To Carl.

The electro-magnetic spectrum consists of more than just light waves.
There are also X-rays, ultraviolet, infrared, radio waves etc. These
are all wavelike energy manifestations which can be described in
frequencies and thus ratios and cents if some sort of accuracy can be
established. Since they are all grouped together in one spectrum it is
possible that some sort of octave equivalence occurs. And if octaves
occur in the electro-magnetic spectrum then other musical phenomena
might also occur.

The answer is yes.

there is equivalence in everything but the medium and out ability to
experience it

On Sat, Jun 21, 2008 at 12:48 PM, robert thomas martin <
robertthomasmartin@...> wrote:

> The electro-magnetic spectrum consists of more than just light waves.
> There are also X-rays, ultraviolet, infrared, radio waves etc. These
> are all wavelike energy manifestations which can be described in
> frequencies and thus ratios and cents if some sort of accuracy can be
> established. Since they are all grouped together in one spectrum it is
> possible that some sort of octave equivalence occurs. And if octaves
> occur in the electro-magnetic spectrum then other musical phenomena
> might also occur.
>
>
>

[Non-text portions of this message have been removed]

At 09:48 AM 6/21/2008, you wrote:
>The electro-magnetic spectrum consists of more than just light waves.
>There are also X-rays, ultraviolet, infrared, radio waves etc. These
>are all wavelike energy manifestations which can be described in
>frequencies and thus ratios and cents if some sort of accuracy can be
>established. Since they are all grouped together in one spectrum it is
>possible that some sort of octave equivalence occurs.

How could there be "octave equivalence" of phenomena humans
can't even perceive?
There are many differences between light and sound. Sound is
longitudinal waves in air. EM is transverse waves in the
electromagnetic field. Therefore it's little surprise that
vision and hearing are also quite different. So while I think
it's a neat idea, I don't think it's likely to be a fertile
direction. Of course if you investigate and come up with
something interesting you will prove me wrong!

-Carl

visible light is perceived just short of an octave....

where is violet heading if not red?

On Sat, Jun 21, 2008 at 12:59 PM, Carl Lumma <carl@...> wrote:

> At 09:48 AM 6/21/2008, you wrote:
> >The electro-magnetic spectrum consists of more than just light waves.
> >There are also X-rays, ultraviolet, infrared, radio waves etc. These
> >are all wavelike energy manifestations which can be described in
> >frequencies and thus ratios and cents if some sort of accuracy can be
> >established. Since they are all grouped together in one spectrum it is
> >possible that some sort of octave equivalence occurs.
>
> How could there be "octave equivalence" of phenomena humans
> can't even perceive?
> There are many differences between light and sound. Sound is
> longitudinal waves in air. EM is transverse waves in the
> electromagnetic field. Therefore it's little surprise that
> vision and hearing are also quite different. So while I think
> it's a neat idea, I don't think it's likely to be a fertile
> direction. Of course if you investigate and come up with
> something interesting you will prove me wrong!
>
> -Carl
>
>
>

[Non-text portions of this message have been removed]

Hi Chris,

At 09:57 AM 6/21/2008, you wrote:
>The answer is yes.
>
>there is equivalence in everything but the medium and out ability to
>experience it

Octave "equivalence" is a psychoacoustic phenomenon. There is
no "equivalence" in sound, it is in the human mind. Therefore
it follows there is no similar equivalence in EM radiation that
we cannot perceive.

-Carl

I am saying that the mathematical techniques used for EM radiation apply

for example http://en.wikipedia.org/wiki/Fourier_transform

this has applications in many places.... not just sound and vise versa

On Sat, Jun 21, 2008 at 1:08 PM, Carl Lumma <carl@...> wrote:

> Hi Chris,
>
> At 09:57 AM 6/21/2008, you wrote:
> >The answer is yes.
> >
> >there is equivalence in everything but the medium and out ability to
> >experience it
>
> Octave "equivalence" is a psychoacoustic phenomenon. There is
> no "equivalence" in sound, it is in the human mind. Therefore
> it follows there is no similar equivalence in EM radiation that
> we cannot perceive.
>
> -Carl
>
>
>

[Non-text portions of this message have been removed]

At 10:16 AM 6/21/2008, you wrote:
>I am saying that the mathematical techniques used for EM radiation apply
>
>for example http://en.wikipedia.org/wiki/Fourier_transform

The Fourier transform is a generic time-domain transform. So?

