Dirty timbres

Hi everybody,

in message #92905 John Moriarty wrote:

"Absolutely. Similar to the way tempering just ratios to fit melodic
purposes and transposition has its payoffs and downturns, so does the
tempering of a timbre. You might end up with a dirty sounding timbre
with consonant triads, as opposed to a pure tone with triads that
make you cringe. Sometimes I prefer one to the other, and sometimes
it's switched."

Why do tempered timbres tend to sound dirty? When I tune the harmonics
of a sustained tone to something of medium accuracy such as 22-equal
I hear a strange warbling in the sound which is reminiscent of
beating but not quite the same. The impression of a single pitch is
robust and no partials pop out as separate. Is it combination tones?

The warbling is alleviated or completely disappears when I introduce
some bandwidth to the (tempered) harmonics à la PADsynth algorithm
of Nasca Paul (ZynAddSubFX, PaulStretch). Why is this?

Kalle

> Why do tempered timbres tend to sound dirty?

To put it simply, we are cognitively biased towards integer relationships of pitch.

We can't really be sure why, but one could argue that it has to do with voice recognition. And perhaps our voices are harmonically related because harmonic overtones are in a pattern that is uncommon enough in nature to be desirable as a recognition tool, and is also easily emulated by simple means (like taught strings and air columns).

We are biased towards this pattern in that we recognize it most as a single tone with pitch, as opposed to a bunch of sine wave pitches heard in harmony or a "noise" with no discernible pitch. Something emitting an overtone series not anywhere close to harmonicity will tend to not to have any distinguishable pitch, but will still have an overall character (think clanging pots and pans or white noise). Some overtone series are imperfect, but still close enough to harmonicity to still have a recognizable pitch. These timbres will tend to have a different character with a less pure sounding tone. Here you can think of over-taught strings, some xylophones and marimbas, and our electronically mapped timbres.

I would like to point out, however, that some extremely inharmonic sounds can sound very cool indeed, even if they are not "pure" sounding. Each tuning's mapped timbre have a unique character to them, and I think that 5-edo and 7-edo mapped timbres sound pretty far out. There is virtually no clashing among partials and they sound spaced out, sort of airy.

> The warbling is alleviated or completely disappears when I introduce
> some bandwidth to the (tempered) harmonics à la PADsynth algorithm
> of Nasca Paul (ZynAddSubFX, PaulStretch). Why is this?

This might have to do with the fact that pitch isn't the only thing that links partials together to create a timbre. The unity of partials in a timbre is also due, in smaller part, by phase, loudness, and some other factors I think. Have you read Sethares' book "Tuning Timbre Spectrum Scale"? He talks about a lot of this sort of thing.

John M

John wrote:

> > Why do tempered timbres tend to sound dirty?
>
> To put it simply, we are cognitively biased towards integer
> relationships of pitch.

Don't tell Bill.

> We can't really be sure why, but one could argue that it has to
> do with voice recognition.

There are very good arguments in that direction. Auditory
neurons tuned to specific features of vocalizations have been
studied extensively in birds, bats, and monkies.

> And perhaps our voices are harmonically related because
> harmonic overtones are in a pattern that is uncommon enough in
> nature to be desirable as a recognition tool,

More likely an accident due to the fact that most means of
producing vocalizations of reasonable duration will obey
simple harmonic motion.

-Carl

--- In tuning@yahoogroups.com, "John Moriarty" <JlMoriart@...> wrote:

> We can't really be sure why, but one could argue that it has to do with voice recognition.

I think it has to do with voices, at any rate, as the human voice is quite regular in its partial tones. Moreover, speech is really often not too far removed from music, as the AutoTune thread should make clear.

On Sat, Sep 18, 2010 at 11:47 PM, genewardsmith
<genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, "John Moriarty" <JlMoriart@...> wrote:
>
> > We can't really be sure why, but one could argue that it has to do with voice recognition.
>
> I think it has to do with voices, at any rate, as the human voice is quite regular in its partial tones. Moreover, speech is really often not too far removed from music, as the AutoTune thread should make clear.

Or these:

http://www.youtube.com/watch?v=22yd2efX9SY&feature=related
http://www.youtube.com/watch?v=9nlwwFZdXck
http://www.youtube.com/watch?v=-RQPeoyqyP4&feature=related

No political commentary intended. This would obviously work
spectacularly with microtonal music. You down to really autotune the
news, Gene? :)

The funny thing is, after you've listened to this a few times, it's
hard to get it to sound like they aren't actually singing.

-Mike

> > To put it simply, we are cognitively biased towards integer
> > relationships of pitch.
>
> Don't tell Bill.

=P I don't think he'd mind. He'd probably just argue that we're more so biased towards a lack of beating than integer relationships overall, and I'l be likely to agree with him. JI with harmonic timbres= little beating, 5-edo with certain gamelan instruments = little beating. Gamelan instruments in JI = lots of beating (i'd assume).
The whole timbre mapping paradigm deals with approximating harmonic timbres anyway.

> More likely an accident due to the fact that most means of
> producing vocalizations of reasonable duration will obey
> simple harmonic motion.

Simple harmonic motion doesn't imply integer relationships though, just sinusoidal variations in pressure. Each partial emitted by a pot struck by a spoon is sounded by a section of the pot undergoing simple harmonic motion right?

John

On 19 September 2010 08:59, John Moriarty <JlMoriart@...> wrote:

>> More likely an accident due to the fact that most means of
>> producing vocalizations of reasonable duration will obey
>> simple harmonic motion.
>
> Simple harmonic motion doesn't imply integer relationships though, just sinusoidal variations in pressure. Each partial emitted by a pot struck by a spoon is sounded by a section of the pot undergoing simple harmonic motion right?

Simple harmonic motion does lead to integer relationships. I don't
think simple harmonic motion applies to the pot at all.

Graham

> Simple harmonic motion does lead to integer relationships. I don't
> think simple harmonic motion applies to the pot at all.

Then maybe I have a skewed definition of the word. When I think of simple harmonic motion, I think of the weight on a spring from physics class that underwent sinusoidal motion when displaced from equilibrium. It is sinusoidal pressure variation that we perceive as a single pitch, and combinations of which we hear as either harmony or timbre.

For a string, certain sections of the string are vibrating sinusoidally. They are related, due to the physics of the string, by integer multiples of the lowest frequency. In a pot struck by a spoon, different sections of the pot are also undergoing sinusoidal vibration and, due to the physics of the pot, they are not related by simple integer ratios of frequency.

Are you saying that simple harmonic motion, or sinusoidal motion, implies similar instances of the same motion at integer multiple frequencies of the fundamental, or is simple harmonic motion not what I am describing it as here?

John

On 19 September 2010 09:33, John Moriarty <JlMoriart@...> wrote:

> Then maybe I have a skewed definition of the word. When I think of simple harmonic motion, I think of the weight on a spring from physics class that underwent sinusoidal motion when displaced from equilibrium. It is sinusoidal pressure variation that we perceive as a single pitch, and combinations of which we hear as either harmony or timbre.

That's simple harmonic motion. It looks like it's defined as being
sinusoidal, but the equations that lead to it can also be solved to
give other harmonic partials. See here:

http://en.wikipedia.org/wiki/Simple_harmonic_motion#Dynamics_of_simple_harmonic_motion

We perceive the set of harmonic partials as a single pitch. In some
cases, like bells, we perceive inharmonic partials as a single pitch.

> For a string, certain sections of the string are vibrating sinusoidally. They are related, due to the physics of the string, by integer multiples of the lowest frequency. In a pot struck by a spoon, different sections of the pot are also undergoing sinusoidal vibration and, due to the physics of the pot, they are not related by simple integer ratios of frequency.

The whole string is vibrating, except for the nodes. No section of
the string vibrates independently of the other parts. Because the
string is thin, it can be compared to harmonic motion. In the real
world, the string won't be infinitely thin or infinitely elastic, so
there will be some inharmonicity.

The pot is vibrating according to its physics. Because the standing
waves aren't constrained to one dimension, it doesn't approximate
harmonic motion. It exhibits complex, inharmonic motion.

> Are you saying that simple harmonic motion, or sinusoidal motion, implies similar instances of the same motion at integer multiple frequencies of the fundamental, or is simple harmonic motion not what I am describing it as here?

The equation for simple harmonic motion can also be solved to get
complex harmonics. That's where harmonic timbres come from. Getting
pure, sinusoidal motion is quite difficult. It's what tuning forks
do. You can also combine an inharmonic body (like a pot) with a
harmonic resonator to bring out its strongest partial.

Graham

> The equation for simple harmonic motion can also be solved to get
> complex harmonics.

Ok cool, thanks for the explanation.

John

On Sun, Sep 19, 2010 at 2:23 AM, Graham Breed <gbreed@...> wrote:
>
> On 19 September 2010 09:33, John Moriarty <JlMoriart@...> wrote:
>
> > Then maybe I have a skewed definition of the word. When I think of simple harmonic motion, I think of the weight on a spring from physics class that underwent sinusoidal motion when displaced from equilibrium. It is sinusoidal pressure variation that we perceive as a single pitch, and combinations of which we hear as either harmony or timbre.
>
> That's simple harmonic motion. It looks like it's defined as being
> sinusoidal, but the equations that lead to it can also be solved to
> give other harmonic partials. See here:
>
> http://en.wikipedia.org/wiki/Simple_harmonic_motion#Dynamics_of_simple_harmonic_motion

Sorry, but where are you seeing this? The second derivative of a
sawtooth wave is not another scaled sawtooth wave. The equation should
hold only for sinusoids and complex exponential sinusoids.

> > For a string, certain sections of the string are vibrating sinusoidally. They are related, due to the physics of the string, by integer multiples of the lowest frequency. In a pot struck by a spoon, different sections of the pot are also undergoing sinusoidal vibration and, due to the physics of the pot, they are not related by simple integer ratios of frequency.
>
> The whole string is vibrating, except for the nodes. No section of
> the string vibrates independently of the other parts. Because the
> string is thin, it can be compared to harmonic motion. In the real
> world, the string won't be infinitely thin or infinitely elastic, so
> there will be some inharmonicity.

