Yahoo Tuning Groups Ultimate Backup tuning A deeper investigation into periodicity buzz

I wanted to test the hypothesis that the time domain "shape" of the
waveform is crucial to generating periodicity buzz. In order to do
this, I sought to come up with the "flattest" harmonic waveform
possible, as per Carl's suggestion.

It is useful to recognize that when we talk about waveforms that have
the same frequency response but generally "look" different in the time
domain, the only thing that differs is the phase response. For
example, the following three waveforms all have the same magnitude
response, which is 1 for all frequencies:

1) A perfect impulse (a Dirac delta distribution)
2) A sine sweep
3) White noise

However, the phase responses will differ for all three of these. If
you look at a graph of frequency vs phase response, the impulse's
phase will be a line, the sine sweep's will be a parabola, and the
white noise's will be random. And in each case, the Fourier transform
for each of these signals will yield a series of sine waves, infinite
in each direction, that "magically" interfere and reinforce and cancel
each other out and yield the original signal. They also sound really
different: the impulse sounds like a "click," a sine sweep is a sine
sweep, and white noise is white noise.

The convolution of any of the above three waveforms with an impulse
train will yield a "periodic" version of that waveform. So a periodic
impulse train, or a periodic sine sweep, or periodic noise. In the
frequency domain, the convolution will cancel out all frequencies
except those which are at integer multiples of the fundamental. So
it's a good idea to come up with periodic versions of the above three
waveforms to evaluate their impact on the periodicity buzz produced.

I'm actually using a variant of this approach, slightly easier to
compute, which is to take a symmetrical chirp that goes from 0 Hz up
to 22050 Hz and back down, and convolve that with an impulse train. So
the base waveform looks like this:

http://www.mikebattagliamusic.com/music/symmetricchirptrain.png

Here's the frequency response of this waveform:

http://www.mikebattagliamusic.com/music/symmetricchirptrainfft.png

The harmonics seem to have random amplitude, but the wave is obviously
still periodic enough and will do as a suitable test waveform for
periodicity buzz. Let's use this signal for our base and see what
happens as we tweak the phase response.

There are four more variants of this wave: one in which the phase is
linear across the board (mimicking an impulse), and three in which the
phase is random (mimicking periodic noise). Here is a graph displaying
the time domain waveform, the magnitude response, and the phase
response for all three:

http://www.mikebattagliamusic.com/music/buzzcomparison.png

Although the chirp phase response looks linear, it is actually ordered
in some kind of pattern that is not easily discernible to me. Either
way, it generates a smooth periodic chirp in the time domain rather
than periodic noise.

Here are the examples:

At 441 Hz:
http://www.mikebattagliamusic.com/music/441periodicchirp.wav
http://www.mikebattagliamusic.com/music/441pseudoimpulse.wav
http://www.mikebattagliamusic.com/music/441periodicnoise.wav
http://www.mikebattagliamusic.com/music/441periodicnoise2.wav
http://www.mikebattagliamusic.com/music/441periodicnoise3.wav

At 220.5 Hz:
http://www.mikebattagliamusic.com/music/220.5periodicchirp.wav
http://www.mikebattagliamusic.com/music/220.5pseudoimpulse.wav
http://www.mikebattagliamusic.com/music/220.5periodicnoise.wav
http://www.mikebattagliamusic.com/music/220.5periodicnoise2.wav
http://www.mikebattagliamusic.com/music/220.5periodicnoise3.wav

At 110.25 Hz:
http://www.mikebattagliamusic.com/music/110.25periodicchirp.wav
http://www.mikebattagliamusic.com/music/110.25pseudoimpulse.wav
http://www.mikebattagliamusic.com/music/110.25periodicnoise.wav
http://www.mikebattagliamusic.com/music/110.25periodicnoise2.wav
http://www.mikebattagliamusic.com/music/110.25periodicnoise3.wav

At 55.125 Hz:
http://www.mikebattagliamusic.com/music/55.125periodicchirp.wav
http://www.mikebattagliamusic.com/music/55.125pseudoimpulse.wav
http://www.mikebattagliamusic.com/music/55.125periodicnoise.wav
http://www.mikebattagliamusic.com/music/55.125periodicnoise2.wav
http://www.mikebattagliamusic.com/music/55.125periodicnoise3.wav

At 27.5625 Hz:
http://www.mikebattagliamusic.com/music/27.5625periodicchirp.wav
http://www.mikebattagliamusic.com/music/27.5625pseudoimpulse.wav
http://www.mikebattagliamusic.com/music/27.5625periodicnoise.wav
http://www.mikebattagliamusic.com/music/27.5625periodicnoise2.wav
http://www.mikebattagliamusic.com/music/27.5625periodicnoise3.wav

Note that as the frequency response gets lower, the phenomenon gets
more apparent, peaking at around 55.125 Hz. The difference is always
the most striking between the "impulse" and the "chirp" equivalents at
each frequency. In the case of 55.125 Hz, I can also actually hear
some kind of imprint of the "noise" in the upper partials, as if they
aren't all onsetting at the same time, but randomly.

I have never heard of anything like this in the psychoacoustics
literature, so I'm not sure how to explain this. This certainly
destroys any notion I had that the cochlear critical band is involved.
So how do we explain this?

Carl has put forward the hypothesis that the entire phenomenon is due
to mainly to time domain processing, which I think can be more
rigorously stated by saying that the brain fails to fully resolve the
signal into a "pitched" component. That is, auditory scene processing
partitions or "leaks" some of the signal into a noise component, where
a nonpitched time-domain analysis is made and which yields the
perception of a periodic nonpitched signal is perceived. This
certainly could be what's happening.

Another hypothesis, which may not be mutually exclusive to the above
one, which is supported by the fact that you can kind of hear some
weird "noise imprint" in some of the "periodic noise" examples, is
that the brain's time-frequency representation is not uniform across
the board. This means that if we're dealing with a waveform at 50 Hz,
and one which has harmonics at 100 Hz, 150 Hz, etc, then the harmonics
can turn on and off "in the middle" of the waveform's period. There is
a lot of reference to this sort of thing in the literature.

So rather than the brain separating an impulse train into a bunch of
harmonic sine waves that stretch across the waveform's period, the
brain would then separate the impulse train into a bunch of harmonic
sine "wavelets" that are time-limited and DO NOT stretch across the
full period of the waveform. For the impulse train, the wavelets would
all be located at the onset of each impulse. For the periodic chirp,
the wavelets would be placed across the waveform in a way that
corresponds with the instantaneous frequency of the chirp. For the
noise, the wavelets would be randomly placed all across the waveform.
It may be that the temporal placement of these wavelets plays a role
in VF detection, and the ones that are too far off for the brain to
make any sense of it are sent to the noise channel.

This is my current understanding, and thus ends my sitrep. Over and out.

-Mike

🔗Michael <djtrancendance@...>

MikeB>"1) A perfect impulse (a Dirac delta distribution)
2) A sine sweep
3) White noise"

In the case of a sine sweep, if I have it right...the phase change is
gradual and thus the mind hears it and relative phase shift...which is heard as
a quick frequency change. So it seems fairly obvious to me why it would sound
different.

The real stumping question to me...is how we hear the impulse (linear phase)
vs. the white noise (random phase).
My best guess is that the white noise wave would work best...since chances are
that if any nearby frequencies phase-cancel out...at least one frequency in a
very near IE virtually indecipherable range with a phasing that does not cancel
out will be there to take over.

