Harmonic Entropy, Cognition, and Perception

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Yes Mike, very perceptive assessment.

It makes sense to me, and may explain why Carl and others who are "tone-deaf" to LucyTuning have trouble appreciating the scalecoding system and the tendency for intervals closer on the spiral of fourths and fifths to sound more consonant.

http://lucytune.com/new_to_lt/pitch_05.html

I didn't consciously perceive this pattern myself until I had been playing LucyTuned instruments and listening to it regularly for a couple of years, although other regular users also seem to observe the pattern, which make total sense from a traditional harmony point of view.

I had been unable to explain scientifically or musically what was happening. I could just "hear" it, so Mike's series of complex steps could be a good rationalisation of what is actually going on.

Thanks for your thoughts Mike.

On 22 Jun 2008, at 14:32, Mike Battaglia wrote:

> I have been noticing a peculiar attitude lately towards the Harmonic > Entropy model and what it purports to do. Namely, that it serves as > a predictive measure of the perception of a dyad, a chord, or of any > sound at all.
>
> The idea was put forth some time ago that many other things besides > the harmonic entropy of the individual dyads of a chord affect the > way the chord is perceived. To name one, the chords played before > and after a chord will affect how the chord is perceived. Not only > does this apply to triads and up, in which it is sometimes accepted > that HE alone falls short, but it also applies to simple dyads as > well. The musical context of an chord, the timbre that the chord is > played with, and the interpolation between the intervals and a faux-> harmonic series will all affect how the perceived. In addition, how > FAMILIAR one is with an interval/chord will affect how it's > perceived. Some of these things Paul addresses directly in his HE > theory; some of them he mentions out of context, but does not > address specifically within the theory; and some of the things he > doesn't mention at all in his writings that I've found.
>
> To put things in perspective: Entropy, as it stands in information > theory, is sort of a measure of "disorder" or "novelty" in a signal. > The string "1111222233334444" has a lower entropy than the string > "816449362516941". Do you see how you immediately found the > "pattern" or "order" in the first string? This principle, applied to > psychoacoustic and physiological mechanisms in the ear and brain, is > how the concept of harmonic entropy works as well. The second string > is the concatenation of the squares from 9^2 down to 1^2, one right > after the other. You might have found the order in that one, and you > might not have. However, now that it's been shown to you, you're > more likely to find it the next time you see it than you were > before. The same also applies to harmonic entropy, and this latter > part is often left out.
>
> The concept of Harmonic Entropy is a brilliant model that describes > the physical and psychoacoustic interactions between the pitch > resolution and the periodicity resolution mechanisms in the ear and > brain. The output from those mechanisms, whether high or low > entropy, eventually ends up in the cerebral cortex, which is another > way of saying that it is perceived by you, the listener. So you are > presented with either a relatively orderly or a relatively > disorderly signal. After that signal appears in your consciousness, > all sorts of higher-order mental functions process it immediately, > before you are even able to focus on it. These processes very > strongly contribute to your perception of the signal when all is > said and done.
>
> Harmonic Entropy models don't really determine the final perception > of anything. Actually assigning the resultant of the model > perceptual qualities such as that it will be perceived as "mistuned" > or "harsh" or something similar is overstepping the boundaries of > what the place and periodicity mechanisms in the brain are > responsible for. Furthermore, it is an extremely rough estimate to > say that "high entropy" will directly translate to "out of tune." In > order to actually describe what happens to create your actual > perception of a chord, it is necessary to look at the picture not > only from a neurological perspective, but from a psychological > perspective as well.
>
> In psychological terms, a "schema" is the set of associations that > you have for a particular phenomenon. For example, think of a > grapefruit. Whatever it is that comes to mind - that a grapefruit is > slightly heavier than a baseball, is yellowish to orangeish, smells > and tastes sour, can squirt in your eye, that it's called a > "grapefruit" -- all of that is part of your schema for a grapefruit. > And whatever you thought of when I just mentioned a "baseball" or > "sour" is what your schemas for baseballs and sourness are. It is > what those things ARE to you.
>
> Harmonic Entropy models can't accurately predict if an interval will > be perceived as an "out of tune" version of another interval because > such a prediction would entail that a person will end up applying a > schema for some general interval that they have (major third) to an > incoming phenomenon (400 cent interval) and then treat that specific > case as a "wrong" version of the original schema (major third that > is too sharp). Attempting, with a purely psychoacoustic model, to > predict the entire outcome of the process of cognition without > taking into account what schemas an individual even has (what > intervals they know), how open an individual is to creating new > schemas, etc. is absurd.
>
> Now, it might be a pretty good estimate to assume that most people > will have only one schema that encapsulates the 400-cent major third > and the 386 one. And it's probably a decent guess to assume that if > a perceptual signal of any type is extremely high entropy, that a > fair amount of people will hear it as being discordant. But these > are just guesses. And they often fall short, especially when you > consider that humans have made it a point to find order in high-> entropy signals for as long as we've been on the earth.
>
> Humans increase their appreciation for music by finding the > intuitive order in progressively higher entropy signals, whether > harmonic or otherwise. This process is at least partly psychological > in nature,and has to do with the building of new schemas. As nobody > is really sure how the aural periodicity mechanism in the brain > analyzes data, it is certainly possible that that mechanism's > adapting and "learning" new ways of analysis helps to contribute to > this process as well. However, regardless of how the specific > process works, it is clear that over time humans do find patterns in > high-entropy signals, thus decreasing theperceptual entropy of a > signal as one becomes acclimated to it over time. This is how > someone who is used to 12-tet builds schemas for new intervals, > chords, and sounds, and in doing so gains an appreciation for > microtonal music over time.
>
> Having made sense of a high entropy chord is the difference between > it being "grating" and "complex." It's the difference between a 19-> tet major third being "mistuned" and "different." It's the > difference between the tritone being "The Devil's Interval (tm)" and > "consonant." In fact, in addition to finding the order in a chord, > the way a particular chord fits into a chord progression or into a > larger overall context is another type of signal with its own entropy.
>
> If someone hears a chord or a harmonic progression that is > completely foreign to them, that they have not yet "made sense" of, > one option is for them could treat it by trying to force it into > their existing schemas for music (often a musician's fallacy), which > will lead them to actually hear it as being "out of tune." > Alternately, they could perhaps "give up" and not try to it at all. > They will hear a completely discordant composition. It's like > reading a book in English when the only language you speak is > Chinese. And just like when you immerse yourself in another > language, they will eventually find the "order" in the signal and > start to hear that song as "making sense" eventually, in what I have > termed the "Chromosounds effect" after Gene Ward Smith's composition > of the same name. This is why a lot of people might not immediately > like a certain microtonal composition - it would literally sound > "out of tune" to them.
>
> That isn't to say that the concept of harmonic entropy is incorrect > or useless. It is perfectly useful. It only describes the first half > of a long and complicated process leading ultimately to cognition.
>
> Some real life ways in which a model in which harmonic entropy alone > is used to predict perceptual results breaks down:
>
> 1) When I listened to a 9/7 supermajor third for the first time, I > thought it was just a really sharp, out of tune major third. Now > I've started to hear how 9/7 functions as separate in its own right. > I used to only have a schema for 5/4, and I tried to fit 9/7 into > 5/4. Then I started to "get used" to the sound of 9/7 and now I hear > it as a sound distinct from 5/4. On the other hand, I can still > treat, musically, 9/7 as a sharp major third, and people will hear > it as a major third - I'm writing a composition now that basically > does just that. So you can, via musical context, cause an interval > to be treated with a different schema than it might be treated if > heard alone.
>
> 2) Those with perfect pitch have a very strong, very noticeable > field of attraction around absolute pitch values that they are used > to (in this case, the notes of 12tet for me). For that example > posted in the other thread, where 4:5:6:7:8:9:10:11 is compressed so > that 11/4 becomes 8/3, I can either hear it as 11/4 on the outside, > or as a C to an F an octave up. If I focus on the sound of the > chord, I hear an otonal octad with 11/4, and if I focus on the outer > notes, I hear C-F, which to me is a perfect fourth, having its own > properties, and so forth.
>
> There are a few unresolved questions here, namely how much of the > learning of a new sound is an adaptation on the part of the > periodicity mechanism and how much is simple "classical" schematic > learning. It must be a little of both, I think, as the schema you > have for an interval might determine whether a chord that you hear > is "annoying" or "exciting," but whether you can even make sense of > that chord at all must have something to do with the periodicity > mechanism.
>
> -Mike
>
>
Charles Lucy
lucy@...

- Promoting global harmony through LucyTuning -

for information on LucyTuning go to:
http://www.lucytune.com

For LucyTuned Lullabies go to:
http://www.lullabies.co.uk

--- In tuning@yahoogroups.com, Charles Lucy <lucy@...> wrote:
>
> Yes Mike, very perceptive assessment.
>
> It makes sense to me, and may explain why Carl and others who
> are "tone-deaf" to LucyTuning

Charles, I would like to remind you that you're making a public
statement about me. Can you do me the respect of explaining
the basis for this claim, i.e. why do you think I am "tone-deaf
to LucyTuning"?

> have trouble appreciating the scalecoding

And why do you think I have "trouble appreciating" scalecoding?
Is that like people who have "trouble appreciating" the need
to invade Iraq?

-Carl

On 22 Jun 2008, at 19:40, Carl Lumma wrote:

> --- In tuning@yahoogroups.com, Charles Lucy <lucy@...> wrote:
> >
> > Yes Mike, very perceptive assessment.
> >
> > It makes sense to me, and may explain why Carl and others who
> > are "tone-deaf" to LucyTuning
>
> > Charles, I would like to remind you that you're making a public
> >statement about me.
>

Yes, I realised that Carl, and expected that you would "wear it as a medal" of pride;-)
>

>
> >Can you do me the respect of explaining
> >the basis for this claim, i.e. why do you think I am "tone-deaf
> >to LucyTuning"?
>

> I think that you are "tone-deaf to LucyTuning" because you are > unable to "hear" what I and others hear. Which I suppose is to be > expected, since you have such a catholic" listening and composition > repertoire, and like many of the JI disciples you seem to measure > everything against small integer frequency ratios, hence you (Just) > don't "get it".
>

>
> > have trouble appreciating the scalecoding
>
> >And why do you think I have "trouble appreciating" scalecoding?
>

No idea; maybe because it's an N.I.H. (not invented here) concept?

> >Is that like people who have "trouble appreciating" the need
> >to invade Iraq?
>

Maybe. I neither see nor ever saw any need to invade Iraq, only desires with ulterior motives, re-enforced by a lack of imagination to find "better" solutions to an ill- perceived problem.

That is what you would expect from me; as you know my feelings about the "soon to depart" regime that the U.S. population and unfortunate others have had to endure for the past 7 odd years.

BTW Have you lined up all your voters for the $50 challenge yet?

You're great fun to wind-up Carl. It's like having a spitting match with a Pavlovian dog; I whistle; you spit and then bark;-)

best wishes

Charles Lucy
lucy@...

- Promoting global harmony through LucyTuning -

for information on LucyTuning go to:
http://www.lucytune.com

For LucyTuned Lullabies go to:
http://www.lullabies.co.uk

Charles wrote:
> > > have trouble appreciating the scalecoding
> >
> > >And why do you think I have "trouble appreciating" scalecoding?
>
> No idea; maybe because it's an N.I.H. (not invented here) concept?

Or maybe because every time its flaws are pointed out to
you (as recently as 2 days ago in our offlist discussion),
you fall silent, only to restate the same claims later.
Let me refresh your memory: I had asked you if you thought
9/8 was more consonant than 5/4. Do you?

> > >Is that like people who have "trouble appreciating" the need
> > >to invade Iraq?
>
> Maybe.

I think it is. When anyone at the CIA said there was no
reason to invade, the Bush cabinet said they had trouble
appreciating the reasons. Likewise, any viewpoint, opinion,
or evidence that doesn't agree with LucyTuning is merely
due to some "trouble" people around you are having.

> You're great fun to wind-up Carl. It's like having a spitting
> match with a Pavlovian dog; I whistle; you spit and
> then bark ;-)

Wink really isn't appropriate after comparing your correspondent
to a dog, Charles.

-Carl

--- In tuning@yahoogroups.com, "Mike Battaglia" <battaglia01@...> wrote:
>
> I have been noticing a peculiar attitude lately towards the Harmonic
Entropy
> model and what it purports to do. Namely, that it serves as a predictive
> measure of the perception of a dyad, a chord, or of any sound at all.
>
...

Hi Mike,

I'm with Carl here. You and Kraig are having a great old time whacking
a straw man. I don't recall anyone claiming all the things you say
were wrongly claimed for Harmonic Entropy. Sure we may not have given
the full list of caveats every time we mentioned it, but all those you
mention have been recognised since the early days. There's no harm in
reminding us of them, but you should know that the _real_ Paul Erlich
was always very aware of them.

-- Dave Keenan

i will withdraw from this discussion all together.

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Dave Keenan wrote:
>
> --- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com>, "Mike > Battaglia" <battaglia01@...> wrote:
> >
> > I have been noticing a peculiar attitude lately towards the Harmonic
> Entropy
> > model and what it purports to do. Namely, that it serves as a predictive
> > measure of the perception of a dyad, a chord, or of any sound at all.
> >
> ...
>
> Hi Mike,
>
> I'm with Carl here. You and Kraig are having a great old time whacking
> a straw man. I don't recall anyone claiming all the things you say
> were wrongly claimed for Harmonic Entropy. Sure we may not have given
> the full list of caveats every time we mentioned it, but all those you
> mention have been recognised since the early days. There's no harm in
> reminding us of them, but you should know that the _real_ Paul Erlich
> was always very aware of them.
>
> -- Dave Keenan
>
>

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me neither.
i would have hoped that if my conceptions of harmonic entropy were wrong i might have learned how.
frankly i have learned absolutely nothing from the discussion about harmonic entropy.
time to move on.

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Mike Battaglia wrote:
>
> I'm not exactly sure what Kraig has to do with this here.
>
>
> At the very least the whole explanation might be helpful for someone > searching the group archives anyway.
>
> -Mike
>
>

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
>
> i will withdraw from this discussion all together.

Just in time! You were at risk of learning something.