I actually did this as an assignment in acoustics class - treat a
string as a bunch of masses with connected springs undergoing simple
harmonic motion. Then you can take the limit as the number of masses
goes to infinity and become closer together and end up getting
individual points on a string, and the resulting behavior can be used
to derive the behavior of a string. I think the context was in our
deriving the wave equation for a string. I don't remember the exact
concept though.

> > Are you saying that simple harmonic motion, or sinusoidal motion, implies similar instances of the same motion at integer multiple frequencies of the fundamental, or is simple harmonic motion not what I am describing it as here?
>
> The equation for simple harmonic motion can also be solved to get
> complex harmonics. That's where harmonic timbres come from. Getting
> pure, sinusoidal motion is quite difficult. It's what tuning forks
> do. You can also combine an inharmonic body (like a pot) with a
> harmonic resonator to bring out its strongest partial.

I would again like to see this - I thought that what produced some of
the overtones of a tuning fork was some kind of inherent nonlinearity,
or that the simple harmonic motion equation was an "idealized" version
that does not apply to a tuning fork. When you hit the fork harder,
you drive the nonlinearity more. That was my understanding, but
perhaps I am wrong.

-Mike

I wrote:
>> The whole string is vibrating, except for the nodes. No section of
>> the string vibrates independently of the other parts. Because the
>> string is thin, it can be compared to harmonic motion. In the real
>> world, the string won't be infinitely thin or infinitely elastic, so
>> there will be some inharmonicity.
>
> I actually did this as an assignment in acoustics class - treat a
> string as a bunch of masses with connected springs undergoing simple
> harmonic motion. Then you can take the limit as the number of masses
> goes to infinity and become closer together and end up getting
> individual points on a string, and the resulting behavior can be used
> to derive the behavior of a string. I think the context was in our
> deriving the wave equation for a string. I don't remember the exact
> concept though.

Sorry, you're right here. Yes, each point was a mass with two springs,
so no, it wouldn't be SHM.

-Mike

On 19 September 2010 10:45, Mike Battaglia <battaglia01@...> wrote:

> Sorry, but where are you seeing this? The second derivative of a
> sawtooth wave is not another scaled sawtooth wave. The equation should
> hold only for sinusoids and complex exponential sinusoids.

Right, I think I'm remembering that wrong. They say "one of the
solutions" but the others are probably only different phases. I don't
see where integers can come out of that equation. So the basic
physical model does give simple harmonic motion, which is sinusoidal.

Vibrating strings follow a different model, where you have a standing
wave in one dimension, and that allows integer frequency harmonics.

> I actually did this as an assignment in acoustics class - treat a
> string as a bunch of masses with connected springs undergoing simple
> harmonic motion. Then you can take the limit as the number of masses
> goes to infinity and become closer together and end up getting
> individual points on a string, and the resulting behavior can be used
> to derive the behavior of a string. I think the context was in our
> deriving the wave equation for a string. I don't remember the exact
> concept though.

As you say later, not simple harmonic motion. But note that there are
physical modeling algorithms that work like this. Csound can do it.

> I would again like to see this - I thought that what produced some of
> the overtones of a tuning fork was some kind of inherent nonlinearity,
> or that the simple harmonic motion equation was an "idealized" version
> that does not apply to a tuning fork. When you hit the fork harder,
> you drive the nonlinearity more. That was my understanding, but
> perhaps I am wrong.

A tuning fork is designed to produce -- and resonate at -- a single
frequency. Obviously it isn't perfect. It is inherently nonlinear.
The shape is designed to remove harmonic partials that could give
false matches.

Graham

On Sun, Sep 19, 2010 at 3:15 AM, Graham Breed <gbreed@...> wrote:
>
> On 19 September 2010 10:45, Mike Battaglia <battaglia01@...> wrote:
>
> > Sorry, but where are you seeing this? The second derivative of a
> > sawtooth wave is not another scaled sawtooth wave. The equation should
> > hold only for sinusoids and complex exponential sinusoids.
>
> Right, I think I'm remembering that wrong. They say "one of the
> solutions" but the others are probably only different phases. I don't
> see where integers can come out of that equation. So the basic
> physical model does give simple harmonic motion, which is sinusoidal.

Yeah, it could be different phases, but they might have been hinting
at also that complex exponentials work as well (e.g. e^(iwt)). Cosines
can be derived as (e^(iwt) + e^(-iwt))/2 and all of that, as well as
phase shifting stuff.

It's just that in general they tend to work the math out for all of
this stuff out with complex exponentials, as it tends to be more
mathematically rigorous. They just present it as being made up of
sines and such, but complex exponentials really form the basis
functions for most of it.

For some reason that I can't quite comprehend, they have decided to
call complex exponentials "phasors." Okay.

> Vibrating strings follow a different model, where you have a standing
> wave in one dimension, and that allows integer frequency harmonics.

Yes, that's right. I wish I could remember the math though.

-Mike

John wrote:

> > Don't tell Bill.
>
> =P I don't think he'd mind. He'd probably just argue that
> we're more so biased towards a lack of beating than integer
> relationships overall, and I'l be likely to agree with him.

I wouldn't. 12-ET introduces plenty of beating and roughness
to get more of those integer relationships. The Hammond organ
was practically beatless but musicians reacted by playing the
damn things through rotating speakers! Then we have this
major/minor thing we've been talking about, where everyone
finds 60:70:84:105 much more discordant than 4:5:6:7 even
though they contain the same intervals and have very nearly
identical roughness.

> Gamelan instruments in JI = lots of beating (i'd assume).

The 'American gamelan school' (e.g. Lou Harrison) built
gamelan tuned in just intonation. To my ear they beat less
than Indonesian gamelan. However to be fair, this may be
due to timbral differences.

> The whole timbre mapping paradigm deals with approximating
> harmonic timbres anyway.

That's true.

> > More likely an accident due to the fact that most means of
> > producing vocalizations of reasonable duration will obey
> > simple harmonic motion.
>
> Simple harmonic motion doesn't imply integer relationships
> though, just sinusoidal variations in pressure.

There also has to be resonance

http://en.wikipedia.org/wiki/Resonator

>Each partial emitted by a pot struck by a spoon is sounded by
>a section of the pot undergoing simple harmonic motion right?

I believe so, yes. But the speed of sound and distances
between nodes may not be the same throughout the pot, so
the resonances may not fit to a single harmonic series.
That's my understanding anyway.

-Carl

Mike wrote:
> I thought that what produced some of
> the overtones of a tuning fork was some kind of inherent nonlinearity,
> or that the simple harmonic motion equation was an "idealized" version
> that does not apply to a tuning fork. When you hit the fork harder,
> you drive the nonlinearity more. That was my understanding, but
> perhaps I am wrong.

Nonlinear response can cause harmonic distortion, like the
harmonic distortion in an expensive tube amplifier. I think
that's due to clipping. That explains why the effect increases
as the system is driven harder.

There's also intermodulation distortion (which causes combination
tones in the inner ear).
http://en.wikipedia.org/wiki/Intermodulation

-Carl

I wrote:

> Nonlinear response can cause harmonic distortion, like the
> harmonic distortion in an expensive tube amplifier. I think
> that's due to clipping. That explains why the effect increases
> as the system is driven harder.
> There's also intermodulation distortion (which causes combination
> tones in the inner ear).
> http://en.wikipedia.org/wiki/Intermodulation

I'm not entirely sure how these relate to the normal modes
explanation that I mentioned earlier (and that Graham just
mentioned; "standing wave in one dimension" of the system).

-Carl

On Sun, Sep 19, 2010 at 4:09 AM, Carl Lumma <carl@...> wrote:
>
> Mike wrote:
> > I thought that what produced some of
> > the overtones of a tuning fork was some kind of inherent nonlinearity,
> > or that the simple harmonic motion equation was an "idealized" version
> > that does not apply to a tuning fork. When you hit the fork harder,
> > you drive the nonlinearity more. That was my understanding, but
> > perhaps I am wrong.
>
> Nonlinear response can cause harmonic distortion, like the
> harmonic distortion in an expensive tube amplifier. I think
> that's due to clipping. That explains why the effect increases
> as the system is driven harder.
>
> There's also intermodulation distortion (which causes combination
> tones in the inner ear).
> http://en.wikipedia.org/wiki/Intermodulation

I was actually going to propose this as a mechanism for why intervals
like neutral seconds sometimes "open up" so much, or why sonorities
like 9:10:11 open up even more: distortion product otoacoustic
emissions (DPOAE's). I came across them while reading the medical
literature for something totally different.

DPOAE's are the mysterious combination tones in the ear that everyone
talks about, and apparently they've been studied to the point that in
audiology, they test for them in babies to make sure their hearing
will work. The ideal frequency ratio for one of the distortion
products to be at optimal volume, 2f1-f2 I believe, is about 11:9.
There are other DPOAE's, but that's the one generally used in the
test. I was reading some research talking about one of the other ones
(2f2-f1), and it seemed like the ideal ratio for that one was going to
be something like 10:11 in normal hearing range, but they didn't test
below like 750 Hz. I stayed up late one night working it all out and
got frustrated by the lack of answers and hence let it go.

If that's true though, then it would explain why intervals around the
size of a neutral second have the peculiar resonance that they do, and
why things like 9:10:11 or 10:11:12 do even more: you have a bunch of
intervals right around the ideal size for 2f2-f1, and the outer dyad
is right around the ideal size for 2f1-f2. And these are even-order
distortion products, so instead of getting a difference tone of 1,
you'll get like ...:6:7:8:9:10:11:12:13:14:... where successive
harmonics are decreasing in volume and much, much lower than the
originals (like 40 dB lower, so about 1/5 as loud).