-Carl

your "so" indicates agreement that the math applies to frequencies
regardless of medium?

we are limited by perception, yes.

but that can be enhanced by electronics

On Sat, Jun 21, 2008 at 1:19 PM, Carl Lumma <carl@...> wrote:

> At 10:16 AM 6/21/2008, you wrote:
> >I am saying that the mathematical techniques used for EM radiation apply
> >
> >for example http://en.wikipedia.org/wiki/Fourier_transform
>
> The Fourier transform is a generic time-domain transform. So?
>
> -Carl
>
>
>

[Non-text portions of this message have been removed]

On Sat, Jun 21, 2008 at 11:22 AM, Chris Vaisvil <chrisvaisvil@...> wrote:
> your "so" indicates agreement that the math applies to frequencies
> regardless of medium?
>
> we are limited by perception, yes.
>
> but that can be enhanced by electronics

Chris, did you read my post about nonlinearity? I could also have used
the argument that the spectral resolution of the eye is much lower
than that of the ear, but I intentionally didn't mention that because
of this objection. The linear-vs-nonlinear thing, however, you can't
really argue with.

Keenan

I'm not sure what you mean about nonlinearity in this context - I perhaps
missed the post

my point is that the math applies across the medium - acoustic -
electromagnetic

if you are saying that ears don't see like eyes..... ????

perception and math are two different things.

On Sat, Jun 21, 2008 at 1:32 PM, Keenan Pepper <keenanpepper@...>
wrote:

> On Sat, Jun 21, 2008 at 11:22 AM, Chris Vaisvil <chrisvaisvil@...<chrisvaisvil%40gmail.com>>
> wrote:
> > your "so" indicates agreement that the math applies to frequencies
> > regardless of medium?
> >
> > we are limited by perception, yes.
> >
> > but that can be enhanced by electronics
>
> Chris, did you read my post about nonlinearity? I could also have used
> the argument that the spectral resolution of the eye is much lower
> than that of the ear, but I intentionally didn't mention that because
> of this objection. The linear-vs-nonlinear thing, however, you can't
> really argue with.
>
> Keenan
>
>

[Non-text portions of this message have been removed]

On Sat, Jun 21, 2008 at 11:39 AM, Chris Vaisvil <chrisvaisvil@...> wrote:
> I'm not sure what you mean about nonlinearity in this context - I perhaps
> missed the post

I think you did. It's in the thread "Electro-magnetic spectrum and
Microtonality?". Why do people keep starting different threads about
the same topic?

> my point is that the math applies across the medium - acoustic -
> electromagnetic
>
> if you are saying that ears don't see like eyes..... ????
>
> perception and math are two different things.

These statements seem vacuous to me.

Keenan

I answered that post....

Any equation that deals with frequency is going to apply

Einstein, whomever, doesn't matter

"Most acoustic systems are essentially nonlinear. That is, if I play
two sine waves at one end of a room, and you listen at the other end
of the room, you will hear not only the two original pitches, but also
difference tones (and harmonics) that are generated spontaneously.
This happens because the acoustic response of the room is nonlinear.
This nonlinearity makes most intervals beat, and the only intervals
that don't beat are simple rational numbers."

light does interfere under certain conditions

.....what of the dual slit experiment?

Room acoustics is not going to generate a new pitch, i.e. harmonics.

phase differences I can see.

and -no- interval would be without beating or harmonics if your proposition
was correct.

in fact a pure sine wave should be impossible to obtain.

On Sat, Jun 21, 2008 at 1:50 PM, Keenan Pepper <keenanpepper@...>
wrote:

> On Sat, Jun 21, 2008 at 11:39 AM, Chris Vaisvil <chrisvaisvil@...<chrisvaisvil%40gmail.com>>
> wrote:
> > I'm not sure what you mean about nonlinearity in this context - I perhaps
> > missed the post
>
> I think you did. It's in the thread "Electro-magnetic spectrum and
> Microtonality?". Why do people keep starting different threads about
> the same topic?
>
> > my point is that the math applies across the medium - acoustic -
> > electromagnetic
> >
> > if you are saying that ears don't see like eyes..... ????
> >
> > perception and math are two different things.
>
> These statements seem vacuous to me.
>
> Keenan
>
>

[Non-text portions of this message have been removed]

In many ways you are complete correct. Waves are waves and regardless
of the medium follow common rules.

Keep in mind however that octave equivalence is a property of the ear
and mind, not of the sound itself. It happens when a sound detector
hears some equivalence between one frequency and double that
frequency. This usually means the detector is at least in part a tuned
resonator. The sound waves pretty much ignore each other while they
travel through the air. The comparison and connection happens in the
ear. Most of the musical properties we know (consonance etc) happen
because of how we perceive sound.