-Carl

Mike wrote:
> Well if I've misunderstood what people were saying about
> harmonic entropy, then I'm happy, as there's no problem.
> Back from my "Music Theory" thread a while ago when I tried
> to get into how psychology and musical context factored
> into the equation, I was generally met with responses to
> the effect that the psychological component was some kind
> of an "alternative theory" to harmonic entropy

Sorry if I gave that impression. Harmonic entropy deals
with low-level effects. The fact that musical context can
overpower low-level effects doesn't mean that a theory of
low-level effects is useless. If you sum over all the
different contexts, you'll be left with the naked case
after all. And if you look at Western music it can be seen
to gravitate to consonances predicted by models like
harmonic entropy. So there's no conflict between a theory
of musical contexts and models of sensory consonance.

> At the very least the whole explanation might be helpful for
> someone searching the group archives anyway.

You probably won't find a whole lot. But you could try
searching for stuff like;

categorical perception
George Miller
magical number
subitizing limit

-Carl

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@...> wrote:
>There's no harm in
> reminding us of them, but you should know that the _real_ Paul Erlich
> was always very aware of them.

I just came across this example while googling "isoharmonic chords".

/tuning/topicId_38310.html#38367

Note Paul's final caveat:
"of course, these kinds of discussions are always imperiled by
unstated considerations of timbre, register, amplitude, audio
reproduction equipment, stereo separation, musical context, musical
training, and acquired taste, which may be different among the
participants . . ."

-- Dave Keenan

> --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@...> wrote:
>>There's no harm in
>> reminding us of them, but you should know that the _real_ Paul Erlich
>> was always very aware of them.
>
> I just came across this example while googling "isoharmonic chords".
>
> /tuning/topicId_38310.html#38367
>
> Note Paul's final caveat:
> "of course, these kinds of discussions are always imperiled by
> unstated considerations of timbre, register, amplitude, audio
> reproduction equipment, stereo separation, musical context, musical
> training, and acquired taste, which may be different among the
> participants . . ."
>
> -- Dave Keenan

Yeah, and from reading Paul's posts and such I can tell that he had a
very, very keen sense of the limits of Harmonic Entropy. He refers to
it as "the simplest possible model that takes in only one factor" to
answer the question "how confused is my brain when it hears a certain
interval?" His models assume that the ability to make sense of
intervals up to numerator N are the same for all intervals, or at
least follow a pattern that has nothing to do with the familiarity of
the interval. And his models also assume that we're dealing with the
response of a "typical listener." So these are a lot of assumptions to
make, especially when you think about the fact that a "typical
listener" could mean someone who grew up on 12-tet, it could mean
someone who grew up in Indonesia listening to Gamelan music, it could
mean someone who grew up in 1/4 comma meantone era, or it could mean
the typical microtonal listener who is not akin to only hearing 9/7 as
a really sharp major third. I don't doubt that Paul wasn't aware of
these limitations.

I'm just trying to study the next step in the process and elucidate
exactly how it works. Why it is that some people hear microtonal music
as "out of tune" and why some people hear don't? The answer I propose
is that it has to do with learning, and is based on the schemata that
one has for an interval, a chord or a sound. A musician will have much
more complex schemata for intervals than a non-musician, who may only
have schemata representing how the interval might function in a song
they remember or a general musical context. But regardless, until
someone hears a mindblowing piece that uses all sorts of
higher-odd-limit septimal chords, melodies and intervals as
intuitively and fluidly as western music has been using 5-limit ones
for years, they are very likely to hear 9/7 as a sharp major third.
Rothenburg's concept of how this applies to melodies is a brilliant
application of the concept; I expect it would apply to intervals and
chord structures as well.

I see a very strong connection between classical and modern theories
of learning and the process by which one stops hearing 9/7 as an out
of tune 5/4. I hypothesize that even the regions that are local maxima
of harmonic entropy - such as around the 11/9 neutral third - can
become as intuitive and consonant as 7/5 has in modern times. After
all, 11/9 is a local maxima of harmonic entropy, but it doesn't have
INFINITE entropy - which means that there is some order to the signal
that the brain and mind could conceivably make sense of and hear in a
musical context. This doesn't mean hearing the ambiguous neutral third
in a musical context in which it functions ambiguously - it means
hearing the neutral third as a rather complex consonance a la 7/5
rather than hearing it as having no consonant value in its own right.

My comments weren't to attack Paul Erlich or Harmonic Entropy at all,
nor were they really to attack anyone or anything in particular except
for a vague notion I have felt emanating here and there that Harmonic
Entropy can actually be used to predict high-level end result
perceptions. Furthermore, if it paves the way for a broader discussion
on how specifically some of these cognitive effects can be harnessed
for musical and tuning purposes, I'm happy. Also, I'm sure that there
are cognitive effects other than learning that play a role into this -
one that Carl Lumma mentioned a long time ago are priming effects, in
which (to use 12-tet terminology) an Eb-Bb dyad is played, and then a
few seconds later a C-G dyad is played. The schema from the Eb-Bb dyad
is still slightly activated and in your short term memory when the
schema for the C-G dyad activates. Is there still a physical Eb-Bb
dyad ringing in the auditory centers somewhere? Maybe, but this effect
can be seen even if the Eb-Bb and C-G dyads are a considerable
distance apart. The schema for Eb-Bb is activated slightly and so you
will remember it later when you hear just C-G, which might remind you
of a "natural minor" or perhaps even "dorian" tonality, as presumably
those notes and root movements are part of the schema you have for
that.

The question here is, is there an absolute cutoff for how long priming
effects last in an individual, or is it dependent on the person? If
someone has never heard dorian mode or minor before, will they still
hear a "minor quality" to the sound? Is there even such a thing as a
"minor quality" for that individual?

Would they build a new schema for minor just from hearing those two
dyads activated separately, or would they first have to hear minor all
by itself, triadically and such, to then later hear the C-G/Eb-Bb dyad
pair as being minor?

Either way, this effect is pretty important, as if it weren't for this
effect, there'd be no such thing as tonality at all. And I expect the
priming and learning effects are really only the tip of the iceberg
with how deep this thread might run and apply to tuning theory and
microtonal music, though for Carl's sake I'll stop short of declaring
this to be a "revolution in thinking" :P

-Mike

Hi Kraig,

I included you because of your fondness for throwing theories in the
trash rather than just recognising their limitations. And in the case
of harmonic entropy, most of the limitations have already been
acknowledged many times by its creator.

It seems to me that what you are proposing re harmonic entropy, would
be analogous to saying that since Erv failed to mention MOS scales
that repeat at the half-octave, we should throw MOS in the trash. No,
we should just extend his theory. I don't know whether or not he did
mention them, I'm just trying to make an analogy to help you see it
from my point of view.

-- Dave Keenan

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
>
> me neither.
> i would have hoped that if my conceptions of harmonic entropy were
wrong
> i might have learned how.
> frankly i have learned absolutely nothing from the discussion about
> harmonic entropy.
> time to move on.
>
>
> /^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
> Mesotonal Music from:
> _'''''''_ ^North/Western Hemisphere:
> North American Embassy of Anaphoria Island <http://anaphoria.com/>
>
> _'''''''_ ^South/Eastern Hemisphere:
> Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>
>
> ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
>
>
>
>
> Mike Battaglia wrote:
> >
> > I'm not exactly sure what Kraig has to do with this here.
> >
> >
> > At the very least the whole explanation might be helpful for someone
> > searching the group archives anyway.
> >
> > -Mike
> >
> >
>

On Sun, Jun 22, 2008 at 7:31 PM, Kraig Grady <kraiggrady@...> wrote:
> me neither.
> i would have hoped that if my conceptions of harmonic entropy were wrong
> i might have learned how.
> frankly i have learned absolutely nothing from the discussion about
> harmonic entropy.
> time to move on.

What do you mean by this?

-Mike

--- In tuning@yahoogroups.com, Charles Lucy <lucy@...> wrote:
>
> Yes Mike, very perceptive assessment.
>
> It makes sense to me, and may explain why Carl and others who are
> "tone-deaf" to LucyTuning have trouble appreciating the scalecoding
> system and the tendency for intervals closer on the spiral of fourths
> and fifths to sound more consonant.
>
> http://lucytune.com/new_to_lt/pitch_05.html
>
> I didn't consciously perceive this pattern myself until I had been
> playing LucyTuned instruments and listening to it regularly for a
> couple of years, although other regular users also seem to observe the
> pattern, which make total sense from a traditional harmony point of
> view.
>
> I had been unable to explain scientifically or musically what was
> happening. I could just "hear" it, so Mike's series of complex steps
> could be a good rationalisation of what is actually going on.
>
> Thanks for your thoughts Mike.

On Sun, Jun 22, 2008 at 10:06 AM, Charles Lucy <lucy@...> wrote:
> Yes Mike, very perceptive assessment.
>
> It makes sense to me, and may explain why Carl and others who are
> "tone-deaf" to LucyTuning have trouble appreciating the scalecoding
system
> and the tendency for intervals closer on the spiral of fourths and
fifths to
> sound more consonant.
> http://lucytune.com/new_to_lt/pitch_05.html
> I didn't consciously perceive this pattern myself until I had been
playing
> LucyTuned instruments and listening to it regularly for a couple of
years,
> although other regular users also seem to observe the pattern, which
make
> total sense from a traditional harmony point of view.
> I had been unable to explain scientifically or musically what was
happening.
> I could just "hear" it, so Mike's series of complex steps could be a
good
> rationalisation of what is actually going on.
> Thanks for your thoughts Mike.

Interesting, and I did come up independently with the same system a
long time ago when I was trying to understand how the modes worked. I
think that what it is is that you build a map of all sorts of
intervals based on stacking one of them. This is the principle behind
a major 7 chord, major 9 chord, major 9 #11 chord, for example:

C E G B D F# A C# E G#, etc. forever.

It's basically that you take a CEG major chord, then you "tile" it up
a fifth to GBD, etc., then up a fifth to DF#A, etc. The pattern of
this chord is that it keeps getting extended by a perfect fifth.

The spiral of perfect fifths is a great example and generalization of
this, as you can "feel" the relationship from each note to the next
one in the circle. Chord progressions like:

Amaj Emaj Bmaj F#maj C#maj

sound particularly beautiful, especially if they are repeated - the
motion from C#maj to Amaj can be heard as a motion by a pythagorean
major third in its own right, rather than just as a motion by a
stretched 5/4. The whole concept of Pythagorean tuning is based on
your ability to feel the map of thirds out into even more remote
intervals.

Here is a mental exercise tf ryou: If you imagine enough 3/2's in your
head, and you imagine the 3/2's as they're played on a piano, you'll
obviously end up back where you started, 12 octaves up. But if you go
by what a 3/2 "feels" like to you, and you very slowly and carefully
imagine 3/2's on top of each other, you WILL end up considerably
sharper than the starting point. You can intuitively feel even that
you will end up sharper than your starting point by about the distance
of the Pythagorean comma if you pay enough attention, and you can feel
where in 12-tet you suddenly "switch" to hearing any given point in
the circle a Pythagorean comma down. Starting at C, when I get to D#,
I suddenly hear it as Eb. There is an almost imperceptible shift in
the way I feel the interval - I stop hearing it at around D# as an
extension away from C and start to hear it as an Eb that is below C
leading back to it. Not below in the octave sense, of course, but
below in terms of the relation along the spiral of fifths.

So from this observation, you can note that even though in temperament
things aren't just, the brain does somewhat treat things in relation
to just intervals, (or maybe to the intervals in the timbre of the
sound being played). I think that the brain builds/you build a "map"
of the intervals that you're familiar with, and that's how you learn
about tonality such as major or minor. It's also how when a piece
moves from C major to G major, you hear that F# as a defining,
contrasting note that signifies to you that something really different
has occured: you have then "learned" something about the quality of
the interval from C to an F# that is a whole tone and a major third
up. Or, rather, you feel it as an "extended" interval - you might not
be able to appreciate the consonance of 45/32 directly, but you do in
fact feel it as a major third above the V chord of a root that is a
modulation by 3/2 away from the root.

This is why quarter tones specifically often sound horribly "wrong" in
a harmonic context at first - they're inaccessible. They haven't been
mapped out yet. They don't fit into the circle of fifths in 12-tet,
and the spiral of fifths for most people stops at the 12-tet circle.
So they don't hear a motion by quarter tone as appearing anywhere in
the spiral of fifths, although naturally it does (approximately). It
also doesn't appear in any motion by major thirds, whole tones, or
anything familiar. There might be certain quarter-tone motions that
"sound good anyway," like the one from C to an F half sharp, and then
from that, one can hear from C to an E half sharp as that first
interval minus a whole tone, and so quarter tones get mapped out.

It's interesting that musicians often find one particular way to map
an interval out and then cling to that as though it were the only way
for it to exist - a lot of musicians treat a major third itself IS the
interval that you get by going four fifths up; not only because they
aren't familiar with the syntonic comma, but because they are clinging
to what they already know.

In general, the three recipes to "blow someone's mind" musically seem
to be the following:

1) Find a way to play an interval or chord or something that people
somehow know about intuitively through their limited feeling out of
the harmonic series, but does not exist in western music currently -
right away they will hear this as sounding like "a higher level of
music" rather than hearing it as "weird and microtonal".
2) Find a way to play an existing interval or chord in a way that
shows people that there are other ways to use these intervals than the
commonly accepted ones, I.E. put a major third on top of a minor chord
for added resonance and let it ring. People will hear their familiar
major third in a very new context.
3) After exploring 1 and 2 for yourself for a long, long time, just
freewrite and express an idea or create feelings that not only use
these principles above, but do so in a way that is as expressive as
the Beatles' song "Let it Be" or the Debussy composition "Reflections
on the Water."

All of these principles not only seem intuitive, but have their basis
in cognitive psychology as well, which maybe helps to show how
incredibly useful combining these two fields can be.

A hypothesis of mine is that those with AP somehow "remember" these
individual notes as being in a certain relation to some home pitch,
but in a different sense than those with stored relative pitch can.
For people with AP, C might be "burned" into the mind as the center of
everything. And then when a new note is encountered, e.g. G 3/2 up
from C, that note ALSO gets "burned" into the mind as well, whereas
those that don't have AP do not have this effect stick into the long
term memory; they might get just the one first note burned into the
mind and then try to remember consciously everything from there.

Also, Charles...
Another thing that I have been realizing as of late is that just like
there is a spiral of 3/2 perfect fifths that leads to remote and
beautiful harmonic arrangements, you can also construct a spiral of
5/4 major thirds, a spiral of 7/4 harmonic sevenths, and so on. Each
one of these spirals has a different feeling than the last one,
especially the major thirds one, which is considerably more dissonant
and complex than the 3/2 one. In LucyTuning, the 5/4 spiral will be
intrinsically related to the 3/2 one, as it's a meantone temperament,
but I would experiment with the 5/4 spiral as well just to see what
musical results you get out of it!