One I made an mp3-type format and ran smack into that issue...I tried only to
use, say, only one sine wave around 200hz, another around 220hz...to summarize a
sound...but everything gained a "stuttering" sound due to phase
cancellation...so I formed bell-shaped-curves of amplitude with random phasing
in the frequencies around those peaks to fix the problem and the stuttering
virtually stopped and it began to sound like two relatively non-beating sine
wave. The randomness "averaged out"...in other words and the effect was
achieved by having a few "linear phase" partials with consistent amplitudes and
randomly phased amplitudes around those to help protect against what happens
when the partial's phases are close enough to opposite to begin canceling out
(in that case the randomly phased frequencies would help "fill in the sound-less
gap of phase cancellation").

>"The harmonics seem to have random amplitude"

If I'm reading you correctly...you seem to be having a very similar problem
to what I had.

>"The convolution of any of the above three waveforms with an impulse train will
>yield a "periodic" version of that waveform. "

Figures you are going for this as periodic wave form as loud overtones +
periodic root tones should mean maximum periodicity buzz.

>"Carl has put forward the hypothesis that the entire phenomenon is due to mainly
>to time domain processing, which I think can be more
rigorously stated by saying that the brain fails to fully resolve the signal
into a "pitched" component. That is, auditory scene processing
partitions or "leaks" some of the signal into a noise component"

Makes sense, especially with phase cancellation effects, that the mind can
not decide where the partials reside and they are heard as "moving" (moving
being a term related to phase and phase cancellation) to the point of being
labeled by the mind as noise. I guess you could say my main concern, so far as
I understand your experiment at the point, is that phase cancellation at
changing frequencies is not adding an extra factor that causes the mind to
categorize more things as noise.

🔗Mike Battaglia <battaglia01@...>

I wrote:
> This certainly destroys any notion I had that the cochlear critical band is involved.

Actually, after thinking more about it, it might still be that
cochlear critical band effects are somehow involved. But I'll get into
that later, and respond to Michael's comments now.

On Tue, Jan 11, 2011 at 11:06 AM, Michael <djtrancendance@...> wrote:
>
> MikeB>"1) A perfect impulse (a Dirac delta distribution)
> 2) A sine sweep
> 3) White noise"
>
> In the case of a sine sweep, if I have it right...the phase change is gradual and thus the mind hears it and relative phase shift...which is heard as a quick frequency change. So it seems fairly obvious to me why it would sound different.

What do you mean by gradual, with respect to what? The reason it
sounds different is that the graph of group delay vs frequency is a
diagonal line, meaning that each frequency takes place slightly after
its nearest lower neighbor.

> The real stumping question to me...is how we hear the impulse (linear phase) vs. the white noise (random phase).

You mean the periodic versions? I posted samples...

> My best guess is that the white noise wave would work best...since chances are that if any nearby frequencies phase-cancel out...at least one frequency in a very near IE virtually indecipherable range with a phasing that does not cancel out will be there to take over.

> One I made an mp3-type format and ran smack into that issue...I tried only to use, say, only one sine wave around 200hz, another around 220hz...to summarize a sound...but everything gained a "stuttering" sound due to phase cancellation...so I formed bell-shaped-curves of amplitude with random phasing in the frequencies around those peaks to fix the problem and the stuttering virtually stopped and it began to sound like two relatively non-beating sine wave.

This sounds interesting, can you post some examples of this?

> The randomness "averaged out"...in other words and the effect was achieved by having a few "linear phase" partials with consistent amplitudes and randomly phased amplitudes around those to help protect against what happens when the partial's phases are close enough to opposite to begin canceling out (in that case the randomly phased frequencies would help "fill in the sound-less gap of phase cancellation").

What do you mean by linear phase partials?

-Mike

🔗Michael <djtrancendance@...>

🔗Mike Battaglia <battaglia01@...>

On Tue, Jan 11, 2011 at 1:29 PM, Michael <djtrancendance@...> wrote:
>
> Me>> The real stumping question to me...is how we hear the impulse (linear phase) vs. the white noise (random phase).
> MikeB>You mean the periodic versions? I posted samples...
>
> As in why we hear what we hear...maybe "how" wasn't a good word choice on my part.

Oh, that's simple. Because the brain isn't performing a frequency
analysis on the data, it's performing a time-frequency analysis on the
data. If you take the Fourier transform of an impulse vs a sine sweep,
the analysis stretches outward to infinity. Over infinity, the exact
series of sine waves that magically add to reconstruct the original
signal end up a series of sine waves at every frequency and with
phases like those described.

> >"What do you mean by linear phase partials?"
> Meaning that the phase will be linear IE it would not rotate at a rate that would change the perception of a frequency at all. IE a 300hz sine wave with a "linear phase" played by itself would sound life a steady frequency...one with slightly non-linear phase that ends up at a slightly further point in its rotation than expected) would come across as, say, 301hz.

That's not what "linear phase" means, that's some kind of linear phase
modulation of the signal. And first off, if the sinusoid is sped up to
sound like 301 Hz, that would still be a linear phase modulation - the
modulating waveform would look like a diagonal line (or a sawtooth
wave, if you allow there to be jumps from +pi to -pi). If you're
modulating the phase of the signal in a way that isn't linear, you're
going to be doing all kinds of stuff to the frequency domain of that
signal - we're moving into the realm of FM and there will be sidebands
and such.

But if a filter is "linear phase," that means that the frequency vs
phase response (w vs angle(F(w))) is a line. We generally look at
frequency vs magnitude response (w vs abs(F(w)))plots, so this is a
bit different.

But every one of the sinusoids in your example would have had to have
the phase chugging along at a constant rate, or else they wouldn't be
sinusoids.

> Actually I've seen many phase vocoders that store frequency in a separate array, and don't simply calculate it from fftbinindex * (22050/fftsize), to take into account that phase shifts affect frequency perception and get extra accuracy in frequency placement over what the FFT bin size allows. If the phase was linear no such method would be needed....

Wow, I didn't realize you were so deep into DSP. Yeah, I learned about
that approach at school, although the explanation I was given is a bit
different. This arises because the actual "best match" to each
frequency sometimes lies between successive DFT bins (which it always
will unless your window size happens to be an exact multiple of the
period of the frequency you want). So the actual best frequency fits
between them, and between successive windows it will look like there's
crazy phase shifting between the "rounded off" bins. However, after
two windows, you can see how the phase has changed and calculate the
actual best frequency.

Very impressive Mike, I didn't realize you were so far into this
stuff! Have you messed with the wavelet transform at all? I want to
load the waveforms in this example up into a CWT and see if the
partials beat periodically. Perhaps we could use a wavelet that has
all harmonics present, and the whole shebang could be used to model
the "second filterbank" in the brain that I was talking about before.

-Mike

🔗Michael <djtrancendance@...>

MikeB> >"What do you mean by linear phase partials?"
Me> "Meaning that the phase will be linear IE it would not rotate at a rate
that would change the perception of a frequency at all. IE a 300hz sine wave
with a "linear phase" played by itself would sound life a steady
frequency...one with slightly non-linear phase that ends up at a slightly
further point in its rotation than expected) would come across as, say, 301hz."
MikeB>"That's not what "linear phase" means, that's some kind of linear phase
modulation of the signal"

In that case, I meant linear phase modulation rather than linear phase.
Argh...so many different terms with virtually the same name.

>"But every one of the sinusoids in your example would have had to have the phase
>chugging along at a constant rate, or else they wouldn't be sinusoids."
Well...if the does not keep chugging along at a constant rate IE it keeps
rotating faster and slower...wouldn't it have the audible effect of

Me>"Actually I've seen many phase vocoders that store frequency in a separate
array, and don't simply calculate it from fftbinindex * (22050/fftsize), to
take into account that phase shifts affect frequency perception and get extra
accuracy in frequency placement over what the FFT bin size allows. If the
phase was linear no such method would be needed...."