To paraphrase if a symphony is played in the forest and there is no
one to hear it there is no music. Music is largely a matter of
perception.

If you want to find equivalence in other spectra you need to think
about how it would eventually be perceived. One simplistic possibility
would be to translate it to sound. According to wikapedia the eye sees
from 400–790 terahertz which is less than an octave so by definition
there will not be octave equivalence in what we see. Also the
detectors in the eye are not based on resonant coupling, at least not
the way we tend to think of it, However we could easily translate
certain frequencies of light into certain frequencies of sound and
then listen to the result

The eye is a much less sophisticated sensor than the ear. The ear can
not only hear over 9 octaves but it can distinguish between
frequencies only a few cents apart. This is a simplification but the
eye basically has two color sensors covering two frequency ranges
with a substantial overlap. The three primary colors are basically:
sensor one sees something, sensor two sees something. both sensors see
something. All other colors are sort of in between these three. As I
said this is a simplification.

On Sat, Jun 21, 2008 at 12:48 PM, robert thomas martin
<robertthomasmartin@...> wrote:
> The electro-magnetic spectrum consists of more than just light waves.
> There are also X-rays, ultraviolet, infrared, radio waves etc. These
> are all wavelike energy manifestations which can be described in
> frequencies and thus ratios and cents if some sort of accuracy can be
> established. Since they are all grouped together in one spectrum it is
> possible that some sort of octave equivalence occurs. And if octaves
> occur in the electro-magnetic spectrum then other musical phenomena
> might also occur.
>
>

--
Steve Morris
barbershopsteve@...
Bass: Boston Wailers
Bass: Sounds Of Concord
Motto: Old age and treachery will always prevail over youth and skill

Chris,

To say "Most acoustic systems are essentially nonlinear" is
technically correct but it begs the point a little. Even though
acoustics has lots of non-linearities in it acoustics is linear to
more than a first approximation. The non-linearities cause only subtle
second or third order effects. You would be more accurate to say

"Most acoustic systems are essentially linear but there are minor
non-linear effects that must be considered."

You can go a long ways and be quite productive pretending that
acoustics is linear because most of it is.

This is similar to the issue of the period of a pendulum. Pendulums
were used for years for high accuracy clocks because "they have the
same period no matter how high they swing." Many of us were taught
this in school. Unfortunately it is not true except as a first
approximation. Pendulums are accurate time keepers only if you keep
them swinging by a roughly constant amount which rule all good
mechanical clock designs enforce. So pendulums are actually non linear
but you can make them appear linear if you use them in constrained
circumstances.

Audio is the same. The non linearities are there but usually you can
ignore them.

By the way the worst non-linearities in music come from non-linear
electronics, not from non-linear acoustical systems. The worst
culprits are microphones and pre-amps.

On Sat, Jun 21, 2008 at 2:14 PM, Chris Vaisvil <chrisvaisvil@...> wrote:
> I answered that post....
>
> Any equation that deals with frequency is going to apply
>
> Einstein, whomever, doesn't matter
>
> "Most acoustic systems are essentially nonlinear. That is, if I play
> two sine waves at one end of a room, and you listen at the other end
> of the room, you will hear not only the two original pitches, but also
> difference tones (and harmonics) that are generated spontaneously.
> This happens because the acoustic response of the room is nonlinear.
> This nonlinearity makes most intervals beat, and the only intervals
> that don't beat are simple rational numbers."
>
> light does interfere under certain conditions
>
> .....what of the dual slit experiment?
>
> Room acoustics is not going to generate a new pitch, i.e. harmonics.
>
> phase differences I can see.
>
> and -no- interval would be without beating or harmonics if your proposition
> was correct.
>
> in fact a pure sine wave should be impossible to obtain.
>
> On Sat, Jun 21, 2008 at 1:50 PM, Keenan Pepper <keenanpepper@...>
> wrote:
>
>> On Sat, Jun 21, 2008 at 11:39 AM, Chris Vaisvil
>> <chrisvaisvil@...<chrisvaisvil%40gmail.com>>
>
>> wrote:
>> > I'm not sure what you mean about nonlinearity in this context - I
>> > perhaps
>> > missed the post
>>
>> I think you did. It's in the thread "Electro-magnetic spectrum and
>> Microtonality?". Why do people keep starting different threads about
>> the same topic?
>>
>> > my point is that the math applies across the medium - acoustic -
>> > electromagnetic
>> >
>> > if you are saying that ears don't see like eyes..... ????
>> >
>> > perception and math are two different things.
>>
>> These statements seem vacuous to me.
>>
>> Keenan
>>
>>
>
> [Non-text portions of this message have been removed]
>
>