Synaesthetically speaking, the 3/2 spiral to me sounds like a
construction "on top" of something, as though you are moving up in
fifths stacked on top of each other, but the 5/4 spiral sounds like
you're moving "forward." It's like going "into" the scene, moving
behind the image of the note to something diagonally up and behind it.
And I haven't gotten into the 7/4 spiral yet, but I imagine that that
would be perceived as a fourth degree of freedom. So whoever says you
can't imagine the fourth dimension might just need to go listen to the
7/4 spiral for a bit.

Again, in terms of how this relates to LucyTuning, it is true that 4
fourths equals a major third, but if you try and hear it as its own
separate interval that stands by itself, you'll hear the depths of the
spiral of thirds and such. I'm trying to figure out if there are modes
and scales that incorporate motions by the spiral of thirds as well -
here's what I've found.

The modes you've listed on your site, from locrian to lydian (and as
you've noticed, there are more), all have one thing in common from a
non-meantone perspective: In the 5-limit JI lattice, they go out into
the 3-direction a few times, and the 5-direction no more than ONE
EXCURSION OUT. This is equivalent to saying they contain two steps in
the spiral of thirds: the step from C-E is equivalent to the step from
G-B, as they are simply separated by a fifth.

All of the melodic minor modes, on the other hand, contain exactly
THREE levels along the 5-axis: that is, they go two excursions out
into the 5-direction. Take this scale, loosely described in 12-tet
notation:

C D E F# G# A B C

That G# can be used as a 25/16 from C, which gives the parent scale a
completely different sound than the diatonic parent scale. The modes
of the harmonic minor and major scales are similar as well. Take this
one, for instance, Lydian #2:

C D# E F# G A B C

One way to get from that C to the D# is as follows:

C->E->B->D#

So it's a motion by 5/4, a 3/2, and another 5/4. Alternatively, in
12-tet, you might hear that C-D# as a C-Eb, so it depends on how
you're mapping that interval out in any given musical context. This
scale, Lydian Augmented #2:

C D# E F# G# A B C

Introduces another 5-limit way to get to that D#, namely C->E->G#->D#.

So this might be the concept of a LucyTuned or meantone spiral of
fifths can be extended to other intervals as well.

An interesting question posed here is, if the diatonic modes can be
generated as a stack of meantone fifths, what properties would scales
based on a magic temperament spiral of major thirds have? You might be
able to build some really consonant scales that way.

-Mike

i doubt it. Cameron, mike and I presented samples . i never saw any coming from the other side to illustrate anything of the supposed unquestionable theory. lets here it sound.
keep repeating Carl, it will make it true!

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Carl Lumma wrote:
>
> --- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com>, Kraig > Grady <kraiggrady@...> wrote:
> >
> > i will withdraw from this discussion all together.
>
> Just in time! You were at risk of learning something.
>
> -Carl
>
>

a simple example.
1.prove to me that nobel mediants are less entropic than harmonic entropy points IN SOUND,.
2. that it is better than helmholtz formula in determining dissonance
3. show me where HE can predict the results of Mike's and/or the last examples i posted.

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Carl Lumma wrote:
>
> --- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com>, Kraig > Grady <kraiggrady@...> wrote:
> >
> > i will withdraw from this discussion all together.
>
> Just in time! You were at risk of learning something.
>
> -Carl
>
>

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
>
> i doubt it. Cameron, mike and I presented samples.
> i never saw any coming from the other side to illustrate
> anything of the supposed unquestionable theory.

Did you read my messages, or Dave's?

> lets here it sound.

I have posted several audio examples in this thread,
and described how I made others. I take it you didn't
listen to them or duplicate them for yourself. It's
also evident that you don't understand the theory you're
attempting to argue with, but instead of asking questions
or having a modicum of humility, you announce that it
should be thrown in the trash. Then to top it off you
accuse us of backing an "unquestionable" theory. It's
not unquestionable but in order to question it you
should probably first understand it, don't you think?

Of course I understand if you aren't interested, as you
said on MMM theory is of limited use to practicing
musicians such as yourself. Fine, but then don't make
outrageous statements about throwing things in the trash!

-Carl

> i doubt it. Cameron, mike and I presented samples . i never saw any
> coming from the other side to illustrate anything of the supposed
> unquestionable theory. lets here it sound.
> keep repeating Carl, it will make it true!

Well, my main idea wasn't to throw out harmonic entropy altogether,
but rather that instead of evaluating entropy curves based on a just
harmonic series, to evaluate the curve based on the harmonic series of
the timbre. It is extremely possible that the entropy of a stretched
chord, from an information standpoint, would decrease if the partials
all coincide, as the brain might be able to "adjust" its periodicity
mechanism slightly to take cues from a stretched harmonic series in a
timbre.

My other point was that harmonic entropy along cannot be used to
predict whether someone will hear a 350 cent neutral third as major,
or minor, or whether they have grown used to 11/9 as its own
consonance, for example, or any of that. I do think that the phantom
fundamental of a dyad plays a role in how low it can go before the
actual flavor of it is lost, which seems to correspond to statements
about how "roughness" dominants the perception of consciousness in
higher registers.

-Mike

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
>
> a simple example.
> 1.prove to me that nobel mediants are less entropic than harmonic
> entropy points IN SOUND,.

I haven't made such a claim, but if you tell me what you
think the noble mediant between 4/3 and 5/4 is, I'll tell
you if it disagrees with harmonic entropy and then synthesize
the two intervals if it does.

> 2. that it is better than helmholtz formula in determining
> dissonance

Helmholtz's formula is like Sethares' and therefore cannot
explain why utonal triads, tetrads, etc. are less consonant
than otonal ones. You can't do that with roughness-based
models without invoking untrue claims about difference
tones.

> 3. show me where HE can predict the results of Mike's and/or
> the last examples i posted.

Those examples are larger chords, which for the millionth
time harmonic entropy doesn't apply to. Average dyadic error
does, and I've already posted my findings there. If you
care to make a coherent reply to those findings I'd be happy
to listen and respond in a civil manner.

-Carl

> > 3. show me where HE can predict the results of Mike's and/or
> > the last examples i posted.
>
> Those examples are larger chords, which for the millionth
> time harmonic entropy doesn't apply to. Average dyadic error
> does, and I've already posted my findings there. If you
> care to make a coherent reply to those findings I'd be happy
> to listen and respond in a civil manner.
>
> -Carl

A few questions here:

When people talk about needing "a better theory to handle triads," are
they specifically talking about needing a model to calculate the
harmonic entropy of triads and such?

Also, the example that I posted a while ago where the beating in the
chord stopped when the intervals were aligned in a stretched-harmonic
series, if difference tones aren't responsible for the original
beating and the stop in the beating subsequently, then what is?

-Mike

There was a big push to imply that Erv was tied to the 2/1octave. As i have said continually for all these years, this was never the case. So while people like to think they are expanding his theory in that direction, they are unfortunately deluded.
You have everything backward it fact. His use far exceeds anything being presented because he is not tied to any notion of consonance. for examples the octave is expedient.
His work with Marcus Hobbs expanding a generator through the continuum might clue us in in that he is more concerned with the pattern MOS unveils than any one application of them.

My problem with HE is not with it ability to find ambiguous points/ areas yet i do not understand how it is an improvement over previous ones.

My problem is with it in regard to the con/dis problems. The assumption that Ambiguous= Dissonance is questionable. The rest of it you can have.
Where A=D if i can shorten this is quite true in 12et and might apply to other ETs in which case it will be useful there.

Helmholtz in appendix XV. p.415-418. Why has no one compared with this. middle of 416 being basis for P.192

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Dave Keenan wrote:
>
> Hi Kraig,
>
> I included you because of your fondness for throwing theories in the
> trash rather than just recognising their limitations. And in the case
> of harmonic entropy, most of the limitations have already been
> acknowledged many times by its creator.
>
> It seems to me that what you are proposing re harmonic entropy, would
> be analogous to saying that since Erv failed to mention MOS scales
> that repeat at the half-octave, we should throw MOS in the trash. No,
> we should just extend his theory. I don't know whether or not he did
> mention them, I'm just trying to make an analogy to help you see it
> from my point of view.
>
> -- Dave Keenan
>
> --- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com>, Kraig > Grady <kraiggrady@...> wrote:
> >
> > me neither.
> > i would have hoped that if my conceptions of harmonic entropy were
> wrong
> > i might have learned how.
> > frankly i have learned absolutely nothing from the discussion about
> > harmonic entropy.
> > time to move on.
> >
> >
> > /^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
> > Mesotonal Music from:
> > _'''''''_ ^North/Western Hemisphere:
> > North American Embassy of Anaphoria Island <http://anaphoria.com/ > <http://anaphoria.com/>>
> >
> > _'''''''_ ^South/Eastern Hemisphere:
> > Austronesian Outpost of Anaphoria > <http://anaphoriasouth.blogspot.com/ > <http://anaphoriasouth.blogspot.com/>>
> >
> > ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
> >
> >
> >
> >
> > Mike Battaglia wrote:
> > >
> > > I'm not exactly sure what Kraig has to do with this here.
> > >
> > >
> > > At the very least the whole explanation might be helpful for someone
> > > searching the group archives anyway.
> > >
> > > -Mike
> > >
> > >
> >
>
>

Mike wrote:
>
> > > 3. show me where HE can predict the results of Mike's
> > > and/or the last examples i posted.
> >
> > Those examples are larger chords, which for the millionth
> > time harmonic entropy doesn't apply to. Average dyadic error
> > does, and I've already posted my findings there. If you
> > care to make a coherent reply to those findings I'd be happy
> > to listen and respond in a civil manner.
>
> A few questions here:
>
> When people talk about needing "a better theory to handle
> triads," are they specifically talking about needing a model
> to calculate the harmonic entropy of triads and such?

After years of working on it on this list and the
harmonic_entropy list, Paul arrived at such a model. But
he never did the calculations (they take days or weeks,
but you only have to do it once)! So we don't have it.
One day, one of us will probably do those calculations.

> Also, the example that I posted a while ago where the beating
> in the chord stopped when the intervals were aligned in a
> stretched-harmonic series, if difference tones aren't
> responsible for the original beating and the stop in the
> beating subsequently, then what is?

I haven't auditioned at every one of your numerous examples,
but the ones I did seem to be explained by difference tones.
But if you use a more normal timbre (like the reed organ in
the wave file I uploaded), the stretched chords beat plenty.

-Carl

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
>
> There was a big push to imply that Erv was tied to the 2/1
> octave. As i have said continually for all these years, this
> was never the case. So while people like to think they are
> expanding his theory in that direction, they are unfortunately
> deluded.

You also changed your story about that at least once. And
there's no extant work of Erv's showing nonoctave periods
that I'm aware of. I wouldn't be surprised if he did play
with them, of course.

> My problem is with it in regard to the con/dis problems.
> The assumption that Ambiguous=Dissonance is questionable.

Who's saying that??

[deleted incomprehensible sentence fragment]
> Helmholtz in appendix XV. p.415-418. Why has no one compared
> with this. middle of 416 being basis for P.192

I was reading that just last week.

-Carl

> Mike wrote:
> >
> > > > 3. show me where HE can predict the results of Mike's
> > > > and/or the last examples i posted.
> > >
> > > Those examples are larger chords, which for the millionth
> > > time harmonic entropy doesn't apply to. Average dyadic error
> > > does, and I've already posted my findings there. If you
> > > care to make a coherent reply to those findings I'd be happy
> > > to listen and respond in a civil manner.
> >
> > A few questions here:
> >
> > When people talk about needing "a better theory to handle
> > triads," are they specifically talking about needing a model
> > to calculate the harmonic entropy of triads and such?
>
> After years of working on it on this list and the
> harmonic_entropy list, Paul arrived at such a model. But
> he never did the calculations (they take days or weeks,
> but you only have to do it once)! So we don't have it.
> One day, one of us will probably do those calculations.

I'll have to look at that.

> > Also, the example that I posted a while ago where the beating
> > in the chord stopped when the intervals were aligned in a
> > stretched-harmonic series, if difference tones aren't
> > responsible for the original beating and the stop in the
> > beating subsequently, then what is?
>
> I haven't auditioned at every one of your numerous examples,
> but the ones I did seem to be explained by difference tones.
> But if you use a more normal timbre (like the reed organ in
> the wave file I uploaded), the stretched chords beat plenty.
>
> -Carl

They did beat, but in a very even and pleasing manner, imo. It almost
sounded like you had run the chord through a leslie or something,
which makes sense if you consider that beating will occur between a
whole harmonic series of partials, and so the beat pseudo-frequencies
will be in a harmonic series, a la FM modulation (minus the negative
sidebands). At least that's one possible explanation.

Chords like that IMO sound even better with a complex and normal
timbre - the beating seems very even, has a lot of shimmer to it, and
yet has a very resonant quality to it. If I were going to resolve V7
to I, rather than to use the metastable 7 over a normal major triad, I
might, depending on the circumstances, just stretch the major triad
out as well for the added harmonic entropy and, paradoxically,
resonance.

Mike wrote:
> They did beat, but in a very even and pleasing manner, imo.

Didn't sound particularly pleasant to me. Again, I tried
numerous nearby chords in tuningspace.

> It almost sounded like you had run the chord through a leslie
> or something, which makes sense if you consider that beating
> will occur between a whole harmonic series of partials, and so
> the beat pseudo-frequencies will be in a harmonic series,
> a la FM modulation (minus the negative sidebands). At least
> that's one possible explanation.

You didn't like my 'interior dyads are still just' explanation?

-Carl

> Mike wrote:
> > They did beat, but in a very even and pleasing manner, imo.
>
> Didn't sound particularly pleasant to me. Again, I tried
> numerous nearby chords in tuningspace.
>
> > It almost sounded like you had run the chord through a leslie
> > or something, which makes sense if you consider that beating
> > will occur between a whole harmonic series of partials, and so
> > the beat pseudo-frequencies will be in a harmonic series,
> > a la FM modulation (minus the negative sidebands). At least
> > that's one possible explanation.
>
> You didn't like my 'interior dyads are still just' explanation?
>
> -Carl

Why does the interior dyads being still just have anything to do with
the chord sounding like it's being run through a rotary speaker?

