HE vs Sethares and why you can't just compare the two models

On Thu, Mar 24, 2011 at 1:31 AM, cityoftheasleep
<igliashon@...> wrote:
>
> > Setharean dissonance is very important. Do you still feel that the
> > chords rank the same way if you use sine waves?
>
> I don't care about sine waves. Why should I?

And this gets us to the crux of the situation.

I don't know if this has ever been explained in plain English, so
maybe a bit of basic psychoacoustic background will help here. You
probably already know some of this but I can't figure out why you
point at the two models as though they're interchangeable - they model
two different, but interlocking, things. So here's exactly what the
"big picture" is, and perhaps this will help you understand how to use
these models and how to use them in your book.

Sethares models stuff that's going on in the ear, and Erlich models
stuff that's going on in the brain. Erlich models how "fused" a chord
sounds, and Sethares models how much the cochlea can split the chord
into individual "notes" at all - and if it can't, Paul's model doesn't
apply. Both are important and you need to understand how they interact
to be able to make judgments from them.

This applies to many of the other models that are thrown as well:
Tenney Height is a really rough rule of thumb to model stuff going on
in the brain, and Plomp and Llevelt's curve models stuff going on in
the ear. John's formula is an attempt to come up with a rough rule of
thumb that models stuff going on in the ear and the brain, although he
doesn't seem to like that explanation too much. You can't just, as
some have done, compare Plomp and Llevelt's curve with HE. I strongly
suspect that some people on here got in a fight early with Carl Lumma
and are now hell-bent on "disproving HE's ironclad grasp on the tuning
list" by showing how much "better" Sethares' model is in certain
cases. But proletariat rebellion aside, they are just two different
models. They don't measure the same thing. If you're going to do that
you might as well throw the 120dB threshold of pain in there as its
own dissonance model and declare it the winner.

The two yield "similar looking" curves for various reasons, but in
your case, the differences are very meaningful and important. And I
think particularly for the kind of music you want to write, Sethares
will likely be a better curve for you to use.

Firstly,

There's the concept of chord "quality." Is it major, is it minor,
happy, sad, what? However you resolve the nuances involving tonalness
and entropy and whether or not HE applies to melody - all of it has to
do with stuff going on in the brain. Why does 5:10:14 sound "sad" and
1:2:3 sound "happy?" Not because of stuff going on in the cochlea, but
stuff in the brain. Further downstream, there's also a bunch of stuff
that has to do with learning, the kind of stuff Rothenberg's written
about, but we're not thinking about that for now.

HE is just one simple model that measures one aspect of this stuff
(ideally timbral fusion, liberally can perhaps be applied to chord
quality in a broader sense). Aside from a few issues with how well it
handles different minor chords, it's definitely a step in the right
direction - a diminished chord is more dissonant than a major chord, a
minor chord is in between, etc. There are a bit of nits to pick about
how accurate HE in its current formulation is, but it's at least a
handy, decent guide to figure out whether a certain chord or interval
will be more appropriate for a church choir or for Slipknot. 4:5:6 is
going to be happier than 10:12:15, and 4000:5001:6000 is going to be
about as happy as 4:5:6.

The fact that some uncertainty exists in pitch perception is a
fantastic musical tool. It means that you can have a father-tempered
fifth that sounds simultaneously like 3/2 and 8/5. It can sound either
rooted or unrooted, and as an artist you can communicate tons of
useful information with that. Sevish has a track on golden hour where
he's in 22-tet and uses the 650 cent interval as a really flat pelog
"fifth"; it sounds like a subdued combination of a fifth and tritone
when you hear it. Really beautiful stuff.

HOWEVER, many people on here just don't like the sound of
higher-entropy intervals - period. Some people hate stuff like I've
outlined above, whereas others like you really like high-error
temperaments. And this is even despite any issues with beating,
because they just don't like the sound of weird "ambiguous" intervals
like that. On the other hand, folks like you don't mind them at all,
and so you've found interesting ways to use these intervals. So you
can use a fifth at like 720 cents which just sounds like a brighter,
wider fifth, and five of them hit the octave. And life is good.

HOLD RIGHT THERE

We never get to any of this beautiful art if the signal never makes it
past the cochlea. If you're a masochist and have nothing to do, go
back to the periodicity buzz gammatone filter thread and check out
what happens to the signal when there's too much roughness -
everything goes to hell. AM, FM, all kinds of stuff gets thrown on the
signal. And for every significantly detuned interval with a complex
timbre, this is happening on -every- otherwise coincident partial. The
cochlea wreaks utter havoc on what's going on and makes it difficult
to figure anything out.