--
Steve Morris
barbershopsteve@...
Bass: Boston Wailers
Bass: Sounds Of Concord
Motto: Old age and treachery will always prevail over youth and skill

Steve Morris wrote:
> By the way the worst non-linearities in music come from non-linear
> electronics, not from non-linear acoustical systems. The worst
> culprits are microphones and pre-amps.
> ... and ears.
Milan

On Sat, Jun 21, 2008 at 12:14 PM, Chris Vaisvil <chrisvaisvil@...> wrote:
> light does interfere under certain conditions
>
> .....what of the dual slit experiment?

This just proves how little you understood what I was saying. In the
double slit experiment, the two waves interfering have exactly the
same wavelength, so you don't need any nonlinearity for interference.
If you try to do the double slit experiment with two lasers of
different wavelengths instead of one laser split in two, you're never
going to see any fringes. Unisons always beat, even in a linear
system, but it takes nonlinearities for other ratios to beat.

> Room acoustics is not going to generate a new pitch, i.e. harmonics.

O RLY ?

> and -no- interval would be without beating or harmonics if your proposition
> was correct.

Excuse me? A simple just interval never beats, because the difference
tones all line up and a new fundamental is created. No amount of
nonlinearity will create beating in this case.

> in fact a pure sine wave should be impossible to obtain.

Well, technically this is true, for the same reason you can't draw a
perfect circle or straight line.

Keenan

On Sat, Jun 21, 2008 at 2:44 PM, aum <aum@...> wrote:
> ... and ears.
> Milan

Exactly what I was about to say.

Keenan

On Sat, Jun 21, 2008 at 2:20 PM, Steve Morris <barbershopsteve@...> wrote:
> Chris,

Actually you're replying to things I said.

> To say "Most acoustic systems are essentially nonlinear" is
> technically correct but it begs the point a little. Even though
> acoustics has lots of non-linearities in it acoustics is linear to
> more than a first approximation. The non-linearities cause only subtle
> second or third order effects. You would be more accurate to say
>
> "Most acoustic systems are essentially linear but there are minor
> non-linear effects that must be considered."
>
> You can go a long ways and be quite productive pretending that
> acoustics is linear because most of it is.

This is true, but if you assume everything is perfectly linear then
there is no reason to believe that JI intervals are anything special
(except for timbres that already have perfectly harmonic overtones
like totally non-stiff strings). The reason JI intervals are special
in general is because of nonlinear effects like harmonic and
difference tone generation.

> This is similar to the issue of the period of a pendulum. Pendulums
> were used for years for high accuracy clocks because "they have the
> same period no matter how high they swing." Many of us were taught
> this in school. Unfortunately it is not true except as a first
> approximation. Pendulums are accurate time keepers only if you keep
> them swinging by a roughly constant amount which rule all good
> mechanical clock designs enforce. So pendulums are actually non linear
> but you can make them appear linear if you use them in constrained
> circumstances.

Aha, but what about the phenomenon of two weakly coupled pendula
locking in phase? If the pendula were perfectly linear, that would
never happen. It's a fundamentally nonlinear phenomenon.

> Audio is the same. The non linearities are there but usually you can
> ignore them.

I claim that if you ignore the nonlinearity you ignore phenomena that
are musically important.

> By the way the worst non-linearities in music come from non-linear
> electronics, not from non-linear acoustical systems. The worst
> culprits are microphones and pre-amps.

Good point, but if you play a loud, precisely tuned chord on an
acoustic guitar, it sounds much fuller and richer than if you sampled
all the separate notes and mixed them together digitally. It's the
nonlinear response of the guitar body that does it.

Keenan

you made the argument that the medium was causing nonlinearity

I thought it took a ring modulator to create +/- tones from two frequencies

and beats were amplitude phenomena created by phase overlap

- not new frequencies.....

and phase overlap is what the dual slit experiment for light is about

I will be glad to be shown wrong - honestly

- however... you would need to change my entire understanding of the physics
of sound.

feel free to email direct if some object to this being on the list.