As for the interior dyads still being just, the 4:5:6:7.something
chord, which is a just major triad with an irrational, noble 7th, on
top, has mostly interior dyads that are just, with the exception of
the ones involving that seventh. However, the 4:5.x:6.x:7.x chord has
no just dyads at all in the chord: I have taken the first chord and
stretched the major triad until the whole thing is in proportion and
sounds like a stretched 4:5:6:7. All of the dyads in the chord are
going to be sharper than just; some of the examples I posted had dyads
that were a full 50 cents sharp or flat and yet still sounded
recognizable and resonant.

-Mike

Sorry, I ran back and read through some of your messages again, and I
think that what you're talking about is that the average dyadic error
is lower for the stretched chord than the first one with just the
stretched harmonic 7th. This is what I'm talking about exactly, just
using different terms. In fact, if you stretch the chord enough, the
4:5:6:7... starts to sound like 7:9:11:13... and then 3:4:5:6:7, all
transposed to the same key. However, it does illustrate an interesting
principle: If any of the dyads in the last chord are made out to be
just, assuming the appropriate timbre, the chord becomes considerably
more discordant.

-Mike

> There was a big push to imply that Erv was tied to the 2/1octave. As i
> have said continually for all these years, this was never the case. So
> while people like to think they are expanding his theory in that
> direction, they are unfortunately deluded.
> You have everything backward it fact. His use far exceeds anything being
> presented because he is not tied to any notion of consonance. for
> examples the octave is expedient.
> His work with Marcus Hobbs expanding a generator through the continuum
> might clue us in in that he is more concerned with the pattern MOS
> unveils than any one application of them.
>
> My problem with HE is not with it ability to find ambiguous points/
> areas yet i do not understand how it is an improvement over previous ones.
>
> My problem is with it in regard to the con/dis problems. The assumption
> that Ambiguous= Dissonance is questionable. The rest of it you can have.
> Where A=D if i can shorten this is quite true in 12et and might apply to
> other ETs in which case it will be useful there.

Well, the concept of saying that high harmonic entropy = ambiguous is
questionable as well. It just means "more ambiguous." To determine
absolutely that every individual will be unable to hear 11/9 as a
consonance in its own right; to categorically state that 11/9 IS
"ambiguous" and will flip flop between 5/4 and 6/5 or something like
it, is absurd without taking into account other factors. I'm not sure
if the periodicity mechanism, which as Paul writes is "not well
understood" and has to do with "a mathematical analysis of patterns of
nerve stimulation", is involved in the process of learning to hear the
identity and consonance in new intervals, or if it is entirely
cognitive; either way, it does happen, and you can learn to hear 11/9
as an interval in its own right.

-Mike

I don't think there is a limit on it, only that some are able to be comprehended quicker. just that 11/9 has more entropy than the others etc.
At one point it diverges from Dan Sterns model which coincides with the scale tree, i am not sure, nor why. it seem nobles would be the most and once again why they are not i also don't grasp. Also at that point and that far into the woods of intervals, it might be hard to tell. /^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Mike Battaglia wrote:
>
> > There was a big push to imply that Erv was tied to the 2/1octave. As i
> > have said continually for all these years, this was never the case. So
> > while people like to think they are expanding his theory in that
> > direction, they are unfortunately deluded.
> > You have everything backward it fact. His use far exceeds anything being
> > presented because he is not tied to any notion of consonance. for
> > examples the octave is expedient.
> > His work with Marcus Hobbs expanding a generator through the continuum
> > might clue us in in that he is more concerned with the pattern MOS
> > unveils than any one application of them.
> >
> > My problem with HE is not with it ability to find ambiguous points/
> > areas yet i do not understand how it is an improvement over previous > ones.
> >
> > My problem is with it in regard to the con/dis problems. The assumption
> > that Ambiguous= Dissonance is questionable. The rest of it you can have.
> > Where A=D if i can shorten this is quite true in 12et and might apply to
> > other ETs in which case it will be useful there.
>
> Well, the concept of saying that high harmonic entropy = ambiguous is
> questionable as well. It just means "more ambiguous." To determine
> absolutely that every individual will be unable to hear 11/9 as a
> consonance in its own right; to categorically state that 11/9 IS
> "ambiguous" and will flip flop between 5/4 and 6/5 or something like
> it, is absurd without taking into account other factors. I'm not sure
> if the periodicity mechanism, which as Paul writes is "not well
> understood" and has to do with "a mathematical analysis of patterns of
> nerve stimulation", is involved in the process of learning to hear the
> identity and consonance in new intervals, or if it is entirely
> cognitive; either way, it does happen, and you can learn to hear 11/9
> as an interval in its own right.
>
> -Mike
>
>

--- In tuning@yahoogroups.com, "Mike Battaglia" <battaglia01@...> wrote:
> I don't doubt that Paul wasn't aware of
> these limitations.

Hee hee. I couldn't fail to disagree with you less. ;-)

> I'm just trying to study the next step in the process and elucidate
> exactly how it works. Why it is that some people hear microtonal music
> as "out of tune" and why some people hear don't? The answer I propose
> is that it has to do with learning, and is based on the schemata that
> one has for an interval, a chord or a sound. A musician will have much
> more complex schemata for intervals than a non-musician, who may only
> have schemata representing how the interval might function in a song
> they remember or a general musical context.
...

A very worthy project.

...
> And I expect the
> priming and learning effects are really only the tip of the iceberg
> with how deep this thread might run and apply to tuning theory and
> microtonal music, though for Carl's sake I'll stop short of declaring
> this to be a "revolution in thinking" :P

I guess we've been aware of these things and listed them as
"contextual factors" that affect musical perception, but as to how
they work exactly, I think this has always just seemed too hard.

So I wish you luck.

-- Dave Keenan

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
>
> There was a big push to imply that Erv was tied to the 2/1octave. As i
> have said continually for all these years, this was never the case. So
> while people like to think they are expanding his theory in that
> direction, they are unfortunately deluded.

That's fine. But I hope you got the point that, whether deluded or
not, they at least desire to expand his theory, rather than throw it
in the trash.

> My problem with HE is not with it ability to find ambiguous points/
> areas yet i do not understand how it is an improvement over previous
ones.
>
> My problem is with it in regard to the con/dis problems. The assumption
> that Ambiguous= Dissonance is questionable.

Yes. It is. Who said it wasn't?

> Helmholtz in appendix XV. p.415-418. Why has no one compared with this.
> middle of 416 being basis for P.192

Can anyone put this on the web, or point to where it already is?

Even if it looks identical to a harmonic entropy curve, HE has an
advantage in being derived from a model having some "neural
plausibility" based on information theory.

-- Dave Keenan

On Mon, Jun 23, 2008 at 5:57 AM, Dave Keenan <d.keenan@...> wrote:
> --- In tuning@yahoogroups.com, "Mike Battaglia" <battaglia01@...> wrote:
>> I don't doubt that Paul wasn't aware of
>> these limitations.
>
> Hee hee. I couldn't fail to disagree with you less. ;-)

Oh my god, I'm buried in a sea of negatives. What is that, 5?

I don't (1)
doubt that Paul wasn't (2)
aware of these limitations.

I couldn't (3)
fail to (4)
disagree (5) with you,
less (6)

Did you construct that sentence specifically to f**k with my head? Oh
my god. I was trying to say that I think Paul WAS aware of these
limitations, but whoa.

>> I'm just trying to study the next step in the process and elucidate
>> exactly how it works. Why it is that some people hear microtonal music
>> as "out of tune" and why some people hear don't? The answer I propose
>> is that it has to do with learning, and is based on the schemata that
>> one has for an interval, a chord or a sound. A musician will have much
>> more complex schemata for intervals than a non-musician, who may only
>> have schemata representing how the interval might function in a song
>> they remember or a general musical context.
> ...
>
> A very worthy project.
>
> ...
>> And I expect the
>> priming and learning effects are really only the tip of the iceberg
>> with how deep this thread might run and apply to tuning theory and
>> microtonal music, though for Carl's sake I'll stop short of declaring
>> this to be a "revolution in thinking" :P
>
> I guess we've been aware of these things and listed them as
> "contextual factors" that affect musical perception, but as to how
> they work exactly, I think this has always just seemed too hard.
>
> So I wish you luck.
>
> -- Dave Keenan

Indeed! Thank you. It's nice to get some encouragement. Right now I'm
just trying to figure out how much of it is cognitive perception and
how much of it is purely psychoacoustic (and is there such a thing as
purely psychoacoustic)? We'll see where it goes.

-Mike

Dave Keenan wrote:

"It seems to me that what you are proposing re harmonic entropy, would
be analogous to saying that since Erv failed to mention MOS scales
that repeat at the half-octave, we should throw MOS in the trash. No,
we should just extend his theory. I don't know whether or not he did
mention them, I'm just trying to make an analogy to help you see it
from my point of view."

For the record, Erv did work with MOS that wrapped around intervals other than an octave. Once, at his kitchen table, and "just for kicks" (a typical Wilson phrase), he took me on a spin through MOS on fourths, fifths and twelfths. As Chalmer's book, then still in manuscript, was of great interest to both of us, the tetrachordal possibilities were explored the most. I believe that this eventually led Wilson to the Parvi/Marwa papers.

Daniel Wolf

--- In tuning@yahoogroups.com, "Mike Battaglia" <battaglia01@...> wrote:
>
> On Mon, Jun 23, 2008 at 5:57 AM, Dave Keenan <d.keenan@...> wrote:
> > --- In tuning@yahoogroups.com, "Mike Battaglia" <battaglia01@> wrote:
> >> I don't doubt that Paul wasn't aware of
> >> these limitations.
> >
> > Hee hee. I couldn't fail to disagree with you less. ;-)
>
> Oh my god, I'm buried in a sea of negatives. What is that, 5?
>
> I don't (1)
> doubt that Paul wasn't (2)
> aware of these limitations.
>
> I couldn't (3)
> fail to (4)
> disagree (5) with you,
> less (6)
>
> Did you construct that sentence specifically to f**k with my head?

Someone else constructed it. I'm just passing it on. It's a beauty
isn't it? :-) I still have no idea what it means.

> Oh
> my god. I was trying to say that I think Paul WAS aware of these
> limitations, but whoa.

Yes. Somehow I knew that.

Did you hear about the linguist giving a lecture and telling how in
some languages a double negative is a positive and in some it is still
a negative, but there is no language in which a double positive is a
negative. And some smart alec up the back calls out sneeringly "Yeah,
right".

-- Dave Keenan

--- In tuning@yahoogroups.com, "Daniel Wolf" <djwolf@...> wrote:
> For the record, Erv did work with MOS that wrapped around intervals
other
> than an octave. Once, at his kitchen table, and "just for kicks" (a
> typical Wilson phrase), he took me on a spin through MOS on fourths,
> fifths and twelfths. As Chalmer's book, then still in manuscript,
was of
> great interest to both of us, the tetrachordal possibilities were
explored
> the most. I believe that this eventually led Wilson to the
Parvi/Marwa
> papers.
>
> Daniel Wolf
>

Thanks for that Daniel. But that wasn't quite the sort of thing I had
in mind. Whatever your target interval of equivalence, you can get a
distributionally even two-step-size scale within it by wrapping the
generator within the whole interval of equivalence (the only way I've
ever seen erv do it), or within the two halves of that interval, or
within the three thirds of that interval etc. These produce distinct
scales. We were never sure whether to call them MOS or not if they
weren't wrapping within the whole interval of equivalence.

I believe George Secor wrote to Erv asking him about this. I seem to
remember that the letter in reply did not appear to address the
question at all.

-- Dave Keenan

That this equation had been put up at least two other times in this discussion basically says that there is no use me posting.
but!
it seems implied by if entropy can be related to the con/dis question at all then how else can it relate except by being ambiguous. if we can assume that entropy = ambiguousness and if not, why!

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Dave Keenan wrote:
>
>
> >
> > My problem is with it in regard to the con/dis problems. The assumption
> > that Ambiguous= Dissonance is questionable.
>
> Yes. It is. Who said it wasn't?
>
>
>

On Mon, Jun 23, 2008 at 8:03 AM, Kraig Grady <kraiggrady@...> wrote:
> That this equation had been put up at least two other times in this
> discussion basically says that there is no use me posting.
> but!
> it seems implied by if entropy can be related to the con/dis question at
> all then how else can it relate except by being ambiguous. if we can
> assume that entropy = ambiguousness and if not, why!

That's what I've been saying - entropy CAN mean ambiguousness, but it
doesn't have to. Local maxima of the curve are harder to process and
make sense of than local minima, but to categorically state that a
local maximum on the curve IS "ambiguous" is a step that you can't
take. You can only assume that entropy = relatively more, or
relatively less ambiguous.

Over time, as you become accustomed to an interval class (such as
9/7), it's entirely possible that you will start to hear it as an
interval in its own right, rather than as a sharp 5/4. The same would
apply to 11/9 as well, even though it corresponds to a local maximum
of harmonic entropy.

Just because something is a local maximum doesn't mean that it is
going to be entirely interpreted as ambiguous. It just means that it's
HARDER for you to "piece together" what interval it is and how it
works. Over time, after repeated exposures in musical contexts, it
becomes considerably less hard. In order for an interval to be
completely and forever ambiguous, and never be able to made sense of,
it would have to have infinite entropy, not just more than the
surrounding points.

Think of it as the Rite of Spring: there is a lot of musical "entropy"
floating around in that piece. The first time you hear it, it might
sound like noise to you. However, after repeated listens, you start to
make sense of it. The same applies to high-entropy intervals - they're
harder to make sense of the first time you hear them, but they get
considerably easier after a while. Harmonic entropy doesn't actually
determine the end result of how ambiguous an interval sounds.

-Mike

so a slight qualifier
more entropy=more ambiguousness.
never thought differently cause 11/9 seems to have little entropy.
with what Sterns presented is as good as any other
So you see it 'evolutionary'.
the things in is that neutral thirds are way more common in the world than just thirds.
The blues is a great illustration of how strong this interval is cause it exist DESPITE the ambient tuning.
where as i cannot think of a culture with neutral thirds where the people are compelled to enter 5/4 and6/5 despite.
So it seems the real driving force is the intervals 'intent' within the culture.
then it finds the acoustical means (pardon the pun) to do so.

in the bland lab of unmusical sonority without meaning, [if we really need to go to that level, assuming it will tell something about the living]

my experience though is that JI is both more consonant but also more dissonant because it can create relationships that will not be mistaken as something else. It is this extreme breath of ability is what makes it useful as a building block. It is the best modular system we have.