They occur at the volume range of normal hearing (50-60 dB SPL I
believe is where the test is done), and are considerably lower, so
they don't really have an identity all their own, just serve to make
the sound slightly more concordant and open it up a bit. So when
Michael Sheiman is talking about difference tones around neutral
seconds, he's probably talking about this. It also has something to do
apparently with nonlinear effects right at the basilar membrane
related to critical band interactions, which is where I jumped off the
bus.

Anyway, once I realized how much I had to research to fully understand
this I gave up, since it isn't really that critically important, but
that was the theory I had. I had a huge thing written about it and
never posted it, but since you bring it up I might as well mention it.

> I'm not entirely sure how these relate to the normal modes
> explanation that I mentioned earlier (and that Graham just
> mentioned; "standing wave in one dimension" of the system).

Nonlinearity isn't involved there, because when you first excite the
pot/spring/tuning fork you're going to excite it with a waveform that
ideally resembles something like an impulse. An ideal impulse would
have a frequency response equal to exactly one for all frequencies,
and then the instrument acts as a waveguide which acoustically filters
the signal. Hence why strings will resonate sympathetically for only
certain frequencies, but not others. The nodes at the end of a string
cause reflections of the wave going up and down the string, which
cancel out every frequency except the standing waves. This is not
coincidentally correlated with the fact that an impulse train has a
frequency response of an idealized comb filter (inelasticity at the
nodes, I believe, is where the rolloff and damping comes from).

So in a sense, instruments behave like subtractive synthesizers,
except instead of removing frequency content from a waveform like a
sawtooth, they remove it from an impulse, in which all frequencies are
present, ideally leaving only ones which are aligned in a harmonic
series.

Nonlinear behavior for a tuning fork I think would arise when the tine
moves so far that an additional compressive force starts to kick in
for extreme deformations, thus destroying superposition. If you hold
one edge of the vibrating tuning fork lightly against a table, it will
chop off the motion of the wave, and hence you'll hear some kind of
"buzzing." This gets infinitely more complicated in ways that I don't
fully understand, but that's the basic idea.

I just found this, too. Some good stuff can be found here:
http://paws.kettering.edu/~drussell/Publications/Rossing-Russell-Fork.pdf

I know that to really formalize this you need to understand something
called a Volterra series, which I have never learned and which scare
the hell out of me. Maybe Gene knows something about them.

-Mike

Could you please explain more?

Daniel Forro

On 19 Sep 2010, at 4:58 PM, Carl Lumma wrote:

> The Hammond organ
> was practically beatless but musicians reacted by playing the
> damn things through rotating speakers!

The electromechanical Hammonds weren't tuned to 12-tET, but to a rational approximation thereof. I don't know about "practically beatless", but they sure are smooth without a Leslie.

--- In tuning@yahoogroups.com, Daniel Forró <dan.for@...> wrote:
>
> Could you please explain more?
>
> Daniel Forro
>
> On 19 Sep 2010, at 4:58 PM, Carl Lumma wrote:
>
> > The Hammond organ
> > was practically beatless but musicians reacted by playing the
> > damn things through rotating speakers!
>

Gamelan are designed to beat, and in a consistent way- it's a very, very trippy thing live, like being underwater.

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> John wrote:
>
> > > Don't tell Bill.
> >
> > =P I don't think he'd mind. He'd probably just argue that
> > we're more so biased towards a lack of beating than integer
> > relationships overall, and I'l be likely to agree with him.
>
> I wouldn't. 12-ET introduces plenty of beating and roughness
> to get more of those integer relationships. The Hammond organ
> was practically beatless but musicians reacted by playing the
> damn things through rotating speakers! Then we have this
> major/minor thing we've been talking about, where everyone
> finds 60:70:84:105 much more discordant than 4:5:6:7 even
> though they contain the same intervals and have very nearly
> identical roughness.
>
> > Gamelan instruments in JI = lots of beating (i'd assume).
>
> The 'American gamelan school' (e.g. Lou Harrison) built
> gamelan tuned in just intonation. To my ear they beat less
> than Indonesian gamelan. However to be fair, this may be
> due to timbral differences.
>
> > The whole timbre mapping paradigm deals with approximating
> > harmonic timbres anyway.
>
> That's true.
>
> > > More likely an accident due to the fact that most means of
> > > producing vocalizations of reasonable duration will obey
> > > simple harmonic motion.
> >
> > Simple harmonic motion doesn't imply integer relationships
> > though, just sinusoidal variations in pressure.
>
> There also has to be resonance
>
> http://en.wikipedia.org/wiki/Resonator
>
> >Each partial emitted by a pot struck by a spoon is sounded by
> >a section of the pot undergoing simple harmonic motion right?
>
> I believe so, yes. But the speed of sound and distances
> between nodes may not be the same throughout the pot, so
> the resonances may not fit to a single harmonic series.
> That's my understanding anyway.
>
> -Carl
>

Yes, I know this as long-years Hammond player - I owned about 6
different models, now I have CV from 1945, M3 from 1960 and digital
clone Korg CX3. Differences in temperament are so small (see: http://
tonalsoft.com/enc/h/hammond-organ.aspx) that it's practically
unhearable, so for sure there are beats, differential tones and
intermodulation distortion. Then there's vibrato or chorus effect
additional.

Sound without Leslie is rough and harmonica like. It's slow Leslie
which adds smoothness IMHO.

Daniel Forro

On 19 Sep 2010, at 7:58 PM, cameron wrote:

> The electromechanical Hammonds weren't tuned to 12-tET, but to a
> rational approximation thereof. I don't know about "practically
> beatless", but they sure are smooth without a Leslie.
>
> --- In tuning@yahoogroups.com, Daniel Forró <dan.for@...> wrote:
>>
>> Could you please explain more?
>>
>> Daniel Forro

The sound of the Leslie is associated so much with the Hammond that I'm probably remembering a slow Leslie (not that wobble-wobble or whizz! whizz!) and not "without a Leslie". If that's the case I'd have to ask to what Carl meant there, too.

--- In tuning@yahoogroups.com, Daniel Forró <dan.for@...> wrote:
>
> Yes, I know this as long-years Hammond player - I owned about 6
> different models, now I have CV from 1945, M3 from 1960 and digital
> clone Korg CX3. Differences in temperament are so small (see: http://
> tonalsoft.com/enc/h/hammond-organ.aspx) that it's practically
> unhearable, so for sure there are beats, differential tones and
> intermodulation distortion. Then there's vibrato or chorus effect
> additional.
>
> Sound without Leslie is rough and harmonica like. It's slow Leslie
> which adds smoothness IMHO.
>
> Daniel Forro
>
> On 19 Sep 2010, at 7:58 PM, cameron wrote:
>
> > The electromechanical Hammonds weren't tuned to 12-tET, but to a
> > rational approximation thereof. I don't know about "practically
> > beatless", but they sure are smooth without a Leslie.
> >
> > --- In tuning@yahoogroups.com, Daniel Forró <dan.for@> wrote:
> >>
> >> Could you please explain more?
> >>
> >> Daniel Forro
>

Hi John,

--- In tuning@yahoogroups.com, "John Moriarty" <JlMoriart@...> wrote:
>
> > Why do tempered timbres tend to sound dirty?
>
> To put it simply, we are cognitively biased towards integer
> relationships of pitch.
>
> We can't really be sure why, but one could argue that it has to do
> with voice recognition. And perhaps our voices are harmonically
> related because harmonic overtones are in a pattern that is
> uncommon enough in nature to be desirable as a recognition tool,
> and is also easily emulated by simple means (like taught strings
> and air columns).
>
> We are biased towards this pattern in that we recognize it most as
> a single tone with pitch, as opposed to a bunch of sine wave
> pitches heard in harmony or a "noise" with no discernible pitch.
> Something emitting an overtone series not anywhere close to
> harmonicity will tend to not to have any distinguishable pitch, but
> will still have an overall character (think clanging pots and pans
> or white noise). Some overtone series are imperfect, but still
> close enough to harmonicity to still have a recognizable pitch.
> These timbres will tend to have a different character with a less
> pure sounding tone. Here you can think of over-taught strings, some
> xylophones and marimbas, and our electronically mapped timbres.

Note that both strings and air columns have natural frequencies that
diverge from a perfect harmonic series (because they aren't really
one-dimensional) but they lock to perfect harmonic series when they
are driven by a continuous excitation like bowing or blowing. When
an electronic timbre with only approximate harmonics decays
relatively rapidly it sounds quite normal, probably because we are
used to hearing such sounds from plucked/struck string instruments.
It's when that kind of timbre is sustained that it sounds a bit
weird.

But as I said even for such sustained almost harmonic timbres the
perception of pitch is robust. This shouldn't be surprising as
the ear picks out a certain accidentally occurring approximate
harmonic series from such a highly inharmonic spectra as those of
timpani.

What I'm asking for is the psychoacoustic basis for the warbling
sensation I'm hearing. Why my auditory system detects inharmonicity
(in the guise of this warbling) even if the pitch is clear?

> > The warbling is alleviated or completely disappears when I
> > introduce some bandwidth to the (tempered) harmonics à la
> > PADsynth algorithm of Nasca Paul (ZynAddSubFX, PaulStretch). Why
> > is this?
>
> This might have to do with the fact that pitch isn't the only thing
> that links partials together to create a timbre. The unity of
> partials in a timbre is also due, in smaller part, by phase,
> loudness, and some other factors I think. Have you read Sethares'
> book "Tuning Timbre Spectrum Scale"? He talks about a lot of this
> sort of thing.

I have read parts of the book and I'm familiar with Sethares' ideas.
I'm speculating that the nonlinearities in the ear are producing
some sort of beating effect when the partials are not exactly
harmonic. Loudness makes combination tones more audible so maybe
when the there is some bandwidth in the harmonics and the energy is
not so narrowly concentrated on the basilar membrane the nonlinear
behaviour is reduced or masked.

