Yahoo Tuning Groups Ultimate Backup tuning Concordance of timbres vs Concordance of chords

This is an impossible discussion to continue in the other thread,
moving it here:

On Sat, Apr 16, 2011 at 6:24 PM, Carl Lumma <carl@...> wrote:
> As a rule,
> adding notes to any rooted chord should not decrease its
> discordance. This rule is entirely consistent with the notion
> that timbres having 12db/oct rolloff are more concordant than
> those having 6db/oct rolloff.

Why? How is it consistent?

> If you want to compare chords and timbres you should compute
> the spectra of the chords assuming some timbre. That has the
> obvious drawback of having to pick a timbre -- a choice that's
> averaged away in the "chord" abstraction.

OK, let's assume sawtooth waves, to make the math easy. I'll crunch
some numbers when I get back.

> The other drawback is that processing may be hierarchical to some degree,
> especially if the individual tones are separated by spatial or
> timing cues (also averaged away in the "chord" abstraction).
> However it might still be interesting. Comparing the spectra
> of chord fundamentals (i.e. picking sine tones for the timbre)
> is what I thought you were doing when I first replied here.
> It's something, but it's not a typical musical situation.

No, but like I said in my last message, if each note has harmonics
then the situation gets even worse. A 4:5:6:7:..:18:19 chord played
with sawtooth waves, where all of the notes are at equal volume, will
have an even harsher spectrum than if it were played with sines. Upper
notes will end up even louder because there will be additive effects
with the harmonics of lower notes. So, spectrally, the rolloff will be
negative.

This may be counterbalanced by the fact that we're not actually
talking about a 1:2:3:4:5:6:7:8:...:infinity "chord," with all
harmonics going on forever, but a finite subset of these (like
harmonics 4:...:19), which is sort of like the last thing sent through
a bandpass filter. If you aren't sure that this will really lead to a
harsher sound, we could load some tests up and see, but I'm in Orlando
now...

> > sources in real life exhibit phase irregularities, differences
> > in inter-aural spatialization cues, F0 estimation will be
> > taking place regardless. If it wasn't, then there'd be no
> > point in us talking meaningfully about "4:5:6" to begin with.
>
> I only brought up phase because it doesn't seem to matter much
> in practice (though it doesn't seem to be entirely inaudible
> either) yet it matters a lot to waveform. So referring to
> timbres by waveform may not be a good idea.

I meant in the generalized sense of a parabolic wave having 1/N^2
rolloff and all harmonics present. We already know exactly when phase
matters and when it doesn't - take the Fourier transform of a signal,
and then from that plot its "phase response." If the phase response is
a line, it'll sound no different. If it's not a line, it will. I
posted some listening examples of my voice sent through different
phase responses a while back to show.

For sustained timbres, you can't get any more out there than being in
a reverberant hall, which adds randomly delayed and filtered copies of
the signal to the original. Each one of those interacts with the
original signal and changes the phase of random parts, so reverb is
equivalent to just taking the original signal and @*#&ing up the phase
of each component. Still doesn't interfere with F0 estimation,
although as we saw it definitely interferes with "periodicity buzz"
(which now needs a new name).

-Mike

🔗Carl Lumma <carl@...>

🔗Mike Battaglia <battaglia01@...>

🔗Carl Lumma <carl@...>

🔗Mike Battaglia <battaglia01@...>

On Sun, Apr 17, 2011 at 7:59 PM, Carl Lumma <carl@...> wrote:
>
> > I don't think I understand.
>
> You don't understand how adding notes to a rooted chord
> adds energy to the upper end of its spectrum?

I don't understand why you say that that doesn't alter its
concordance, and that this is consistent with the knowledge that
increasing energy to the upper end of the spectrum of a note does
alter its concordance.

> >> Can you dig up the link?
> >
> > /tuning/topicId_95522.html#95568
>
> Oh, I remember that. I have a rudimentary 10-partial
> additive synth and I can tell the difference if I have
> one of the prominent partials at 90deg vs 180 deg. Is
> the phase response different? I should add that it may
> be due to combination tones or other artifacts in the
> audio pipeline of this thing.

Yes, the phase response will be different. There will be a crazy spike
in the phase response at whichever partial it is that's changing. I
notice that this can sometimes cause weird spatialization effects to
occur.

> >> > Still doesn't interfere with F0 estimation,
> >> > although as we saw it definitely interferes with
> >> > "periodicity buzz" (which now needs a new name).
> >>
> >> Why does it need a new name?
> >
> > Because it doesn't actually have anything to do with
> > periodicity.
>
> Oh no?

Oh no, and I went over this already. I spent weeks on this. Check out
the threads on periodicity buzz from a few months ago, where I posted
examples that destroyed this exact hypothesis. Periodicity buzz will
happen for any chord in which each adjacent note is separated by the
same difference in frequency, linearly speaking in Hz (the same effect
can happen for chords in which adjacent notes are separated by
frequency differences that are harmonically related, but it isn't as
neat). It has more to do with equal beating than anything, or perhaps
equal roughness is a better way to describe it.

-Mike

🔗Carl Lumma <carl@...>

🔗Mike Battaglia <battaglia01@...>

🔗Carl Lumma <carl@...>

🔗Mike Battaglia <battaglia01@...>

On Sun, Apr 17, 2011 at 9:02 PM, Carl Lumma <carl@...> wrote:
>
> > Are you asking me why it would be less concordant to begin with?
> > I'm confused here.
>
> Yes. I didn't say I knew, I just said it's consistent with
> the general rule about chords I proposed (which itself is
> consistent with Tenney height and pretty much every investigation
> done on chords that I'm aware of).
>
> > > > Oh no, and I went over this already. I spent weeks on this.
> > >
> > > I was afraid you were thinking of that thread. I didn't
> > > agree with, pretty much anything you did in that thread.
> >
> > As I recall, the matter ended pretty conclusively, but feel
> > free to apply logic liberally.
>
> What makes you think it ended conclusively? It looked to me
> like you were posting in a vacuum.

It ended conclusively because I tested all of the other hypotheses
that were being thrown around, as well as some that I came up with to
play devil's advocate, and they all ended up disproven by various
listening examples. I was hardly posting in a vacuum and was
interacting with plenty of people at the time. What actually happened
is

- You jumped on early, threw out a hypothesis that time-domain
processing in the brain was involved, I threw out that the cochlea was
involved. I later addressed this in the listening tests
- I started doing some basic tests with impulse trains
- You didn't see what impulse trains had to do with periodicity buzz
- I explained, but you didn't seem to like the answer, so we went back
and forth on that for a while
- I decided gammatone filters would be useful
- I remember you vaguely disliked gammatone filters for some reason,
but didn't state why. As I already know what the drawbacks to
gammatone filtering are and saw that they didn't apply, I kept going
- You jumped off the conversation
- ??? HERE BE DRAGONS (this is where a series of like a thousand
listening examples were posted with feedback from plenty of people)
- Months later, here we are, you're still back where you jumped off,
I'm like 20MB of listening tests later

As are no doubt aware by now, my singular pet peeve is when I do work
and people try to criticize it without actually knowing what the work
is. This is doubly so when I spent as much time on it as I did. I am
always accepting of criticism and don't really have any attachments to
particular. Feel free to dissect anything that I've done, and to be
honest I think I have answers for anything that you can throw at me at
this point, because I threw most things I could think of at myself.
But please try and familiarize yourself with the work that I've done
before throwing criticism at it.

> Early on, I disagreed that
> the buzz sounds you were synthesizing were necessarily related
> to periodicity buzz. Your hypothesis that equal-frequency
> spacing causes the effect is plausible, but I haven't seen
> much evidence that it's true.

I posted tons of listening examples, with titles like "LISTENING
EXAMPLES, PERIODICITY BUZZ! PLEASE LISTEN!", involving equally-spaced
irrational chords that exhibited "periodicity buzz." They involved
things like phi and sqrt(2). That should have settled this matter.
Feel free to go read through the thread again.

-Mike

🔗Michael <djtrancendance@...>

🔗Carl Lumma <carl@...>

🔗Mike Battaglia <battaglia01@...>

On Sun, Apr 17, 2011 at 9:46 PM, Carl Lumma <carl@...> wrote:
>
> It didn't. Here's what actually happened.
>
> - You posted 10,000 posts of vague mush.
> - I couldn't keep up.

It's "vague mush" if you don't understand the mathematics or concepts
involved, yes. I was as precise as you could possibly hope for, but no
more precise. This means that I didn't preemptively read your mind and
guess what you do or don't know. The presumption is that you will
actually read the things that I post and ask questions about them.
Feel free at any time to come back down to earth with the rest of us
and try that.

> You ought to be able to state concisely whatever it
> is you think you demonstrated.

Periodicity buzz is synchronized roughness. Roughness is amplitude
modulation that occurs on the cochlea when the two notes are close
enough to get caught in the critical band between each note, but not
on the notes themselves. This behavior is predicted by not only
gammatone filters, and certainly by more advanced cochlear models, but
even with ERBs. For example:

The ERB at middle C is about 24.7*(4.37*.261 + 1) = ~53 Hz. This means
it's about ~26 Hz in either direction. 7/6, if played at middle C with
sines, will yield Eb at 7/6 * 261 = ~305 Hz. Will this get caught in
the critical band at C?

305 - 261 = 44 Hz

It would need to be < 26 Hz to cause beating over there, so no, it
won't. Will it get caught in the critical band at Eb? Well, the
critical bandwidth at Eb is 24.7*(4.37*.305+ 1) = 58 Hz, so that
equates to ~29 Hz in either direction. So no, it won't get caught
there either. But what about the mean of 305 and 261 Hz, which is 283
Hz? The critical bandwidth there is 55 Hz, so ~27 Hz in either
direction. Let's find out:

283 + 27 = 310 Hz - check
283 - 27 = 256 Hz - check

So while there will be no actual AM at the peak resonance for 310 or
256 Hz on the cochlea, there will be AM occurring on the cochlea
between them. When you have a chord like 4:5:6, the 4:5 and the 5:6
will be beating in unison with one another, and this creates the
characteristic sound of "periodicity buzz." When you have 7:8:10, the
8:10 is beating twice as fast as the 7:8, and you have periodicity
buzz in which the beating is in a 2:1 ratio, which still cool.
16:18:21 will give you buzz that is in a 3:2 polyrhythm, and that's
not as nice.

When you have 5 evenly spaced notes (in Hz) with an outer dyad of phi,
you will still get periodicity buzz, because they'll all be beating at
the same rate. Listening examples exist for all of this and plenty
more.

The whole thing is very sensitive to phase, and I posted gammatone
filterbank plots that explored how the phase response changes all of
this. They generally predicted the behavior of the listening examples
well.

This may be a good place to start:
/tuning/topicId_95699.html#95699

> - Nobody else gave a darn.

Haha... I was getting great feedback from Petr, I believe from Kalle,
Jacques Dudon, from Gene, even Michael S was involved. I won't claim
it was the discovery of the year, but it was a productive discussion
that I enjoyed. The term "drat" was defined from what happened, and
the whole thing spurred some kind of sync-beating phase for a little
bit that everyone was into. This may be another thing that you're
unaware of because you tuned it out. But now it may be my turn to tune
this thread out.

> The fact that you're
> instead recounting some kind of drama indicates to
> me that haven't got anything.

I see you have decided to ignore my request to actually read the thread... LOL.

Furthermore, you seem to have taken my honest plea to read my work
before criticizing as an opportunity to respond with insults and
condescension! That's a shame.