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Mike Battaglia wrote:
>
> On Mon, Jun 23, 2008 at 8:03 AM, Kraig Grady <kraiggrady@... > <mailto:kraiggrady%40anaphoria.com>> wrote:
> > That this equation had been put up at least two other times in this
> > discussion basically says that there is no use me posting.
> > but!
> > it seems implied by if entropy can be related to the con/dis question at
> > all then how else can it relate except by being ambiguous. if we can
> > assume that entropy = ambiguousness and if not, why!
>
> That's what I've been saying - entropy CAN mean ambiguousness, but it
> doesn't have to. Local maxima of the curve are harder to process and
> make sense of than local minima, but to categorically state that a
> local maximum on the curve IS "ambiguous" is a step that you can't
> take. You can only assume that entropy = relatively more, or
> relatively less ambiguous.
>
> Over time, as you become accustomed to an interval class (such as
> 9/7), it's entirely possible that you will start to hear it as an
> interval in its own right, rather than as a sharp 5/4. The same would
> apply to 11/9 as well, even though it corresponds to a local maximum
> of harmonic entropy.
>
> Just because something is a local maximum doesn't mean that it is
> going to be entirely interpreted as ambiguous. It just means that it's
> HARDER for you to "piece together" what interval it is and how it
> works. Over time, after repeated exposures in musical contexts, it
> becomes considerably less hard. In order for an interval to be
> completely and forever ambiguous, and never be able to made sense of,
> it would have to have infinite entropy, not just more than the
> surrounding points.
>
> Think of it as the Rite of Spring: there is a lot of musical "entropy"
> floating around in that piece. The first time you hear it, it might
> sound like noise to you. However, after repeated listens, you start to
> make sense of it. The same applies to high-entropy intervals - they're
> harder to make sense of the first time you hear them, but they get
> considerably easier after a while. Harmonic entropy doesn't actually
> determine the end result of how ambiguous an interval sounds.
>
> -Mike
>
>

> Well, the concept of saying that high harmonic entropy = ambiguous
> is questionable as well. It just means "more ambiguous." To
> determine absolutely that every individual will be unable to hear
> 11/9 as a consonance in its own right; to categorically state that
> 11/9 IS "ambiguous" and will flip flop between 5/4 and 6/5 or
> something like it, is absurd without taking into account other
> factors.

Mike, I'm really getting tired of the straw men. I'm used to
it from Kraig but I can't handle the two of you at once. If
you want to have a discussion about this, can we please keep it
a two-way one?

-Carl

> > Helmholtz in appendix XV. p.415-418. Why has no one compared
> > with this. middle of 416 being basis for P.192
>
> Can anyone put this on the web, or point to where it already is?

Dave, I discussed this at length some days ago in reply to
John Chalmers. It's on Google books. Just search for it.

-Carl

Kraig wrote:
> entropy = ambiguousness and if not, why!

Entropy is a precise term with a precise definition.
"Ambiguousness" is not. If somebody says they're the
same, I assume that amounts to their definition of
the latter word. If somebody says they're different,
I'll be inclined to ask how they define ambiguousness.

I have said a thousand times and I'll say again, that
MOST (but NOT necessarily ALL) of what we experience
as concordance and discordance in sounds *taken OUT
of musical context* can be described by 2 values: an
entropy value and a roughness/beating value. I'm
happy to explain what I mean by that, but Erlich and
Sethares already do it so well....

By the way Mike, Easley Blackwood long ago suggested
the terms concordance and discordance be used to
address the notion of consonance and dissonance without
musical context (since consonance and dissonance are
actually musical terms). We tried that for a while
on this list but it didn't stick. Maybe we should
try again?

In psychoacoustics, they tried "sensory dissonance".
But then THAT term became associated with the pet
theory of the people who proposed it, namely the
roughness theory. So it's tainted now as well.

Also, we need to keep terms for both consonance and
dissonance, as they are NOT inverses.

Note to revolutionaries: Next time you want to attack
a conspiracy on this list, please refer back to this
message for material to attack. Here's the link for
your reference:

/tuning/topicId_77580.html#77653

Thanks,

-Carl

> but to categorically state that a
> local maximum on the curve IS "ambiguous" is a step that you can't
> take.

Mike: please see my first paragraph in

/tuning/topicId_77580.html#77653

and get back to me. We can't possible succeed until we
agree on the basics of what's to be expected from language.

> You can only assume that entropy = relatively more, or
> relatively less ambiguous.

Are you thinking aloud here, or what?

> Just because something is a local maximum doesn't mean that it is
> going to be entirely interpreted as ambiguous. It just means that
> it's HARDER for you to "piece together" what interval it is and
> how it works.

I agree. So what?

-Carl

On Mon, Jun 23, 2008 at 1:19 PM, Carl Lumma <carl@...> wrote:
>> Well, the concept of saying that high harmonic entropy = ambiguous
>> is questionable as well. It just means "more ambiguous." To
>> determine absolutely that every individual will be unable to hear
>> 11/9 as a consonance in its own right; to categorically state that
>> 11/9 IS "ambiguous" and will flip flop between 5/4 and 6/5 or
>> something like it, is absurd without taking into account other
>> factors.
>
> Mike, I'm really getting tired of the straw men. I'm used to
> it from Kraig but I can't handle the two of you at once. If
> you want to have a discussion about this, can we please keep it
> a two-way one?
>
> -Carl

I was responding to Kraig's post about how harmonic entropy and
ambiguousness and dissonance were related. Everything I say isn't some
kind of tag teaming of me and Kraig vs. you. A lot of people on the
board have made the exact assumption that harmonic entropy maxima ARE
absolutely ambiguous, not least of all Paul Erlich himself:

"Note also that there is a definite maximum at around 348 cents. This
means that harmonically, the brain interprets the neutral third with a
variety of ratios, none of which is predominant enough to allow the
brain to make a decision."

Which isn't quite the truth, as it is quite possible that the brain
ultimately could make a decision as it grows more accustomed to that
interval. Just because you understand this already doesn't mean
everyone does, and it's those people I was responding to.

On Mon, Jun 23, 2008 at 1:38 PM, Carl Lumma <carl@...> wrote:
> Kraig wrote:
>> entropy = ambiguousness and if not, why!
>
> Entropy is a precise term with a precise definition.
> "Ambiguousness" is not. If somebody says they're the
> same, I assume that amounts to their definition of
> the latter word. If somebody says they're different,
> I'll be inclined to ask how they define ambiguousness.

Indeed. Precisely what I was trying to explain to Kraig myself before
you labeled it as a straw man attack on you.

> I have said a thousand times and I'll say again, that
> MOST (but NOT necessarily ALL) of what we experience
> as concordance and discordance in sounds *taken OUT
> of musical context* can be described by 2 values: an
> entropy value and a roughness/beating value. I'm
> happy to explain what I mean by that, but Erlich and
> Sethares already do it so well....

Indeed.

> By the way Mike, Easley Blackwood long ago suggested
> the terms concordance and discordance be used to
> address the notion of consonance and dissonance without
> musical context (since consonance and dissonance are
> actually musical terms). We tried that for a while
> on this list but it didn't stick. Maybe we should
> try again?

Ah, except I thought it was "accordance." Either way, I find the term
more appropriate than using consonance and dissonance, as both of
those are perceptual qualities which as we've been discussing are
beyond the scope of how far harmonic entropy can really go.

> In psychoacoustics, they tried "sensory dissonance".
> But then THAT term became associated with the pet
> theory of the people who proposed it, namely the
> roughness theory. So it's tainted now as well.
>
> Also, we need to keep terms for both consonance and
> dissonance, as they are NOT inverses.

Indeed. I agree.

> Note to revolutionaries: Next time you want to attack
> a conspiracy on this list, please refer back to this
> message for material to attack. Here's the link for
> your reference:
>
> /tuning/topicId_77580.html#77653

"Shocking eyewitness reports are coming in of a 'straw man' being
brutally assaulted on the yahoo tuning list:
news at 11."

-Mike

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
>
> That this equation had been put up at least two other times in this
> discussion basically says that there is no use me posting.
> but!
> it seems implied by if entropy can be related to the con/dis
question at
> all then how else can it relate except by being ambiguous. if we can
> assume that entropy = ambiguousness and if not, why!

Entropy = ambiguity seems fairly safe to say, but not even Paul Erlich
claimed Entropy/Ambiguity = Dissonance. He only said it was one
component of dissonance.

-- Dave Keenan

--- In tuning@yahoogroups.com, "Mike Battaglia" <battaglia01@...> wrote:
> The same applies to high-entropy intervals - they're
> harder to make sense of the first time you hear them, but they get
> considerably easier after a while. Harmonic entropy doesn't actually
> determine the end result of how ambiguous an interval sounds.

OK. I can go along with that.

-- Dave Keenan

--- In tuning@yahoogroups.com, "Mike Battaglia" <battaglia01@...> wrote:
> A lot of people on the
> board have made the exact assumption that harmonic entropy maxima ARE
> absolutely ambiguous, not least of all Paul Erlich himself:
>
> "Note also that there is a definite maximum at around 348 cents. This
> means that harmonically, the brain interprets the neutral third with a
> variety of ratios, none of which is predominant enough to allow the
> brain to make a decision."
>
> Which isn't quite the truth, as it is quite possible that the brain
> ultimately could make a decision as it grows more accustomed to that
> interval. Just because you understand this already doesn't mean
> everyone does, and it's those people I was responding to.
>

By Paul saying "the brain" here and not "the person" i think we can
take it that he's talking about some low level processing that can
certainly be overridden by higher level factors.

But interestingly, if you just reduce the "s" parameter of the model,
that relates to the person's pitch discrimination, 9:11 appears as a
notch in its own right. But I agree with you that it doesn't have to,
it can just be learned by repetition, and I expect Paul would agree.

-- Dave Keenan

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> > > Helmholtz in appendix XV. p.415-418. Why has no one compared
> > > with this. middle of 416 being basis for P.192
> >
> > Can anyone put this on the web, or point to where it already is?
>
> Dave, I discussed this at length some days ago in reply to
> John Chalmers. It's on Google books. Just search for it.
>
> -Carl

Hi Carl,

I tried following the leads you gave then, but got nowhere. All I
could find were references to the book, and a few pages, not the whole
book as a PDF. There must be something I'm not understanding about
Google Books.

-- Dave Keenan

Entropy has not a precise definition in relation to perception. it is a law of thermodynamics.
just because it is a 'scientific' word, this means nothing

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Carl Lumma wrote:
>
> Kraig wrote:
> > entropy = ambiguousness and if not, why!
>
> Entropy is a precise term with a precise definition.
>
>
>

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
>
> Entropy has not a precise definition in relation to perception. it is a
> law of thermodynamics.
> just because it is a 'scientific' word, this means nothing

Kraig,

Entropy also has a precise definition in relation to information
theory. It is this meaning that Harmonic Entropy invokes, and
information processing is clearly related to perception.
See http://en.wikipedia.org/wiki/Information_entropy

-- Dave Keenan

information is 'related'. that is all that can be said.
information theory is another ball of wax that had its moment in the sun being applied to music. it didn't seem to last long or lead anywhere. hence its relationship to music is fuzzy at best.

....is a measure of the uncertainty
uncertain and ambiguous are close enough for me

is this the formula used then? otherwise one is just taking a poetic analogy. not that there isn't value in that

but we have really gotten into left field. if i have questions i will direct them at Paul where i am sure they would be cleared up much easier.
I ask questions and get no answers and are referred to attacking straw men.
i am tired of my question being diverted into such trivial points as above.

this time i really am out of discussing it

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Dave Keenan wrote:
>
> --- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com>, Kraig > Grady <kraiggrady@...> wrote:
> >
> > Entropy has not a precise definition in relation to perception. it is a
> > law of thermodynamics.
> > just because it is a 'scientific' word, this means nothing
>
> Kraig,
>
> Entropy also has a precise definition in relation to information
> theory. It is this meaning that Harmonic Entropy invokes, and
> information processing is clearly related to perception.
> See http://en.wikipedia.org/wiki/Information_entropy > <http://en.wikipedia.org/wiki/Information_entropy>
>
> -- Dave Keenan
>
>

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
> is this the formula used then? otherwise one is just taking a poetic
> analogy. not that there isn't value in that

Harmonic Entropy is calculated using the formula for
information-theoretic entropy, as defined by Claude Shannon. Other
assumptions are involved in obtaining the probabilities to feed into
that formula.

-- Dave Keenan

Don't cultures that use neutral thirds use them primarily melodically,
not in vertical harmony? If so, I don't think anyone would expect
Harmonic Entropy to be relevant. And if they are used harmonically, or
against a drone, then isn't their very balancing between 5:6 and 4:5 a
possible explanation for their relative stability?

-- Dave Keenan

--- In tuning@...m, Kraig Grady <kraiggrady@...> wrote:
>
> so a slight qualifier
> more entropy=more ambiguousness.
> never thought differently cause 11/9 seems to have little entropy.
> with what Sterns presented is as good as any other
> So you see it 'evolutionary'.
> the things in is that neutral thirds are way more common in the world
> than just thirds.
> The blues is a great illustration of how strong this interval is cause
> it exist DESPITE the ambient tuning.
> where as i cannot think of a culture with neutral thirds where the
> people are compelled to enter 5/4 and6/5 despite.
> So it seems the real driving force is the intervals 'intent' within
the
> culture.
> then it finds the acoustical means (pardon the pun) to do so.
>
> in the bland lab of unmusical sonority without meaning, [if we really
> need to go to that level, assuming it will tell something about the
living]
>
> my experience though is that JI is both more consonant but also more
> dissonant because it can create relationships that will not be mistaken
> as something else. It is this extreme breath of ability is what
makes it
> useful as a building block. It is the best modular system we have.
>
> /^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
> Mesotonal Music from:
> _'''''''_ ^North/Western Hemisphere:
> North American Embassy of Anaphoria Island <http://anaphoria.com/>
>
> _'''''''_ ^South/Eastern Hemisphere:
> Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
>
> That this equation had been put up at least two other times in this
> discussion basically says that there is no use me posting.
> but!
> it seems implied by if entropy can be related to the con/dis
question at
> all then how else can it relate except by being ambiguous. if we can
> assume that entropy = ambiguousness and if not, why!