Kalle

--- In tuning@yahoogroups.com, "cameron" <misterbobro@...> wrote:
>
> The electromechanical Hammonds weren't tuned to 12-tET, but to a rational approximation thereof.

From the Scala archive:

! hammond12.scl
!
Hammond organ scale, 1/1=277.0731707 Hz, A=440, see hammond.scl for the ratios
12
!
5494/5183
1435/1278
5658/4757
984/781
1517/1136
2009/1420
3936/2627
451/284
2747/1633
4428/2485
3485/1846
2/1

Hi Cameron,

> Gamelan are designed to beat,

Yes, that may very well be true. I know Kraig Grady
believes this, and both of you probably know more about
it than me.

However in this case, it's besides the point what they're
designed to do. The claim was, tuning a gamelan in JI
should make it beat more. In fact, the American gamelan
seem to beat less.

-Carl

Daniel wrote:

> > The Hammond organ
> > was practically beatless but musicians reacted by playing the
> > damn things through rotating speakers!
>
> Could you please explain more?

Sure. To pick up on the rest of the thread, yes they were
tuned to the scale Gene just posted, but it doesn't matter what
scale they were tuned to. What matters is that the tone wheels
each produce a decent sinusoid, and therefore the scale the
organ is tuned to and the harmonics of the organ's timbre are
identical. Therefore, the instrument produces many beatless
intervals (e.g. major 3rds), prior to the addition of overdriven
amps and other effects, which were used copiously along with
tremolo and Leslie to make the things warble like a barn swallow
on crack. I take this as a tidbit of historical evidence
against John's claim that musicians favor beatlessness over
onalness. Cameron's claim that gamelan are designed to beat
would be another such tidbit, if true.

You think a harmonica sounds rough? There is no hope for you.
:) Incidentally, many diatonic harmonicas are tuned in JI.
Some even in the 7-limit.

-Carl

Hi Kalle,

> What I'm asking for is the psychoacoustic basis for the warbling
> sensation I'm hearing. Why my auditory system detects inharmonicity
> (in the guise of this warbling) even if the pitch is clear?

Sorry, could you repeat what it is you're listening to?

If you really have sines, aren't playing them too loud, and
have intervals wider than a critical band, you should not
hear warbling.

-Carl

Mike wrote:

> DPOAE's are the mysterious combination tones in the ear that
> everyone talks about, and apparently they've been studied to
> the point that in audiology, they test for them in babies to
> make sure their hearing will work.

Yes, this is standard now. Both my kids had it. However I
believe they test for EOAEs not DPOAEs. DPOAEs are artifacts
due to nonlinearities in the ear. EOAEs are created by
specialized hair cells in the cochlea.

> If that's true though, then it would explain why intervals
> around the size of a neutral second have the peculiar resonance
> that they do,

I'm not sure I notice a particular resonance with neutral
seconds.

> They occur at the volume range of normal hearing (50-60 dB SPL I
> believe is where the test is done), and are considerably lower,
> so they don't really have an identity all their own, just serve
> to make the sound slightly more concordant and open it up a bit.

I don't see how you're getting this.

> > I'm not entirely sure how these relate to the normal modes
> > explanation that I mentioned earlier (and that Graham just
> > mentioned; "standing wave in one dimension" of the system).
>
> Nonlinearity isn't involved there, because when you first excite
> the pot/spring/tuning fork you're going to excite it with a
> waveform that ideally resembles something like an impulse.
> An ideal impulse would have a frequency response equal to exactly
> one for all frequencies, and then the instrument acts as a
> waveguide which acoustically filters the signal.

Right, got that.

> Hence why strings will resonate sympathetically for only certain
> frequencies, but not others. The nodes at the end of a string
> cause reflections of the wave going up and down the string, which
> cancel out every frequency except the standing waves.

Yep. OK, so the two aren't related.

> So in a sense, instruments behave like subtractive synthesizers
> except instead of removing frequency content from a waveform
> like a sawtooth, they remove it from an impulse, in which all
> frequencies are present, ideally leaving only ones which are
> aligned in a harmonic series.

Ok, yeah.

> Nonlinear behavior for a tuning fork I think would arise when
> the tine moves so far that an additional compressive force
> starts to kick in for extreme deformations, thus destroying
> superposition.

If amplitude of the impulse exceeds the ability of the fork
to respond (linear response), the signal gets clipped, right?

> I just found this, too. Some good stuff can be found here:
> http://paws.kettering.edu/~drussell/Publications/Rossing-
> Russell-Fork.pdf

It seems to say what I just said about clipping, and also
there's mode shifting due to the spring constant being
different at different accelerations (amplitudes).

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> Hi Kalle,
>
> > What I'm asking for is the psychoacoustic basis for the warbling
> > sensation I'm hearing. Why my auditory system detects inharmonicity
> > (in the guise of this warbling) even if the pitch is clear?
>
> Sorry, could you repeat what it is you're listening to?
>
> If you really have sines, aren't playing them too loud, and
> have intervals wider than a critical band, you should not
> hear warbling.

But I do hear it! I uploaded an example to my files called
"Warbling". It's 8 seconds of a 220 Hz tone with 6 harmonics and then
the same with harmonics tuned to 12-equal.

Kalle

On Sun, Sep 19, 2010 at 5:20 PM, Carl Lumma <carl@...> wrote:
>
> Mike wrote:
>
> > DPOAE's are the mysterious combination tones in the ear that
> > everyone talks about, and apparently they've been studied to
> > the point that in audiology, they test for them in babies to
> > make sure their hearing will work.
>
> Yes, this is standard now. Both my kids had it. However I
> believe they test for EOAEs not DPOAEs. DPOAEs are artifacts
> due to nonlinearities in the ear. EOAEs are created by
> specialized hair cells in the cochlea.

Which are EOAE's? I though DPOAE's were a subclass of EOAE's.

> > If that's true though, then it would explain why intervals
> > around the size of a neutral second have the peculiar resonance
> > that they do,
>
> I'm not sure I notice a particular resonance with neutral
> seconds.

The exact point of maximum resonance differs with everyone. For me,
neutral seconds have a weird quality to them, especially when they're
stacked; they seem to "open up" more than triads like 4:5:6 do. This
is, I thought, because they're still harmonic, but rough. This is
true, and is apparently actually what leads to DPOAE's existing
(nonlinear behavior where critical bands interact). I didn't study it
enough to describe beyond that, maybe you know more about it.

> > They occur at the volume range of normal hearing (50-60 dB SPL I
> > believe is where the test is done), and are considerably lower,
> > so they don't really have an identity all their own, just serve
> > to make the sound slightly more concordant and open it up a bit.
>
> I don't see how you're getting this.

Because if that's true, then 10:11:12 becomes
(7:8:9):10:11:12:(13:14:15) in which the tones in parentheses are
about 1/4-1/5 the volume (if this is where your ears are tuned to
produce the frequencies at that ratio). This is equivalent to adding
some very, very slight even-order distortion to the signal, which is a
sound we really like. This is what people refer to when they speak
about the "warmth" of tape. It's like putting very, very slight
amounts of distortion on a guitar - not enough to cause the presence
of additional harmonic tones, just enough to add a very subtle effect.

> > Hence why strings will resonate sympathetically for only certain
> > frequencies, but not others. The nodes at the end of a string
> > cause reflections of the wave going up and down the string, which
> > cancel out every frequency except the standing waves.
>
> Yep. OK, so the two aren't related.

I was thinking about this, and it might be related for longitudinal
waves, where the notes might act to "clip" the signal, but I'm not
sure.

> > Nonlinear behavior for a tuning fork I think would arise when
> > the tine moves so far that an additional compressive force
> > starts to kick in for extreme deformations, thus destroying
> > superposition.
>
> If amplitude of the impulse exceeds the ability of the fork
> to respond (linear response), the signal gets clipped, right?

Yeah, that's what I mean. For extreme deformations, when the tine is
way out there, the properties of the metal might be such that an
additional compressive force beyond the normal idealized restoring
force starts to kick in and bring it back even more strongly to where
it started. It would probably not be as much of a hard clipping as a
soft clipping, but it would be nonlinear for all intents and purposes.

More likely what it is is that the restoring force itself is probably
not going to be linearly proportional to displacement for extreme
displacements. So you could view the real restoring force as a
combination of the idealized linear restoring force, and an additional
super-restoring force that serves to "compress" the waveform at high
frequencies, "clipping" it in a sense.

> > I just found this, too. Some good stuff can be found here:
> > http://paws.kettering.edu/~drussell/Publications/Rossing-
> > Russell-Fork.pdf
>
> It seems to say what I just said about clipping, and also
> there's mode shifting due to the spring constant being
> different at different accelerations (amplitudes).

I was in agreement with you on the clipping - when you talk about the
mode shifting, you mean how you can get the fork into "clang" mode?

-Mike

Mike wrote:

> Which are EOAE's? I though DPOAE's were a subclass of EOAE's.

No, completely different. Look them up.

> This is true, and is apparently actually what leads to DPOAE's
> existing (nonlinear behavior where critical bands interact).

No, I don't think DPOAEs have anything to do with critical
bands. They have to do with the ear drum and associated bones
and stuff. Correct me if I'm wrong.

>>> They occur at the volume range of normal hearing (50-60 dB SPL I
>>> believe is where the test is done), and are considerably lower,
>>> so they don't really have an identity all their own, just serve
>>> to make the sound slightly more concordant and open it up a bit.
>>
>> I don't see how you're getting this.
>
> Because if that's true, then 10:11:12 becomes
> (7:8:9):10:11:12:(13:14:15) in which the tones in parentheses are
> about 1/4-1/5 the volume (if this is where your ears are tuned to
> produce the frequencies at that ratio).

1/5th the amplitude or 1/5 the loudness?

> just enough to add a very subtle effect.

Yes, I think usually pretty subtle.