-Mike

🔗Carl Lumma <carl@...>

Mike wrote:

> The ERB at middle C is about 24.7*(4.37*.261 + 1) = ~53 Hz.
> This means it's about ~26 Hz in either direction. 7/6, if
> played at middle C with sines, will yield Eb at
> 7/6 * 261 = ~305 Hz. Will this get caught in the critical
> band at C?
> 305 - 261 = 44 Hz
> It would need to be < 26 Hz to cause beating over there,
> so no, it won't. Will it get caught in the critical band
> at Eb? Well, the critical bandwidth at Eb is
> 24.7*(4.37*.305+ 1) = 58 Hz, so that equates to ~29 Hz in
> either direction. So no, it won't get caught there either.
> But what about the mean of 305 and 261 Hz, which is 283 Hz?

Not that I see the relevance to periodicity buzz, but you're
doing it wrong. The excitation on the basilar membrane from
these two pitches does overlap, since 26 + 29 > 44. The
roughness is a function of the overlapping energy relative to
the total energy and in this case is quite small. The energy
from each stimulus falls off by an additive factor of about
-3.82dB per bin, where an ERB contains about 60 bins.

Overlap produces roughness but not perceived AM, until tones
are separated by < 1/2CB. This can be shown by synthesizing
dyads of sine waves that are not JI, do not have periodicity
buzz, but do have overlap and roughness. Compare to
450hz:525hz, which are JI, do have PB, and have no overlap
and no roughness.

> When you have a chord like 4:5:6, the 4:5 and the 5:6 will
> be beating in unison with one another, and this creates the
> characteristic sound of "periodicity buzz."

And what happens to your beat rates for near-JI tempered
chords (which still exhibit periodicity buzz)?

> Haha... I was getting great feedback from Petr, I believe from
> Kalle, Jacques Dudon, from Gene, even Michael S was involved.
> I won't claim it was the discovery of the year,

That's good because whatever you discovered, it doesn't
seem to have anything to do with periodicity buzz.

-Carl

🔗Mike Battaglia <battaglia01@...>

On Wed, Apr 20, 2011 at 5:46 AM, Carl Lumma <carl@...> wrote:
>
> Not that I see the relevance to periodicity buzz, but you're
> doing it wrong. The excitation on the basilar membrane from
> these two pitches does overlap, since 26 + 29 > 44. The
> roughness is a function of the overlapping energy relative to
> the total energy and in this case is quite small. The energy
> from each stimulus falls off by an additive factor of about
> -3.82dB per bin, where an ERB contains about 60 bins.

That's what I said. There will be "no interaction" at either C or Eb
on the basilar membrane, but there will be interaction between them.
Hence you have "roughness," but not "beating." I thought I said this
in the post you're replying to...

I wrote:
> So while there will be no actual AM at the peak resonance for 310 or
> 256 Hz on the cochlea, there will be AM occurring on the cochlea
> between them.

Ah yes! I did. It was in the sentence directly after where you cut off
the quote you're replying to.

> Overlap produces roughness but not perceived AM, until tones
> are separated by < 1/2CB.

Roughness is barely perceptual AM. If you have more than one dyad
producing roughness at the same rate and in phase with one another, it
can become audible, whether or not the dyads are just or not (assuming
sines for now).

> This can be shown by synthesizing
> dyads of sine waves that are not JI, do not have periodicity
> buzz, but do have overlap and roughness. Compare to
> 450hz:525hz, which are JI, do have PB, and have no overlap
> and no roughness.

I'm not at a computer with MATLAB now, but how about these?

http://www.mikebattagliamusic.com/music/alt567buzz.wav
http://www.mikebattagliamusic.com/music/alt78910buzz.wav
http://www.mikebattagliamusic.com/music/mysterybuzz.wav
http://www.mikebattagliamusic.com/music/mystery2buzz.wav

Use good headphones - in each WAV file, there are four different
sub-examples, with the first being repeated at the end to form five.
Do you hear any buzz in these chords, and if so, does it sound like
the buzz is varying from sub-example to sub-example? Which one is
strongest?

Then try this one:

http://www.mikebattagliamusic.com/music/buzztempering.wav

Which chords are JI, and which ones are near-JI but tempered?

> > When you have a chord like 4:5:6, the 4:5 and the 5:6 will
> > be beating in unison with one another, and this creates the
> > characteristic sound of "periodicity buzz."
>
> And what happens to your beat rates for near-JI tempered
> chords (which still exhibit periodicity buzz)?

If they're tempered in such a way that for a:b:c, b-a = c-b, they'll
still exhibit periodicity buzz. If c-b and b-a are in a 2:1 ratio,
it'll still exhibit buzz. If c-b and b-a are in a 3:2 ratio, it'll
still buzz, but less coherently. etc.

-Mike

🔗Carl Lumma <carl@...>

Mike Battaglia <battaglia01@...> wrote:

> Ah yes! I did. It was in the sentence directly after where
> you cut off the quote you're replying to.

Yes, I saw. But you apparently reached the conclusion by
incorrect means, by calculating the critical bandwidth at the
midpoint between two stimuli. If that's not what you did,
I'm sorry. Either way, I demonstrated the correct method.

> > Overlap produces roughness but not perceived AM, until tones
> > are separated by < 1/2CB.
>
> Roughness is barely perceptual AM.

Er- no, it isn't. If you explain why you think so maybe I
can explain why it isn't in a way that's meaningful to you.
But we can't expect do that kind of thing ad infinitum and
still manage to conclude something about periodicity buzz
before we're old and gray.

> > This can be shown by synthesizing
> > dyads of sine waves that are not JI, do not have periodicity
> > buzz, but do have overlap and roughness. Compare to
> > 450hz:525hz, which are JI, do have PB, and have no overlap
> > and no roughness.
>
> I'm not at a computer with MATLAB now, but how about these?
> http://www.mikebattagliamusic.com/music/alt567buzz.wav
> http://www.mikebattagliamusic.com/music/alt78910buzz.wav

The file names make it seem like these aren't dyads.

> http://www.mikebattagliamusic.com/music/mysterybuzz.wav
> http://www.mikebattagliamusic.com/music/mystery2buzz.wav

Not interested in mysteries, sorry. Try the example I gave
and see if you can reproduce the result I got.

> > And what happens to your beat rates for near-JI tempered
> > chords (which still exhibit periodicity buzz)?
>
> If they're tempered in such a way

I didn't ask about a restricted case, I asked you to provide
the predictions of your model for arbitrary tempered chords
that exhibit periodicity buzz. First though you'll have to
clear the JI (7:6) example above, which seems to falsify it
immediately. (I raised this issue early in the previous
thread and am still waiting for your response.)

-Carl

🔗Mike Battaglia <battaglia01@...>

On Wed, Apr 20, 2011 at 5:54 PM, Carl Lumma <carl@...> wrote:
>
> Mike Battaglia <battaglia01@...> wrote:
>
> > Ah yes! I did. It was in the sentence directly after where
> > you cut off the quote you're replying to.
>
> Yes, I saw. But you apparently reached the conclusion by
> incorrect means, by calculating the critical bandwidth at the
> midpoint between two stimuli. If that's not what you did,
> I'm sorry. Either way, I demonstrated the correct method.

That's not incorrect at all if we're using ERBs, because they're rectangular.

> > > Overlap produces roughness but not perceived AM, until tones
> > > are separated by < 1/2CB.
> >
> > Roughness is barely perceptual AM.
>
> Er- no, it isn't. If you explain why you think so maybe I
> can explain why it isn't in a way that's meaningful to you.
> But we can't expect do that kind of thing ad infinitum and
> still manage to conclude something about periodicity buzz
> before we're old and gray.

The sensation of "roughness" occurs when a critical band interaction
occurs between the two notes on the basilar membrane, but not at the
notes themselves. Or, if you'd like a more precise definition that
doesn't require making recourse to ERBs, it's as you said, when the
interaction occurs and the region of overlap is small, energy-wise,
compared to the total energy being passed by rest of the filter/s. The
gammatone filter plots gave a nicely visual diagram of this.

> > > This can be shown by synthesizing
> > > dyads of sine waves that are not JI, do not have periodicity
> > > buzz, but do have overlap and roughness. Compare to
> > > 450hz:525hz, which are JI, do have PB, and have no overlap
> > > and no roughness.
> >
> > I'm not at a computer with MATLAB now, but how about these?
> > http://www.mikebattagliamusic.com/music/alt567buzz.wav
> > http://www.mikebattagliamusic.com/music/alt78910buzz.wav
>
> The file names make it seem like these aren't dyads.
>
> > http://www.mikebattagliamusic.com/music/mysterybuzz.wav
> > http://www.mikebattagliamusic.com/music/mystery2buzz.wav
>
> Not interested in mysteries, sorry.

This is silly and makes communication impossible. These "mystery"
names are from files that I synthesized months ago. I didn't bother to
change the names. They're from the thread that I posted a long time
ago, which I note that you still haven't read. The "mystery" was
revealed in the thread following. Go read it.

The funniest part of this is that the above wav files completely
destroy your hypothesis that periodicity buzz is actually related to
periodicity, but you've chosen to put your fingers in your ears and go
"la la la la I won't listen la la la." This may be a good time to
decide if you primarily want to "know the truth" or to "play games."

> Try the example I gave and see if you can reproduce the result I got.

With sine waves, it buzzes, and it also buzzes if you go with 450 Hz
and 519 Hz, which is about 247 cents.

> > > And what happens to your beat rates for near-JI tempered
> > > chords (which still exhibit periodicity buzz)?
> >
> > If they're tempered in such a way
>
> I didn't ask about a restricted case, I asked you to provide
> the predictions of your model for arbitrary tempered chords
> that exhibit periodicity buzz.

You don't seem to be understanding anything I write. They aren't going
to buzz unless they're tempered in the way that I wrote above. If you
don't temper them as I described, they're going to exhibit a warbling
buzz as the critical band interactions drift in and out of sync with
one another. If you play clever tricks with the phase response, you
can also attenuate or in some cases eliminate the buzz. Since you seem
to be on top of this, I assume I won't need to provide an explanation
for why that might be.

-Mike

🔗Carl Lumma <carl@...>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

>> Yes, I saw. But you apparently reached the conclusion by
>> incorrect means, by calculating the critical bandwidth at the
>> midpoint between two stimuli. If that's not what you did,
>> I'm sorry. Either way, I demonstrated the correct method.
>
> That's not incorrect at all if we're using ERBs,

Yes, it is.

> The funniest part of this is that the above wav files
> completely destroy your hypothesis that periodicity buzz is
> actually related to periodicity, but you've chosen to put your
> fingers in your ears and go "la la la la I won't listen
> la la la." This may be a good time to decide if you primarily
> want to "know the truth" or to "play games."

I don't know which hypothesis of mine you're referring to.
If you synthesized them months ago, I heard them months ago.

> > Try the example I gave and see if you can reproduce the
> > result I got.
>
> With sine waves, it buzzes,

So your idea about roughness causing the phenomenon stands
where?

> > I didn't ask about a restricted case, I asked you to provide
> > the predictions of your model for arbitrary tempered chords
> > that exhibit periodicity buzz.
>
> You don't seem to be understanding anything I write. They
> aren't going to buzz unless they're tempered in the way
> that I wrote above.

But they do, so your idea is falsified twice so far
in this message.

> If you don't temper them as I described, they're going to
> exhibit a warbling buzz as the critical band interactions
> drift in and out of sync with one another.

I've never observed this. If your model is one tenth
what you say it is, you'll be able to predict the warbling
in the buzz and synthesize examples showing your
predictions correct.

-Carl

🔗Mike Battaglia <battaglia01@...>

On Wed, Apr 20, 2011 at 6:39 PM, Carl Lumma <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> >> Yes, I saw. But you apparently reached the conclusion by
> >> incorrect means, by calculating the critical bandwidth at the
> >> midpoint between two stimuli. If that's not what you did,
> >> I'm sorry. Either way, I demonstrated the correct method.
> >
> > That's not incorrect at all if we're using ERBs,
>
> Yes, it is.