Karl,

Some of the confusion about what is claimed for HE may come from the
fact that it is a theory about some low level processing of the
signals coming from the ear, and we say that the output of this
imagined subsystem corresponds to the level of "ambiguity" in a
certain mathematically well-defined sense. And then someone thinks we
are talking about a conscious experience of ambiguity, which is not
necessarily the case at all.

We imagine there might be some clusters of neurons that take the raw
signals coming from the cochleas and do some processing to try to
determine whether various partials are part of a single tone or not.
And we imagine these clusters sending an unconscious signal on to
other parts of the brain to give the level of uncertainty as to
whether these partials might be part of a single tone. This might be
used by some other part of the brain that tries to "separate" sounds
from multiple sources. One can easily imagine the survival value of
such ability explaining why it might have evolved.

It would be very difficult to talk about this if were not allowed to
"anthropomorphise" to get suitable names for the subsystems and
signals. But then people readily make the mistake of assuming we're
talking about a person's direct conscious experience when we're only
talking about one component that may feed into higher level processing
that in turn depends on learnt factors and finally gives rise to the
conscious experience.

Mike B,

You talked about stretching the harmonic entropy along with stretched
partials. Harmonic Entropy doesn't stretch. It's considered to be a
different component from the one that is supposed to explain that
effect, which is the Plomp/Levelt/Sethares "sensory dissonance" model.
This can be calculated by applying a critical band function such as
that described in Dave Benson's free book (10 MB)
http://www.maths.abdn.ac.uk/~bensondj/html/music.pdf
to all the pairs of partials of all the tones together. The
calculation is explained in detail in Sethares "Tuning Timbre Spectrum
Scale", a computer program on CD is included.

This "sensory dissonance" calculation can handle triads and up too.
You can even include the difference tones.

Some fun stuff here.
http://en.wikipedia.org/wiki/Consonance_and_dissonance

-- Dave Keenan

> I was responding to Kraig's post about how harmonic entropy and
> ambiguousness and dissonance were related. Everything I say isn't
> some kind of tag teaming of me and Kraig vs. you. A lot of people
> on the board have made the exact assumption that harmonic entropy
> maxima ARE absolutely ambiguous,

Again, I think this is just a fantasy of yours until I see
some evidence to the contrary. Paul doesn't say anything
like this in the quote you gave, either.

-Carl

Mike wrote:
> > By the way Mike, Easley Blackwood long ago suggested
> > the terms concordance and discordance be used to
> > address the notion of consonance and dissonance without
> > musical context (since consonance and dissonance are
> > actually musical terms). We tried that for a while
> > on this list but it didn't stick. Maybe we should
> > try again?
>
> Ah, except I thought it was "accordance." Either way, I
> find the term more appropriate than using consonance and
> dissonance, as both of those are perceptual qualities
> which as we've been discussing are beyond the scope of
> how far harmonic entropy can really go.

1. What does "accordance" have to do with how far
harmonic entropy can go?
2. Proposing "consonance" and "dissonance" be replaced
by a single term seems odd in light of the fact that
you subsequently agree with me that two terms are
necessary since they're not inverses:

> > Also, we need to keep terms for both consonance and
> > dissonance, as they are NOT inverses.
>
> Indeed. I agree.

-Carl

> But interestingly, if you just reduce the "s" parameter of the model,
> that relates to the person's pitch discrimination, 9:11 appears as a
> notch in its own right. But I agree with you that it doesn't have to,
> it can just be learned by repetition, and I expect Paul would agree.
>
> -- Dave Keenan

Of course we now now that there is no level so low that it is
not subject to top-down feedback (seeing as SOAEs can be heard
and recorded from outside the ear!).

-Carl

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@...> wrote:
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@> wrote:
> >
> > > > Helmholtz in appendix XV. p.415-418. Why has no one compared
> > > > with this. middle of 416 being basis for P.192
> > >
> > > Can anyone put this on the web, or point to where it already is?
> >
> > Dave, I discussed this at length some days ago in reply to
> > John Chalmers. It's on Google books. Just search for it.
> >
> > -Carl
>
> Hi Carl,
>
> I tried following the leads you gave then, but got nowhere. All I
> could find were references to the book, and a few pages, not the
> whole book as a PDF. There must be something I'm not understanding
> about Google Books.

If you search Google Books for "sensations of tone" it is the
first result.

http://books.google.com

(Or choose Books after a web search.)

-Carl

everytime i try to get off this subject you resort to misrepresentations and insults. this conversation is not doing anyone any good and is useless. let us move on.

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Carl Lumma wrote:
>
> when you wax
> pontifactory for three paragraphs, or declare in a mistyped
> sentence fragment that all should be trashed, based on something
> having to do with "ambiguousness", you're mainly full of shit.
>
> -Carl
>
>

> Mike B,
>
> You talked about stretching the harmonic entropy along with stretched
> partials. Harmonic Entropy doesn't stretch. It's considered to be a
> different component from the one that is supposed to explain that
> effect, which is the Plomp/Levelt/Sethares "sensory dissonance" model.
> This can be calculated by applying a critical band function such as
> that described in Dave Benson's free book (10 MB)
> http://www.maths.abdn.ac.uk/~bensondj/html/music.pdf
> to all the pairs of partials of all the tones together. The
> calculation is explained in detail in Sethares "Tuning Timbre Spectrum
> Scale", a computer program on CD is included.

OK, I see the distinction now. Harmonic entropy is probably better off
describing how when you stretch the partials, there is a certain point
at which 4:5:6:7 will eventually become 4.5:6:7.5:9 (which is the same
as 9:12:15:18).

> This "sensory dissonance" calculation can handle triads and up too.
> You can even include the difference tones.
>
> Some fun stuff here.
> http://en.wikipedia.org/wiki/Consonance_and_dissonance

Ah, that article is great. A lot of the ideas I'd been putting out in
this thread seem to be already described in that article. Which I very
much like.

> Don't cultures that use neutral thirds use them primarily melodically,
> not in vertical harmony? If so, I don't think anyone would expect
> Harmonic Entropy to be relevant. And if they are used harmonically, or
> against a drone, then isn't their very balancing between 5:6 and 4:5 a
> possible explanation for their relative stability?

This question is equivalent to the question of how much of the
learning process of interval recognition is cognitive in nature and
how much is part of the periodicity mechanism or some other
subconscious feature adapting to more efficiently process new sounds.
It's equivalent to the question: "does the part of the brain that
processes incoming harmonic information have a fixed efficiency rate,
or an adaptable efficiency rate?" As I have seen in myself a strong
tendency to start to hear 9/7 as its own interval with its own
"sound," and not just a sharp 5/4, I strongly suspect it actually DOES
have something to do with an increase in pitch discrimination in
certain interval areas. If not, I would simply hear 9/7 as a sharp
5/4, and that is what 9/7 would BECOME to me, just as 11/9 would
become "the ambiguous third" people of those cultures. But, from my
own experience, although 9/7 can serve as a sharp major third, it can
also serve as 9/7, which suggests to me that there is some deeper
process at work adapting to these intervals.right?

So it is certainly true that 11/9 could remain "ambiguous" and that
that is what the actual interval could BECOME to them, i.e. that would
be a part of their schema for it - but it is also certainly true that
they might have found an intuitive use for 11/9 that is distinct from
this ambiguity. Sort of how a minor third can have a lot of uses - in
the blues it's often used to sound like a very flat major third, but
sometimes also in the blues it's almost serving a 19/16 function over
a 5/4, and it can also be used as simply minor, as an interval in its
own right, so on and so on. I believe, although this is just my
hypothesis, that the process by which intervallic recognition becomes
easier may correlate specifically to a widening of pitch
discrimination, or an altering of that "s"/sigma parameter, around
certain intervals and areas which are most thoroughly explored
musically. I'd have to do listening tests before I could make that
distinction though, and I'm not sure how I'd be able to objectively
assess the harmonic entropy component while filtering out conscious
distorting of the process and cognitive labeling and such, or exactly
how that fits in.

The key here is understanding the function of the periodicity
mechanism better, I think, and in a few of Paul's posts I see he has
it labeled as "not clearly understood." Maybe some research has been
done since then that would elucidate the situation.

-Mike

> The key here is understanding the function of the periodicity
> mechanism better, I think, and in a few of Paul's posts I see he has
> it labeled as "not clearly understood." Maybe some research has been
> done since then that would elucidate the situation.

I don't know what era you're reading from, but Paul found
Peter Cariani's work circa 2000 I think (for instance
"Neurobiological Foundations for the Theory of Harmony in
Western Tonal Music") and I've done a lot more digging
since then.

-Carl

This is driving me nuts. The only thing I get when I do that is a
limited preview. Could it be because I'm in Australia? Copyright laws
or something?

-- Dave Keenan

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
> If you search Google Books for "sensations of tone" it is the
> first result.
>
> http://books.google.com
>
> (Or choose Books after a web search.)
>
> -Carl
>

i have the same problem when i just tried

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Dave Keenan wrote:
>
> This is driving me nuts. The only thing I get when I do that is a
> limited preview. Could it be because I'm in Australia? Copyright laws
> or something?
>
> -- Dave Keenan
>
> --- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com>, "Carl > Lumma" <carl@...> wrote:
> > If you search Google Books for "sensations of tone" it is the
> > first result.
> >
> > http://books.google.com <http://books.google.com>
> >
> > (Or choose Books after a web search.)
> >
> > -Carl
> >
>
>

> Again, I think this is just a fantasy of yours until I see
> some evidence to the contrary. Paul doesn't say anything
> like this in the quote you gave, either.
>
> -Carl

OK, to name an example off of the top of my head, all of the talk
about metastable intervals recently involved the assumption that they
are perceptually ambiguous intervals. If by "ambiguous" people didn't
mean "perceptually ambiguous" but rather meant "precognitively
ambiguous" or something, then I have simply misunderstood what they're
saying. However, from that conversation, I remember getting the vibe
quite a few times that people often referred to these intervals as
being "ambiguous," and I am simply pointing out that they might also
serve a unique function that is decidedly NOT "ambiguous" in nature,
once the ear/brain system learns how to process those intervals.
Somebody, might have been Dave, referred to them as new types of
consonance, and I think he was right on with that.

To name another one, someone else mentioned a while ago that the ear
interprets the minor third as an out of tune major third in a triad,
and the justification used was in A minor, that since people still
properly hear the A as the "root" of the chord, that that corresponds
to hearing an "A" phantom fundamental and that the C is interpreted as
an out of tune C#. Being as the same applies for an A-C interval by
itself (which, if played alone, usually does sound like A minor with A
as the root), I would expect the statement to translate over to purely
dyadic harmonic entropy as well. This is an interesting theory, and
the rationale sounds good, but it's an unfalsifiable statement.

Someone also referred to having a 4:5:6 chord with a 16/9 on top would
sound like the 16/9 was essentially an out of tune 7/4. While this
MIGHT be true for just the 16/9 dyad itself, it is certainly not true
for the entire chord. In fact, in my experience, the 16/9 and 7/4
dyads alone have completely different characters to me. When I first
heard 7/4, I heard it as an out of tune 16/9, so that has something to
say about how familiarity affects the strength of an interval's field
of attraction.

>> Ah, except I thought it was "accordance." Either way, I
>> find the term more appropriate than using consonance and
>> dissonance, as both of those are perceptual qualities
>> which as we've been discussing are beyond the scope of
>> how far harmonic entropy can really go.
> 1. What does "accordance" have to do with how far
> harmonic entropy can go?
> 2. Proposing "consonance" and "dissonance" be replaced
> by a single term seems odd in light of the fact that
> you subsequently agree with me that two terms are
> necessary since they're not inverses:

I meant that I thought the terms were "accordance" and "discordance"
rather than "concordance" and "discordance." Whatever we use, I think
that MUSICALLY, we should use two terms. I think of consonance as
though it is an entire spectrum of different sounds, some which are
easy to grasp ("more consonant", like major thirds and such) and some
which are harder to grasp ("less consonant", like 7/5 and such).
"Dissonance," as it's usually used historically, is used to describe
sounds that people are unable to "grasp" (which may correspond to a
failure of the periodicity and place mechanisms to process
high-entropy information). A major third used to be considered a
dissonance. A tritone used to be considered a dissonance. In jazz
playing today, a b9 unless it's over the root is considered to be a
dissonance. Some of the best music out there uses dissonant intervals
in a decidedly dissonant way - i.e. it sounds unstable as part of its
charm - and some of the best music shows you how sounds you previously
thought to be dissonant are actually complex consonances and fit
together in a certain way. So it has something to do with musical
context, and consonant intervals can also be used in a way that sounds
dissonant as well - such as serialistic music, for example.

However, within the context of information theory, I wouldn't be
opposed to really only using the term "accordance" to represent the
both of those (since you brought it up and I like the name now). After
all, we are simply trying to evaluate how ordered the signal is, or
how high the entropy is. To be honest, I would think the only actual
term representing some kind of absolute descriptive value that we need
to use is "entropy." Concordance and discordance are just two terms to
mention how relatively high or low the entropy is.

So you can say that a given interval might be more or less
concordant/discordant than another interval, i.e. that a major third
is more concordant than a neutral third, but to give different
intervals absolute values such as "concordant" or "discordant" in and
of themselves doesn't make much sense IMO.

Really I'm starting to realize that it all boils down to that sigma
parameter - if that parameter can vary across pitch space, then it
might change quite a bit in a relatively short amount of time for a
certain interval, making the precise nature of what these HE curves
convey slightly more complicated than if it doesn't.

> Of course we now now that there is no level so low that it is
> not subject to top-down feedback (seeing as SOAEs can be heard
> and recorded from outside the ear!).

Can you explain what you mean by this?

-Mike

Carl Lumma wrote:
> It's a quantity used in many fields including thermodynamics,
> computer science, physics, biology, neuroscience, etc. It's
> usually expressed in units of nats or in bits. It happens to
> to be one of the most useful concepts known to man. But none
> of that is germane to my point, which was: when you wax
> pontifactory for three paragraphs, or declare in a mistyped
> sentence fragment that all should be trashed, based on something
> having to do with "ambiguousness", you're mainly full of shit.

Look man, if you want to bash Grady, can you go make a bash Grady
thread, or take it offlist? I hate that every god damned post on this
forum has to eventually degrade into the same negative, hateful,
counterproductive bullshit. I don't agree with the view that HE or
information theory is useless either, but you don't see me saying that
he's "full of shit" over it.