> > > I just found this, too. Some good stuff can be found here:
> > > http://paws.kettering.edu/~drussell/Publications/Rossing-
> > > Russell-Fork.pdf
> >
> > It seems to say what I just said about clipping, and also
> > there's mode shifting due to the spring constant being
> > different at different accelerations (amplitudes).
>
> I was in agreement with you on the clipping - when you talk
> about the mode shifting, you mean how you can get the fork into
> "clang" mode?

I was just repeating what I read in the linked paper.

-Carl

On Sun, Sep 19, 2010 at 6:24 PM, Carl Lumma <carl@...> wrote:
>
> Mike wrote:
>
> > Which are EOAE's? I though DPOAE's were a subclass of EOAE's.
>
> No, completely different. Look them up.

Alrighty.

> > This is true, and is apparently actually what leads to DPOAE's
> > existing (nonlinear behavior where critical bands interact).
>
> No, I don't think DPOAEs have anything to do with critical
> bands. They have to do with the ear drum and associated bones
> and stuff. Correct me if I'm wrong.

This is something I saw reference to over the place, but see here:

See: http://saha.searle.northwestern.edu/bibcat/pdf/437.pdf

"Nonlinear distortion arises from the action of the cochlear
amplifier producing a wave-related mechanical interaction
on the basilar membrane and depends on inherent
physiological nonlinearities of the cochlear amplifier."

So the distortion occurs on the basilar membrane, and hence it must
occur at the place where the two frequencies interact. This is also
responsible for why f2 is usually lowered, since the interaction is
occuring in the "tail" of f1, so the aim is to equalize them. This is
what I understood while reading, anyway.

> > Because if that's true, then 10:11:12 becomes
> > (7:8:9):10:11:12:(13:14:15) in which the tones in parentheses are
> > about 1/4-1/5 the volume (if this is where your ears are tuned to
> > produce the frequencies at that ratio).
>
> 1/5th the amplitude or 1/5 the loudness?

Loudness, but actually, now that I'm reading this, I realize I'm doing
it wrong. They're 40 dB down, and 10 dB is about a doubling of
loudness. So they're about 1/16 as loud, but there's a lot of them.

-Mike

I wrote:

> > Which are EOAE's? I though DPOAE's were a subclass
> > of EOAE's.
>
> No, completely different. Look them up.
[snip]
> No, I don't think DPOAEs have anything to do with critical
> bands. They have to do with the ear drum and associated
> bones and stuff. Correct me if I'm wrong.

I was wrong, sorry! Yes, DPOAEs are a subclass of EOAEs.
And all OAEs are produced in the inner ear; none in the
middle ear like I said. Specifically, by the action of
outer hair cells and the basilar membrane.

I'm still not clear on the distinction between nonlinear
response and active amplification. It is known that the
outer hair cells are an active system, receiving downward
signals from the brain. It is literally true that when
you're listening for something, your ear is more sensitive
to it (I don't mean to imply this is necessarily under
conscious control, though it may be).

It's funny because I just saw something about this last
week or something. Here it is:

http://arxiv.org/PS_cache/arxiv/pdf/1009/1009.2034v1.pdf

They claim to finally explain how the cochlea achieves the
huge amplification it does. They explain the entire thing
in terms you (Mike) are more likely to understand than me,
but I'm extremely impressed by this paper and suspect it
will become a landmark in the field. The short answer to
my is that the nonlinearity is nonlinearity of the cochlear
amplifier.

> This is something I saw reference to over the place, but see here:
> See: http://saha.searle.northwestern.edu/bibcat/pdf/437.pdf

I think it's safe to say my cite blows this away. :)

> "Nonlinear distortion arises from the action of the cochlear
> amplifier producing a wave-related mechanical interaction
> on the basilar membrane and depends on inherent
> physiological nonlinearities of the cochlear amplifier."

...However it still would have answered my question.

> So the distortion occurs on the basilar membrane,

Not exactly. It (mostly) occurs in the response of the outer
hair cells, due to the limited rate that action potentials can
change (if I understand correctly).

> So they're about 1/16 as loud, but there's a lot of them.

I don't think they're responsible for what you attributed
to them, but I could be wrong.

-Carl

When I went to a gamelan concert, more years ago than I care to think about, the deliberate beating was specifically described and demonstrated (the concert being held at USC, which had a gamelan class). IIRC it was a Balinese gamelan. A fellow musician of mine who spent some time in Indonesia recently verifies that the gamelan indeed do a soft "wagga-wagga-wagga" consistently throughout the concerts.

About JI beating more, I don't understand. Of course "JI" has to be defined, rational intervals can beat like mad. Harrison's American gamelan didn't beat like an Indonesian gamelan (I went to his lectures and demonstrations in the Santa Cruz/Capitola area of course), but the comparison may not be apt, because a gamelan orchestra has two facing sets of instruments which are deliberately tuned to consistently beat. The inherent beating of a single set, spectra contra tuning that is, I don't know.

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> Hi Cameron,
>
> > Gamelan are designed to beat,
>
> Yes, that may very well be true. I know Kraig Grady
> believes this, and both of you probably know more about
> it than me.
>
> However in this case, it's besides the point what they're
> designed to do. The claim was, tuning a gamelan in JI
> should make it beat more. In fact, the American gamelan
> seem to beat less.
>
> -Carl
>

Oh it wobbles alright. I don't get it- is someone saying that it doesn't?

--- In tuning@yahoogroups.com, "Kalle Aho" <kalleaho@...> wrote:
>
>
>
>
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@> wrote:
> >
> > Hi Kalle,
> >
> > > What I'm asking for is the psychoacoustic basis for the warbling
> > > sensation I'm hearing. Why my auditory system detects inharmonicity
> > > (in the guise of this warbling) even if the pitch is clear?
> >
> > Sorry, could you repeat what it is you're listening to?
> >
> > If you really have sines, aren't playing them too loud, and
> > have intervals wider than a critical band, you should not
> > hear warbling.
>
> But I do hear it! I uploaded an example to my files called
> "Warbling". It's 8 seconds of a 220 Hz tone with 6 harmonics and then
> the same with harmonics tuned to 12-equal.
>
> Kalle
>

I see- Carl said sines, not too loud. Your tone has some upper partials, and it does indeed wobble as you say. It's a nice effect, though I think other detunings would be even nicer.

--- In tuning@yahoogroups.com, "cameron" <misterbobro@...> wrote:
>
>
> Oh it wobbles alright. I don't get it- is someone saying that it doesn't?
>
>
> --- In tuning@yahoogroups.com, "Kalle Aho" <kalleaho@> wrote:
> >
> >
> >
> >
> >
> > --- In tuning@yahoogroups.com, "Carl Lumma" <carl@> wrote:
> > >
> > > Hi Kalle,
> > >
> > > > What I'm asking for is the psychoacoustic basis for the warbling
> > > > sensation I'm hearing. Why my auditory system detects inharmonicity
> > > > (in the guise of this warbling) even if the pitch is clear?
> > >
> > > Sorry, could you repeat what it is you're listening to?
> > >
> > > If you really have sines, aren't playing them too loud, and
> > > have intervals wider than a critical band, you should not
> > > hear warbling.
> >
> > But I do hear it! I uploaded an example to my files called
> > "Warbling". It's 8 seconds of a 220 Hz tone with 6 harmonics and then
> > the same with harmonics tuned to 12-equal.
> >
> > Kalle
> >
>

Gene wrote :

> From the Scala archive:
>
> ! hammond12.scl
> !
> Hammond organ scale, 1/1=277.0731707 Hz, A=440, see hammond.scl for > the ratios
> 12
> !
> 5494/5183
> 1435/1278
> 5658/4757
> 984/781
> 1517/1136
> 2009/1420
> 3936/2627
> 451/284
> 2747/1633
> 4428/2485
> 3485/1846
> 2/1

Amazing !!!
These are so complex I can't even figurate out the number of teeth for each note.
All I see is that the denominators are multiples of 71 by 73, 18, 67, 11, 16, 20, 37, 4, 23, 35, 26, and that all numerators are multiple of 41 by 67, 35, 69, 24, 37, 49, 96, 11, 67, 108, 85. And that's only for the first octave.
No way to generate it from one wheel, or the teeth would have been VERY small and the speed very slow !
I guess he used several wheels in gears - ? But why so complex ratios then ?

See in comparison my "one wheel" 12-tet succedaneum, default tuning for Ethno2 :

! synchronous_12.scl
!
Synchronous-beating alternative to 12-ET
12
!
373/352
395/352
419/352
887/704
235/176
249/176
527/352
559/352
37/22
157/88
1329/704
2/1
! 704 746 790 838 887 940 996 1054 1118 1184 1256 1329
! cycle of fourths beats from C:F = 1 2 1 1 2 4 3 6 8 8 8 32

- - - - - - -
Jacques

Cameron wrote:

> About JI beating more, I don't understand. Of course "JI" has
> to be defined, rational intervals can beat like mad.

Rational is not just. Just intonation only includes those
rational numbers which can be represented as fractions of
*small* whole numbers, and which are generally *beatless*
when performed with typical timbres like violins or trumpets
or human voices.

John's idea is that the goal of Indonesian gamelan tuning
is to match the inharmonic timbres of the instruments to
*reduce* beating (Sethares makes this case in his book).
Thus, tuning the gamelan in JI would increase beating.
Except that's not what happened. However that's probably
because the American gamelan I've heard produced timbres
closer to sine tones, due to resonator design. It also
may be the case that gamelan tuning doesn't reduce beating
in the first place.

-Carl

Kalle wrote:

> > If you really have sines, aren't playing them too loud, and
> > have intervals wider than a critical band, you should not
> > hear warbling.
>
> But I do hear it! I uploaded an example to my files called
> "Warbling". It's 8 seconds of a 220 Hz tone with 6 harmonics
> and then the same with harmonics tuned to 12-equal.

Thanks, I hear it too, and yes I think it probably is
combination tones beating against partials. What are you
using to synthesize it? Can you make a version where
the partials come in one by one?