MikeB>"Wow, I didn't realize you were so deep into DSP. "

Thank you and...indeed. For a while I was obsessed with the idea of taking
sound files and reducing them to only partials that were "in-tune"...a bit like
auto-tune only, of course, I used microtonal scales and added extra
partials/area to help account for reproducing the effect of noise. Oh
yeah...and then aligning the resulting partials to more-or-less the curve of
human hearing (using about 16 "blocks" for all the frequencies...each who's
average amplitude matches the curve of human hearing) so I could play the result
very loudly without hurting my ears as much as an unprocessed sound file. And
then I found a phase vocoder library that seemed to finally be able to
manipulate sound enough to handle that sort of thing and started figuring out
how the code worked...learning a good deal about DSP terms and applications
along the way.

I abandoned the project when I had two issues
A) Trouble figuring out an algorithm to determine which pre-defined schema
frequency (IE one in a scale) to match each partial in a wave file
to...especially when the partial is right-smack in between two notes of a scale
(which tone in the scale should I add the amplitude of the partial value to).
Plus there was the problem of, if there are multiple partials between two
scale/schema points...how much should I weight each of them to determining the
scale-point amplitude (not to mention phase)?
B) The other issue was the compression algorithm. My "hack" on doing
compression involved taking a 2048...taking 100 or so "scale frequencies" spread
through all 2048 bins that match my scale schema, pitch shifting the results
into the first/lowest 100 or so bins, and saving the result as a much lower HZ
wave file IE 100/2048*22050hz = about 1076hz..about a 20 to 1 rate of
compression. Since the "compressed" output is a wave file, of course, you can
then shove the output into a FLAC encoder and get another factor of 2 or so of
compression.
However, as it turns out, even using a Short-Time-frame-FFT, there were
major accuracy issues on encode and decode (the fact each of these steps
requires using two slightly phase-warping sFFTs, of course, did not help).
Apparently just because I put accurate values into the first 100 bins does not
mean I get anything near accurate values on the way out: everything sounded
horribly distorted and the phasing way off.

If you have any hacks for such or ways to describe why the pitch shifting
downward (encode) and/or reverse pitch-shifting (decode) would garble the
signal, or any creative hacks for the other problems I encountered which went
above my head, though...I'm all ears.

MikeB>"the actual best frequency fits between them, and between successive
windows it will look like there's crazy phase shifting between the "rounded off"
bins."
Exactly...and the mind reads the phase shift over the windowed fading
between the FFT windows as a frequency shift.

>"Have you messed with the wavelet transform at all? "
No but maybe I should. Honestly...I've stuck with FFTs because there's so
much documentation on them that even I, a person who learned about DSP from
internet reading and knowledge of coding alone with no formal training, could
figure out.

I looked at some Wavelet code...but, for the life of me, I couldn't even
figure out how to do the equivalent of what I did with FFTs....IE derive both
the real and imaginary part of the results from which to derive phase and
amplitude...let alone do "inverse Wavelets" when I'm done with my analysis to
convert results back to the time domain. I realize Wavelet should do a much
more accurate and less "phase warped" job than FFTs, however...and that I was
using somewhat old-school technology that way.

If you could teach me to be a "wavelet Ninja" though...that would be awesome.
:-)

🔗Mike Battaglia <battaglia01@...>

On Tue, Jan 11, 2011 at 3:41 PM, Michael <djtrancendance@...> wrote:
>
> >"But every one of the sinusoids in your example would have had to have the phase chugging along at a constant rate, or else they wouldn't be sinusoids."
> Well...if the does not keep chugging along at a constant rate IE it keeps rotating faster and slower...wouldn't it have the audible effect of
> Me>"Actually I've seen many phase vocoders that store frequency in a separate array, and don't simply calculate it from fftbinindex * (22050/fftsize), to take into account that phase shifts affect frequency perception and get extra accuracy in frequency placement over what the FFT bin size allows. If the phase was linear no such method would be needed...."

No, because the actually peak frequency doesn't just result from an
average of the two nearby ones... each FFT bin actually has the
frequency response of a sinc function, and the zeroes of the sinc
function are the other FFT bins. When you take the FFT of a sine that
has a bin corresponding to it, you get an impulse in the frequency
domain, because all of the zeroes are lining up with the other bins.
When the frequency fits between two bins, you get a sinc function that
is "sampled" at each bin. I think we're on two different pages here.

> MikeB>"Wow, I didn't realize you were so deep into DSP. "
>
> If you have any hacks for such or ways to describe why the pitch shifting downward (encode) and/or reverse pitch-shifting (decode) would garble the signal, or any creative hacks for the other problems I encountered which went above my head, though...I'm all ears.

I have some ideas, why don't you send me a more thorough explanation
offlist, perhaps along with some code? Were you programming this with
MATLAB?

> MikeB>"the actual best frequency fits between them, and between successive windows it will look like there's crazy phase shifting between the "rounded off" bins."
> Exactly...and the mind reads the phase shift over the windowed fading between the FFT windows as a frequency shift.

I don't think the mind is actually doing an STFT, but rather a
multiresolution scheme, and I think that the phase shifting is an
artifact of the particular time-frequency math we're using with the
STFT. The phase shift depends on the window size that you use, and I
think there's a different window size for every frequency in the
brain, and that's what leads to periodicity buzz.

> I looked at some Wavelet code...but, for the life of me, I couldn't even figure out how to do the equivalent of what I did with FFTs....IE derive both the real and imaginary part of the results from which to derive phase and amplitude...let alone do "inverse Wavelets" when I'm done with my analysis to convert results back to the time domain. I realize Wavelet should do a much more accurate and less "phase warped" job than FFTs, however...and that I was using somewhat old-school technology that way.

I'm not sure phase is even involved. Maybe if you use a complex
wavelet like the complex morlet wavelet. Look at the continuous
wavelet transform on wikipedia for more info.

> If you could teach me to be a "wavelet Ninja" though...that would be awesome. :-)

Haha, I'm definitely not a wavelet ninja. I think we'll all have to
become wavelet ninjas to explain periodicity buzz though. Maybe we
should branch off into some strict signal processing forums and report
back.

-Mike

🔗Mike Battaglia <battaglia01@...>

Sorry, it looks like some people were having problems because of the
nonuniform sample rate. I reuploaded all of the samples at 44100 Hz.
The most distinct difference seems to be between the "periodic chirp"
and the "pseudo-impulse" waveforms, and in the lower register. Some
highlights:

At 110.25 Hz:
http://www.mikebattagliamusic.com/music/110.25periodicchirp.wav
http://www.mikebattagliamusic.com/music/110.25pseudoimpulse.wav

At 55.125 Hz:
http://www.mikebattagliamusic.com/music/55.125periodicchirp.wav
http://www.mikebattagliamusic.com/music/55.125pseudoimpulse.wav

At 27.5625 Hz:
http://www.mikebattagliamusic.com/music/27.5625periodicchirp.wav
http://www.mikebattagliamusic.com/music/27.5625pseudoimpulse.wav

The chirp one seems to have a "spitting" sound, and the impulse one
has a "buzzing" sound. Furthermore, the noise waveforms actually
change the timbre of the sound, which proves that the phase response
of an incoming signal has some kind of bearing on timbral perception
and/or the VF mechanism. The phase response here, when mixed with a
multiresolution/wavelet analysis, can be intuitively thought of as
"where" along the period of the waveform the harmonics actuall occur.

I think that periodicity buzz will show up if these waveforms are run
through a CWT.

-Mike

On Tue, Jan 11, 2011 at 4:59 AM, Mike Battaglia <battaglia01@...> wrote:
> I wanted to test the hypothesis that the time domain "shape" of the
> waveform is crucial to generating periodicity buzz.