Unfortunately, most of the interesting "in between" intervals up there
happen to be the ones that wreak havoc on the signal the most. So what
do we do if we want to use 15-tet, but the fifth beats so much that
you can't just hear it as a wide fifth and get it overwith? There are
a few ways to solve this problem:

1) Be careful with the timbres you use such that the harmonics that
would otherwise beat don't end up being strongest
2) Put effects on the signal to smear it and make your ear less
sensitive to beating in general
3) Make more use of arpeggiation and less use of concurrent harmonies
(assuming my stronger hypothesis)
Use specialized, detuned timbres
4) Use a sync-beating or an omni-sync beating (RI) tuning, which is
hit or miss in terms of how well theory can predict its crappiness
right now. But sometimes it can make a high-error tuning sound less
crappy; you fix things in the cochlea so now you can play around
better with these higher entropy intervals
5) Use specialized, detuned timbres

phew.

THE POINT

The point is that individual tolerance varies for both of these. Some
people can't stand ambiguous, higher entropy intervals, and some
people don't mind them. So when we're talking about which model
predicts what chords sound "better," we need to figure out what we, as
individuals, think "better" means. Grandiose statements about
Sethares' curve or HE or Plomp and Llevelt's curve or whatever being
"The One True Dissonance Curve" are MEANINGLESS unless you define
exactly what type of "dissonant" aural characteristic you're trying to
model. Minor chords vs major chords rank equally on Sethares model,
but very differently in HE. On the other hand, 720 cents is clearly in
the field of attraction for 3/2, but if you're using a timbre that has
strong second and third harmonics you're going to hate that interval
with a passion because of precisely the kind of thing that Sethares
claims to model.

Lastly, people often complain that it seems like they're being bullied
into trusting the model over their own ears. But none of these are
supposed to be more accurate than your ears. They're supposed to be
ways for a computer to "listen" to a thousand tunings at once and make
heuristic judgments about which ones will be the most musically
useful. We're in the phase where we're overwhelmed by the infinity of
tunings out there and are trying to find the ones that we think fit
the criteria that will be musically useful.

So someone who doesn't mind a bit of harmonic ambiguity but hates
beating might want to stick more with Sethares' model (perhaps this
applies to Igs). On the other hand, someone who knows they're going to
go entirely by the harmonic "flavor" of the chords and intervals they
want to use, and play with timbres until they manage to make it sound
OK, should probably use HE and not pay much attention to Sethares. But
as there's clearly some variation in which percept people prioritize
for actual music-making, statements about which is "more relevant" are
meaningless.

-Mike

Mike, I'd like to thank you for taking the time to write all that out (most of it was very clear), but I'm afraid it still isn't very helpful.

I understand that Sethares is all about the cochlea and HE is all about the brain. The problem in music is that the ear and brain work together simultaneously. If the partials are having a clusterf*** in the cochlea, the brain can't do its job at all, but there are also some chords where the proportions are so screwy the brain can't make heads or tails of it even when you present it with the individual frequencies on a silver platter. I get this, you get this, we're good so far.

The issue I have is that both curves--Sethares and HE--share the same independent variable: the relative frequencies of the notes making up the intervals. As you vary these frequencies, the different curves go up or down in different places. The "relative importance" of each curve at a given point is proportional to the level of discordance it predicts at that point: when an interval or chord has high HE, the Sethares curve is irrelevant, and where the interval has high Setharesian dissonance, the HE curve is irrelevant. But because these are curves, that means the relevance of each model varies continuously, so there will be points where it's sort of a crapshoot as to which one is more relevant.

What I want is a unified measure of discordance, one which takes both curves into account and where I don't have to guess at which one is more relevant at which point. I *don't* want to ignore one in favor of the other, because I think that's a musically stupid decision to make. They both matter, but no one has (as of yet) shown me a way to unify them such that we can have a single curve that predicts/models the absolute perceptual discordance of an interval or chord based on the single independent variable of frequency (or frequencies) relative to a fixed "root" tone.

An incomplete measure is of no use to me.

