporal coding of tonal information . . .
>
>> I'm currently thrashing through...
>>
>> http://lumma.org/stuff/MissingPitchTemplates.zip
>>
>> ...did you refer me to it?
>
>No; interestingly it uses "periodicity" where others use "place",
>to mean the same thing (e.g., Goldstein's theory).

I guess I found it on my own. I finished it last night. I don't
understand certain bits, mostly referring to things I haven't read.
And it seems to leave a lot of questions unanswered. But the basic
premise is very provokative!

>> >> and roughness by critical band effects, my experience tells me
>> >> that the two can coexist up to a point, beyond which roughness
>> >> only remains.
>> >
>> >Hmm . . . can you elaborate on this please?
>>
>> I imagine one could, with harmonic complex tones, play a 7:4 and
>> then introduce a third tone that beats with either the 7 or 4, to
>> the point where the original interval is indistinguishable.
>
>Indistinguishable? You mean like a 1:1?

I see that instead of "that beats with" I should have written
"offset by a small amount from". And instead of "indistinguishable",
"the periodicity buzz of the original dyad disappears".

-Carl