...No. Work it out.

> > The funniest part of this is that the above wav files
> > completely destroy your hypothesis that periodicity buzz is
> > actually related to periodicity, but you've chosen to put your
> > fingers in your ears and go "la la la la I won't listen
> > la la la." This may be a good time to decide if you primarily
> > want to "know the truth" or to "play games."
>
> I don't know which hypothesis of mine you're referring to.
> If you synthesized them months ago, I heard them months ago.

la la la la la

> > > Try the example I gave and see if you can reproduce the
> > > result I got.
> >
> > With sine waves, it buzzes,
>
> So your idea about roughness causing the phenomenon stands
> where?

Whoa there! Don't skip over the fact that this alone falsifies any
notion of periodicity buzz having to do with "periodicity."

Anyways, it stands with the fact that ERBs are pretty crude
approximations to what actually occurs in the cochlea, and that things
like gammatone filters, which are orders of magnitude more accurate,
predict the proper behavior.

> > > I didn't ask about a restricted case, I asked you to provide
> > > the predictions of your model for arbitrary tempered chords
> > > that exhibit periodicity buzz.
> >
> > You don't seem to be understanding anything I write. They
> > aren't going to buzz unless they're tempered in the way
> > that I wrote above.
>
> But they do, so your idea is falsified twice so far
> in this message.

Uh, which idea was falsified, and how was it falsified? Give me a
concrete example. That tempered sine wave dyads exhibit periodicity
buzz is something that the idea predicts, because there is going to be
a single rate of AM, and it will be in sync with itself. The model's
predictions work even better when you get into triads, tetrads, etc,
although you'd have to actually listen to the examples to know that.

What actually has been falsified several times, now however, is the
notion that periodicity buzz has anything to do with "periodicity." I
note that you yourself posted an example at one point with a dyad
where the notes were played with full stereo separation, exhibiting no
buzz, vs one where the notes were played in mono, exhibiting buzz. How
do you explain that?

> > If you don't temper them as I described, they're going to
> > exhibit a warbling buzz as the critical band interactions
> > drift in and out of sync with one another.
>
> I've never observed this. If your model is one tenth
> what you say it is, you'll be able to predict the warbling
> in the buzz and synthesize examples showing your
> predictions correct.

So first you refuse to listen to my synthesized examples, and then you
claim that I need to synthesize them? LOL!

I did specifically what you demand right here:

I wrote:
> http://www.mikebattagliamusic.com/music/buzztempering.wav

> Which chords are JI, and which ones are near-JI but tempered?

You didn't respond to this. But go ahead, which ones are JI, and which
ones are near-JI but tempered? Use good headphones, and keep the
volume low.

-Mike

🔗Carl Lumma <carl@...>

Mike wrote:

> ...No. Work it out.

Boy, this is fun.

> > > > Try the example I gave and see if you can reproduce the
> > > > result I got.
> > >
> > > With sine waves, it buzzes,
> >
> > So your idea about roughness causing the phenomenon stands
> > where?
>
> Whoa there! Don't skip over the fact that this alone
> falsifies any notion of periodicity buzz having to do with
> "periodicity."

I didn't coin the term. Meanwhile: answer the question.

> Anyways, it stands with the fact that ERBs are pretty crude
> approximations to what actually occurs in the cochlea,

Yes. I usually use CBs, which are slightly better and good
enough for what I use them for.

> and that things like gammatone filters, which are orders of
> magnitude more accurate, predict the proper behavior.

When you post something that requires gammatone filters
to get right, I'll let you know.

> > But they do, so your idea is falsified twice so far
> > in this message.
>
> Uh, which idea was falsified, and how was it falsified?

Your idea that some vague combination of basilar membrane
overlap / roughness / beat synchrony has something to do with periodicity buzz. It's falsified by a sound that has none
of those thing but still buzzes.

> Give me a concrete example.

I did, and you confirmed it. The record of that is above.

> That tempered sine wave dyads

or tempered complex-tone chords...

> exhibit periodicity buzz is something that the idea predicts,
> because there is going to be a single rate of AM, and it will
> be in sync with itself. The model's predictions work even
> better when you get into triads, tetrads, etc, although you'd
> have to actually listen to the examples to know that.

You've yet to post a single prediction of your model along
with an example that someone could listen to in order to
check it. Yet you go around typing crap like "la la la la".

> What actually has been falsified several times, now however,
> is the notion that periodicity buzz has anything to do with
> "periodicity."

That hasn't been falsified, though I don't claim to know what
causes periodicity buzz.

> I note that you yourself posted an example at one point with
> a dyad where the notes were played with full stereo separation,
> exhibiting no buzz, vs one where the notes were played in mono,
> exhibiting buzz. How do you explain that?

I haven't tried to explain it yet. It did falsify an earlier
idea about PB originating centrally. But it's even more
valuable as an aid for pining down what periodicity buzz
sounds like, so we can build confidence we're listening for
the same thing.

You seem to imply that "periodicity" means some particular
hearing process, when it can be interpreted much more generally.
So the name has not been shown to be inappropriate. Nor has
it been shown appropriate. I use it because it's the only
name I know for the phenomenon.

> So first you refuse to listen to my synthesized examples,

I have listened to them. I think I said that.

> and then you claim that I need to synthesize them? LOL!

An example is an example of something. Your "examples"
are random files with no meaning.

> I did specifically what you demand right here:
>
> > http://www.mikebattagliamusic.com/music/buzztempering.wav
> > Which chords are JI, and which ones are near-JI but tempered?

I didn't demand you make a cryptic quiz. I demanded you
cough up predictions for the model you supposedly have.

-Carl

🔗Mike Battaglia <battaglia01@...>

On Wed, Apr 20, 2011 at 7:42 PM, Carl Lumma <carl@...> wrote:
>
> Mike wrote:
>
> > ...No. Work it out.
>
> Boy, this is fun.

ERBs are symmetrical approximations of the auditory filter. Hence,
since they're symmetrical, they predict not only the danger zone of
interaction for a tone with adjacent tones, but the width of the
auditory filter at a certain point on the basilar membrane.

> > Whoa there! Don't skip over the fact that this alone
> > falsifies any notion of periodicity buzz having to do with
> > "periodicity."
>
> I didn't coin the term.

Phew! Now we're getting somewhere.

> Meanwhile: answer the question.

Does my answer right after the sentence you quoted count?

> > Anyways, it stands with the fact that ERBs are pretty crude
> > approximations to what actually occurs in the cochlea,
>
> Yes. I usually use CBs, which are slightly better and good
> enough for what I use them for.

How exactly are you using CBs? Are you modeling things where there's a
variance in magnitude response within the two -3dB cutoff points, but
that beyond that you model the auditory filter as passing no energy at
all?

> > > But they do, so your idea is falsified twice so far
> > > in this message.
> >
> > Uh, which idea was falsified, and how was it falsified?
>
> Your idea that some vague combination of basilar membrane
> overlap / roughness / beat synchrony has something to do with periodicity buzz. It's falsified by a sound that has none
> of those thing but still buzzes.

This doesn't falsify anything of the sort! It means that you are
pushing the limits of what ERBs are supposed to predict, and as I've
said (and shown) things like gammatone filterbanks predict the correct
behavior where they fail. Both ERBs and CBs (as you seem to be using
them) are designed to be useful rules of thumb in approximating the
behavior of grossly apparent critical band interactions. They aren't
designed to predict the perceptual quality of minimal variances in
amplitude right at the edge of where the ERB predicts roughness should
occur. Things that model the auditory filter as having an infinite
frequency response do predict things properly, such as gammatone
filters. Using less accurate models of the cochlea to "falsify"
behaviors that more accurate models predict doesn't make any sense,
especially when the limitations of the less accurate models are known
from the outset.

Here's a JASA reference where researchers have demonstrated the same
findings that I have, model roughness the same way, do the same tests
with phase, etc:
http://audition.ens.fr/dp/pdfs/pressnitzer-1999-roughness_phase.pdf

Just look at experiment #1, as experiment #2 is more obliquely related.

> > That tempered sine wave dyads
>
> or tempered complex-tone chords...

Complex-tone chords, if the timbre is perfectly periodic, will only
exhibit perfectly even "buzz" if you're playing a JI or RI chord. If
you're using a detuned timbre, this behavior should change.

> > What actually has been falsified several times, now however,
> > is the notion that periodicity buzz has anything to do with
> > "periodicity."
>
> That hasn't been falsified, though I don't claim to know what
> causes periodicity buzz.

I am openminded to the possibility that all of the gammatone
filterbank predictions, the listening tests, and my general reasoning
and understanding of what goes on in the cochlea has led me to follow
a red herring. I'm not really that attached to anything. However, that
periodicity buzz actually involves "periodicity" has been falsified in
the minds of everyone who listened to the listening tests, which is a
group I hope that you join soon!

> > I note that you yourself posted an example at one point with
> > a dyad where the notes were played with full stereo separation,
> > exhibiting no buzz, vs one where the notes were played in mono,
> > exhibiting buzz. How do you explain that?
> You seem to imply that "periodicity" means some particular
> hearing process, when it can be interpreted much more generally.

How so?

> You've yet to post a single prediction of your model along
> with an example that someone could listen to in order to
> check it. Yet you go around typing crap like "la la la la".
//snip
> An example is an example of something. Your "examples"
> are random files with no meaning.
//snip
>
> I didn't demand you make a cryptic quiz. I demanded you
> cough up predictions for the model you supposedly have.

Emotions are running hot in this thread, and I'm not going to let your
bias cloud the results. I'd like to know what the samples sound like
to you. But, if you really want to cheat and corrupt my data set, you
could always just CLICK THE LINK TO THE THREAD I posted, where I say
EXACTLY WHAT THE EXAMPLES ARE. This is something you should already
know, as even a psychoacoustic authority on such a high horse as yours
should familiarize himself with the work he's attempting to criticize.
At least, that's how I like to do things.

But hey, I'm hoping that you won't cheat, and that you'll just say
what the examples sound like. Then again, if your results differ from
everyone else's, as well as the referenced study's, that'll say
something about how tuning list bias affects listening tests.

-Mike

🔗Carl Lumma <carl@...>

Mike wrote:

> ERBs are symmetrical approximations of the auditory filter. Hence,
> since they're symmetrical, they predict not only the danger zone
> of interaction for a tone with adjacent tones, but the width of
> the auditory filter at a certain point on the basilar membrane.

Ok, what I realize you've been getting at is

(cf + 24)/2 + (cf' + 24)/2 = c(f+f')/2 + 24

What I've been trying to say, what I thought I said, is that
the roughness depends on the power present at the overlap,
and the power at the edges of an ERB or CB or whatever depends
on its center frequency.

> How exactly are you using CBs? Are you modeling things where
> there's a variance in magnitude response within the two -3dB
> cutoff points, but that beyond that you model the auditory
> filter as passing no energy at all?

I assume each partial's power is totally absorbed by its CB,
by setting the membrane response at the CF so the number of
constant-log-frequency-width bins available takes the power
to 0dB at the edges.

> > Your idea that some vague combination of basilar membrane
> > overlap / roughness / beat synchrony has something to do with
> > periodicity buzz. It's falsified by a sound that has none
> > of those thing but still buzzes.
>
> This doesn't falsify anything of the sort! It means that you
> are pushing the limits of what ERBs are supposed to predict,

I've listened to wider intervals than 7:6 (such as 6:5, 9:7,
and 7:5) at 1/1s up to 750Hz, so there's no question of
overlap. The buzz becomes faster but not softer. Try it!

> Here's a JASA reference where researchers have demonstrated the
> same findings that I have, model roughness the same way, do the
> same tests with phase, etc:
> http://audition.ens.fr/dp/pdfs/pressnitzer-1999-roughness_phase.pdf
> Just look at experiment #1, as experiment #2 is more obliquely
> related.