-Igs

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Thu, Mar 24, 2011 at 1:31 AM, cityoftheasleep
> <igliashon@...> wrote:
> >
> > > Setharean dissonance is very important. Do you still feel that the
> > > chords rank the same way if you use sine waves?
> >
> > I don't care about sine waves. Why should I?
>
> And this gets us to the crux of the situation.
>
> I don't know if this has ever been explained in plain English, so
> maybe a bit of basic psychoacoustic background will help here. You
> probably already know some of this but I can't figure out why you
> point at the two models as though they're interchangeable - they model
> two different, but interlocking, things. So here's exactly what the
> "big picture" is, and perhaps this will help you understand how to use
> these models and how to use them in your book.
>
> Sethares models stuff that's going on in the ear, and Erlich models
> stuff that's going on in the brain. Erlich models how "fused" a chord
> sounds, and Sethares models how much the cochlea can split the chord
> into individual "notes" at all - and if it can't, Paul's model doesn't
> apply. Both are important and you need to understand how they interact
> to be able to make judgments from them.
>
> This applies to many of the other models that are thrown as well:
> Tenney Height is a really rough rule of thumb to model stuff going on
> in the brain, and Plomp and Llevelt's curve models stuff going on in
> the ear. John's formula is an attempt to come up with a rough rule of
> thumb that models stuff going on in the ear and the brain, although he
> doesn't seem to like that explanation too much. You can't just, as
> some have done, compare Plomp and Llevelt's curve with HE. I strongly
> suspect that some people on here got in a fight early with Carl Lumma
> and are now hell-bent on "disproving HE's ironclad grasp on the tuning
> list" by showing how much "better" Sethares' model is in certain
> cases. But proletariat rebellion aside, they are just two different
> models. They don't measure the same thing. If you're going to do that
> you might as well throw the 120dB threshold of pain in there as its
> own dissonance model and declare it the winner.
>
> The two yield "similar looking" curves for various reasons, but in
> your case, the differences are very meaningful and important. And I
> think particularly for the kind of music you want to write, Sethares
> will likely be a better curve for you to use.
>
> Firstly,
>
> There's the concept of chord "quality." Is it major, is it minor,
> happy, sad, what? However you resolve the nuances involving tonalness
> and entropy and whether or not HE applies to melody - all of it has to
> do with stuff going on in the brain. Why does 5:10:14 sound "sad" and
> 1:2:3 sound "happy?" Not because of stuff going on in the cochlea, but
> stuff in the brain. Further downstream, there's also a bunch of stuff
> that has to do with learning, the kind of stuff Rothenberg's written
> about, but we're not thinking about that for now.
>
> HE is just one simple model that measures one aspect of this stuff
> (ideally timbral fusion, liberally can perhaps be applied to chord
> quality in a broader sense). Aside from a few issues with how well it
> handles different minor chords, it's definitely a step in the right
> direction - a diminished chord is more dissonant than a major chord, a
> minor chord is in between, etc. There are a bit of nits to pick about
> how accurate HE in its current formulation is, but it's at least a
> handy, decent guide to figure out whether a certain chord or interval
> will be more appropriate for a church choir or for Slipknot. 4:5:6 is
> going to be happier than 10:12:15, and 4000:5001:6000 is going to be
> about as happy as 4:5:6.
>
> The fact that some uncertainty exists in pitch perception is a
> fantastic musical tool. It means that you can have a father-tempered
> fifth that sounds simultaneously like 3/2 and 8/5. It can sound either
> rooted or unrooted, and as an artist you can communicate tons of
> useful information with that. Sevish has a track on golden hour where
> he's in 22-tet and uses the 650 cent interval as a really flat pelog
> "fifth"; it sounds like a subdued combination of a fifth and tritone
> when you hear it. Really beautiful stuff.
>
> HOWEVER, many people on here just don't like the sound of
> higher-entropy intervals - period. Some people hate stuff like I've
> outlined above, whereas others like you really like high-error
> temperaments. And this is even despite any issues with beating,
> because they just don't like the sound of weird "ambiguous" intervals
> like that. On the other hand, folks like you don't mind them at all,
> and so you've found interesting ways to use these intervals. So you
> can use a fifth at like 720 cents which just sounds like a brighter,
> wider fifth, and five of them hit the octave. And life is good.
>
> HOLD RIGHT THERE
>
> We never get to any of this beautiful art if the signal never makes it
> past the cochlea. If you're a masochist and have nothing to do, go
> back to the periodicity buzz gammatone filter thread and check out
> what happens to the signal when there's too much roughness -
> everything goes to hell. AM, FM, all kinds of stuff gets thrown on the
> signal. And for every significantly detuned interval with a complex
> timbre, this is happening on -every- otherwise coincident partial. The
> cochlea wreaks utter havoc on what's going on and makes it difficult
> to figure anything out.
>
> Unfortunately, most of the interesting "in between" intervals up there
> happen to be the ones that wreak havoc on the signal the most. So what
> do we do if we want to use 15-tet, but the fifth beats so much that
> you can't just hear it as a wide fifth and get it overwith? There are
> a few ways to solve this problem:
>
> 1) Be careful with the timbres you use such that the harmonics that
> would otherwise beat don't end up being strongest
> 2) Put effects on the signal to smear it and make your ear less
> sensitive to beating in general
> 3) Make more use of arpeggiation and less use of concurrent harmonies
> (assuming my stronger hypothesis)
> Use specialized, detuned timbres
> 4) Use a sync-beating or an omni-sync beating (RI) tuning, which is
> hit or miss in terms of how well theory can predict its crappiness
> right now. But sometimes it can make a high-error tuning sound less
> crappy; you fix things in the cochlea so now you can play around
> better with these higher entropy intervals
> 5) Use specialized, detuned timbres
>
> phew.
>
> THE POINT
>
> The point is that individual tolerance varies for both of these. Some
> people can't stand ambiguous, higher entropy intervals, and some
> people don't mind them. So when we're talking about which model
> predicts what chords sound "better," we need to figure out what we, as
> individuals, think "better" means. Grandiose statements about
> Sethares' curve or HE or Plomp and Llevelt's curve or whatever being
> "The One True Dissonance Curve" are MEANINGLESS unless you define
> exactly what type of "dissonant" aural characteristic you're trying to
> model. Minor chords vs major chords rank equally on Sethares model,
> but very differently in HE. On the other hand, 720 cents is clearly in
> the field of attraction for 3/2, but if you're using a timbre that has
> strong second and third harmonics you're going to hate that interval
> with a passion because of precisely the kind of thing that Sethares
> claims to model.
>
> Lastly, people often complain that it seems like they're being bullied
> into trusting the model over their own ears. But none of these are
> supposed to be more accurate than your ears. They're supposed to be
> ways for a computer to "listen" to a thousand tunings at once and make
> heuristic judgments about which ones will be the most musically
> useful. We're in the phase where we're overwhelmed by the infinity of
> tunings out there and are trying to find the ones that we think fit
> the criteria that will be musically useful.
>
> So someone who doesn't mind a bit of harmonic ambiguity but hates
> beating might want to stick more with Sethares' model (perhaps this
> applies to Igs). On the other hand, someone who knows they're going to
> go entirely by the harmonic "flavor" of the chords and intervals they
> want to use, and play with timbres until they manage to make it sound
> OK, should probably use HE and not pay much attention to Sethares. But
> as there's clearly some variation in which percept people prioritize
> for actual music-making, statements about which is "more relevant" are
> meaningless.
>
> -Mike
>