🔗Mike Battaglia <battaglia01@...>

Also, on second thought, this doesn't have to be taking place in the
brain at all - the cochlea has its own mixed time-frequency
representation going on, inherent in the fact that the critical bands
have different widths at different frequency registers.

-Mike

On Tue, Jan 11, 2011 at 5:57 PM, Mike Battaglia <battaglia01@...> wrote:
> Sorry, it looks like some people were having problems because of the
> nonuniform sample rate. I reuploaded all of the samples at 44100 Hz.
> The most distinct difference seems to be between the "periodic chirp"
> and the "pseudo-impulse" waveforms, and in the lower register. Some
> highlights:
>
>
> At 110.25 Hz:
> http://www.mikebattagliamusic.com/music/110.25periodicchirp.wav
> http://www.mikebattagliamusic.com/music/110.25pseudoimpulse.wav
>
> At 55.125 Hz:
> http://www.mikebattagliamusic.com/music/55.125periodicchirp.wav
> http://www.mikebattagliamusic.com/music/55.125pseudoimpulse.wav
>
> At 27.5625 Hz:
> http://www.mikebattagliamusic.com/music/27.5625periodicchirp.wav
> http://www.mikebattagliamusic.com/music/27.5625pseudoimpulse.wav
>
> The chirp one seems to have a "spitting" sound, and the impulse one
> has a "buzzing" sound. Furthermore, the noise waveforms actually
> change the timbre of the sound, which proves that the phase response
> of an incoming signal has some kind of bearing on timbral perception
> and/or the VF mechanism. The phase response here, when mixed with a
> multiresolution/wavelet analysis, can be intuitively thought of as
> "where" along the period of the waveform the harmonics actuall occur.
>
> I think that periodicity buzz will show up if these waveforms are run
> through a CWT.
>
> -Mike
>
>
>
> On Tue, Jan 11, 2011 at 4:59 AM, Mike Battaglia <battaglia01@...> wrote:
>> I wanted to test the hypothesis that the time domain "shape" of the
>> waveform is crucial to generating periodicity buzz.
>

🔗Carl Lumma <carl@...>

🔗Mike Battaglia <battaglia01@...>

On Tue, Jan 11, 2011 at 7:12 PM, Carl Lumma <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> >
> > I wanted to test the hypothesis that the time domain "shape" of the
> > waveform is crucial to generating periodicity buzz. In order to do
> > this, I sought to come up with the "flattest" harmonic waveform
> > possible, as per Carl's suggestion.
>
> That wasn't my suggestion. I suggested creating random-phase
> versions of the stimuli I posted.

Oh. Well then I guess it was my suggestion. I'm still trying to figure
out how to apply this technique to stuff besides buzz waveforms - I
guess a convolution of the sample I posted with a 5:6:7 made of sines
would do the trick. I'll work on that, but I'd like to apply the CWT
to the examples I posted first to see what comes up.

> > In the frequency domain, the convolution will cancel out all
> > frequencies except those which are at integer multiples of the
> > fundamental. So it's a good idea to come up with periodic
> > versions of the above three waveforms to evaluate their impact
> > on the periodicity buzz produced.
>
> Can you explain what you think any of this has to do with
> periodicity buzz? I'm not sure I hear any in your examples,
> and I certainly don't in most ordinary (harmonic) timbres.

You seemed to have a different opinion when I played the "buzz"
waveform a while ago, which sparked you onto this new train of thought
that it was only the time domain that mattered. That's a harmonic
timbre with a pretty clear "buzzing" sound to me.

The important result here is that, mostly in the lower registers, the
"pseudo-impulse" and "symmetrical chirp" examples sound different. The
VF is the same, but you can hear different things happening in the
upper partials. I hear a bunch of "hard clicks" with the impulse, and
some kind of "spitting" sound with the chirp one. This is important
because it proves that the brain really is performing a
multiresolution analysis on the signal - meaning that there is a
different window size for each frequency.

> > I have never heard of anything like this in the psychoacoustics
> > literature,
>
> What would it have said if you did?

What do you mean?

-Mike

🔗Mike Battaglia <battaglia01@...>

On Tue, Jan 11, 2011 at 6:24 PM, Mike Battaglia <battaglia01@...> wrote:
> Also, on second thought, this doesn't have to be taking place in the
> brain at all - the cochlea has its own mixed time-frequency
> representation going on, inherent in the fact that the critical bands
> have different widths at different frequency registers.
>
> -Mike

To elaborate on this - this is the only thing that makes any sense at
all right now. The multiresolution analysis is a natural artifact of
the different damping coefficients of different hairs in the cochlea,
and when you slam these hairs with an impulse, they decay. It so
happens that, since the critical band gets wider as you get higher,
and hence the frequency resolution gets worse, the time resolution
gets better.

So everything I said about the analogy with the VF "filterbank" and
slapping the trumpet still applies here, but in the cochlea. The
harmonics decay rapidly as the impulses strike them, and are re-struck
each impulse. There will thus be some AM going on in the upper
harmonics of a buzz waveform, which will make the VF sound like it's
buzzing as more harmonics are added and removed hundreds of times each
second, and yet also create the sensation of them harmonics themselves
changing in amplitude. This also explains why the phenomenon doesn't
occur when the harmonics are split between the two ears.

When the buzz waveform is convolved with a chirp, as is what happened
above, all of the harmonics don't onset and decay at the same time,
but rather "sweep" upwards and back down. This is most noticeable in
the lower register (I didn't really hear much difference in the upper
register), which can yield some useful information about how exactly
the multiresolution analysis is set up.

So a good test to perform is:

1) Perform a CWT on these examples, using this waveform as the mother
wavelet: http://en.wikipedia.org/wiki/Gammatone
2) See if this approach shows AM in the upper partials. If not, try
the minimum-phase version of the Gammatone waveform
3) Generate new examples with a perfectly flat frequency response;
i.e. no random amplitude like I posted
4) Convolve these with waveforms like 5:6:7 made of sines to make Carl happy
5) See what comes of it.

I'll work on that next.

-Mike

🔗Mike Battaglia <battaglia01@...>

🔗Carl Lumma <carl@...>

🔗Michael <djtrancendance@...>

🔗Mike Battaglia <battaglia01@...>

I'll respond to all of these at once:

On Tue, Jan 11, 2011 at 9:47 PM, Carl Lumma <carl@...> wrote:
>
> Mike wrote:
> > To elaborate on this - this is the only thing that makes any
> > sense at all right now. The multiresolution analysis is a
> > natural artifact of the different damping coefficients of
> > different hairs in the cochlea, and when you slam these hairs
> > with an impulse, they decay. It so happens that, since the
> > critical band gets wider as you get higher, and hence the
> > frequency resolution gets worse, the time resolution
> > gets better.
>
> Mike, slow down. Critical bands get narrower in higher
> registers, not wider.

What? Since when? http://en.wikipedia.org/wiki/File:ERB_vs_frequency.svg

You mean they get narrower logarithmically, in cents, right? But
linearly, in Hz, which is what's important for what I'm describing,
they get larger in the upper register.

> > So everything I said about the analogy with the VF "filterbank"
> > and slapping the trumpet still applies here, but in the cochlea.
>
> I don't think so. The cochlea is an actively-amplified device...

See the gammatone picture I sent in the next picture - you can observe
the exact behavior I'm talking about.

> My own investigations sparked that. I have never understood
> how a "buzz waveform" is significant here.

A buzz wave is 1:2:3:4:5:6:7:8:9:10:..., with all notes at equal
volume. It's the derivative of a sawtooth wave. It also sounds like
what it's called - "buzz." Periodicity buzz eventually turns into
this. This is a very difficult problem to solve; I thought it would be
helpful in understanding the system to begin the investigation here,
and then to look at subsets of this waveform (e.g. chords) later.