I looked at this before. They are talking about roughness,
not periodicity buzz! Is there some particular section of
this paper that you think is related?

> Complex-tone chords, if the timbre is perfectly periodic, will
> only exhibit perfectly even "buzz" if you're playing a JI or RI
> chord.

Then why do tempered chords buzz almost indistinguishably
from JI chords? Now, if you were to calculate the predicted
buzz for a bunch of chords, we could listen and see what's
going on...

> that periodicity buzz actually involves "periodicity"
> has been falsified in the minds of everyone who listened to the
> listening tests, which is a group I hope that you join soon!

Just a couple of messages ago you were talking about simple
buzz ratios in chords. If that's not periodic I don't know
what is!

> Emotions are running hot in this thread, and I'm not going to
> let you bias cloud the results. I'd like to know what the
> samples sound like to you.

I have idea what you want me to listen for or why, so I can't
comply even if I wanted to.

> But hey, I'm hoping that you won't cheat,

I can't cheat at something I don't understand.

> Then again, if your results differ from everyone else's,

Just to be clear, I don't have any periodicity buzz results.
Above I was talking about a general roughness model I put
together years ago.

-Carl

🔗Carl Lumma <carl@...>

🔗Mike Battaglia <battaglia01@...>

🔗Carl Lumma <carl@...>

🔗Mike Battaglia <battaglia01@...>

On Thu, Apr 21, 2011 at 2:24 AM, Carl Lumma <carl@...> wrote:
>
> Ok, what I realize you've been getting at is
>
> (cf + 24)/2 + (cf' + 24)/2 = c(f+f')/2 + 24
>
> What I've been trying to say, what I thought I said, is that
> the roughness depends on the power present at the overlap,
> and the power at the edges of an ERB or CB or whatever depends
> on its center frequency.

In real life, the frequency response of the auditory filter is
infinite in extent. There is always overlap, but it will drop below
the threshold of detectability at some point. ERBs aren't going to
tell you exactly what that point is, because they're linear and don't
take into account any cochlear amplification at low volumes, and
because they're rectangular.

The whole point of an ERB is that it takes the infinite energy
response of the auditory filter and tells you how wide a rect filter
would have to be to pass the same energy. You can then use this to set
up something like a gammatone filterbank by setting each gammatone
filter's total energy to be equivalent to the ERB's. It is not the
case that the actual auditory filter has a frequency response that
suddenly drops off at the edges, a la ERB.

> > This doesn't falsify anything of the sort! It means that you
> > are pushing the limits of what ERBs are supposed to predict,
>
> I've listened to wider intervals than 7:6 (such as 6:5, 9:7,
> and 7:5) at 1/1s up to 750Hz, so there's no question of
> overlap. The buzz becomes faster but not softer. Try it!

There is always overlap. The Gammatone filterbank predicts the proper behavior

http://www.mikebattagliamusic.com/music/gammatone-7-5-buzz.png

As well as with sqrt(2)

http://www.mikebattagliamusic.com/music/gammatone-sqrt-2-buzz.png

Note that the "black" areas are actually where the filterbank is most
active, and "white" areas are where it's least active. So there's only
a small amount of interaction, but it's there. Now, gammatone models
have two drawbacks, both of which need to be addressed

1) Gammatone filters are linear, which leads to two separate issues:
1a) Most importantly, this means that they don't take into account the
varying response of the auditory filter with respect to volume. At low
volumes, the frequency response of the filter narrows, which would
lead to less overlap. However, at low volumes, the cochlea tends to
amplify what you do have, which counteracts the effects of the above.
1b) It also means that gammatone filters don't model combination
tones, which would reinforce even beating only at periodic ratios.
However, in my experiments and listening tests, one of which you'll
find below again in this thread, I still noted that linearly even
triads buzz more clearly than periodic triads that are not linearly
even.

and 2) The actual auditory filter is asymmetrical. This doesn't have
much bearing on anything, though, as if you ran the filterbank with
asymmetrical filters instead of gammatone filters, the interaction
area would just be moved up a bit - the apex of interaction just
wouldn't be at the mean of the two frequencies.

> I looked at this before. They are talking about roughness,
> not periodicity buzz! Is there some particular section of
> this paper that you think is related?

See

"Experimental studies seeking to quantify roughness perception have
often studied the effects of the frequency composition of stimuli
Plomp and Levelt, 1965; Plomp and Steeneken, 1968; Kameoka and
Kuriyagawa, 1969. The presence of frequency components within the
limits of a critical band is considered, in these studies, to be the
source of the beats that produce the percept of roughness.
Consequently, models of roughness perception have been proposed that
are based on the spectral composition of energy falling within
critical bands Hutchinson and Knopoff, 1978. A different approach to
roughness is to study the influence of temporal parameters by means of
amplitude-modulated stimuli Mathes and Miller, 1947; Terhardt, 1974;
Fastl, 1977. A dependence of roughness on the frequency and depth of
the modulation was demonstrated. The interpretation proposed is that
roughness is determined by the envelope fluctuations of the signal
within an auditory filter. These results have inspired another kind of
model in which roughness estimates are based on the rms value of the
signal envelope after auditory filtering and after a
modulation-frequency bandpass filter Aures, 1985; Daniel and Weber,
1997."

They then proceed to do exactly the same tests with phase as I do, but
we're not there yet in this discussion.

> > Complex-tone chords, if the timbre is perfectly periodic, will
> > only exhibit perfectly even "buzz" if you're playing a JI or RI
> > chord.
>
> Then why do tempered chords buzz almost indistinguishably
> from JI chords? Now, if you were to calculate the predicted
> buzz for a bunch of chords, we could listen and see what's
> going on...
//snip
> Just a couple of messages ago you were talking about simple
> buzz ratios in chords. If that's not periodic I don't know
> what is!
//snip
> I have idea what you want me to listen for or why, so I can't
> comply even if I wanted to.
//snip
> I can't cheat at something I don't understand.

OK, just start with this one:
http://www.mikebattagliamusic.com/music/buzztempering.wav

Some of these chords should buzz perfectly, and some of them should
have warbly buzz. Your job is to say which ones buzz perfectly, and
which ones have warbly buzz. Some sample options:

1) buzz, warbly buzz, warbly buzz
2) buzz, buzz, warbly buzz
3) buzz, warbly buzz, buzz
4) something else

-Mike

🔗Carl Lumma <carl@...>

--- Mike Battaglia <battaglia01@...> wrote:

> In real life, the frequency response of the auditory filter is
> infinite in extent.

In real life, nothing has infinite frequency response.

> ERBs aren't going to tell you exactly what that point is,
> because they're linear and don't take into account any
> cochlear amplification at low volumes, and because they're
> rectangular.

The discrete model I chose should closely approximate
auditory filter response, because I based it Dick Lyon's
ideal auditory filter.

> There is always overlap. The Gammatone filterbank predicts
> the proper behavior
> http://www.mikebattagliamusic.com/music/gammatone-7-5-buzz.png

What's the proper behavior, and how is this image
predicting it? Believe it or not, the people who read
this list are not telepaths.

> Now, gammatone models
> have two drawbacks, both of which need to be addressed

First address what gammatone filters have to do with
periodicity buzz.

> > I looked at this before. They are talking about roughness,
> > not periodicity buzz! Is there some particular section of
> > this paper that you think is related?
>
> See
> "Experimental studies seeking to quantify roughness perception
> have often studied the effects of the frequency composition of
> stimuli Plomp and Levelt, 1965; Plomp and Steeneken, 1968;
> Kameoka and Kuriyagawa, 1969. The presence of frequency
> components within the limits of a critical band is considered,
> in these studies, to be the source of the beats that produce
> the percept of roughness.

Yup.

> Consequently, models of roughness perception have been proposed
> that are based on the spectral composition of energy falling
> within critical bands Hutchinson and Knopoff, 1978. A different
> approach to roughness is to study the influence of temporal
> parameters by means of amplitude-modulated stimuli Mathes and
> Miller, 1947; Terhardt, 1974; Fastl, 1977. A dependence of
> roughness on the frequency and depth of the modulation was
> demonstrated. The interpretation proposed is that roughness is
> determined by the envelope fluctuations of the signal within
> an auditory filter. These results have inspired another kind of
> model in which roughness estimates are based on the rms value
> of the signal envelope after auditory filtering and after a
> modulation-frequency bandpass filter Aures, 1985; Daniel and
> Weber, 1997."

Where's the part about periodicity buzz?

> OK, just start with this one:
> http://www.mikebattagliamusic.com/music/buzztempering.wav
> Some of these chords should buzz perfectly, and some of them
> should have warbly buzz. Your job is to say which ones buzz
> perfectly, and which ones have warbly buzz.

I have no idea what "warbly buzz" is but if pressed I'd say
none of them has it.

-Carl

🔗Mike Battaglia <battaglia01@...>

On Sat, Apr 23, 2011 at 10:44 PM, Carl Lumma <carl@...> wrote:
>
> In real life, nothing has infinite frequency response.

No. In real life, everything has an infinite frequency response.

> > ERBs aren't going to tell you exactly what that point is,
> > because they're linear and don't take into account any
> > cochlear amplification at low volumes, and because they're
> > rectangular.
>
> The discrete model I chose should closely approximate
> auditory filter response, because I based it Dick Lyon's
> ideal auditory filter.

I don't know who Dick Lyon is, but I know what ERBs are, and their
drawbacks are as I listed in the last post.

> > There is always overlap. The Gammatone filterbank predicts
> > the proper behavior
> > http://www.mikebattagliamusic.com/music/gammatone-7-5-buzz.png
>
> What's the proper behavior, and how is this image
> predicting it? Believe it or not, the people who read
> this list are not telepaths.

This is a gammatone filterbank plot of 7/5, and the image shows
amplitude modulation occuring on the cochlea between the two tones.

> > Now, gammatone models
> > have two drawbacks, both of which need to be addressed
>
> First address what gammatone filters have to do with
> periodicity buzz.

I've been addressing that the whole time, so I don't know why you're
suddenly confused. Gammatone filters model the cochlea better than
ERBs, and thus will predict better when and where amplitude modulation
will occur. The hypothesis we're testing is that periodicity buzz is
actually synchronized AM in the cochlea.

> > Consequently, models of roughness perception have been proposed
> > that are based on the spectral composition of energy falling
> > within critical bands Hutchinson and Knopoff, 1978. A different
> > approach to roughness is to study the influence of temporal
> > parameters by means of amplitude-modulated stimuli Mathes and
> > Miller, 1947; Terhardt, 1974; Fastl, 1977. A dependence of
> > roughness on the frequency and depth of the modulation was
> > demonstrated. The interpretation proposed is that roughness is
> > determined by the envelope fluctuations of the signal within
> > an auditory filter. These results have inspired another kind of
> > model in which roughness estimates are based on the rms value
> > of the signal envelope after auditory filtering and after a
> > modulation-frequency bandpass filter Aures, 1985; Daniel and
> > Weber, 1997."
>
> Where's the part about periodicity buzz?

They said

"The presence of frequency components within the limits of a critical
band is considered, in these studies, to be the source of the beats
that produce the percept of roughness."

As one of your criticisms was that roughness isn't related to AM,
here's a reference in the literature that seems to assume it is. Then,
here are four more references that back up the same assertion:

> > A different
> > approach to roughness is to study the influence of temporal
> > parameters by means of amplitude-modulated stimuli Mathes and
> > Miller, 1947; Terhardt, 1974; Fastl, 1977. A dependence of
> > roughness on the frequency and depth of the modulation was
> > demonstrated. The interpretation proposed is that roughness is
> > determined by the envelope fluctuations of the signal within
> > an auditory filter.