On Sat, Jun 21, 2008 at 5:32 PM, Keenan Pepper <keenanpepper@...>
wrote:

> On Sat, Jun 21, 2008 at 12:14 PM, Chris Vaisvil <chrisvaisvil@...<chrisvaisvil%40gmail.com>>
> wrote:
> > light does interfere under certain conditions
> >
> > .....what of the dual slit experiment?
>
> This just proves how little you understood what I was saying. In the
> double slit experiment, the two waves interfering have exactly the
> same wavelength, so you don't need any nonlinearity for interference.
> If you try to do the double slit experiment with two lasers of
> different wavelengths instead of one laser split in two, you're never
> going to see any fringes. Unisons always beat, even in a linear
> system, but it takes nonlinearities for other ratios to beat.
>
> > Room acoustics is not going to generate a new pitch, i.e. harmonics.
>
> O RLY ?
>
> > and -no- interval would be without beating or harmonics if your
> proposition
> > was correct.
>
> Excuse me? A simple just interval never beats, because the difference
> tones all line up and a new fundamental is created. No amount of
> nonlinearity will create beating in this case.
>
> > in fact a pure sine wave should be impossible to obtain.
>
> Well, technically this is true, for the same reason you can't draw a
> perfect circle or straight line.
>
> Keenan
>
>

[Non-text portions of this message have been removed]

>> Room acoustics is not going to generate a new pitch, i.e. harmonics.
>
>O RLY ?

Actually Keenan I think Chris and Steve are right here. In
typical rooms, the worst that happens is that you get standing
waves at low frequencies and attenuation (damn carpet!) at
high ones. No significant nonlinearities. As Milan said,
the greatest source of them in musical situations is the ear
itself.

>Excuse me? A simple just interval never beats, because the difference
>tones all line up and a new fundamental is created.

More of this. Simple just intervals can and do beat whenever
partials fall within a critical band. 5/4 in the bass will
beat because the critical band is wider there. In the middle
register, most septimal intervals will beat (though in this
case the beating will be in relatively high partials compared
to the beating of mistuned intervals like 5ths and 3rds... it
is therefore weaker in amplitude, and the beats will be nicely
synchronized, giving them a pleasant sound known in the old
republic as "periodicity buzz").

Difference tones reinforcing the fundamental have ALMOST NOTHING
to do with consonance judgements. The most important thing
in consonance judgements is virtual pitch, which is a consequence
of high-order processing in the brain and has nothing to do
with intermodulation distortion.

>No amount of nonlinearity will create beating in this case.

Beating is the consequence of failure of spectral resolution
of the basilar membrane.

-Carl

Keenan wrote:
>The reason JI intervals are special
>in general is because of nonlinear effects like harmonic and
>difference tone generation.

Wow, I had no idea until recently how pervasive this myth was.
See my previous message.

-Carl

On Sat, Jun 21, 2008 at 6:37 PM, Carl Lumma <carl@...> wrote:
> Actually Keenan I think Chris and Steve are right here. In
> typical rooms, the worst that happens is that you get standing
> waves at low frequencies and attenuation (damn carpet!) at
> high ones. No significant nonlinearities. As Milan said,
> the greatest source of them in musical situations is the ear
> itself.

Well, you may be right there. On the other hand, when I was helping
Wayne Vitale tune my university's gamelan, I could hear beats between
two single gangsa keys an octave apart, and they don't naturally have
octave overtones. It also really made a difference if I moved my head
around.

> More of this. Simple just intervals can and do beat whenever
> partials fall within a critical band. 5/4 in the bass will
> beat because the critical band is wider there. In the middle
> register, most septimal intervals will beat (though in this
> case the beating will be in relatively high partials compared
> to the beating of mistuned intervals like 5ths and 3rds... it
> is therefore weaker in amplitude, and the beats will be nicely
> synchronized, giving them a pleasant sound known in the old
> republic as "periodicity buzz").

I've never heard a 5/4 beat. It sounds muddy in the bass, but I can't
hear beats occurring at a specific tempo.

Anyway, I was careful to say "simple". Maybe I should have just said
"octaves don't beat", because I was really just trying to respond to
this statement:

"-no- interval would be without beating or harmonics if your
proposition was correct"

> Difference tones reinforcing the fundamental have ALMOST NOTHING
> to do with consonance judgements. The most important thing
> in consonance judgements is virtual pitch, which is a consequence
> of high-order processing in the brain and has nothing to do
> with intermodulation distortion.

Since this is after all the "Make Micro Music" list, I'll ask: What
practical consequences does this have?

> Beating is the consequence of failure of spectral resolution
> of the basilar membrane.

This doesn't make sense. If it's only present in your ear, how come
you can see it clearly on an oscilloscope?