-Carl

On Mon, Sep 20, 2010 at 2:32 AM, Carl Lumma <carl@...> wrote:
>
> I was wrong, sorry! Yes, DPOAEs are a subclass of EOAEs.
> And all OAEs are produced in the inner ear; none in the
> middle ear like I said. Specifically, by the action of
> outer hair cells and the basilar membrane.

I think I'm still confused about the distinction between inner and
outer hair cells. Inner hair cells are the ones that transmit the
information, ultimately, to the brain? As in, where the place theory
is concerned with, where critical bands form, etc? And outer hair
cells simply act as a cochlear amplifier?

> I'm still not clear on the distinction between nonlinear
> response and active amplification.

Well, in an idealized sense: let's say the incoming pressure wave
varies over time with a function f(x). The amplifier takes this value
and spits out a new one for whatever pressure it is fed as input.
Let's say its input-output function is called a(x).

Imagine if for any input, it feeds the same thing as output. This is
hardly an amplifier at all, just a simple unity gain buffer. If you
come up with a graph matching inputs to outputs, where inputs are the
x axis, and outputs are the y axis. Every input value has a unique
output value. Well, (1,1) is going to be a point on the resulting
function, as is (2,2), and (3,3), and so on. In fact, any point on the
line y=x will be there, so the graph will just look like a y=x graph,
a line with slope 1. Which is hardly surprising, since I just defined
the amplification function as output = input. Now let's say I have
output = 2 * input. The graph will look like y=2x, and so on.

Let's now say that I make the input-output function something that is
not a line Like abs(x). This means negative input values become
positive output values, which is a full-wave rectifier. You now have a
"nonlinear" response, which has, as you'd expect, an input-output
function that is not a line. This will end up actually generating new
frequencies at the output in the form of intermodulation distortion
and harmonic distortion. Harmonic distortion is intermodulation
distortion occurring between a tone and itself (e.g. 2f is just the
sum tone of f and f). The true definition of "linearity" just
generalizes this to take into account phase shifts, filtering, etc and
so on, which are still linear. Anything obeying the principle of
superposition is linear.

Now let's say our input-output is something like arctan(x), or
cuberoot(x) so that a huge, range of input values ends up producing a
much smaller range of output values. For arctan(x), there's a finite
output level that is reached as the input level goes to infinity,
since arctan(12031029301923 psi) is pi/2. This would be a
"compressive" nonlinear response, and is actually, in effect, soft
clipping. If you sent a sine into this signal with an amplitude of
1378014371438104380108741, it will just turn into a near-square wave
with an amplitude of pi/2.

Active amplification without introducing nonlinearity, on the other
hand, would be an active "changing" of the input-output function so
that it's no longer a line of slope 1, but a line of slope 8000 when
soft sounds are played, and a line of slope 0.03 when loud sounds are
played. However, if you remember the generalization of linearity I
mentioned before, then it means that linearity doesn't apply here.
This actually is a technically nonlinear system anyway.

Actually, here's a pretty intuitive example of the two I just came up
with: the difference between a nonlinear response and active
amplification is the difference between clipping the waveform at a low
amplitude and putting a compressor on it. Both limit the dynamic range
of the waveform, but in different ways.

> http://arxiv.org/PS_cache/arxiv/pdf/1009/1009.2034v1.pdf
>
> They claim to finally explain how the cochlea achieves the
> huge amplification it does. They explain the entire thing
> in terms you (Mike) are more likely to understand than me,
> but I'm extremely impressed by this paper and suspect it
> will become a landmark in the field. The short answer to
> my is that the nonlinearity is nonlinearity of the cochlear
> amplifier.

In this paper, as I understand it, they are saying that the cochlear
amplification system uses both: on the basilar membrane, at the peak
frequency of the critical band, there's a compressive nonlinearity
distorting the hell out of the hair bundle motion only at moderate
amplitudes. At high amplitudes, this doesn't happen, and at low
amplitudes, it also doesn't happen. This generates a ton of harmonics
as far as the actual motion of the hair cell at that part of the
critical band goes, but those harmonics would have to then reflect off
of the hair and be emitted and received at higher pitches on the
basilar membrane for us to hear them - the movement of a hair cell on
the basilar membrane in a pattern that is not sinusoidal does not, in
and of itself, change the timbre of what we're hearing. We do, but
they're extremely quiet, and this is what DPOAE's are - when you have
a compressive nonlinearity occuring at the peak of a critical band,
and you place another frequency nearby such that this stimulates the
same hair cell too, you have the hair cell being stimulated by two
frequencies and exhibiting behavior and bam, combination tones. The
behavior of the other, more important part of the cochlear amplifier
might enhance this.

This nonlinearity occurs because forces in the ear at the hair cell
literally act to stop the motion of the hair cell if it gets too loud,
but then turn on "completely" to stop it as much as possible once the
signal gets loud enough, and in the middle range, you have a situation
where it's turning on only for the higher pressure values in the same
wave, hence the nonlinear input-output mapping (or "transfer
function"). This doesn't account for the ridiculous gain that is seen
in mammalian cochlear amplification. The new discovery of this paper
seems to be that at the forces acting to constrain the motion of the
hair cell also cause an equal and opposite reaction on the basilar
membrane itself, causing it to vibrate and essentially act as a
speaker re-transmitting the sound. This then causes the hair cells
corresponding to the sound to vibrate, and the individual hair bundles
to contract and try to constrain its motion, which causes the entire
basilar membrane vibrate and emit sound, which stimulates the hair
cells, which make the entire basilar membrane vibrate and emit sounds,
and so on through a very clever feedback mechanism that I want to
immediately replicate and put on an acoustic guitar and sell under the
name "Dobro." It may also explain why sometimes the timbral quality of
a sound becomes "clearer" at lower volumes.

The last thing I see in the paper is that this can be disabled by the
outer hair cells: the outer hair cells are electromotile and can move
in just such a way in response to the incoming waveform so as to
absorb this feedback and nullify the basilar membrane response. They
can apparently do this in a way that is frequency selective and
nullifies high frequencies, thus making the basilar membrane more
susceptible to feedback low frequencies.

That's what I got out of it, anyway. So DPOAE's occur at the critical
band, the basilar membrane acts as a dobro guitar, outer hair cells
serve to NULLIFY the feedback at the basilar membrane, and this
feedback is occuring at the nonlinear range where hair bundle forces
compressing the signal at the critical band (where DPOAE's are
generated) are in sync with the waveform itself, causing the basilar
membrane to occur. Damn, that is complicated.

-Mike

Mike wrote:

> I think I'm still confused about the distinction between inner and
> outer hair cells. Inner hair cells are the ones that transmit the
> information, ultimately, to the brain?

Yep.

> As in, where the place theory is concerned with, where critical
> bands form, etc? And outer hair cells simply act as a cochlear
> amplifier?

Pretty much.

> which causes the entire
> basilar membrane vibrate and emit sound, which stimulates the hair
> cells, which make the entire basilar membrane vibrate and emit
> sounds, and so on through a very clever feedback mechanism that
> I want to immediately replicate and put on an acoustic guitar and
> sell under the name "Dobro."

Heh, interesting connection. I suppose all hollow body
electrics get their sustain from a similar mechanism.

-Carl

On Mon, Sep 20, 2010 at 5:19 AM, Carl Lumma <carl@...> wrote:
>
> > As in, where the place theory is concerned with, where critical
> > bands form, etc? And outer hair cells simply act as a cochlear
> > amplifier?
>
> Pretty much.

Yes, but after all of the reading I just did, it seems they actually
take the opposite role. Or at least that's what this new paper says.
The outer hair cells form a "ratchet" mechanism, as I understand it
(http://arxiv.org/PS_cache/arxiv/pdf/1003/1003.5557v1.pdf) that acts
as a damper for this basilar membrane feedback mechanism. The hair
bundle forces acting on inner hair cells to compress the amplitude
response at the peak of the critical band are what transmit the motion
back to the basilar membrane, which the outer hair cells either
disable by absorbing the brunt of that force, or don't interfere with
and allow to feed back.

> Heh, interesting connection. I suppose all hollow body
> electrics get their sustain from a similar mechanism.

Ha. Yes.

-Mike

I guess you heard Harrison's American Gamelan at Mills? The other one is at Harvard these days. The one I've heard is darn boingy-mellow, a far cry from the thick metallic tropical sounds.

As a side note, I played a Harrison guitar piece in a student ensemble, on regular 12-tET guitars, and the feel of the piece was very similar to his Just works- so, I think it's fair to say he had his own thing going compositionally, probably more important to him than specific tunings.

Anyway, it's entirely possible that one set in the gamelan really is tuned to reduce beating, that is, Just in terms of altered partials, as Sethares says. For the deliberate beating that I heard demonstrated and explained was the beating of one set against the other. Lessee...

from Wikipedia:
"Balinese gamelan instruments are commonly played in pairs which are tuned slightly apart to produce interference beats, ideally at a consistent speed for all pairs of notes in all registers. It is thought that this contributes to the very "busy" and "shimmering" sound of gamelan ensembles. In the religious ceremonies that contain gamelan, these interference beats are meant to give the listener a feeling of a god's presence or a stepping stone to a meditative state."

This is exactly what I learned and experienced. Some might say that "Stepping stone to a meditative state" is quite similar to bogeying a goodly portion of a Thai stick and putting "Crimson in Clover" on endless repeat... BTW I wasn't referring to the student ensemble, in which my girlfriend at the time played, but to visiting musicians from Bali. Could have been playing the USC instruments though.

Regardless: lots of beating, yes.