> > > > I have never heard of anything like this in the psychoacoustics
> > > > literature,
> > >
> > > What would it have said if you did?
> >
> > What do you mean?
>
> I'm trying to figure out what you're talking about, and thought
> it might help if you actually said what it is.

Did you listen to the examples? Did you notice that, especially at low
frequencies, you can hear a different "type" of buzz between the chirp
train and the impulse train? I have never heard of anything indicating
that that's possible for periodic signals, or that to change the phase
of each harmonic in a timbre can actually alter the perception of the
resulting sound. I suppose it's implicit in statements made that the
brain performs a multiresolution analysis.

> Cochlear transforms are big business (see the Audience paper
> I just linked to). But I don't know what they have to do with
> the price of periodicity buzz. -Carl

Well, we'll see what happens when we run 5:6:7 with different phases
through the gammatone wavelet transform. If it doesn't accurately
describe what we hear, then that's the end of that one, and it'll have
to be something in the brain.

I missed the paper you linked to, where is it? I don't remember you
linking to a paper in this thread...

-Mike

🔗Mike Battaglia <battaglia01@...>

On Tue, Jan 11, 2011 at 10:05 PM, Mike Battaglia <battaglia01@...> wrote:
>
>> My own investigations sparked that. I have never understood
>> how a "buzz waveform" is significant here.
>
> A buzz wave is 1:2:3:4:5:6:7:8:9:10:..., with all notes at equal
> volume. It's the derivative of a sawtooth wave. It also sounds like
> what it's called - "buzz." Periodicity buzz eventually turns into
> this. This is a very difficult problem to solve; I thought it would be
> helpful in understanding the system to begin the investigation here,
> and then to look at subsets of this waveform (e.g. chords) later.

Also, if this isn't absolutely clear, then let's put it this way: a
sine wave has no periodicity buzz, 8:9 has some periodicity buzz,
8:9:10 has more, 8:9:10:11:12:13:14 has even more. Since it seems that
buzz increases as more harmonics are added, it stands to reason that
an "idealized perfect buzz" chord would be
1:2:3:4:5:6:7:8:9:10:11:etc.

It just so happens that if all of the notes in this chord have equal
volume, the waveform that's produced is an impulse train, and I
thought it profound that the name for this waveform in my DSP textbook
is a "buzz" wave. The key realization here is that when you listen to
this wave, it actually sounds like "buzz" - kind of like a sawtooth
sounds buzzy, but even harsher (since this is the derivative of a
sawtooth wave - check out what differentiation does to the frequency
domain of a signal).

The "periodicity buzz" generated by a sonority such as 5:6:7:8:9 with
sines transforms into the characteristic buzz of a buzz wave as the
other harmonics are added. Thus the reason that sawtooth waves sound
buzzy and the reason that 5:6:7:8:9 displays periodicity buzz are
fundamentally the same reason, whatever it is. So why is this? Why
exactly DO sawtooth waves sound buzzy, anyway?

-Mike

🔗Mike Battaglia <battaglia01@...>

On Tue, Jan 11, 2011 at 4:59 AM, Mike Battaglia <battaglia01@...> wrote:
>
> Carl has put forward the hypothesis that the entire phenomenon is due
> to mainly to time domain processing, which I think can be more
> rigorously stated by saying that the brain fails to fully resolve the
> signal into a "pitched" component. That is, auditory scene processing
> partitions or "leaks" some of the signal into a noise component, where
> a nonpitched time-domain analysis is made and which yields the
> perception of a periodic nonpitched signal is perceived. This
> certainly could be what's happening.

It should also be mentioned, after further rumination on this, that
the nonuniform time-frequency response of the ear could also lead to
the noise component of this as well. Look at this picture again:

http://www.mathworks.com/matlabcentral/fx_files/15313/1/GAMMA.png

Note in the highest register that the hair cells decay completely by
the time that each impulse is sounded, and they're all getting slammed
pretty uniformly. So as far as the upper register is concerned, this
might as well be noise - recurring, nonpitched, high-pass filtered
noise. And that's exactly what I hear when I listen to the examples I
posted, at least for the impulse train.

This provides for a plausible method by which some of this signal
could get filtered into a noise component. But wait, I said that an
impulse train ONLY has frequencies that are integer multiples of the
fundamental - so how could this waveform be stimulating the hair cells
in the ear such that the whole mass of high frequencies gets smacked
around at once? The answer is the phases for successive "smacks" will
be aligned for the hair cells that correspond to the frequencies in
the chord, and the phases for the ones that don't will not be aligned.
If the resonance of the hairs didn't decay so quickly, the smacks
would overlap and we'd see interference and all would cancel except
the frequencies in the chord - except that doesn't happen here,
because they decay so quickly, and by the time the next smack has
rolled around, the brain has "forgotten" about the phase of the
previous smack. High time resolution, low frequency resolution.

One question that I have is - does the frequency of the buzz
correspond to the VF of the chord, or to the difference tones between
successive notes in the chord? I think the latter, but let's save that
for later.

-Mike

🔗Carl Lumma <carl@...>

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

> > Mike, slow down. Critical bands get narrower in higher
> > registers, not wider.
>
> What? Since when?
> http://en.wikipedia.org/wiki/File:ERB_vs_frequency.svg
>
> You mean they get narrower logarithmically, in cents, right? But
> linearly, in Hz, which is what's important for what I'm describing,
> they get larger in the upper register.

Ok yeah, sorry.

> Periodicity buzz eventually turns into this.

Huh?

> > I'm trying to figure out what you're talking about, and thought
> > it might help if you actually said what it is.
>
> Did you listen to the examples?

Yes - they don't sound much like periodicity buzz.

> I suppose it's implicit in statements made that the
> brain performs a multiresolution analysis.

Have you read
http://dicklyon.com/tech/Hearing/ImportanceOfTime-SlaneyLyon.pdf
?

> > Cochlear transforms are big business (see the Audience paper
> > I just linked to). But I don't know what they have to do with
> > the price of periodicity buzz. -Carl
>
> Well, we'll see what happens when we run 5:6:7 with different
> phases through the gammatone wavelet transform. If it doesn't
> accurately describe what we hear, then that's the end of that
> one, and it'll have to be something in the brain.

How will we know if it describes what we hear or not?

> I missed the paper you linked to, where is it? I don't remember
> you linking to a paper in this thread...

The one you commented on with regard to the failure of
dichotic periodicity buzz.

-Carl

🔗Carl Lumma <carl@...>

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

> a sine wave has no periodicity buzz, 8:9 has some
> periodicity buzz, 8:9:10 has more, 8:9:10:11:12:13:14 has
> even more.

That is far from clear.

> It just so happens that if all of the notes in this chord have
> equal volume, the waveform that's produced is an impulse train,

Yes.

> The key realization here is that when you listen to
> this wave, it actually sounds like "buzz" -

Yes, it sounds like buzzing, but not necessarily like
periodicity buzz.

> Why exactly DO sawtooth waves sound buzzy, anyway?

Good question.

> Look at this picture again:
> http://www.mathworks.com/matlabcentral/fx_files/15313/1/GAMMA.png

What is the input here? The page doesn't say.

> One question that I have is - does the frequency of the buzz
> correspond to the VF of the chord, or to the difference tones
> between successive notes in the chord? I think the latter, but
> let's save that for later.

In the example I posted, I definitely hear a buzz frequency
corresponding to the waveform period. I feel like I may also
be hearing some faster buzz rates superimposed, but it's
hard to tell.

-Carl

🔗Mike Battaglia <battaglia01@...>

On Tue, Jan 11, 2011 at 11:23 PM, Carl Lumma <carl@...> wrote:
>
> > Periodicity buzz eventually turns into this.
>
> Huh?