Keenan

I would like to say that beat tones are -not- harmonics.

Anyway, I was careful to say "simple". Maybe I should have just said
"octaves don't beat", because I was really just trying to respond to
this statement:

"-no- interval would be without beating or harmonics if your
proposition was correct"

Your original statement was that room acoustics caused harmonics - this it
not so.

On trax in space we did an interesting experiment - took a microtonal song
and substituted a pure sinewave for a piano sample

The intervals all sounded pure - except the tritone.... which was
interesting because it didn't "beat" per se...

I'm still trying to figure out what all this means.

My interest is not in the perfect microtonal scale

and certainly not JI

but to develop harmony in 19 or 22 TET

On Sun, Jun 22, 2008 at 6:55 PM, Keenan Pepper <keenanpepper@...>
wrote:

> On Sat, Jun 21, 2008 at 6:37 PM, Carl Lumma <carl@...<carl%40lumma.org>>
> wrote:
> > Actually Keenan I think Chris and Steve are right here. In
> > typical rooms, the worst that happens is that you get standing
> > waves at low frequencies and attenuation (damn carpet!) at
> > high ones. No significant nonlinearities. As Milan said,
> > the greatest source of them in musical situations is the ear
> > itself.
>
> Well, you may be right there. On the other hand, when I was helping
> Wayne Vitale tune my university's gamelan, I could hear beats between
> two single gangsa keys an octave apart, and they don't naturally have
> octave overtones. It also really made a difference if I moved my head
> around.
>
> > More of this. Simple just intervals can and do beat whenever
> > partials fall within a critical band. 5/4 in the bass will
> > beat because the critical band is wider there. In the middle
> > register, most septimal intervals will beat (though in this
> > case the beating will be in relatively high partials compared
> > to the beating of mistuned intervals like 5ths and 3rds... it
> > is therefore weaker in amplitude, and the beats will be nicely
> > synchronized, giving them a pleasant sound known in the old
> > republic as "periodicity buzz").
>
> I've never heard a 5/4 beat. It sounds muddy in the bass, but I can't
> hear beats occurring at a specific tempo.
>
> Anyway, I was careful to say "simple". Maybe I should have just said
> "octaves don't beat", because I was really just trying to respond to
> this statement:
>
> "-no- interval would be without beating or harmonics if your
> proposition was correct"
>
> > Difference tones reinforcing the fundamental have ALMOST NOTHING
> > to do with consonance judgements. The most important thing
> > in consonance judgements is virtual pitch, which is a consequence
> > of high-order processing in the brain and has nothing to do
> > with intermodulation distortion.
>
> Since this is after all the "Make Micro Music" list, I'll ask: What
> practical consequences does this have?
>
> > Beating is the consequence of failure of spectral resolution
> > of the basilar membrane.
>
> This doesn't make sense. If it's only present in your ear, how come
> you can see it clearly on an oscilloscope?
>
> Keenan
>
>

[Non-text portions of this message have been removed]

Keenan wrote:

>> More of this. Simple just intervals can and do beat whenever
>> partials fall within a critical band. 5/4 in the bass will
>> beat because the critical band is wider there. In the middle
>> register, most septimal intervals will beat (though in this
>> case the beating will be in relatively high partials compared
>> to the beating of mistuned intervals like 5ths and 3rds... it
>> is therefore weaker in amplitude, and the beats will be nicely
>> synchronized, giving them a pleasant sound known in the old
>> republic as "periodicity buzz").
>
>I've never heard a 5/4 beat. It sounds muddy in the bass, but I can't
>hear beats occurring at a specific tempo.
//
>> Beating is the consequence of failure of spectral resolution
>> of the basilar membrane.
>
>This doesn't make sense. If it's only present in your ear, how come
>you can see it clearly on an oscilloscope?

Sorry, I meant "roughness" above, not beating.

>> Difference tones reinforcing the fundamental have ALMOST NOTHING
>> to do with consonance judgements. The most important thing
>> in consonance judgements is virtual pitch, which is a consequence
>> of high-order processing in the brain and has nothing to do
>> with intermodulation distortion.
>
>Since this is after all the "Make Micro Music" list, I'll ask: What
>practical consequences does this have?

It leads to models of consonance that correctly predict the
consonance of chords, which in turn can be used to justify things
like Tenney Height, which can be used to create tuning schemes
like TOP, which can be used to make music.