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> Cameron wrote:
>
> > About JI beating more, I don't understand. Of course "JI" has
> > to be defined, rational intervals can beat like mad.
>
> Rational is not just. Just intonation only includes those
> rational numbers which can be represented as fractions of
> *small* whole numbers, and which are generally *beatless*
> when performed with typical timbres like violins or trumpets
> or human voices.
>
> John's idea is that the goal of Indonesian gamelan tuning
> is to match the inharmonic timbres of the instruments to
> *reduce* beating (Sethares makes this case in his book).
> Thus, tuning the gamelan in JI would increase beating.
> Except that's not what happened. However that's probably
> because the American gamelan I've heard produced timbres
> closer to sine tones, due to resonator design. It also
> may be the case that gamelan tuning doesn't reduce beating
> in the first place.
>
> -Carl
>

Here is exact description how it is done:

http://b3world.com/hammond-techinfo.html

http://www.electricdruid.net/index.php?page=info.hammond

Yes, it's amazing.

Daniel Forro

On 20 Sep 2010, at 5:23 PM, Jacques Dudon wrote:

>
>
> Gene wrote :
>
>> From the Scala archive:
>>
>> ! hammond12.scl
>> !
>> Hammond organ scale, 1/1=277.0731707 Hz, A=440, see hammond.scl >> for the ratios
>> 12
>> !
>> 5494/5183
>> 1435/1278
>> 5658/4757
>> 984/781
>> 1517/1136
>> 2009/1420
>> 3936/2627
>> 451/284
>> 2747/1633
>> 4428/2485
>> 3485/1846
>> 2/1
>
>
> Amazing !!!
> These are so complex I can't even figurate out the number of teeth > for each note.
> All I see is that the denominators are multiples of 71 by 73, 18, > 67, 11, 16, 20, 37, 4, 23, 35, 26, and that all numerators are > multiple of 41 by 67, 35, 69, 24, 37, 49, 96, 11, 67, 108, 85. And > that's only for the first octave.
> No way to generate it from one wheel, or the teeth would have been > VERY small and the speed very slow !
> I guess he used several wheels in gears - ? But why so complex > ratios then ?
>
> See in comparison my "one wheel" 12-tet succedaneum, default tuning > for Ethno2 :
>
> ! synchronous_12.scl
> !
> Synchronous-beating alternative to 12-ET
> 12
> !
> 373/352
> 395/352
> 419/352
> 887/704
> 235/176
> 249/176
> 527/352
> 559/352
> 37/22
> 157/88
> 1329/704
> 2/1
> ! 704 746 790 838 887 940 996 1054 1118 1184 1256 1329
> ! cycle of fourths beats from C:F = 1 2 1 1 2 4 3 6 8 8 > 8 32
>
> - - - - - - -
> Jacques

> a gamelan orchestra has two facing sets of instruments which are deliberately tuned to consistently beat. The inherent beating of a single set, spectra contra tuning that is, I don't know.

Sethares (I'm pretty sure) analyzed both sets of gamelan tunings and then found the dissonance curves to match up best with the tunings when they were crossed with harmonic timbres, not just the other instruments. The instruments beat very interestingly together, but each is at a dissonance minimum with its tuning when played in combination with the few harmonic timbres used in those ensembles like the voice and some bowed instruments. I'm not really sure if this is a good responses to your post, but it seemed relevant.

John

--- In tuning@yahoogroups.com, "cameron" <misterbobro@...> wrote:
>
> I guess you heard Harrison's American Gamelan at Mills?

I don't think I've ever heard gamelan at Mills actually.
I saw Harrison, along with one (IIRC) of his instruments,
at SJ State. I also heard some stuff at Claremont college,
from Bill Alves students I think. But mostly recordings
from the JI Network days. American Gamelan is kinda dead.

> The other one is at Harvard these days. The one I've heard
> is darn boingy-mellow, a far cry from the thick metallic
> tropical sounds.

Yes. It sounds like they get pretty close to sines.

> from Wikipedia:
> "Balinese gamelan instruments are commonly played in pairs
> which are tuned slightly apart to produce interference beats,
> ideally at a consistent speed for all pairs of notes in all
> registers. It is thought that this contributes to the very
> "busy" and "shimmering" sound of gamelan ensembles. In the
> religious ceremonies that contain gamelan, these interference
> beats are meant to give the listener a feeling of a god's
> presence or a stepping stone to a meditative state."
>
> This is exactly what I learned and experienced.

Ok, thanks. Lots of theories on this stuff, and I never
believe more than half of any one of them. But if I can
get Cam + Wiki the same day, that's something.

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> Kalle wrote:
>
> > > If you really have sines, aren't playing them too loud, and
> > > have intervals wider than a critical band, you should not
> > > hear warbling.
> >
> > But I do hear it! I uploaded an example to my files called
> > "Warbling". It's 8 seconds of a 220 Hz tone with 6 harmonics
> > and then the same with harmonics tuned to 12-equal.
>
> Thanks, I hear it too, and yes I think it probably is
> combination tones beating against partials. What are you
> using to synthesize it? Can you make a version where
> the partials come in one by one?

Done. It's called "Warbling2". I used Goldwave, I'm pretty good with
its' Expression Evaluator. :)

Kalle

--- In tuning@yahoogroups.com, "cameron" <misterbobro@...> wrote:
>
> I see- Carl said sines, not too loud. Your tone has some upper
> partials, and it does indeed wobble as you say. It's a nice effect,
> though I think other detunings would be even nicer.

No doubt they would. I wasn't trying to produce a nice effect, in fact
I find it a bit annoying. The question is why does it wobble?

It's 6 sines at a 1:2:2^(19/12):4:2^(28/12):2^(31/12) relationship.
The frequency of 1 is 220 Hz. The relative amplitudes are
1, 5/12, 2/9, 1/8, 1/15, 1/36 which come from the pattern
1/1*(6/6), 1/2*(5/6), 1/3*(4/6), 1/4*(3/6), 1/5*(2/6), 1/6*(1/6).

Now none of the frequencies are within the same critical bandwidth so
there shouldn't be any beating in the usual sense. So why do we hear
it?

Kalle

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:

>
> > from Wikipedia:
> > "Balinese gamelan instruments are commonly played in pairs
> > which are tuned slightly apart to produce interference beats,
> > ideally at a consistent speed for all pairs of notes in all
> > registers. It is thought that this contributes to the very
> > "busy" and "shimmering" sound of gamelan ensembles. In the
> > religious ceremonies that contain gamelan, these interference
> > beats are meant to give the listener a feeling of a god's
> > presence or a stepping stone to a meditative state."
> >
> > This is exactly what I learned and experienced.
>
> Ok, thanks. Lots of theories on this stuff, and I never
> believe more than half of any one of them. But if I can
> get Cam + Wiki the same day, that's something.
>
> -Carl
>

Could be just Bali- and even just one region of Bali, for all we know. If I get to Indonesia (we have art/music partners in Indonesia and the Phillipines) I'll surely make a point of listening for this.

-Cameron

On 20 September 2010 23:10, John Moriarty <JlMoriart@...> wrote:

> Sethares (I'm pretty sure) analyzed both sets of gamelan tunings and then
> found the dissonance curves to match up best with the tunings when they
> were crossed with harmonic timbres, not just the other instruments. The
> instruments beat very interestingly together, but each is at a dissonance
> minimum with its tuning when played in combination with the few harmonic
> timbres used in those ensembles like the voice and some bowed instruments.
> I'm not really sure if this is a good responses to your post, but it seemed
> relevant.

I don't have the reference here, but here's how I remember it:
Sethares analyzed the timbre of one type of instrument (sarong?),
crossed it with standard harmonic timbres, and showed that 9 note
equal temperament was a good tuning for minimizing dissonance.
There's a great variability of gamelan tunings. You'll have to check
the book to see if those tuning changes tracked the timbres.

Note that this thread's fallen into the fallacy of assuming minimizing
dissonance is the same as minimizing beating. That isn't true. You
can say that JI minimizes beats. Dissonance is caused by roughness,
which is what you get when beats get faster than a certain frequency
(about 15 Hz). Minimizing dissonance with a temperament is generally
about getting clashes out of the roughness region and into the beating
region. You shouldn't be surprised if a temperament beats. But
strong, coherent beats will still likely come from mistuned unisons,
as widely reported with gamelans.

Graham

Oh, almost forgot: one thing we can take as granted is that detailed, consistent specifics of tuning and spectra are NOT a defining characteristic of "gamelan". Gamelan percussion is also made of wood and bamboo; these far less expensive gamelan being within the means of villages, it is probably safe to assume that they constitute a majority. Therefore any universal statements about "gamelan" based on analysis of spectra of metal gamelan would almost certainly be false.

--- In tuning@yahoogroups.com, "cameron" <misterbobro@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@> wrote:
>
> >
> > > from Wikipedia:
> > > "Balinese gamelan instruments are commonly played in pairs
> > > which are tuned slightly apart to produce interference beats,
> > > ideally at a consistent speed for all pairs of notes in all
> > > registers. It is thought that this contributes to the very
> > > "busy" and "shimmering" sound of gamelan ensembles. In the
> > > religious ceremonies that contain gamelan, these interference
> > > beats are meant to give the listener a feeling of a god's
> > > presence or a stepping stone to a meditative state."
> > >
> > > This is exactly what I learned and experienced.
> >
> > Ok, thanks. Lots of theories on this stuff, and I never
> > believe more than half of any one of them. But if I can
> > get Cam + Wiki the same day, that's something.
> >
> > -Carl
> >
>
> Could be just Bali- and even just one region of Bali, for all we know. If I get to Indonesia (we have art/music partners in Indonesia and the Phillipines) I'll surely make a point of listening for this.
>
> -Cameron
>

Gentlemen,

--- In tuning@yahoogroups.com, "cameron" <misterbobro@...> wrote:
> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@> wrote:
> > Ok, thanks. Lots of theories on this stuff, and I never
> > believe more than half of any one of them. But if I can
> > get Cam + Wiki the same day, that's something.
>
> Could be just Bali- and even just one region of Bali, for all we know. If I get to Indonesia (we have art/music partners in Indonesia and the Phillipines) I'll surely make a point of listening for this.