Note "envelope fluctuations of the signal within an auditory filter."
If the frequencies are separated by a constant difference, then these
envelope fluctuations will be in sync with one another, unless you
play with the phase, which notably destroys it. The tests in the study
I cited were done on single sinusoids that were being modified with
AM, which will always produce such triads.

> > OK, just start with this one:
> > http://www.mikebattagliamusic.com/music/buzztempering.wav
> > Some of these chords should buzz perfectly, and some of them
> > should have warbly buzz. Your job is to say which ones buzz
> > perfectly, and which ones have warbly buzz.
>
> I have no idea what "warbly buzz" is but if pressed I'd say
> none of them has it.

You don't hear any sort of warbling, beating, or a chorus-like effect
in the last example?

-Mike

🔗Carl Lumma <carl@...>

--- Mike Battaglia <battaglia01@...> wrote:

> > In real life, nothing has infinite frequency response.
>
> No. In real life, everything has an infinite frequency response.

No physical system has infinite frequency response.

> > First address what gammatone filters have to do with
> > periodicity buzz.
>
> I've been addressing that the whole time, so I don't know why
> you're suddenly confused.

Perhaps someone else can explain your idea here.

> The hypothesis we're testing is that periodicity buzz is
> actually synchronized AM in the cochlea.

Define synchronized. Why, of the infinitude of sounds that
produce AM in the cochlea, do only a tiny subset of them
produce periodicity buzz?

> "The presence of frequency components within the limits of a
> critical band is considered, in these studies, to be the source
> of the beats that produce the percept of roughness."

Right, roughness.

> As one of your criticisms was that roughness isn't related to AM,
> here's a reference in the literature that seems to assume it is.

Yeah, it's wrong (the AM is obviously related, but roughness
is not the 'sound' of it as they seem to say). But that's
beside the point.

> Note "envelope fluctuations of the signal within an auditory
> filter."

Note, nowhere in this paper is periodicity buzz, or anything
remotely like it, mentioned.

> If the frequencies are separated by a constant difference,
> then these envelope fluctuations will be in sync with one
> another, unless you play with the phase, which notably
> destroys it.

Yeah ok, you've got some predictions to make and experiments
to perform. You can proxy the latter by posting examples
here, but you should recognize that what you've posted so far
aren't examples of anything.

> You don't hear any sort of warbling, beating, or a chorus-like
> effect in the last example?

I hear a chorus-like warble. It doesn't seem to interact
with the periodicity buzz.

-Carl

🔗Mike Battaglia <battaglia01@...>

On Mon, Apr 25, 2011 at 6:04 AM, Carl Lumma <carl@...> wrote:
>
> --- Mike Battaglia <battaglia01@...> wrote:
>
> > > In real life, nothing has infinite frequency response.
> >
> > No. In real life, everything has an infinite frequency response.
>
> No physical system has infinite frequency response.

I'm not sure why you continue to assert this inaccurate statement
without providing any supporting arguments, but it's wrong. Every
physical system has an infinite frequency response. There is no
physical system that will simply thermodynamically uncouple itself
from an incoming signal at a certain frequency. I think what you mean
to say is that no physical system will contain a component that has
infinite or absolutely zero mechanical compliance, which is the sort
of thing that might actually lead to a complete attenuation of some
frequency somewhere. But we live in a universe dominated by the second
law of thermodynamics, and this is not the case.

> > The hypothesis we're testing is that periodicity buzz is
> > actually synchronized AM in the cochlea.
>
> Define synchronized. Why, of the infinitude of sounds that
> produce AM in the cochlea, do only a tiny subset of them
> produce periodicity buzz?

Sounds of the type a:a+b:a+2b will produce periodicity buzz because
the beating between them will both be at frequency b, and so you have
lots of places on the cochlea all beating simultaneously at b. This
can be confounded by altering the phase response of the signal so that
the peaks of the AM no longer align with one another.

> > "The presence of frequency components within the limits of a
> > critical band is considered, in these studies, to be the source
> > of the beats that produce the percept of roughness."
>
> Right, roughness.

Which is periodicity buzz.

> > As one of your criticisms was that roughness isn't related to AM,
> > here's a reference in the literature that seems to assume it is.
>
> Yeah, it's wrong (the AM is obviously related, but roughness
> is not the 'sound' of it as they seem to say). But that's
> beside the point.

You need to back this up with an argument, and provide an explanation
of what you think that roughness is.

> > Note "envelope fluctuations of the signal within an auditory
> > filter."
>
> Note, nowhere in this paper is periodicity buzz, or anything
> remotely like it, mentioned.

Periodicity buzz is caused by envelope fluctuations of the signal
within an auditory filter. Later on, down the page, they test
sinusoids that have AM on them, which will produce a triad. By playing
around with the phase response, they can change the quality of the
roughness produced, which is the same thing I was doing by messing
with the phase response to alter whether or not there's a strong buzz.

> > If the frequencies are separated by a constant difference,
> > then these envelope fluctuations will be in sync with one
> > another, unless you play with the phase, which notably
> > destroys it.
>
> Yeah ok, you've got some predictions to make and experiments
> to perform. You can proxy the latter by posting examples
> here, but you should recognize that what you've posted so far
> aren't examples of anything.

These predictions and experiments have already been performed. I'm
humoring you by taking you through my work again. Being as you seem to
be the last person on the list who believes in stuff like this, and
fancy yourself the last bit of psychoacoustic resistance against this
idea, I'd expect you'd be more willing to cooperate by reading the
material. But the question is, why should I continue to do so if
you're not? Newcomers will join the list, I'll point them to the
thread on this stuff, they'll read it, and understand, and life will
go on.

> > You don't hear any sort of warbling, beating, or a chorus-like
> > effect in the last example?
>
> I hear a chorus-like warble. It doesn't seem to interact
> with the periodicity buzz.

What do you mean "interact" with the periodicity buzz?

-Mike

🔗Carl Lumma <carl@...>

--- Mike Battaglia <battaglia01@...> wrote:

> > No physical system has infinite frequency response.
>
> I'm not sure why you continue to assert this inaccurate
> statement without providing any supporting arguments, but
> it's wrong.

This is OT so I won't go into it further. Take a physics
course if you're interested. There was no need to top off
being wrong by writing some nonsense about thermodynamics
by the way.

> > Define synchronized. Why, of the infinitude of sounds that
> > produce AM in the cochlea, do only a tiny subset of them
> > produce periodicity buzz?
>
> Sounds of the type a:a+b:a+2b will produce periodicity buzz
> because the beating between them will both be at frequency b,
> and so you have lots of places on the cochlea all beating
> simultaneously at b.

What's the significance of the size of b?

> > Right, roughness.
>
> Which is periodicity buzz.

Excuse me?

> You need to back this up with an argument, and provide an
> explanation of what you think that roughness is.

Har. You're the one making the novel claims. Or trying to.

> Periodicity buzz is caused by envelope fluctuations of the
> signal within an auditory filter.

So for a lone 7:5, what will the rate and intensity of the
periodicity buzz be with 5=200Hz, 5=400Hz, 5=600Hz, & 5=800Hz?

> Being as you seem to be the last person on the list who
> believes in stuff like this, and fancy yourself the last bit
> of psychoacoustic resistance against this idea,

I don't know what gave you either impression. First, I don't
think anyone here other than you has understood what you're
doing here. I could be wrong, and I'd very much welcome their
input. Second, I have no desire to resist in any way research
into periodicity buzz.

> > > You don't hear any sort of warbling, beating, or a
> > > chorus-like effect in the last example?
> >
> > I hear a chorus-like warble. It doesn't seem to interact
> > with the periodicity buzz.
>
> What do you mean "interact" with the periodicity buzz?

The periodicity buzz is unaffected by the addition of the
warble. -Carl

🔗Mike Battaglia <battaglia01@...>

On Mon, Apr 25, 2011 at 4:17 PM, Carl Lumma <carl@...> wrote:
>
> This is OT so I won't go into it further. Take a physics
> course if you're interested. There was no need to top off
> being wrong by writing some nonsense about thermodynamics
> by the way.

Mmmm... no. I'm not going to let you back out of this one. To have a
filter that has a finite frequency response would require having
infinite rolloff. Infinite rolloff filters are a physical
impossibility. Not only is it false that every real-life filter has a
finite frequency response, but this actually poses a problem that
engineers have to solve all the time. Like the ones I was assigned for
homework... as an undergrad student... three years ago.

You run up against this when it comes to the Shannon sampling theorem.
To avoid aliasing, you have to first filter out all of the frequencies
above the Nyquist frequency, while keeping those above it. You WANT a
finite-response filter in this case - a "brickwall" filter - but they
don't exist, so people have spent lots of time developing things like
elliptical filters and tricks with oversampling which prove to be good
enough. There is no useful real-life filter that just so happens to
have a finite frequency response which will take care of this for us.
National Semiconductor has a datasheet explaining this

http://sacdlab.cn/Demo/Nyquist-Kotelnikov_teorem_info_2.pdf

If you actually want to achieve infinite rejection for a specific
frequency, you're limited to tricks like this

http://jap.aip.org/resource/1/japiau/v18/i8/p691_s1?isAuthorized=no

and

http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=1125867

These people did not spent all of that time working out all of these
techniques because they just weren't aware that in real life, perfect
and infinite attenuation lies all around us.

> > Sounds of the type a:a+b:a+2b will produce periodicity buzz
> > because the beating between them will both be at frequency b,
> > and so you have lots of places on the cochlea all beating
> > simultaneously at b.
>
> What's the significance of the size of b?

As b increases, the frequency of the buzz should both increase in
speed and decrease in volume.

> > > Right, roughness.
> >
> > Which is periodicity buzz.
>
> Excuse me?

This paper shows that your roughness model is flawed and is more in
line with what I'm saying. Your roughness model is the same one that
Hutchinson et. al proposes, and this paper has a pretty thorough
review of how that model was improved on with subsequent experiments,
has been refined generally in with how I claim it works, and then
performs an experiment to refine it further which is exactly the same
one I performed with phases in the other thread. So you cannot
dismiss, a priori, critical band interactions being the source of
periodicity buzz, just because your flawed roughness model says so.

Your response that I have to first prove that roughness is related to
periodicity buzz, as a stepping stone to show that modern models of
roughness support periodicity buzz being cochlear in origin, is
fallacious and circular.

> > You need to back this up with an argument, and provide an
> > explanation of what you think that roughness is.
>
> Har. You're the one making the novel claims. Or trying to.

Uh... lol. This is what just happened:

1) You made a claim about how roughness works, based on your model
which has errors approximating the rolloff of the real-life auditory
filter
2) I refuted your claim with a lit reference, which contains three
further references to Terhardt, Mathes and Miller, and Fastl. It also
has a reference to Hutchinson et. all, which proposes the same model
for roughness that you do, and addresses how further studies have
improved on this hypothesis and instead support my model. Then it does
the same experiment that I did, and further provides evidence for my
point
3) You respond that the authors of this paper, as well as Terhardt,
Mathes and Miller, Fastl, and every other author mentioned, "are
wrong" while giving no argument
4) I ask you to back this up with an argument of why it's wrong
5) You try to shift the burden of proof to me

???

> > Periodicity buzz is caused by envelope fluctuations of the
> > signal within an auditory filter.
>
> So for a lone 7:5, what will the rate and intensity of the
> periodicity buzz be with 5=200Hz, 5=400Hz, 5=600Hz, & 5=800Hz?

If 5 is 200 Hz, 7/5 should be 280 Hz, so the buzz should be 80 Hz. If
5 is 400 Hz, 7/5 should be 560 Hz, so the buzz should be 160 Hz.
Likewise, it should then go to 240 Hz and 320 Hz, respectively.