-Mike

Mike Battaglia wrote:
> Look man, if you want to bash Grady, can you go make a bash Grady
> thread, or take it offlist? I hate that every god damned post on this
> forum has to eventually degrade into the same negative, hateful,
> counterproductive bullshit. I don't agree with the view that HE or
> information theory is useless either, but you don't see me saying that
> he's "full of shit" over it.
>
> -Mike
That's our Carl...isn't he charming?

--
* David Beardsley
* http://biink.com

Carl and i have come to an agreement!

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

David Beardsley wrote:
>
> Mike Battaglia wrote:
> > Look man, if you want to bash Grady, can you go make a bash Grady
> > thread, or take it offlist? I hate that every god damned post on this
> > forum has to eventually degrade into the same negative, hateful,
> > counterproductive bullshit. I don't agree with the view that HE or
> > information theory is useless either, but you don't see me saying that
> > he's "full of shit" over it.
> >
> > -Mike
> That's our Carl...isn't he charming?
>
> -- > * David Beardsley
> * http://biink.com <http://biink.com>
>
>

Dave Keenan wrote:
> But interestingly, if you just reduce the "s" parameter of the model,
> that relates to the person's pitch discrimination, 9:11 appears as a
> notch in its own right. But I agree with you that it doesn't have to,
> it can just be learned by repetition, and I expect Paul would agree.
>
> -- Dave Keenan

Some more thoughts on this.

I was just writing in response to Margo's thread that when I come to
perceive the relationship between two justly tuned intervals as being
whole unto itself, I get a sense of "depth" to the interval. 3/2, and
stacks of 3/2's, are much more shallow than 5/4, which sounds like
it's going "in" more or "back" or "deep" or something. I
synaesthetically perceive it to be the aural equivalent of the visual
process by which the brain puts parallax imagery between two eyes
together to form one three dimensional image. The distance by which
the two images diverge correlates with the brain's propensity and
ability to merge the two images into a cohesive, three dimensional
whole. Similarly, the harmonic "distance" by which the two tones
diverge correlates with the brain's propensity to merge the two tones
together into a cohesive interval. I use the term distance here to
mean in some kind of multi-dimensional JI space, and not distance in
cents or in pitch.

So if I perceive my ability to place increasingly higher-limit
harmonic intervals as an increase in awareness of "depth," and as I
perceive my ability to determine finer and finer pitch variations as
an increase of resolution (as in a monitor), could it be that this
sensation of depth is the actual experience of the periodicity
mechanism working?

So a few questions I have from this observation:

1) Are there any models of harmonic entropy that incorporate a free
variable that describes the ability of the periodicity mechanism to
operate, as there is with the ability of the place mechanism? Is that
what the "N" parameter is for?

and 2) has any experimentation ever been done on with having the sigma
value vary across the pitch spectrum? I'm thinking along the lines of
having sigma "peaks" at 100, 200, 300 ... up to 1200 cents to simulate
the harmonic entropy of an average listener who has been mainly
exposed to 12-tet... Of course, some other intervals would likely be
thrown in as well to make it really authentic, like perhaps some
smaller peaks for the just intervals, like one at 7/4 and one at 350
cents. I can already tell you that my pitch discrimination at around
350 cents is much stronger than my pitch discrimination at 550/600
cents, for example -- I sometimes get 550 and 600 cent intervals
confused, especially if they're at the top of a chord (although
considerably less so recently), but I rarely ever actually confuse 350
for 400 cents.

It might be interesting to generate a sigma curve and multiply THAT
into the equation rather than keeping sigma constant. You could plot a
variety of the most common scales and intervals you've heard and do
some kind of regression analysis to get a sigma curve, then see if the
result holds any resemblance to how you first heard microtonal music
when you were previously only exposed to 12tet or whatever your
background is. Might provide a decent model of how accordant music
from other cultures will be to us and how accordant western music will
be to those in other cultures. So we might be able to compute an HE
"map" for a specific person this way.

It might also be interesting to see if there is an optimal level of
harmonic entropy that makes intervals easiest to learn as well, as
opposed to ones that are already learned and ones that might just
sound like noise for quite a while until they are placed.

-Mike

I agree. Carl's post was another of his "insulting people rather than their ideas" lapses.

I currently have a $50 claim against him for doing this to me, in response to his $50 offer of about a week ago.

Maybe Grady should initiate his own claim $50 against Carl too.

Unfortunately, it is a little difficult to get Carl to actually deliver the "prize", as he goes off into some obscure voting routine and attempts to put claimants through all sorts of hoops instead of admitting his "lapse" and paying up as he had suggested that he would.

I appreciate Carl's devil's advocate function, yet I am becoming doubtful about whether the time-wasting required is worth the effort for a "promised" $50;-)

On second thoughts; apologies to those who are distressed by the negative nonsense; let's continue exploring ideas, and just treat the personal attacks as (un?) necessary noise.

On 24 Jun 2008, at 06:41, Mike Battaglia wrote:

> Carl Lumma wrote:
> > It's a quantity used in many fields including thermodynamics,
> > computer science, physics, biology, neuroscience, etc. It's
> > usually expressed in units of nats or in bits. It happens to
> > to be one of the most useful concepts known to man. But none
> > of that is germane to my point, which was: when you wax
> > pontifactory for three paragraphs, or declare in a mistyped
> > sentence fragment that all should be trashed, based on something
> > having to do with "ambiguousness", you're mainly full of shit.
>
> Look man, if you want to bash Grady, can you go make a bash Grady
> thread, or take it offlist? I hate that every god damned post on this
> forum has to eventually degrade into the same negative, hateful,
> counterproductive bullshit. I don't agree with the view that HE or
> information theory is useless either, but you don't see me saying that
> he's "full of shit" over it.
>
> -Mike
>
>
Charles Lucy
lucy@...

- Promoting global harmony through LucyTuning -

for information on LucyTuning go to:
http://www.lucytune.com

For LucyTuned Lullabies go to:
http://www.lullabies.co.uk

yes I think we just need to work on productive things here. there are going to be such dead locks possibly we can all learn to nib them sooner than later.

There is something rather funny that the argument was over 'entropy'. since that is what it invoked it seems :)

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Charles Lucy wrote:
>
> I agree. Carl's post was another of his "insulting people rather than > their ideas" lapses.
>
>
> I currently have a $50 claim against him for doing this to me, in > response to his $50 offer of about a week ago.
>
> Maybe Grady should initiate his own claim $50 against Carl too.
>
> Unfortunately, it is a little difficult to get Carl to actually > deliver the "prize", as he goes off into some obscure voting routine > and attempts to put claimants through all sorts of hoops instead of > admitting his "lapse" and paying up as he had suggested that he would.
>
> I appreciate Carl's devil's advocate function, yet I am becoming > doubtful about whether the time-wasting required is worth the effort > for a "promised" $50;-)
>
> On second thoughts; apologies to those who are distressed by the > negative nonsense; let's continue exploring ideas, and just treat the > personal attacks as (un?) necessary noise.
>
>
>
> On 24 Jun 2008, at 06:41, Mike Battaglia wrote:
>
>> Carl Lumma wrote:
>> > It's a quantity used in many fields including thermodynamics,
>> > computer science, physics, biology, neuroscience, etc. It's
>> > usually expressed in units of nats or in bits. It happens to
>> > to be one of the most useful concepts known to man. But none
>> > of that is germane to my point, which was: when you wax
>> > pontifactory for three paragraphs, or declare in a mistype! d
>> > s entence fragment that all should be trashed, based on something
>> > having to do with "ambiguousness", you're mainly full of shit.
>>
>> Look man, if you want to bash Grady, can you go make a bash Grady
>> thread, or take it offlist? I hate that every god damned post on this
>> forum has to eventually degrade into the same negative, hateful,
>> counterproductive bullshit. I don't agree with the view that HE or
>> information theory is useless either, but you don't see me saying that
>> he's "full of shit" over it.
>>
>> -Mike
>>
>
> Charles Lucy
> lucy@... <mailto:lucy@...>
>
> - Promoting global harmony through LucyTuning -
>
> for information on LucyTuning go to:
> http://www.lucytune.com <http://www.lucytune.com>
>
> For LucyTuned Lullabies go to:
> http://www.lullabies.co.uk <http://www.lullabies.co.uk>
>
>
>
>

The need to invade Iraq? What rotten twisted unholy need is that?

Oz.

On Jun 22, 2008, at 9:40 PM, Carl Lumma wrote:

> --- In tuning@yahoogroups.com, Charles Lucy <lucy@...> wrote:
>>
>> Yes Mike, very perceptive assessment.
>>
>> It makes sense to me, and may explain why Carl and others who
>> are "tone-deaf" to LucyTuning
>
> Charles, I would like to remind you that you're making a public
> statement about me. Can you do me the respect of explaining
> the basis for this claim, i.e. why do you think I am "tone-deaf
> to LucyTuning"?
>
>> have trouble appreciating the scalecoding
>
> And why do you think I have "trouble appreciating" scalecoding?
> Is that like people who have "trouble appreciating" the need
> to invade Iraq?
>
> -Carl

greed.
home of the new saudi empire,
since they are the ones paying for it , albeit indirectly with bail out.
The US is merely their blackwater.

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Ozan Yarman wrote:
>
> The need to invade Iraq? What rotten twisted unholy need is that?
>
> Oz.
>
>
> > Messages in this topic > </tuning/topicId_77580.html#77580;_ylc=X3oDMTM0NXJxdWs4BF9TAzk3MzU5NzE0BGdycElkAzcwNjA1BGdycHNwSWQDMTcwNTg5Nzc1MwRtc2dJZAM3Nzc1OQRzZWMDZnRyBHNsawN2dHBjBHN0aW1lAzEyMTQzNTM1MTEEdHBjSWQDNzc1ODA-> > (73) > </tuning/post;_ylc=X3oDMTJvbG1tOWU3BF9TAzk3MzU5NzE0BGdycElkAzcwNjA1BGdycHNwSWQDMTcwNTg5Nzc1MwRtc2dJZAM3Nzc1OQRzZWMDZnRyBHNsawNycGx5BHN0aW1lAzEyMTQzNTM1MTE-?act=reply&messageNum=77759>

Dave,

On Jun 24, 2008, at 5:17 AM, Dave Keenan wrote:

> Don't cultures that use neutral thirds use them primarily melodically,
> not in vertical harmony?

That conception is right in the case of Maqam music. But, one can surely use them in dissonant, or even quasi-consonant chords.

> If so, I don't think anyone would expect
> Harmonic Entropy to be relevant. And if they are used harmonically, or
> against a drone, then isn't their very balancing between 5:6 and 4:5 a
> possible explanation for their relative stability?
>

Oh, but neutral thirds are hardly stable in Maqam music. Instead, they flounder about as the melody requires them. In Saba, Huzzam, Qarjighar and Ushshaq, one can observe how perdes segah, saba, hisar, evdj and shehnaz that form middle seconds with the diatonic natural notes below them flex up and down. Quantizing these neutral thirds was one of the hardest tasks during my doctorate thesis.

> -- Dave Keenan
>

Oz.

> --- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
>>
>> so a slight qualifier
>> more entropy=more ambiguousness.
>> never thought differently cause 11/9 seems to have little entropy.
>> with what Sterns presented is as good as any other
>> So you see it 'evolutionary'.
>> the things in is that neutral thirds are way more common in the world
>> than just thirds.
>> The blues is a great illustration of how strong this interval is >> cause
>> it exist DESPITE the ambient tuning.
>> where as i cannot think of a culture with neutral thirds where the
>> people are compelled to enter 5/4 and6/5 despite.
>> So it seems the real driving force is the intervals 'intent' within
> the
>> culture.
>> then it finds the acoustical means (pardon the pun) to do so.
>>
>> in the bland lab of unmusical sonority without meaning, [if we really
>> need to go to that level, assuming it will tell something about the
> living]
>>
>> my experience though is that JI is both more consonant but also more
>> dissonant because it can create relationships that will not be >> mistaken
>> as something else. It is this extreme breath of ability is what
> makes it
>> useful as a building block. It is the best modular system we have.
>>
>> /^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
>> Mesotonal Music from:
>> _'''''''_ ^North/Western Hemisphere:
>> North American Embassy of Anaphoria Island <http://anaphoria.com/>
>>
>> _'''''''_ ^South/Eastern Hemisphere:
>> Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>> >
>
>
>
> ------------------------------------
>
> You can configure your subscription by sending an empty email to one
> of these addresses (from the address at which you receive the list):
> tuning-subscribe@yahoogroups.com - join the tuning group.
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>
>
>

--- In tuning@yahoogroups.com, Ozan Yarman <ozanyarman@...> wrote:
>
> The need to invade Iraq? What rotten twisted unholy need is that?
>
> Oz.

Hiya Oz,

I think Carl was almost certainly being facetious here....

-AKJ

> On Jun 22, 2008, at 9:40 PM, Carl Lumma wrote:
>
> > --- In tuning@yahoogroups.com, Charles Lucy <lucy@> wrote:
> >>
> >> Yes Mike, very perceptive assessment.
> >>
> >> It makes sense to me, and may explain why Carl and others who
> >> are "tone-deaf" to LucyTuning
> >
> > Charles, I would like to remind you that you're making a public
> > statement about me. Can you do me the respect of explaining
> > the basis for this claim, i.e. why do you think I am "tone-deaf
> > to LucyTuning"?
> >
> >> have trouble appreciating the scalecoding
> >
> > And why do you think I have "trouble appreciating" scalecoding?
> > Is that like people who have "trouble appreciating" the need
> > to invade Iraq?
> >
> > -Carl
>

Thanks Oz,

That certainly supports the idea that the cultural use of neutral
thirds has little or nothing to do with the coincidence of 9th and
11th harmonics.

I did say "relative" stability. How much variation did you find? Can
you give a standard deviation in cents, or some rough idea?