   In 32TET I can stack 1/1 7/6 3/2 = 6:7:9 triads and 1/1 9/7 3/2 (14:18:21) triads to form a 7 tone scale with 5 triads in the form of such-above triads.  What's the formal name for this scale?
  And boy does that scale sound jazz/bluesy...and loaded with near-perfect 5ths.   Only problem is...there are two tiny clustered dyads...so it acts more like a 5-tone scale melodically.

On Thu, Mar 24, 2011 at 11:32 AM, cityoftheasleep
<igliashon@...> wrote:
>
> The issue I have is that both curves--Sethares and HE--share the same independent variable: the relative frequencies of the notes making up the intervals. As you vary these frequencies, the different curves go up or down in different places. The "relative importance" of each curve at a given point is proportional to the level of discordance it predicts at that point: when an interval or chord has high HE, the Sethares curve is irrelevant, and where the interval has high Setharesian dissonance, the HE curve is irrelevant. But because these are curves, that means the relevance of each model varies continuously, so there will be points where it's sort of a crapshoot as to which one is more relevant.
>
> What I want is a unified measure of discordance, one which takes both curves into account and where I don't have to guess at which one is more relevant at which point. I *don't* want to ignore one in favor of the other, because I think that's a musically stupid decision to make. They both matter, but no one has (as of yet) shown me a way to unify them such that we can have a single curve that predicts/models the absolute perceptual discordance of an interval or chord based on the single independent variable of frequency (or frequencies) relative to a fixed "root" tone.
>
> An incomplete measure is of no use to me.
>
> -Igs

I understand what you want, but there is no such thing as "absolute
perceptual discordance" in this case, because the two curves just
measure different parameters. Which one is more important at the end
of the day probably boils down to individual preference: some like
high-entropy intervals, some don't. Since you generally do, I'd
suggest you play around with various averages of the two curves,
probably giving more weight to Sethares' curve.