> > Being as you seem to be the last person on the list who
> > believes in stuff like this, and fancy yourself the last bit
> > of psychoacoustic resistance against this idea,
>
> I don't know what gave you either impression. First, I don't
> think anyone here other than you has understood what you're
> doing here. I could be wrong, and I'd very much welcome their
> input.

I was interacting with plenty of people while this was still going on,
and most people seemed to get the concept. Now you come into this
months later and insist that "nobody knows what I'm talking about." I
think you mean "I don't understand what you're talking about." You
also have some kind of invented story about how "I was posting in a
vacuum and nobody cared," which I think really means "I tuned out of
the discussion." Since I think you're a smart guy, I don't mind taking
the time to walk you through my work, especially because I generally
value your feedback and don't claim that it is complete.

It's very annoying when, instead of being open-minded and asking me
questions about my work, you like to play this game where we pretend
there's like a panel of researchers, all of whom are looking down
condescendingly on my "leaps of logic." In actuality there's only you,
and sometimes you don't understand concepts that I'm familiar with or
learned in school and see them as illogical jumps. Since I'm not
psychic and don't know what you already do or don't know, I generally
just say things and encourage you to ask questions. Maybe I'm wrong
sometimes, but we will never get anywhere if we continually play these
sorts of self-serving games where we subtly reframe this very
high-level discussion in terms of different social contexts to see
who's playing the fool.

Here's a useful algorithm summing up how instead I wish discussions
between us played out:

http://3.bp.blogspot.com/-X0Wqb_7_dPM/TYdOHyNylxI/AAAAAAAAAHs/gi7ykODJYG8/s1600/FlowchartDebate.jpg

These are the rules of discussion that I'd like to lay down for future
debate with you. I am always happy to discuss my ideas and change
them, but not if every conversation has to be as irritating as this
one has become. If you don't like these terms, then I'd be happy to
not discuss this at all, as I'm already satisfied that I've provided
some theoretical justification for Kraig and Erv Wilson's ideas on
proportional beating, that Jacques Dudon appreciated the research and
we had some discussions about how it tied in with what he did, that it
reopened the conversation about rational intonation and sync-beating
chords, that Kalle, Michael, Gene, and everyone else who responded to
my examples basically heard them the same way I did, that it got Petr
back on the list and he seemed to recognize my exasperation with your
posts at the time. I'm also satisfied in that I haven't seen you raise
a point yet that I couldn't address with the model, and whether I
convince you or not, people who join the list in the future who
understand the math will know what I mean.

-Mike

🔗genewardsmith <genewardsmith@...>

🔗Daniel Nielsen <nielsed@...>

🔗Mike Battaglia <battaglia01@...>

🔗genewardsmith <genewardsmith@...>

🔗Mike Battaglia <battaglia01@...>

🔗Carl Lumma <carl@...>

--- Mike Battaglia <battaglia01@...> wrote:

> > This is OT so I won't go into it further. Take a physics
> > course if you're interested. There was no need to top off
> > being wrong by writing some nonsense about thermodynamics
> > by the way.
>
> Mmmm... no. I'm not going to let you back out of this one.
> To have a filter that has a finite frequency response would
> require having infinite rolloff. Infinite rolloff filters
> are a physical impossibility.

What you're saying assumes continuous symmetries that do not
exist in nature. For a system like a string to have infinite
frequency response it would need to be infinitely flexible.

> You WANT a finite-response filter in this case - a
> "brickwall" filter - but they don't exist,

Of course they exist - sampling itself is an example. It
makes a bad filter because of the aliasing. But I didn't say
filter, I said physical system.

> > What's the significance of the size of b?
>
> As b increases, the frequency of the buzz should both
> increase in speed and decrease in volume.

Ok, have you tested this?

> So you cannot dismiss, a priori, critical band interactions
> being the source of periodicity buzz, just because your flawed
> roughness model says so.

I don't think you know what my "roughness model" is so I don't
think you know that it's flawed. It predicts nothing about
periodicity buzz as far as I can tell.

> > > Periodicity buzz is caused by envelope fluctuations of
> > > the signal within an auditory filter.
> >
> > So for a lone 7:5, what will the rate and intensity of
> > the periodicity buzz be with 5=200Hz, 5=400Hz, 5=600Hz,
> > & 5=800Hz?
>
> If 5 is 200 Hz, 7/5 should be 280 Hz, so the buzz should
> be 80 Hz. If 5 is 400 Hz, 7/5 should be 560 Hz, so the buzz
> should be 160 Hz. Likewise, it should then go to 240 Hz
> and 320 Hz, respectively.

Which of these is "within an auditory filter"? Or more
precisely, what relative amplitudes do you predict for
the buzz?

> I was interacting with plenty of people while this was still
> going on, and most people seemed to get the concept.

You're claiming support for your work. I think I've asked
twice for more on that. My impression was that Jacques and
Michael didn't understand what you were saying but by all
means, point to posts where they demonstrate understanding
and give their endorsement. Frankly I don't think you've
posted enough details for anyone to be able to endorse it
but maybe I'm all wet.

> It's very annoying when, instead of being open-minded and
> asking me questions about my work, you like to play this
> game

The impression you give is not one of openness, but rather
of a desire to be adversarial.

-Carl

🔗Mike Battaglia <battaglia01@...>

On Tue, Apr 26, 2011 at 4:53 AM, Carl Lumma <carl@...> wrote:
>
> What you're saying assumes continuous symmetries that do not
> exist in nature. For a system like a string to have infinite
> frequency response it would need to be infinitely flexible.

For a string to have a frequency response that actually reaches 0 at a
certain point and stays that way, it would need to exhibit infinite
stiffness against a stimulus of a wide range of frequencies. The
motion of a string will decay exponentially, and this exponential time
decay will create spreading regions around each peak in the frequency
domain, and each exponentially shaped region will go on forever. The
same applies to the decaying motion of the hairs in the ear.

The point about string harmonics is tangential, because the decaying
motion of the string will itself produce an infinite frequency
response via spreading, and this is the mechanism I was referring to
when I spoke about the infinite frequency response of the hairs in the
ear (their motion decays). But for posterity's sake, the Fourier
Transform is an algorithm that transforms a signal into a
representation where it is the sum of sinusoids. For some physical
system's motion, it will come up with a series of sine waves that,
when added back together, magically reconstructs the original signal.
Just because in real life, sawtooth waves can't actually jump from -1
to 1 infinitely quickly, doesn't mean that the amplitude of the
harmonics just tapers off to zero. It means that your speaker cone
exhibits some mechanical compliance - if it were infinitely stiff, it
would be able to jump from -1 to 1 infinitely quickly, but it's not.
Compliance is analogous to capacitance

http://www.swarthmore.edu/NatSci/echeeve1/Ref/LPSA/Analogs/ElectricalMechanicalAnalogs.html

So you're just low pass filtering the signal. But, even if you sent
10000000 Hz through your speaker, assuming no other filtering
components exist in the system (another impossibility) the cone will
move a little, tiny fraction of a bit, literally until you get into
things like quantum mechanics. The cone does not have infinite
stiffness, but it doesn't have infinite compliance either, which would
require infinite flexibility, as you already agree is impossible. So
the harmonics will never decay to zero entirely, they'll just be
attenuated a bit.

> > You WANT a finite-response filter in this case - a
> > "brickwall" filter - but they don't exist,
>
> Of course they exist - sampling itself is an example. It
> makes a bad filter because of the aliasing. But I didn't say
> filter, I said physical system.

Sampling is not a filter in the sense that the word filter is
generally used, and the frequency response of a sampled signal is
going to be infinite in extent. In fact, if it wasn't infinite in
extent before sampling, it will definitely be infinite in extent after
sampling. When you sample, you are taking the frequency spectrum and
convolving it with an impulse train that spikes at the sampling
frequency and all of its harmonics. If the bandwidth of your signal is
greater than half the sampling frequency, the negative frequencies
will tile over into the baseband and you get aliasing. Sampling causes
periodicity in the spectrum (not periodicity in the waveform, but in
the spectrum) at the sampling frequency. When you reconstruct the
signal, if you want to attenuate everything but the baseband, you need
to filter. To actually get rid of everything but the baseband would
require a brickwall filter, which I just said doesn't exist, although
you can get arbitrarily close to it. So what they do instead is hold
each sample until the beginning of the next one "sample and hold,"
which dampens the sidebands, but doesn't attenuate them infinitely.
This is tangential, but you should know this anyway, as I predict
variations of this point will keep coming up again and again in this
discussion.

How this relates to auditory filtering: I am using the word filter to
describe a system that alters the frequency response of the input,
usually by taking things away and boosting other things. This is
consistent with how the term is used here

http://en.wikipedia.org/wiki/Filter_%28signal_processing%29

In this extent, the hair cells in the ear are filters, because they
attenuate certain frequencies and pass others. They are mechanical and
acoustical filters. A mechanical-electrical duality exists, as per the
link in the last paragraph - so yes, the hair cells in the ear are
filters, which is why they are called "auditory filters." And no, they
will not produce infinite attenuation anywhere. I hope we can get off
of this subject now and get back to roughness.

> > > What's the significance of the size of b?
> >
> > As b increases, the frequency of the buzz should both
> > increase in speed and decrease in volume.
>
> Ok, have you tested this?

The increase in speed is something I have examples of somewhere in
that thread. Generally, it decreases in volume. Once you get to a
certain point, the volume seems to level off, but huge increases will
still drop it. For really wide intervals, I doubt you'd hear anything.

> > So you cannot dismiss, a priori, critical band interactions
> > being the source of periodicity buzz, just because your flawed
> > roughness model says so.
>
> I don't think you know what my "roughness model" is so I don't
> think you know that it's flawed. It predicts nothing about
> periodicity buzz as far as I can tell.

You keep using assertions about how auditory filters don't overlap in
real life, based on ERBs (!), to prove that it periodicity buzz
couldn't possibly in a million years be related to roughness.

> > If 5 is 200 Hz, 7/5 should be 280 Hz, so the buzz should
> > be 80 Hz. If 5 is 400 Hz, 7/5 should be 560 Hz, so the buzz
> > should be 160 Hz. Likewise, it should then go to 240 Hz
> > and 320 Hz, respectively.
>
> Which of these is "within an auditory filter"? Or more
> precisely, what relative amplitudes do you predict for
> the buzz?

I have no way to predict the actual amplitude change of the buzz at
all right now, I'd need more accurate auditory filter models to do
that and I haven't gotten that far. I can predict that the buzz will
probably decrease in volume as you get higher, but I don't know how
much it will decrease or how perceptually audible it will be. If it
doesn't do that, or if the buzz increases in higher registers, then
I'd really have to take a much harder look at things, see how
A-weighting or combination tones might play into it, but I doubt it
will.

> > I was interacting with plenty of people while this was still
> > going on, and most people seemed to get the concept.
>
> You're claiming support for your work. I think I've asked
> twice for more on that. My impression was that Jacques and
> Michael didn't understand what you were saying but by all
> means, point to posts where they demonstrate understanding
> and give their endorsement. Frankly I don't think you've
> posted enough details for anyone to be able to endorse it
> but maybe I'm all wet.

My impression was that Michael got the main point that linear spacing
predicted buzz more than periodicity, which is the strength of my
model. If it turns out that all of this stuff about the cochlea is a
complete red herring, which I don't think so, I'm still happy to have
figured that out. Jacques Dudon was also understanding of that point.
Kalle caught on as well. Petr wrote a good post about it here

/tuning/topicId_95728.html#95728

He seemed to be on the same page as me at the time. If what you are
arguing is that there may be a better explanation for this behavior
than cochlear interactions, I'd be happy to discuss that. At the time,
it seemed that your main point was that you weren't convinced that
this is true, but thought yourself entitled to not have to listen to
the examples and see.