The "buzz" that you're hearing when you hear this waveform, which is what
has led them to call it a "buzz" wave, is periodicity buzz. Read my second
message for a further explanation.

> > Did you listen to the examples?
>
> Yes - they don't sound much like periodicity buzz.

They're 1:2:3:4:5:6:7:8:9:10:11:12:13:14:15:16:etc. If this doesn't sound
like periodicity buzz to you, then that would mean that periodicity buzz
doesn't increase as more notes are added to a harmonic series, which means
the maximum buzz would peak somewhere after which it would go down. I'm open
to this possibility, but I'd have to see some proof first, as this sounds
like a pretty buzzy waveform to me. Sounds more to me like the periodicity
buzz for any chord that you hear is just a low-pass-filtered version of this
kind of buzz.

> > I suppose it's implicit in statements made that the
> > brain performs a multiresolution analysis.
>
> Have you read
> http://dicklyon.com/tech/Hearing/ImportanceOfTime-SlaneyLyon.pdf
> ?

Wow, this is a great paper! The "correlogram" is basically the same thing
I've been talking about for ages with the 1/N^2 rolloff filterbank, except
instead of a 1/N^2 rolloff, it would have no rolloff at all, sounds like.
I've been wondering, recently, if the 1/N^2 rolloff is really necessary
anyway. Although without it, a sine wave could just as easily match any of
its subharmonics as a VF as it could itself as the fundamental.

> > > Cochlear transforms are big business (see the Audience paper
> > > I just linked to). But I don't know what they have to do with
> > > the price of periodicity buzz. -Carl
> >
> > Well, we'll see what happens when we run 5:6:7 with different
> > phases through the gammatone wavelet transform. If it doesn't
> > accurately describe what we hear, then that's the end of that
> > one, and it'll have to be something in the brain.
>
> How will we know if it describes what we hear or not?

I'm going to run the impulse train examples first, but if I see amplitude
modulation in the upper partials for the pseudo-impulse one, and a
siren-like sweep for the chirp train one, I'll be sold that this is the
right direction to plow ahead into.

> > I missed the paper you linked to, where is it? I don't remember
> > you linking to a paper in this thread...
>
> The one you commented on with regard to the failure of
> dichotic periodicity buzz.

Oh yeah. I didn't actually read it, because by the time you posted it, I was
already convinced that it had something to do with the cochlea. I'll go back
through it and check it out.

I just read it. Jesus, they have a "fast cochlear transform?" Why would you
so surreptitiously throw that into an otherwise unassuming discussion? :P
But they don't post the algorithm. Either way, I'm convinced that this is
the way to go.

> > a sine wave has no periodicity buzz, 8:9 has some
> > periodicity buzz, 8:9:10 has more, 8:9:10:11:12:13:14 has
> > even more.
>
> That is far from clear.

In the examples I posted, it is clear. 8:9:10:11:12:13:14 definitely buzzes
more than 8:9:10. Maybe it reaches some kind of a peak somewhere before
1:2:3:4:5:6:7..., but I haven't seen evidence to indicate that. If you have
any I'd be happy to spend more hours running more MATLAB tests to work that
in.

> > The key realization here is that when you listen to
> > this wave, it actually sounds like "buzz" -
>
> Yes, it sounds like buzzing, but not necessarily like
> periodicity buzz.

Have you listened to how the two transform into one another? Play around
with sines and you'll hear it. Periodicity buzz sounds exactly to me like a
band-pass filtered version of buzz wave buzz.

> > Why exactly DO sawtooth waves sound buzzy, anyway?
>
> Good question.

OK, well I think this is why, and that they're related. Seems like a
reasonable assumption to make. If you have any counterevidence I'd be happy
to throw it away.

> > Look at this picture again:
> > http://www.mathworks.com/matlabcentral/fx_files/15313/1/GAMMA.png
>
> What is the input here? The page doesn't say.

Looks like an impulse train to me, since you can clearly see the
characteristic gammatone impulse response after each "smack."

> > One question that I have is - does the frequency of the buzz
> > correspond to the VF of the chord, or to the difference tones
> > between successive notes in the chord? I think the latter, but
> > let's save that for later.
>
> In the example I posted, I definitely hear a buzz frequency
> corresponding to the waveform period. I feel like I may also
> be hearing some faster buzz rates superimposed, but it's
> hard to tell.

Which example that you posted?

So here's a question then: the odd-harmonic-only version of a "buzz"
waveform, which is a differentiated square wave, adds an upside-down impulse
directly between each impulse. So instead of the wave looking like
_|_|_|_|_|_|_|_|_|_, it looks like

_|_ _|_ _|_ _|_
| | |

(view with fixed-width font)

However, it's not that you're FLIPPING every other impulse (which would make
the period half of what it is), but rather inserting an upside-down impulse
between each buzz wave impulse. The theory that you'd hear the buzz
frequency correspond to the VF means that you'd hear a buzz-unit (a buzzon?)
once per period, and the theory that you'd hear the buzz frequency
correspond to the difference tone means that you'd hear a buzzon once per
impulse, whether upside down or not. So if I generate an odd-harmonic buzz
waveform, and the buzz sounds twice as fast, then that means the difference
tones are what's being heard, not the VF.

-Mike

🔗Carl Lumma <carl@...>

Mike wrote:

> The "buzz" that you're hearing when you hear this waveform,
> which is what has led them to call it a "buzz" wave, is
> periodicity buzz.

How do you know?

> > Yes - they don't sound much like periodicity buzz.
>
> They're 1:2:3:4:5:6:7:8:9:10:11:12:13:14:15:16:etc. If this
> doesn't sound like periodicity buzz to you, then that would mean
> that periodicity buzz doesn't increase as more notes are added
> to a harmonic series, which means the maximum buzz would peak
> somewhere after which it would go down.

It doesn't sound like periodicity buzz to me, full stop.
As to what that means, I'm not sure.

> I'm open to this possibility, but I'd have to see some
> proof first,

You're the one making the claims, bub.

> as this sounds like a pretty buzzy waveform to me.

Rubbing my false teeth together sounds buzzy. So what!

> I just read it. Jesus, they have a "fast cochlear transform?"
> Why would you so surreptitiously throw that into an otherwise
> unassuming discussion? :P But they don't post the algorithm.
> Either way, I'm convinced that this is the way to go.

It's propriety. One of my best friends was employee #3.
I've drugged him several times to try to get him to spill
the beans, but he won't budge. (You can get a lot of details
on the FCT from Lloyd's thesis, and papers he published at
Interval research. But they have a lot more interesting
stuff than just the FCT.)

> > That is far from clear.
>
> In the examples I posted, it is clear. 8:9:10:11:12:13:14
> definitely buzzes more than 8:9:10.

Says you. Links? (I'm not even going to try to find them
in your barrage)

> > > Why exactly DO sawtooth waves sound buzzy, anyway?
> >
> > Good question.
>
> OK, well I think this is why, and that they're related. Seems
> like a reasonable assumption to make. If you have any
> counterevidence I'd be happy to throw it away.

They may very well be related, but I'm not buying that it's
the impulse response of gammatone filters. First, I'm not
sure quite what you mean. Second, gammatone filters are only
crude approximations to what goes on in the cochlea.

> > > http://www.mathworks.com/matlabcentral/fx_files/
> > > 15313/1/GAMMA.png
> >
> > What is the input here? The page doesn't say.
>
> Looks like an impulse train to me, since you can clearly see the
> characteristic gammatone impulse response after each "smack."

Don't you think it would be good to find out before
drawing conclusions?