-Carl

At 05:24 PM 6/22/2008, you wrote:
>Keenan wrote:
>
>>> More of this. Simple just intervals can and do beat whenever
>>> partials fall within a critical band. 5/4 in the bass will
>>> beat because the critical band is wider there. In the middle
>>> register, most septimal intervals will beat (though in this
>>> case the beating will be in relatively high partials compared
>>> to the beating of mistuned intervals like 5ths and 3rds... it
>>> is therefore weaker in amplitude, and the beats will be nicely
>>> synchronized, giving them a pleasant sound known in the old
>>> republic as "periodicity buzz").
>>
>>I've never heard a 5/4 beat. It sounds muddy in the bass, but I can't
>>hear beats occurring at a specific tempo.
>//
>>> Beating is the consequence of failure of spectral resolution
>>> of the basilar membrane.
>>
>>This doesn't make sense. If it's only present in your ear, how come
>>you can see it clearly on an oscilloscope?
>
>Sorry, I meant "roughness" above, not beating.

Sorry, I'm doing a poor job here. The point is that the ear
does a time domain transform on sound. Reinforcement and
cancellation occurs regardless of the interval between two
sines. If that interval is narrower than a critical band
we hear one tone with beats and if it's much wider we hear
two tones with no beats (and in between we hear two tones
with roughness). That's what I meant by "failure of the
spectral resolution of the basilar membrane".

-Carl

> Sorry, I'm doing a poor job here. The point is that the ear
> does a time domain transform on sound. Reinforcement and
> cancellation occurs regardless of the interval between two
> sines. If that interval is narrower than a critical band
> we hear one tone with beats and if it's much wider we hear
> two tones with no beats (and in between we hear two tones
> with roughness). That's what I meant by "failure of the
> spectral resolution of the basilar membrane".
>
> -Carl

Do you mean a frequency domain transform? Or am I confused?

Or are you saying that the signal from the basilar membrane is already
in the frequency domain and is then sent back into the time domain?
Because I'm tossing around the idea that the basilar membrane signal
actually goes to the brain already IN the time domain, and that as the
different cilia vibrate, rather than switching different frequency
channels and critical bands "on" in the brain, the nerves under the
cilia are stimulated in a pattern analogous to the vibration itself.
Sort of like a tape recorder, rather than a multiplexer. I don't know
if this has been proven wrong or right, but it would explain a few
things, namely why there are binaural beat frequencies.

-Mike

--- In MakeMicroMusic@yahoogroups.com, "Mike Battaglia"
<battaglia01@...> wrote:
>
> > Sorry, I'm doing a poor job here. The point is that the ear
> > does a time domain transform on sound. Reinforcement and
> > cancellation occurs regardless of the interval between two
> > sines. If that interval is narrower than a critical band
> > we hear one tone with beats and if it's much wider we hear
> > two tones with no beats (and in between we hear two tones
> > with roughness). That's what I meant by "failure of the
> > spectral resolution of the basilar membrane".
> >
> > -Carl
>
> Do you mean a frequency domain transform?

Yes I think so, sorry. I can never remember if you name
the source or destination domains with that language. :(

> Or are you saying that the signal from the basilar membrane is
> already in the frequency domain and is then sent back into the
> time domain?

I wasn't saying that, but from each 'bin' on the basilar
membrane, a time-domain signal does indeed get sent to
the brain.

> Because I'm tossing around the idea that the basilar membrane
> signal actually goes to the brain already IN the time domain,
> and that as the different cilia vibrate, rather than switching
> different frequency channels and critical bands "on" in the
> brain, the nerves under the cilia are stimulated in a pattern
> analogous to the vibration itself.

You don't have to kick it around because it's an established
fact. However which bin each "spike train" gets sent from is
also communicated to the brain and is also important to
perception (some very clever experiments where the basilar
membrane is stimulated in specific places at atypical
frequencies for those places show this).

> I don't know if this has been proven wrong or right, but it
> would explain a few things, namely why there are binaural
> beat frequencies.

Actually, the ways in which data from the two ears are combined
in the brain are well understood at this point. You can see
a block diagram here:

http://lloydwatts.com/neuroscience.shtml

Much of this diagram has now been modeled in silicon, but
unfortunately the details are being kept proprietary.
On the other hand, you'll soon be able to buy cellphones
that use it to clean up calls -- both the incoming and
outgoing audio, without special microphones touching your
cheek or any of that.

-Carl

On Sat, Jun 21, 2008 at 5:50 PM, Keenan Pepper <keenanpepper@...> wrote:
>> Chris,
>
> Actually you're replying to things I said.

Oops. Sorry to both of you for the confusion.