> > It's very annoying when, instead of being open-minded and
> > asking me questions about my work, you like to play this
> > game
>
> The impression you give is not one of openness, but rather
> of a desire to be adversarial.

This may be because in the very beginning of this conversation, I
asked you to read the thread and familiarize myself with the work
before criticizing it. You responded by calling me a drama queen and
taunted me that this meant I "probably had nothing." After posting the
link to the thread twice, you refused every single time to read it,
and kept telling me that I had posted no examples or predictions which
I obviously know that I have. After posting the examples something
like three times, you refused to listen to them because you didn't
know the answers, which you missed because you didn't click the link
to the thread I gave. Now you've finally listened to them today, so
your comments are actually starting to make sense. I can't imagine
that the way I've acted is not in line with how you'd expect a
reasonable human being to react to behavior like that.

If you have a better way of explaining this behavior than cochlear
interactions, I'd love to hear it, but so far all of the evidence I've
seen supports it. And if you can come up with an example of a chord
that buzzes evenly, with no additional chorus, and that auditory
filtering can't explain, you'll have convinced me of something. So
far, I haven't found one, and I spent lots of time looking. So for
now, this is the explanation that seems most reasonable and that the
evidence continues to support. Maybe you can improve on the paradigm.

-Mike

🔗Carl Lumma <carl@...>

--- Mike Battaglia <battaglia01@...> wrote:

> For a string to have a frequency response that actually
> reaches 0 at a certain point and stays that way, it would
> need to exhibit infinite stiffness against a stimulus of a
> wide range of frequencies.

Like I said, take a physics course. To get a string to
respond at higher and higher frequencies you must drive
it harder, until you reach the Planck scale where driving
harder doesn't do anything. Of course you destroy the
string long before that.

> Sampling is not a filter in the sense that the word filter
> is generally used,

Right.

> and the frequency response of a sampled signal is
> going to be infinite in extent.
> When you reconstruct the signal, if you want to attenuate
> everything but the baseband, you need to filter.

The sampled signal contains no information above Nyquist.
The fact that various reconstruction techniques put stuff
up there is immaterial.

> > > As b increases, the frequency of the buzz should both
> > > increase in speed and decrease in volume.
> >
> > Ok, have you tested this?
>
> The increase in speed is something I have examples of
> somewhere in that thread. Generally, it decreases in volume.

My hunch is that the decrease in volume you would predict is
much greater than observed.

> You keep using assertions about how auditory filters don't
> overlap in real life,

I certainly haven't said that!

> I have no way to predict the actual amplitude change of the
> buzz at all right now, I'd need more accurate auditory filter
> models to do that and I haven't gotten that far. I can
> predict that the buzz will probably decrease in volume as
> you get higher, but I don't know how much it will decrease
> or how perceptually audible it will be.

It's not clear to me if you think the buzz is entirely due
to AM within filters. If it is, the intensity of the buzz
should drop off very rapidly with interval width.

> > You're claiming support for your work. I think I've asked
> > twice for more on that. My impression was that Jacques and
> > Michael didn't understand what you were saying but by all
> > means, point to posts where they demonstrate understanding
> > and give their endorsement. Frankly I don't think you've
> > posted enough details for anyone to be able to endorse it
> > but maybe I'm all wet.
[snip]
> Petr wrote a good post about it here
> /tuning/topicId_95728.html#95728

He mentions an offlist discussion you had with him back during
Rick's GCD thread. He also seems to mention the first examples
you were producing - the impulse trains that were supposedly
examples of periodicity buzz. Finally, he mentions combination
tones. I don't see a word about what we're presently
discussing and I'm surprised you've linked to this message in
response to my request.

> He seemed to be on the same page as me at the time. If what
> you are arguing is that there may be a better explanation for
> this behavior than cochlear interactions, I'd be happy to
> discuss that. At the time, it seemed that your main point was
> that you weren't convinced that this is true, but thought
> yourself entitled to not have to listen to the examples and see.

As I've said now several times, I listened to all your examples
when you posted them - some of them more than once.

> This may be because in the very beginning of this conversation,
> I asked you to read the thread and familiarize myself with the
> work before criticizing it. You responded by calling me a drama
> queen and taunted me that this meant I "probably had nothing."

I'm still waiting for something that could back up the claims
you've made.

> kept telling me that I had posted no examples or predictions
> which I obviously know that I have.

Here's an important point: I still haven't been able to find a
single prediction/example from you on this.

> If you have a better way of explaining this behavior than
> cochlear interactions,

I don't, and said I did. I'm trying to understand yours!

-Carl

🔗Mike Battaglia <battaglia01@...>

On Tue, Apr 26, 2011 at 3:30 PM, Carl Lumma <carl@...> wrote:
>
> > For a string to have a frequency response that actually
> > reaches 0 at a certain point and stays that way, it would
> > need to exhibit infinite stiffness against a stimulus of a
> > wide range of frequencies.
>
> Like I said, take a physics course. To get a string to
> respond at higher and higher frequencies you must drive
> it harder, until you reach the Planck scale where driving
> harder doesn't do anything. Of course you destroy the
> string long before that.

I never said otherwise, and even mentioned the quantum argument
further down in my post. But you brought this point up in response to
my assertion that there will still be overlap between auditory filters
that are out of ERB range. I thought at the time you were arguing my
point as it applies to the cochlea, not making a spurious objection
about quantum mechanics.

> > and the frequency response of a sampled signal is
> > going to be infinite in extent.
> > When you reconstruct the signal, if you want to attenuate
> > everything but the baseband, you need to filter.
> The sampled signal contains no information above Nyquist.
> The fact that various reconstruction techniques put stuff
> up there is immaterial.

A more mathematically rigorous way of looking at it is that the
sampled signal contains the baseband continually reflected about
Nyquist and going up forever. But this is kind of a silly debate, as
the discrete array of samples doesn't mean anything until you put it
back in the time domain. If you actually want to use sinc
interpolation, you cut everything above Nyquist. If your preferred
view on it is that you want to think of the array of samples as
already being sinc interpolated by default in the continuous time
domain, fine, but that's not how I learned it and I think it makes the
math more confusing.

In general it's more intuitive to think of it as sampling in one
domain = periodicity in the other domain, with sampled time domain
signals and Fourier series for periodic waveforms being the canonical
examples of this. Then, sinc filtering to cut everything above nyquist
is only one way to treat the sampled signal. I think it's a more
intuitive paradigm. But now we're really far out there, because my
original point was that when you reconstruct the signal, in real-life,
you can't brickwall filter it.

> > The increase in speed is something I have examples of
> > somewhere in that thread. Generally, it decreases in volume.
>
> My hunch is that the decrease in volume you would predict is
> much greater than observed.
//snip
> It's not clear to me if you think the buzz is entirely due
> to AM within filters. If it is, the intensity of the buzz
> should drop off very rapidly with interval width.

I wouldn't be surprised, but I haven't not taking into account any
kind of cochlear amplification effects, etc. The resulting AM waveform
located between the locations on the cochlea will exhibit constructive
and destructive interference. I had worked it out at one point that
the constructive side of this should always be above the masking curve
by definition, and the destructive side always below it. So it should
always be audible in theory, but at what point you stop hearing it at
all is something I haven't tested.

I think that
1) The concept of a phase-dependent buzz that occurs with linear
spacing can be shown to be a general facet of the behavior of
filterbanks that cover the entire spectrum without any gaps
2) Different filterbanks will predict how the buzz tapers off with
respect to volume in different ways; e.g. gammatone filters will
predict different specific behavior than ERBs, but all should predict
the same general big picture that buzz occurs at a point intermediate
to the two frequencies in the filterbank, increases in speed as the
frequencies get farther apart, and decrease in volume
3) The cochlea is the obvious filterbank in the auditory system to
attribute this behavior to
4) Gammatone filter modeling, which isn't 100% accurate but has most
of the vital features of the actual auditory filter, predicts very
well when and where buzz will occur
5) Its predictions aren't 100% accurate with respect to little details
like the exact amplitude curve of buzz with respect to distance, but
in the larger picture its predictions are good enough for government
work, and where they break down can usually be explained by imagining
the plots with asymmetrical filters and nonlinear effects
6) The work done so far supports the hypothesis that the cochlea is
the origin, and I have yet to see a better model suggested that data
supports over this one

That is where I'm at. I'm not making predictions about the exact buzz
difference frequency-amplitude curve, because I have no way to make
such predictions and I don't see how they're relevant to the bigger
picture. We don't know all of the details of the cochlear
nonlinearities, and I have no way of modeling how exactly cochlear
amplification at low volume works.

I've seen a lot about this "double critical band" theory in the
psychoacoustics literature, which suggests a second set of filters in
the auditory midbrain (I think). If this is true, then that could be
another source of buzz. For now, since I haven't seen any evidence of
that, the simplest suggestion is that the cochlea is where it's at.
Furthermore, the entire wealth of literature we have on the subject
assumes that there's only one filterbank and does roughness
experiments to determine its properties, and all of that would have to
completely change if a second spectral filtering mechanism were
involved. So I see no reason to buy into anything like that.

> > Petr wrote a good post about it here
> > /tuning/topicId_95728.html#95728
>
> He mentions an offlist discussion you had with him back during
> Rick's GCD thread. He also seems to mention the first examples
> you were producing - the impulse trains that were supposedly
> examples of periodicity buzz. Finally, he mentions combination
> tones. I don't see a word about what we're presently
> discussing and I'm surprised you've linked to this message in
> response to my request.

So you can't see the mathematical relationship between the impulse
trains and periodicity buzz? Petr seems to address this in his post

> People like Mike B have dedicated a large amount of their time to
> make examples of the matters they try to document both in sound and in
> words. If someone isn't as involved in Hilbert transforms or other phase
> shifts as Mike might be, I hope there are other ways they might respond than
> things like "I was asking about *this* and you're answering with *that*
> which has absolutely nothing to do with it" when it actually *has* something
> to do with it.

> As I've said now several times, I listened to all your examples
> when you posted them - some of them more than once.

You said that, but refused to respond with data on how you heard them,
insisting I didn't give you the answers and you didn't want to answer
my "cryptic" quiz. Since the answers were right in the thread I linked
to, I called bullshit.

> > kept telling me that I had posted no examples or predictions
> > which I obviously know that I have.
>
> Here's an important point: I still haven't been able to find a
> single prediction/example from you on this.

The buzztempering example predicts that linear spacing generates
periodicity buzz, and that the periodic one without linear spacing
will have buzz rates that slowly drift in and out of sync with one
another, causing a chorus-y effect. To that extend it was right. Both
of these approximate 5:7:9, so your generalized notion of periodicity
has nothing to do with anything.

> > If you have a better way of explaining this behavior than
> > cochlear interactions,
>
> I don't, and said I did. I'm trying to understand yours!

You're also fond of strongly and sometimes spuriously asserting the
truth of the null hypothesis after every sentence in my post just for
the sake of playing devil's advocate.

-Mike

🔗Carl Lumma <carl@...>

--- Mike Battaglia <battaglia01@...> wrote:

> But you brought this point up in response to my assertion
> that there will still be overlap between auditory filters
> that are out of ERB range. I thought at the time you were
> arguing my point as it applies to the cochlea, not making
> a spurious objection about quantum mechanics.

You often speak about Fourier theory as if it were an exact
representation of reality. I mentioned this aside about
"physical systems" to try to broach the subject... of the
fact that the cochlea does not contain any perfect filters.
It's a mechanical system with response thresholds that may
be relevant to music research.

> > The sampled signal contains no information above Nyquist.
> > The fact that various reconstruction techniques put stuff
> > up there is immaterial.
>
> A more mathematically rigorous way of looking at it is that
> the sampled signal contains the baseband continually
> reflected about Nyquist and going up forever.

You can interpret it that way, but the reflections don't
contain information about the signal.