> > In the example I posted, I definitely hear a buzz frequency
> > corresponding to the waveform period. I feel like I may also
> > be hearing some faster buzz rates superimposed, but it's
> > hard to tell.
>
> Which example that you posted?

Sorry, let me rephrase that. In every example of periodicity
buzz I've ever heard, I believe I hear a buzz rate corresponding
to the approximate (if tempered) waveform period. I feel there
may also be faster buzz rates superimposed, but it's hard to
tell for sure.

> The theory that you'd hear the buzz frequency correspond to
> the VF means that you'd hear a buzz-unit (a buzzon?) once per
> period, and the theory that you'd hear the buzz frequency
> correspond to the difference tone means that you'd hear
> a buzzon once per impulse, whether upside down or not. So if
> I generate an odd-harmonic buzz waveform, and the buzz sounds
> twice as fast, then that means the difference tones are what's
> being heard, not the VF.

Ok, I'm down.

-Carl

🔗Mike Battaglia <battaglia01@...>

On Wed, Jan 12, 2011 at 2:11 AM, Carl Lumma <carl@...> wrote:
>
> > They're 1:2:3:4:5:6:7:8:9:10:11:12:13:14:15:16:etc. If this
> > doesn't sound like periodicity buzz to you, then that would mean
> > that periodicity buzz doesn't increase as more notes are added
> > to a harmonic series, which means the maximum buzz would peak
> > somewhere after which it would go down.
>
> It doesn't sound like periodicity buzz to me, full stop.
> As to what that means, I'm not sure.

It means that you have split the spectrum of buzz into different
perceptual categories.

> > I'm open to this possibility, but I'd have to see some
> > proof first,
>
> You're the one making the claims, bub.

My observation is that periodicity buzz increases as more harmonics
are added, and never reaches a "maximum" point where it starts going
back down. I have told you precisely what listening test to do to
reach that observation for yourself, but it doesn't seem like you're
willing to do that.

The waveforms I posted start at 441 Hz and go up to the first 100
harmonics, at equal volume, before the harmonics drop out of the range
of human hearing. This puts this chord in, I guess, the 99-limit.
Unless you have a lot of experience with the qualitative flavor of
periodicity buzz, and how the sound of it changes from the 7-limit up
to the 99-limit, then saying "this doesn't sound like the periodicity
buzz I'm used to" isn't yielding any useful information. Do what I
told you and mess around with 5:6:7 and transform it into
1:2:3:4:5:6:7:8:9:etc and you will see that the buzz transforms from
5:6:7's "periodicity" buzz to the buzz waveform's "non-periodicity"
buzz, which is clearly still periodicity buzz.

At least, that is what I hear. If that's not what you hear, then
please describe what you hear.

> > as this sounds like a pretty buzzy waveform to me.
>
> Rubbing my false teeth together sounds buzzy. So what!

5:6:7 sounds buzzy. So what?

> > I just read it. Jesus, they have a "fast cochlear transform?"
> > Why would you so surreptitiously throw that into an otherwise
> > unassuming discussion? :P But they don't post the algorithm.
> > Either way, I'm convinced that this is the way to go.
>
> It's propriety. One of my best friends was employee #3.
> I've drugged him several times to try to get him to spill
> the beans, but he won't budge. (You can get a lot of details
> on the FCT from Lloyd's thesis, and papers he published at
> Interval research. But they have a lot more interesting
> stuff than just the FCT.)

They posted the magnitude response of each transfer function, which
should be enough for if one really wanted to explore this.

> > > That is far from clear.
> >
> > In the examples I posted, it is clear. 8:9:10:11:12:13:14
> > definitely buzzes more than 8:9:10.
>
> Says you. Links? (I'm not even going to try to find them
> in your barrage)

I didn't post links. I meant in those examples - 8:9:10 and
8:9:10:11:12:13:14. Since it takes me a while to make and upload
examples, and you can clearly generate your own, feel free to compare
them for yourself.

> > > > Why exactly DO sawtooth waves sound buzzy, anyway?
> > >
> > > Good question.
> >
> > OK, well I think this is why, and that they're related. Seems
> > like a reasonable assumption to make. If you have any
> > counterevidence I'd be happy to throw it away.
>
> They may very well be related, but I'm not buying that it's
> the impulse response of gammatone filters. First, I'm not
> sure quite what you mean.

What, specifically, are you confused about?

> Second, gammatone filters are only
> crude approximations to what goes on in the cochlea.

They don't have to be perfect approximations. They just have to
roughly match the time-frequency response of the cochlea for this to
work.

> > Looks like an impulse train to me, since you can clearly see the
> > characteristic gammatone impulse response after each "smack."
>
> Don't you think it would be good to find out before
> drawing conclusions?

No. You have a basic knowledge of DSP, you can look at the signal and
see what it's doing and come to the same educated guess I did. It's
really irrelevant, because I'm going to download it and find out for
myself anyway.

> > The theory that you'd hear the buzz frequency correspond to
> > the VF means that you'd hear a buzz-unit (a buzzon?) once per
> > period, and the theory that you'd hear the buzz frequency
> > correspond to the difference tone means that you'd hear
> > a buzzon once per impulse, whether upside down or not. So if
> > I generate an odd-harmonic buzz waveform, and the buzz sounds
> > twice as fast, then that means the difference tones are what's
> > being heard, not the VF.
>
> Ok, I'm down.

This is going to have to be later though.

-Mike

🔗genewardsmith <genewardsmith@...>

🔗Mike Battaglia <battaglia01@...>

On Wed, Jan 12, 2011 at 3:51 PM, genewardsmith
<genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> > I'm trying to figure out what you're talking about, and thought
> > it might help if you actually said what it is.
>
> I'd like to know how all of this relates to Mike's insistence that phase of partials has no audible effect.

That's not what I said. I said that you will hear no difference
between two signals if the group delay is constant for each frequency.
Since group delay is the derivative of phase, then this means that if
you take a zero-phase signal, and you change the phase response
linearly across the spectrum, then you won't hear a difference.

I'm deliberately dealing with non-linear-phase transfer functions
here. A chirp, for example, has parabolic phase. I think we'd all
agree that a chirp, white noise, and an impulse sound different, and I
never said otherwise.

What we really hear as being different is when group delay varies from
frequency to frequency. Group delay is the derivative of phase
response, so if phase response is linear, group delay will be
constant. More about that here:
http://en.wikipedia.org/wiki/Group_delay_and_phase_delay

So here's an example: let's say that you have a chord
1:2:3:4:5:6:7:8:9:10:11:12:..., made with cosines, and the phase of
each is 0. So the phase vs frequency plot will be 0, 0, 0, 0, 0, 0, 0,
0, 0, - a line. Then let's say you make the same chord, but this time
the phase of each is 90 degrees: 90, 90, 90, 90, 90, 90, 90, 90, 90,
90, etc. Still a line, shouldn't sound any different. Now let's say
you make the same chord, but this time the phases are distributed like
this: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 - still a line,
shouldn't sound any different (or rather, it'll correspond to a
delayed version of the original signal - this is what a non-constant,
linear phase shift produces).

Now let's say you make the same chord, but this time the phases are
distributed like this: 0, 1, 2, 4, 8, 16, etc - parabolic. This should
sound different, and it does. It apparently sounds most different at
lower frequencies, which you can hear in the examples I posted.

If you'd like I could just work up some examples for you, so that you
can hear for yourself.

-Mike

🔗Mike Battaglia <battaglia01@...>

I wrote:
> If you'd like I could just work up some examples for you, so that you
> can hear for yourself.

I did some just for fun, and to demonstrate what I'm talking about.
Here's the original waveform:

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

It's true, I am a real person. Now I'll do stuff to the phase response
of this signal. You will hear, very clearly, what is audible and what
is not.