One of the true mentors of my life, Danlee Mitchell, has spent the last 10+ years pretty deeply immersed in the music and arts of Bali (and, to a somewhat lesser extent, Java), spending a good part of each summer there. (Those of you familiar with the life of composer Harry Partch may also recognize Mitchell from his long-time association with Partch) I'll ask him what he knows and has studied and asked about the pairs tunings in these instruments/orchestras. If I get any worthwhile info (beyond what Cam has mentioned) I'll post it back here.

BTW, he has done some *incredible* documentation of performances over there, most recently with 3-camera shoots. The videos are remarkable, and he swears he's going to make them available some day. I hope!

Cheers,
Jon

Kalle wrote:

> Done. It's called "Warbling2". I used Goldwave, I'm pretty
> good with its' Expression Evaluator. :)

Goldwave, what a blast from the past. I didn't know it had
an expression evaluator. :)

> It's 6 sines at a 1:2:2^(19/12):4:2^(28/12):2^(31/12)
> relationship.
> The frequency of 1 is 220 Hz. The relative amplitudes are
> 1, 5/12, 2/9, 1/8, 1/15, 1/36

I don't hear as much warbling this time. I also don't hear
it much until the 3rd partial enters (the first tempered
partial). Whatever it is, it seems it's in the file. It's
apparently visible in the waveform display starting when
the 3rd partial enters.

I synthesized the first 5 partials in Adobe Audition 3 and
got much the same result. Actually the warbling is slightly
less intense, sounding almost like phase rotation or
something.

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> Kalle wrote:
>
> > Done. It's called "Warbling2". I used Goldwave, I'm pretty
> > good with its' Expression Evaluator. :)
>
> Goldwave, what a blast from the past. I didn't know it had
> an expression evaluator. :)
>
> > It's 6 sines at a 1:2:2^(19/12):4:2^(28/12):2^(31/12)
> > relationship.
> > The frequency of 1 is 220 Hz. The relative amplitudes are
> > 1, 5/12, 2/9, 1/8, 1/15, 1/36
>
> I don't hear as much warbling this time. I also don't hear
> it much until the 3rd partial enters (the first tempered
> partial).

It would be weird if you did hear warbling before that.

The first time I listened to it I noticed the warbling even more. In
fact I had to compare the files to see if there was a difference
in the amplitudes but there wasn't.

> Whatever it is, it seems it's in the file. It's
> apparently visible in the waveform display starting when
> the 3rd partial enters.

What do you mean it's in the file?

Yes, there's a waveform display in Goldwave too and the changes in
the waveform nicely match what I'm hearing.

> I synthesized the first 5 partials in Adobe Audition 3 and
> got much the same result. Actually the warbling is slightly
> less intense, sounding almost like phase rotation or
> something.

But isn't the warbling some kind of phase rotation as the relative
phases between partials are changing?

As you seem to imply that phase rotation has a sound i.e. sounds a
certain way, are you saying we are able to hear it directly (not
through the beating of combination tones or something else)?

At the start of this thread I claimed that the pitch sensation is
robust and it is in the sense that there is only one pitch. But on
the other hand I'm now actually hearing a slight wobble in pitch.

Kalle

Hi Kalle,

> > Whatever it is, it seems it's in the file. It's
> > apparently visible in the waveform display starting when
> > the 3rd partial enters.
>
> What do you mean it's in the file?
> Yes, there's a waveform display in Goldwave too and the changes in
> the waveform nicely match what I'm hearing.

I mean, since the waveform display shows it, it is
probably not combination tones.

> > I synthesized the first 5 partials in Adobe Audition 3 and
> > got much the same result. Actually the warbling is slightly
> > less intense, sounding almost like phase rotation or
> > something.
>
> But isn't the warbling some kind of phase rotation as the
> relative phases between partials are changing?

Sounds right.

> As you seem to imply that phase rotation has a sound i.e. sounds a
> certain way, are you saying we are able to hear it directly (not
> through the beating of combination tones or something else)?

Static phase relations are not distinguishable, but changing
phase relations are definitely audible.

> At the start of this thread I claimed that the pitch sensation is
> robust and it is in the sense that there is only one pitch. But on
> the other hand I'm now actually hearing a slight wobble in pitch.

That I do not hear.

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:

> > As you seem to imply that phase rotation has a sound i.e. sounds a
> > certain way, are you saying we are able to hear it directly (not
> > through the beating of combination tones or something else)?
>
> Static phase relations are not distinguishable, but changing
> phase relations are definitely audible.

Is this the phenomenon of second-order beats?

> > At the start of this thread I claimed that the pitch sensation is
> > robust and it is in the sense that there is only one pitch. But on
> > the other hand I'm now actually hearing a slight wobble in pitch.
>
> That I do not hear.

Well, that's interesting. There's some fluctuation in loudness too and
this could explain the pitch change as I tend to hear a slight pitch
change with the variation of loudness when listening to relatively
simple tones composed of only a few sinusoids.

Kalle

Kalle wrote:

> > Static phase relations are not distinguishable, but changing
> > phase relations are definitely audible.
>
> Is this the phenomenon of second-order beats?

I don't know. But I've twisted the phase knob myself and
heard it. I wish I understood this phenomenon better. -Carl

On Wed, Sep 22, 2010 at 4:02 PM, Carl Lumma <carl@...> wrote:
>
> Kalle wrote:
>
> > > Static phase relations are not distinguishable, but changing
> > > phase relations are definitely audible.
> >
> > Is this the phenomenon of second-order beats?
>
> I don't know. But I've twisted the phase knob myself and
> heard it. I wish I understood this phenomenon better. -Carl

In general, people can hear phase differences in two areas:
1) When the slope of frequency v phase isn't linear across the
frequency spectrum vs a signal in which it is
2) When you start to introduce something like phase modulation, which
is what you're talking about

1 is the reason why an impulse, a sine sweep, and white noise sound
completely different, despite having the same magnitude response, but
a signal sounds the same if you phase shift everything by 90 degrees.

2 is kind of cheating, because as you know the "phase" of a wave is
always changing anyway - the phase just means the current position
that you're at in the sine wave. That is, frequency is the constant
rate at which the phase is changing (in radians per second, or Hz, or
something).

So if you start slowly turning a phase knob to slowly add your own
additional offset, you're effectively increasing the frequency of the
sine wave (and if you change it in a discontinuous way, you'll add
some high frequencies as it "jumps"). If you turn the knob to the
right, and then you stop, although the absolute phase has been
altered, the constant phase increment will stop, and the frequency
will go back down. Since nobody has the ability to do this with a
steady hand and can turn the phase knob at an exact, precise, constant
rate, it will instead just sound like the pitch is wobbling a bit
and/or changing in timbre if discontinuities are introduced. And the
pitch wobbling can cause flanging effects as partials start to collide
and such.

-Mike

There some connection with the fact why Yamaha FM (Frequency Modulation) synthesis is in reality PM (Phase Modulation).

Daniel Forro

On 23 Sep 2010, at 12:43 PM, Mike Battaglia wrote:
> That is, frequency is the constant
> rate at which the phase is changing (in radians per second, or Hz, or
> something).

Mike wrote:

> So if you start slowly turning a phase knob to slowly add your own
> additional offset, you're effectively increasing the frequency of
> the sine wave (and if you change it in a discontinuous way, you'll
> add some high frequencies as it "jumps"). If you turn the knob to
> the right, and then you stop, although the absolute phase has been
> altered, the constant phase increment will stop, and the frequency
> will go back down. Since nobody has the ability to do this with a
> steady hand and can turn the phase knob at an exact, precise,
> constant rate, it will instead just sound like the pitch is wobbling
> a bit and/or changing in timbre if discontinuities are introduced.
> And the pitch wobbling can cause flanging effects as partials start
> to collide and such.

Ok thanks, that makes sense. -C.

In my poor knowledge flanging effect is caused by mixing of direct and identical but delayed signal, where the delay time (usually less than 20 msec) is changed (manually, by envelope or by periodic modulation). I hear for the first time that it can be made by "pitch wobbling" where "partials start to collide and such".

Daniel Forro

On 23 Sep 2010, at 12:43 PM, Mike Battaglia wrote:
> And the
> pitch wobbling can cause flanging effects as partials start to collide
> and such.

On Thu, Sep 23, 2010 at 1:30 AM, Daniel Forró <dan.for@...> wrote:
>
> There some connection with the fact why Yamaha FM (Frequency
> Modulation) synthesis is in reality PM (Phase Modulation).

Right, yes. This is something I actually need to read up on again; I
don't remember exactly what I learned. Basically, the idea is that it
is they end up being the same thing (since phase and frequency are
connected by an integral), but that from a computational standpoint
it's far easier to deal with modulating the phase than the frequency
if the oscillators are digital and/or wavetables are involved.

On Thu, Sep 23, 2010 at 4:30 AM, Daniel Forró <dan.for@tiscali.cz> wrote:
>
> In my poor knowledge flanging effect is caused by mixing of direct
> and identical but delayed signal, where the delay time (usually less
> than 20 msec) is changed (manually, by envelope or by periodic
> modulation). I hear for the first time that it can be made by "pitch
> wobbling" where "partials start to collide and such".

I meant "flanging" in just a rough sense, but if you want to get into
concept - right, the delay time is being changed. A constant change in
delay time is also equivalent to a change in frequency. That is, if
you keep decreasing the delay of a signal at a constant rate, that's
the same thing as just playing it more slowly (and hence decreasing
the pitch slightly).

So a flanger takes a signal and copies it, and then keeps modulating
the delay time of the second sample. This means that the second sample
is going to be played at a slower speed briefly as it keeps getting
delayed and delayed at a constant rate, and then once it reaches some
maximum deviation it's going to be played at a faster rate to catch
back up (this is a negative delay), and then so on.

However, maybe it doesn't make sense to call it a "flanger" if you
just modulate the phase of a single note and not double the original.
The point is you're going to hear weird sorts of effects happening as
partials drift in and out of tune with one another, which may very
well sound something like a flanger (or perhaps a phaser).

-Mike