> If you actually want to use sinc interpolation, you cut
> everything above Nyquist. If your preferred view on it is
> that you want to think of the array of samples as already
> being sinc interpolated by default in the continuous time
> domain, fine, but that's not how I learned it and I think
> it makes the math more confusing.

The sampled data can be viewed as fundamental and without
need for reconstruction. From a continuous functions
perspective, of course (most of) what you've written is
accurate.

> > It's not clear to me if you think the buzz is entirely due
> > to AM within filters. If it is, the intensity of the buzz
> > should drop off very rapidly with interval width.
>
> I wouldn't be surprised, but I haven't not taking into account
> any kind of cochlear amplification effects, etc.

I don't think you need to. At > ERB separations, the
overlapping tails are very short and the amplitude of any
mixing must be small and I would imagine the Matlab gammatone
kit handles that out of the box. One of my major tests all
along is, why do largish sine tone dyads still buzz?

Another has been -- rephrased in light of your linear evenness
idea -- what's the 'linear evenness' of a dyad? Why do some
dyads buzz more than others (of approximately the same size
and register)?

Now, if we give up the idea of auditory filters and just say
that the brain can 'see' the entire response of the basilar
membrane in the time domain... wouldn't that explain both of
the above tests?*

* More rigorous listening is needed to determine the actual
outcome of those tests, which I'm assuming here for the
purpose of discussion.

> e.g. gammatone filters will
> predict different specific behavior than ERBs,

Now that things seem to be calmer, I'll take the opportunity
to say that by "ERB" I never meant the rect filters that you
were freaking out about. I meant the widths of those filters
only - which incidentally, are often used to set the widths of
the gammatones in models like the one you're using.

> 3) The cochlea is the obvious filterbank in the auditory system
> to attribute this behavior to

I'm saving this numbered list for now. To me it looks like
you've assumed filterbank from the beginning, since that's
the hammer you had.

> I have no way of modeling how exactly cochlear
> amplification at low volume works.

Now might be a good time to have a look at the link I
posted earlier:

>> By the way, here's a good explanation of why the ear bothers
>> to do spectral separation in the first place
>> http://www.technologyreview.com/blog/arxiv/26666/

> > Here's an important point: I still haven't been able to find
> > a single prediction/example from you on this.
>
> The buzztempering example predicts that linear spacing generates
> periodicity buzz,

That's true. And I'd like to hear more of those.

-Carl

🔗Mike Battaglia <battaglia01@...>

On Tue, Apr 26, 2011 at 5:32 PM, Carl Lumma <carl@...> wrote:
>
> > But you brought this point up in response to my assertion
> > that there will still be overlap between auditory filters
> > that are out of ERB range. I thought at the time you were
> > arguing my point as it applies to the cochlea, not making
> > a spurious objection about quantum mechanics.
>
> You often speak about Fourier theory as if it were an exact
> representation of reality. I mentioned this aside about
> "physical systems" to try to broach the subject... of the
> fact that the cochlea does not contain any perfect filters.
> It's a mechanical system with response thresholds that may
> be relevant to music research.

I agree with you on the concept, but I think you are applying it the
wrong way. The sinusoids that the Fourier transform bases itself off
of are abstract idealizations that do not exist in nature - literally
they are sine waves that stretch from -infinity to infinity with no
change. They are not real. And if you want to think about frequencies
changing over time, then you're getting away from the Fourier
transform.

There is a point that I'm trying to make as well, and it's come up
before as well: is that these frequencies are not actual, real
entities that need to be limited by physical processes. They are
abstract ideas. The Fourier transform is a mathematical algorithm that
generates an infinite summation of these abstract ideas that magically
add back together to yield the original signal. It's like a Taylor
series or something. That's all it is, no more and no less.

In reality, a system can in real life exhibit motion. If you take the
Fourier transform of this motion, you'll generally end up with an
infinite series that, when you add all the terms back together,
magically adds up to generate the original motion again. The terms of
this series will generally taper off in weighting as the frequency
tends towards infinity, but never quite reach zero (except "at"
infinity). This applies to real-life systems as well. Working quantum
effects into it means you'd need to apply Shannon sampling theory in a
way I haven't done, but I guess quantum physicists do it all the time.
But that's completely off topic.

> > > The sampled signal contains no information above Nyquist.
> > > The fact that various reconstruction techniques put stuff
> > > up there is immaterial.
> >
> > A more mathematically rigorous way of looking at it is that
> > the sampled signal contains the baseband continually
> > reflected about Nyquist and going up forever.
>
> You can interpret it that way, but the reflections don't
> contain information about the signal.

They contain the same information as the baseband.

> The sampled data can be viewed as fundamental and without
> need for reconstruction. From a continuous functions
> perspective, of course (most of) what you've written is
> accurate.

All of it was accurate and I'd be happy to debate you for hours and
hours over this, but maybe we should take this tangent of the
conversation offlist.

> > I wouldn't be surprised, but I haven't not taking into account
> > any kind of cochlear amplification effects, etc.
>
> I don't think you need to. At > ERB separations, the
> overlapping tails are very short and the amplitude of any
> mixing must be small and I would imagine the Matlab gammatone
> kit handles that out of the box. One of my major tests all
> along is, why do largish sine tone dyads still buzz?

Can you give an example? The 7/5 example you gave was predicted by the
gammatone plot.

The obvious explanation for behavior like this is that we have
completely ignore combination tones, so far which will enrich the
spectrum in such a way that causes more buzz no matter what you do. We
could probably work some tests out for this.

Another explanation, possibly sketchy, I've been tossing around for it
is - if there's constructive and destructive interference taking
place, then the constructive side of it will by definition be above
the natural response of the auditory filter (and hence audible and not
masked) and the destructive side will be below it and masked. When it
stops being audible starts then being a matter of categorical
perception, not critical band effects, and if you're hyper-focusing on
it you might hear something even for wide dyads. I haven't worked the
math out so don't quote me on that yet.

> Another has been -- rephrased in light of your linear evenness
> idea -- what's the 'linear evenness' of a dyad? Why do some
> dyads buzz more than others (of approximately the same size
> and register)?

With sine waves? Can you make an example of when this occurs?

> Now, if we give up the idea of auditory filters and just say
> that the brain can 'see' the entire response of the basilar
> membrane in the time domain... wouldn't that explain both of
> the above tests?*

That still wouldn't explain why there's buzz, no. This also suggests
that this is not the case:

/tuning/topicId_95634.html#95634

There's another point that needs to be made here about "time domain"
vs "frequency domain" processing, but maybe I'll save that for later.

> > e.g. gammatone filters will
> > predict different specific behavior than ERBs,
>
> Now that things seem to be calmer, I'll take the opportunity
> to say that by "ERB" I never meant the rect filters that you
> were freaking out about. I meant the widths of those filters
> only - which incidentally, are often used to set the widths of
> the gammatones in models like the one you're using.

You said that there'd be "no overlap," and the point I was making was
that there would always be overlap. And I'm the one who brought up
that gammatone filters are based on ERBs :)

> > 3) The cochlea is the obvious filterbank in the auditory system
> > to attribute this behavior to
>
> I'm saving this numbered list for now. To me it looks like
> you've assumed filterbank from the beginning, since that's
> the hammer you had.

At first I thought it had to do with multiresolution analysis
artifacts, but now I think it just has to do with filterbank, yes.
Maybe one way of thinking about it is that if you take a sine wave and
apply AM to it - but AM in which the envelope goes from 1 to 0, not 1
to -1 - you end up with a "linearly spaced" triad that will exhibit
buzz. The buzz is related to this duality, and the exact relation is
determined by the characteristics of the auditory filter.

> > I have no way of modeling how exactly cochlear
> > amplification at low volume works.
>
> Now might be a good time to have a look at the link I
> posted earlier:
>
> >> By the way, here's a good explanation of why the ear bothers
> >> to do spectral separation in the first place
> >> http://www.technologyreview.com/blog/arxiv/26666/

I read it, but I don't how we could use this to make predictions about
the perceptual quality of low-volume buzz. Also, if you remember when
I said there are an infinite number of ways that we can produce
time-frequency plots, I tend to think of the cochlea as being just one
way to do that (or, more accurately, one half of one way to do that).

> > > Here's an important point: I still haven't been able to find
> > > a single prediction/example from you on this.
> >
> > The buzztempering example predicts that linear spacing generates
> > periodicity buzz,
>
> That's true. And I'd like to hear more of those.

Phew. Next time, if you'd admit stuff like this when it comes up, I
wouldn't keep thinking that you disagreed with my points. Jesus.

-Mike

🔗Carl Lumma <carl@...>

--- Mike Battaglia <battaglia01@...> wrote:

> > You can interpret it that way, but the reflections don't
> > contain information about the signal.
>
> They contain the same information as the baseband.

Aliasing is non-reversible (usually). There's no way to
recover information about the baseband from components
above Nyquist.

Probably the easiest way to characterize the frequency
response of the sampling process is to look at the DFT
of the samples -- you get frequency domain coefficients
up to Nyquist.

> The obvious explanation for behavior like this is that we
> have completely ignore combination tones,

I've been cautious of them the whole time, but of course
they can never be completely eliminated.

> Can you give an example? The 7/5 example you gave was
> predicted by the gammatone plot.

Can we see that plot?

> > Another has been -- rephrased in light of your linear evenness
> > idea -- what's the 'linear evenness' of a dyad? Why do some
> > dyads buzz more than others (of approximately the same size
> > and register)?
>
> With sine waves? Can you make an example of when this occurs?

It's the "7/5 example" you mention above!

> > >> By the way, here's a good explanation of why the ear
> > >> bothers to do spectral separation in the first place
> > >> http://www.technologyreview.com/blog/arxiv/26666/
>
> I read it, but I don't how we could use this to make
> predictions about the perceptual quality of low-volume buzz.

I don't either, but it is informative about the cochlea.

-Carl

🔗Mike Battaglia <battaglia01@...>

On Tue, Apr 26, 2011 at 8:28 PM, Carl Lumma <carl@...> wrote:
>
> --- Mike Battaglia <battaglia01@...> wrote:
>
> > > You can interpret it that way, but the reflections don't
> > > contain information about the signal.
> >
> > They contain the same information as the baseband.
>
> Aliasing is non-reversible (usually). There's no way to
> recover information about the baseband from components
> above Nyquist.

I mean that they contain the same information as the baseband + all of
the aliasing components. The reason aliasing occurs is that you are
taking your sample's frequency response, reflecting it about the
y-axis (to handle negative frequencies), shifting it over so it's now
centered around the sampling frequency instead of 0 Hz, and adding it
to the original. All of the negative frequencies that exceed Nyquist
then end up looping back into the baseband. Repeat this process
forever with the sampling frequency's harmonics. The National
Semiconductor paper I linked you to had a good visual diagram of this.

> Probably the easiest way to characterize the frequency
> response of the sampling process is to look at the DFT
> of the samples -- you get frequency domain coefficients
> up to Nyquist.

You mean that you get frequency domain coefficients up to the sampling
frequency, but that the second half of the resulting array will be the
same as the negative frequencies up to negative Nyquist. The second
half of the array will also be a phase-inverted version of the first
half of the array. This will not be the case for complex (ie. real +
imaginary) signals. This is not up for debate :)

> > The obvious explanation for behavior like this is that we
> > have completely ignore combination tones,
>
> I've been cautious of them the whole time, but of course
> they can never be completely eliminated.

We can do some tests at low volume to see how this all changes.

> > Can you give an example? The 7/5 example you gave was
> > predicted by the gammatone plot.
>
> Can we see that plot?

It's the one I posted earlier, and then the sqrt(2) plot; the one in
which you responded that the people of this list are not psychic and
don't know what it is, etc.

-Mike

Concordance of timbres vs Concordance of chords

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