Linear phase:
http://www.mikebattagliamusic.com/music/realperson90.wav - all sines
put 90 degrees out of phase, sounds identical to the original
http://www.mikebattagliamusic.com/music/realpersonlphase.wav - all
sines shifted in phase linearly with respect to frequency. This
creates a uniform group delay for each frequency, so the entire signal
is delayed in time. The way I did it makes the portion of the signal
that is delayed past the end of the array "wrap around" to the
beginning, so you first hear the end and not the beginning. Still no
audible difference in sound quality.

Nonlinear phase:
http://www.mikebattagliamusic.com/music/realpersonparabolic.wav - The
phase of each sine is shifted quadratically with respect to frequency.
This means that each impulse becomes a sine sweep. I sound like I'm in
space with laser guns shooting all around me.
http://www.mikebattagliamusic.com/music/realpersondnoise.wav - The
phase of each sine is shifted randomly. I accomplished this by
convolving the signal with decaying white noise. There is now
magically reverb on my voice. This is how reverb works.
http://www.mikebattagliamusic.com/music/realpersonnoise.wav - The
phase of each sine is shifted randomly. I accomplished this by
convolving the signal with nondecaying white noise. Every frequency
that was anywhere in the signal is now simultaneously everywhere at
the same time. This is like an infinite sustaining reverb effect.

So there you go, now you can hear what matters and what doesn't.

-Mike

🔗Chris Vaisvil <chrisvaisvil@...>

Nice set of examples Mike.

Where did you learn about the results these manipulations would have?
(i.e. are you an audio engineer?)

Chris

On Wed, Jan 12, 2011 at 6:51 PM, Mike Battaglia <battaglia01@...>wrote:

>
>
> I wrote:
> > If you'd like I could just work up some examples for you, so that you
> > can hear for yourself.
>
> I did some just for fun, and to demonstrate what I'm talking about.
> Here's the original waveform:
>
> http://www.mikebattagliamusic.com/music/realperson.wav
>
> It's true, I am a real person. Now I'll do stuff to the phase response
> of this signal. You will hear, very clearly, what is audible and what
> is not.
>
> Linear phase:
> http://www.mikebattagliamusic.com/music/realperson90.wav - all sines
> put 90 degrees out of phase, sounds identical to the original
> http://www.mikebattagliamusic.com/music/realpersonlphase.wav - all
> sines shifted in phase linearly with respect to frequency. This
> creates a uniform group delay for each frequency, so the entire signal
> is delayed in time. The way I did it makes the portion of the signal
> that is delayed past the end of the array "wrap around" to the
> beginning, so you first hear the end and not the beginning. Still no
> audible difference in sound quality.
>
> Nonlinear phase:
> http://www.mikebattagliamusic.com/music/realpersonparabolic.wav - The
> phase of each sine is shifted quadratically with respect to frequency.
> This means that each impulse becomes a sine sweep. I sound like I'm in
> space with laser guns shooting all around me.
> http://www.mikebattagliamusic.com/music/realpersondnoise.wav - The
> phase of each sine is shifted randomly. I accomplished this by
> convolving the signal with decaying white noise. There is now
> magically reverb on my voice. This is how reverb works.
> http://www.mikebattagliamusic.com/music/realpersonnoise.wav - The
> phase of each sine is shifted randomly. I accomplished this by
> convolving the signal with nondecaying white noise. Every frequency
> that was anywhere in the signal is now simultaneously everywhere at
> the same time. This is like an infinite sustaining reverb effect.
>
> So there you go, now you can hear what matters and what doesn't.
>
> -Mike
>
>

🔗Michael <djtrancendance@...>

Chris>"Nice set of examples Mike.
Where did you learn about the results these manipulations would have?
(i.e. are you an audio engineer?)"

I am not a sound engineer (at least beyond as a hobby) at all but thank you!

This is mostly self-taught from online tutorials...not any sort of formal
academic courses. I did kind of cheat because I found an open source phase
vocoder I built the whole thing from (which handled all the FFT windowing and
such). The one other thing I "stole" was Bill Sethares open source program for
calculating dissonance based on a cumulative set of dyads...but how I applied
that to turn it into a compressor and how I did the harmonic realigning...was a
mix of lots of reading, imagination, trial-and-error, and luck. :-)

That and a general knowledge of beating from reading on Sethares
before...though (as I've learned in my history on this list)...I'm still
probably not going to be trusted as knowing anything about those
things....though it's a nice thought. :-)

BTW, if anyone wants to pick up the source code for this (and/or ask me about
specifics concerning the algorithm) and perfect it (IE get rid of the lack of
clean attack and lack of quick fading/short-delay for the harmonic alignment
effect)...go right ahead...

I don't have much ego at all invested in this 7+ year old code any
more...and care more that someone makes the software fulfill its goal of
retuning any type of sound file to a microtonal scale cleanly and, yes,
hopefully make it easier to make/process microtonal music.

🔗Carl Lumma <carl@...>

🔗Michael <djtrancendance@...>

🔗genewardsmith <genewardsmith@...>

🔗Michael <djtrancendance@...>

🔗Mike Battaglia <battaglia01@...>

🔗Carl Lumma <carl@...>

🔗Chris Vaisvil <chrisvaisvil@...>

yes, this was to Mike B - not michael

I quoted his entire message....

Chris

On Thu, Jan 13, 2011 at 4:22 PM, Chris Vaisvil <chrisvaisvil@...>wrote:

> Nice set of examples Mike.
>
> Where did you learn about the results these manipulations would have?
> (i.e. are you an audio engineer?)
>
> Chris
>
>
> On Wed, Jan 12, 2011 at 6:51 PM, Mike Battaglia <battaglia01@gmail.com>wrote:
>
>>
>>
>> I wrote:
>> > If you'd like I could just work up some examples for you, so that you
>> > can hear for yourself.
>>
>> I did some just for fun, and to demonstrate what I'm talking about.
>> Here's the original waveform:
>>
>> http://www.mikebattagliamusic.com/music/realperson.wav
>>
>> It's true, I am a real person. Now I'll do stuff to the phase response
>> of this signal. You will hear, very clearly, what is audible and what
>> is not.
>>
>> Linear phase:
>> http://www.mikebattagliamusic.com/music/realperson90.wav - all sines
>> put 90 degrees out of phase, sounds identical to the original
>> http://www.mikebattagliamusic.com/music/realpersonlphase.wav - all
>> sines shifted in phase linearly with respect to frequency. This
>> creates a uniform group delay for each frequency, so the entire signal
>> is delayed in time. The way I did it makes the portion of the signal
>> that is delayed past the end of the array "wrap around" to the
>> beginning, so you first hear the end and not the beginning. Still no
>> audible difference in sound quality.
>>
>> Nonlinear phase:
>> http://www.mikebattagliamusic.com/music/realpersonparabolic.wav - The
>> phase of each sine is shifted quadratically with respect to frequency.
>> This means that each impulse becomes a sine sweep. I sound like I'm in
>> space with laser guns shooting all around me.
>> http://www.mikebattagliamusic.com/music/realpersondnoise.wav - The
>> phase of each sine is shifted randomly. I accomplished this by
>> convolving the signal with decaying white noise. There is now
>> magically reverb on my voice. This is how reverb works.
>> http://www.mikebattagliamusic.com/music/realpersonnoise.wav - The
>> phase of each sine is shifted randomly. I accomplished this by
>> convolving the signal with nondecaying white noise. Every frequency
>> that was anywhere in the signal is now simultaneously everywhere at
>> the same time. This is like an infinite sustaining reverb effect.
>>
>> So there you go, now you can hear what matters and what doesn't.
>>
>> -Mike
>>
>>
>
>