-- Dave Keenan

--- In tuning@yahoogroups.com, Ozan Yarman <ozanyarman@...> wrote:
>
> Dave,
>
>
> On Jun 24, 2008, at 5:17 AM, Dave Keenan wrote:
>
> > Don't cultures that use neutral thirds use them primarily melodically,
> > not in vertical harmony?
>
>
> That conception is right in the case of Maqam music. But, one can
> surely use them in dissonant, or even quasi-consonant chords.
>
>
> > If so, I don't think anyone would expect
> > Harmonic Entropy to be relevant. And if they are used harmonically, or
> > against a drone, then isn't their very balancing between 5:6 and 4:5 a
> > possible explanation for their relative stability?
> >
>
>
> Oh, but neutral thirds are hardly stable in Maqam music. Instead, they
> flounder about as the melody requires them. In Saba, Huzzam, Qarjighar
> and Ushshaq, one can observe how perdes segah, saba, hisar, evdj and
> shehnaz that form middle seconds with the diatonic natural notes below
> them flex up and down. Quantizing these neutral thirds was one of the
> hardest tasks during my doctorate thesis.
>
>
> > -- Dave Keenan
> >
>
>
> Oz.

Dear Dave,

Indeed, the neutral thirds of Maqam music are more diversified than the ratio 11:9 can encompass. As far as I can tell, middle second intervals roam the mujannab zone between 14:13 and 11:10. This is a region 37 cents wide. Then again, it is possible to broaden the zone and take 15:14 and 10:9 as the extremes. In that case, we acquire a zone that is 63 cents wide!

I conjecture that high prime limit and relatively simple integer ratios such as 14:13, 27:25, 13:12, 12:11, 35:32, 11:10, 54:49 are at play. Then again, instead of middle seconds, we might be looking at neutral thirds, in which case, the performer could be searching for 17:14, 39:32, 11:9, 27:22, 16:13, 21:17 and 31:25.

So many ratios imply the necessity to temper pitches and represent diverse middle seconds as well as neutral thirds with few, yet, variagated microtones that are reasonably spaced. That is how I arrived at 79 MOS 159-tET. Check out page 95 of my doctorate dissertation. There, you will see how the 79-tone tuning approximates many RI intervals.

Oz.

On Jun 25, 2008, at 2:23 PM, Dave Keenan wrote:

> Thanks Oz,
>
> That certainly supports the idea that the cultural use of neutral
> thirds has little or nothing to do with the coincidence of 9th and
> 11th harmonics.
>
> I did say "relative" stability. How much variation did you find? Can
> you give a standard deviation in cents, or some rough idea?
>
> -- Dave Keenan
>
>
> --- In tuning@yahoogroups.com, Ozan Yarman <ozanyarman@...> wrote:
>>
>> Dave,
>>
>>
>> On Jun 24, 2008, at 5:17 AM, Dave Keenan wrote:
>>
>>> Don't cultures that use neutral thirds use them primarily >>> melodically,
>>> not in vertical harmony?
>>
>>
>> That conception is right in the case of Maqam music. But, one can
>> surely use them in dissonant, or even quasi-consonant chords.
>>
>>
>>> If so, I don't think anyone would expect
>>> Harmonic Entropy to be relevant. And if they are used >>> harmonically, or
>>> against a drone, then isn't their very balancing between 5:6 and >>> 4:5 a
>>> possible explanation for their relative stability?
>>>
>>
>>
>> Oh, but neutral thirds are hardly stable in Maqam music. Instead, >> they
>> flounder about as the melody requires them. In Saba, Huzzam, >> Qarjighar
>> and Ushshaq, one can observe how perdes segah, saba, hisar, evdj and
>> shehnaz that form middle seconds with the diatonic natural notes >> below
>> them flex up and down. Quantizing these neutral thirds was one of the
>> hardest tasks during my doctorate thesis.
>>
>>
>>> -- Dave Keenan
>>>
>>
>>
>> Oz.
>
>
>
> ------------------------------------
>
> You can configure your subscription by sending an empty email to one
> of these addresses (from the address at which you receive the list):
> tuning-subscribe@yahoogroups.com - join the tuning group.
> tuning-unsubscribe@yahoogroups.com - leave the group.
> tuning-nomail@yahoogroups.com - turn off mail from the group.
> tuning-digest@yahoogroups.com - set group to send daily digests.
> tuning-normal@yahoogroups.com - set group to send individual emails.
> tuning-help@yahoogroups.com - receive general help information.
> Yahoo! Groups Links
>
>
>

Ozan/Aaron...

> > The need to invade Iraq? What rotten twisted unholy need is that?
> >
> > Oz.
>
> Hiya Oz,
>
> I think Carl was almost certainly being facetious here....
>
> -AKJ

Not exactly facetious... this post explains what I meant:
/tuning/topicId_77580.html#77588

-Carl

Carl, what does your support of the political twistings, squirmings and lies of the Bush cabinet have anything to do with tuning?

Oz.

On Jun 25, 2008, at 8:23 PM, Carl Lumma wrote:

> Ozan/Aaron...
>
>>> The need to invade Iraq? What rotten twisted unholy need is that?
>>>
>>> Oz.
>>
>> Hiya Oz,
>>
>> I think Carl was almost certainly being facetious here....
>>
>> -AKJ
>
> Not exactly facetious... this post explains what I meant:
> /tuning/topicId_77580.html#77588
>
> -Carl
>

On Wed, Jun 25, 2008 at 2:18 PM, Ozan Yarman <ozanyarman@...> wrote:
> Carl, what does your support of the political twistings, squirmings
> and lies of the Bush cabinet have anything to do with tuning?
>
> Oz.

I think that Carl's saying that he -doesn't- support the Bush
administration. You might be misunderstanding here.

-Mike

battaglia01 wrote (on the 23rd):

> An interesting question posed here is, if the diatonic modes can be
> generated as a stack of meantone fifths, what properties would scales
> based on a magic temperament spiral of major thirds have? You might be
> able to build some really consonant scales that way.

The main property is that they have lots of small semitones. The 7 note magic MOS has steps of a small semitone (approximating 25:24 but tempered to be even smaller) and a minor third (approximating 6:5). That's very unbalanced which will cause problems, especially if you try to fit tunes from your head to it. It's still possible to use it in music but so far nobody has.

My rule is that a magic scale shouldn't have two small semitones next to each other. You can use such runs in music but you can always take one note out of the scale and then treat it as a chromaticism. Scales should be a bit more stable.

If the MOS scales don't work out, then, another approach is to take a major triad and transpose it by major thirds. I'll use meantone notation because the magic comma isn't required. So start with G-B-D and move it down a major third to get Eb-G-Bb. Then move the G major up a major third and you have B-D#-F#. The scale is

G Bb B D D# Eb F# G

D-D# and D#-Eb are both small semitones (1 step in 19-equal, both approximating 25:24 in magic). So this breaks the rule I set above. The solution is to take out the D#. We don't need it because B major can be replaced with B minor or B supermajor (B-Eb-F# with B-Eb approximating 7:9). That leaves us with a 6 note scale.

G Bb B D Eb F# G

There are two steps sizes that approximate 6:5 here: between (G and Bb) and (B and D). Adding two notes then gives an 8 note scale with no steps larger than a subminor third:

G (Ab) Bb B (C) D Eb F# G

On a 5-limit lattice it looks like:

; B---F#
; / \ /
; (C)--G---D
; / \ / \ /
;(Ab)--Eb--Bb

With 225:224 tempered out that gives a full 9-limit tetrad on Ab. That's the logic for using C and Ab instead of C# and A. I leave the extra notes in parentheses because you can treat them as second class citizens if you think 8 notes is too many. Write tunes based on the 6 note core and using C and Ab less frequently as passing notes or to reinforce the harmony.

Generally, I think magic scales have to be taken with a pinch of chromatic salt. There's no point having all those notes and only using seven of them after all.

Another trick is that, if the scale has a big gap in it, you can write tunes smaller than an octave. Then you can fill in the gap with transpositions. This is different to the traditional idea of transposing scales, where new notes are interpreted as modifications of the old ones.

Graham

"I think the theory of Maqam music and other "ethnic" genres around the
world are much neglected by the alternative tuning list community."

I believe that this is far from the case. If you look into the history of the list, you will find a non-trivial engagement from the very beginning with tunings outside of western common practice -- in my case, I've posted some about Ancient Greek and Hellenistic, Karnatic, and Mainland SE Asian tunings, as well as Central Javanese, Sundanese and Bali Aga tunings. (I have also done field research in tunings in Ireland, Hungary, Erdely, and Central Mexico.) What I have appreciated about this list is that there has not been a casual mixing of aesthetic projects: search for temperaments, for example, that are optimal by one measure or another for common practice tonal music has been clearly viewed as restricted to a particular repertoire, not imperialistically applicable to some imagined "all music".

Getting a handle a maqam music, as you identify it, is a particularly daunting task for a list with a largely western and anglophone membership. One is faced with two and a half thousand years of written scholarship and while this list has some members -- John Chalmers, for example -- who are rather expert on one or another portion of that literature, the contemporary literature in Greek, Turkish, Arabic, Persian etc. is large, difficult to access, and when accessible, not translated. Moreover, there is a virtual hornet's nests of controversies, many of a strictly non-musical nature, into which one does not enter easily. For example, while some recognize the contours of a pan-Mediterranean musical tradition with roots stretching from Greece to the Horn of Africa and from Egypt to Persia, and its development in Hellenistic, Byzantine, and Islamicate environments -- a viewpoint which may be so braod as to ignore vital distinctions, others choose to exclude elements, restricting it to an Islamic or Byzantine theory, a viewpoint that fails on the one hand to account for contradictory pockets of activity within the broad texture (the extraordinary Caucasian traditions, for example) as well as the historical fact of persistant cross-ethnic collaboration and synthesis (just consider the large number of Jews and Christians active as Ottoman court musicians!).

An ethnomusicologist sometimes falls into a damned if you do/damned if you don't trap: if we don't pay enough attention to a particular music and culture, we are exclusionary, if not Eurocentric or even racist, but if we pay too much attention, or get too creative with a culture other than our own, it is imperialism, and no matter how much one learns about a culture, an outsider will nver be trusted as dealing fairly with the local sensitivities. But one persists, and although some naive things have been written here, the approach has been both interested and respectfully appropriate.

--
Dr. Daniel Wolf
Composer
Frankfurt

Dear Daniel, here is a very late reply:

Your efforts to reflect and introduce tunings of "exotic" musical genres to this list are commendable. It is also terrific that historical European temperaments are not viewed by members of this community as categorically applicable to world musics, though I admit that the proximity of the Ottoman court to the Western world did at a certain point render meantone temperaments, particularly the Telemann-Mozart methodology of 9 commas to the whole tone & 55 commas to the octave, a valid basis for explaining the theory of maqams (as can be seen in the example of Antoine Murat). While I am not particularly fond of the definition "Art Music", I shall venture to say that Western tonal common-practice music and maqam music of the Ottoman court, its periphery, and Turkish posterity are on a par as regards artistic refinement in such areas as rhythm, melody, texture and form.

You are right that the majority of documents on Middle Eastern music theory penned in Arabic, Persian and old Turkish are quite inaccessible to the majority of Anglophones, which probably renders my complaint falling flat on its face. I must also confess my limitations for not knowing Arabic, Persian or old Turkish script. My only advantage to other members is the inflation of modern Turkish literature on the subject of maqam music and translations of old works.

Nevertheless, I do not agree with your view on Islamic (or, as you put it, Islamicate) music theory not embracing Jews and Christians of the region. While it would be unthinkable in a Byzantine court or Papal district for a Muslim music practitioner to be tolerated, let alone be given high positions, the cultural atmosphere advocated by my religion gave birth to a civilization where even non-Muslims became part of the imperial community. The Caucasian traditions you speak of boast no seperate music theory that I know of until the advent of the Soviets and imposition of 12-tone parlance. The same goes for the Balkans. Tanburi Harutin, Dimitrie Kantemir, Hamparsum Limonjiyan are but a few of the distinguished names ratifying my claims. A single excursion into Armenian and Greek documents of 18th Century Turkey reveal that Armenians use the same perde names, instruments, maqams and forms that were popular among Turks.

The drawback you described can be overcome if objective scholarship is applied to the field.

Cordially,
Oz.

On Jun 30, 2008, at 12:08 PM, Daniel Wolf wrote:

> "I think the theory of Maqam music and other "ethnic" genres around > the
> world are much neglected by the alternative tuning list community."
>
> I believe that this is far from the case. If you look into the > history of
> the list, you will find a non-trivial engagement from the very > beginning
> with tunings outside of western common practice -- in my case, I've > posted
> some about Ancient Greek and Hellenistic, Karnatic, and Mainland SE > Asian
> tunings, as well as Central Javanese, Sundanese and Bali Aga > tunings. (I
> have also done field research in tunings in Ireland, Hungary, > Erdely, and
> Central Mexico.) What I have appreciated about this list is that > there
> has not been a casual mixing of aesthetic projects: search for
> temperaments, for example, that are optimal by one measure or > another for
> common practice tonal music has been clearly viewed as restricted to a
> particular repertoire, not imperialistically applicable to some > imagined
> "all music".
>
> Getting a handle a maqam music, as you identify it, is a particularly
> daunting task for a list with a largely western and anglophone
> membership. One is faced with two and a half thousand years of > written
> scholarship and while this list has some members -- John Chalmers, for
> example -- who are rather expert on one or another portion of that
> literature, the contemporary literature in Greek, Turkish, Arabic, > Persian
> etc. is large, difficult to access, and when accessible, not > translated.
> Moreover, there is a virtual hornet's nests of controversies, many > of a
> strictly non-musical nature, into which one does not enter easily. > For
> example, while some recognize the contours of a pan-Mediterranean > musical
> tradition with roots stretching from Greece to the Horn of Africa > and from
> Egypt to Persia, and its development in Hellenistic, Byzantine, and
> Islamicate environments -- a viewpoint which may be so braod as to > ignore
> vital distinctions, others choose to exclude elements, restricting > it to
> an Islamic or Byzantine theory, a viewpoint that fails on the one > hand to
> account for contradictory pockets of activity within the broad texture
> (the extraordinary Caucasian traditions, for example) as well as the
> historical fact of persistant cross-ethnic collaboration and synthesis
> (just consider the large number of Jews and Christians active as > Ottoman
> court musicians!).
>
> An ethnomusicologist sometimes falls into a damned if you do/damned > if you
> don't trap: if we don't pay enough attention to a particular music and
> culture, we are exclusionary, if not Eurocentric or even racist, but > if we
> pay too much attention, or get too creative with a culture other > than our
> own, it is imperialism, and no matter how much one learns about a > culture,
> an outsider will nver be trusted as dealing fairly with the local
> sensitivities. But one persists, and although some naive things > have been
> written here, the approach has been both interested and respectfully
> appropriate.
>
>
> --> Dr. Daniel Wolf
> Composer
> Frankfurt