> This is true, but if you assume everything is perfectly linear then
> there is no reason to believe that JI intervals are anything special
> (except for timbres that already have perfectly harmonic overtones
> like totally non-stiff strings). The reason JI intervals are special
> in general is because of nonlinear effects like harmonic and
> difference tone generation.

What are you trying to say here? Harmonic series relationships are linear.

> Aha, but what about the phenomenon of two weakly coupled pendula
> locking in phase? If the pendula were perfectly linear, that would
> never happen. It's a fundamentally nonlinear phenomenon.

I don't get your aha. How is this relevant to this thread.

> I claim that if you ignore the nonlinearity you ignore phenomena that
> are musically important.

I claim that most musically important phenomena are linear and based
in harmonic series which come from harmonic analysis (which is linear)
taught in every differential equations class for the last 100 years
and are used as the basis for almost any music theory course you can
take. (By the way when I use the word theory I don't mean "uncertain
idea." I mean it in the sense of "well documented, accepted and
understood" as in theory of gravitation or theory of evolution.)

Of course add my claim to your claim, add $.50 and we still don't have
enough for a decent cup of coffee. What either of us believe or claim
is unimportant.. The facts are fairly well understood and written down
in relevent papers and textx.x

Linear just means that waves do not interact as they pass through each
other. Over wide ranges sound waves are linear as they pass through
the air. Reflections off hard surfaces are basically linear. Strange
shaped objects (like guitars and violins) are acoustically non linear
which is a good thing or they would have a duller more flat sound.

As has been stated elsewhere in this thread the really important
source of acoustic non-linearity is in the ear.

> > I claim that if you ignore the nonlinearity you ignore phenomena that
> > are musically important.
>
> I claim that most musically important phenomena are linear and based
> in harmonic series which come from harmonic analysis (which is linear)
> taught in every differential equations class for the last 100 years
> and are used as the basis for almost any music theory course you can
> take. (By the way when I use the word theory I don't mean "uncertain
> idea." I mean it in the sense of "well documented, accepted and
> understood" as in theory of gravitation or theory of evolution.)

To name some musically important phenomena that have to do with
nonlinearity and deviation from a strict harmonic series:

1) the stretching of a piano tuning to match the stretched timbre of
the instrument
2) the altering of a B3 timbre to match 12-tet
3) the phantom fundamental in the 32' pipe organ stop, which is
actually an octave and a fifth sounding in unison above that stop
4) anything having anything to do with overdriven guitar

Musically important is relative to what has already been done. Some of
the most interesting musical effects I've ever heard were when David
Cross from King Crimson ran his violin through a distortion unit and
made all kinds of crazy noises with it. Though I suppose it's a matter
of taste, I find the nonlinear side of acoustics very musically
interesting.

-Mike

Mike wrote:
> 2) the altering of a B3 timbre to match 12-tet

That doesn't have to do with nonlinearity I'm afraid.

-Carl

> Mike wrote:
> > 2) the altering of a B3 timbre to match 12-tet
>
> That doesn't have to do with nonlinearity I'm afraid.
>
> -Carl

It has to do with deviating from a strict harmonic series towards a
musical effect though, which is one of the other things that Steve
mentioned in his post.

-Mike

Mike,

When stated this way I totally agree. There are many important
non-linear phenomena. I was only disagreeing with the earlier broader
statement that "there is nothing musically significant in JI if you
ignore non-linearities."

On Mon, Jun 23, 2008 at 1:20 AM, Mike Battaglia <battaglia01@...> wrote:
>> > I claim that if you ignore the nonlinearity you ignore phenomena that
>> > are musically important.
> To name some musically important phenomena that have to do with
> nonlinearity and deviation from a strict harmonic series:
>
> 1) the stretching of a piano tuning to match the stretched timbre of
> the instrument
> 2) the altering of a B3 timbre to match 12-tet
> 3) the phantom fundamental in the 32' pipe organ stop, which is
> actually an octave and a fifth sounding in unison above that stop
> 4) anything having anything to do with overdriven guitar
>
> Musically important is relative to what has already been done. Some of
> the most interesting musical effects I've ever heard were when David
> Cross from King Crimson ran his violin through a distortion unit and
> made all kinds of crazy noises with it. Though I suppose it's a matter
> of taste, I find the nonlinear side of acoustics very musically
> interesting.
>
> -Mike
>

--
Steve Morris
barbershopsteve@...
Bass: Boston Wailers
Bass: Sounds Of Concord
Motto: Old age and treachery will always prevail over youth and skill