You should try either max(Sethares, HE) or, more elegantly, Sethares *
HE, that'll probably do the trick. That'll give you a resulting curve
that's only low in dissonance when both HE and Sethares are low, and
high when either one spikes. Then we can call it the Igliashon Jones
Composite Dissonance Parameter or something.

-Mike

>"I strongly suspect that some people on here got in a fight early with Carl Lumma

and are now hell-bent on "disproving HE's ironclad grasp on the tuning list" by showing how much "better" Sethares' model is in certain cases"

    Hahaha...well I'm not rebelling...I'm simply trying to say HE is not G-d.  :-D  The answer to every other thing on this list is "HE says" or "Tenney Height says"...and people are often called crazy if they ever disagree with that.
  There are, of course, gaping holes in Sethares' theory too.
  The main one for me is how equal-beating "periodic" dyads sound more stable to the brain (as opposed to the ear)...and that it misses the concept of fields of attraction from HE (IE play anything between 9/7 and 5/4 and you'll see it getting drawn toward one or the other).
  And that's even if HE seems to fail badly in that sort of brain modeling sometimes IE why does 22/15 sound so much more stable to me than 40/27 even though 40/27 is the one much closer to 3/2?!  Well that, and it doesn't seem to explain the fact that inverting a chord from major/minor makes it more tense (which Sethares seems to indirectly imply by the fact critical band is gentler to smaller gaps if they are at higher frequencies).

>"They don't measure the same thing."
  No they don't, but they both seem to have huge roles in determining things like what chords can be used for resolve vs. tension points in composition.   You can't just say "this scale does well with regards to HE, so it must be ideal concerning resolve"...or the same with Sethares' model.  Of course, both the ear and brain contribute to that "Zen" effect we get from good music. :-)

>"Why does 5:10:14 sound "sad" and 1:2:3 sound "happy?" Not because of stuff going on in the cochlea, but stuff in the brain."
   Right, but that's one example where critical band effects are nearly equal. 

>"We never get to any of this beautiful art if the signal never makes it past the cochlea. If you're a masochist and have nothing to do, go back to the periodicity buzz gammatone filter thread and check out what happens to the signal when there's too much roughness -

everything goes to hell."

Right, which leads us right back to using Sethares ("the ear") before he worry that much about tweaking the HE ("the brain") that happens once we get passed it, correct?

>"4) Use a sync-beating or an omni-sync beating (RI) tuning, which is

hit or miss in terms of how well theory can predict its crappiness

right now."

   This reminds me, I really should make an algorithm for my adaptive JI program to make higher limit chords (especially over 19 odd limit or so) equal-beating.  Any idea how to do this (IE taken a triad find the nearest equal-beating equivalent)?

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

> You should try either max(Sethares, HE) or, more elegantly, Sethares *
> HE, that'll probably do the trick. That'll give you a resulting curve
> that's only low in dissonance when both HE and Sethares are low, and
> high when either one spikes.

Right, you've said this before and I've said I'd like to do this but I don't have any idea how. I don't even know how either of the curves are mathematically defined, let alone how to take the product of the two of them.

-Igs

Igs>>"What I want is a unified measure of discordance, one which takes both curves into account and where I don't have to guess at which one is more relevant at which point. I *don't* want to ignore one in favor of the other, because I think that's a musically stupid decision to make. They both matter, but no one has (as of yet) shown me a way to unify them such that we can have a single curve that predicts/models the absolute perceptual discordance of an interval or
chord based on the single independent variable of frequency (or frequencies) relative to a fixed "root" tone.>>

I'm pretty sure (not 100%) that my Interval Calculator program will do the trick. It measures concordance, not discordance. Any just interval (x and y < 256) with a positive result should be good. Any tempered interval within 6.776 cents (256/255) of a good just interval should also be good. As regards chords, if all of the dyads in the chord are good then the chord should be good.

A lot of people on the list think the program is a load of crap but I doubt if a single one of them has actually tested it. You could be the first to test it. Try it and see what you think. You can download it from the JohnOSullivan folder in the Files section or from my website...

http://www.johnsmusic7.com

There's a version for both Mac OSX and PCs.

John.

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> Mike, I'd like to thank you for taking the time to write all that out (most of it was very clear), but I'm afraid it still isn't very helpful.
>
> I understand that Sethares is all about the cochlea and HE is all about the brain. The problem in music is that the ear and brain work together simultaneously. If the partials are having a clusterf*** in the cochlea, the brain can't do its job at all, but there are also some chords where the proportions are so screwy the brain can't make heads or tails of it even when you present it with the individual frequencies on a silver platter. I get this, you get this, we're good so far.
>
> The issue I have is that both curves--Sethares and HE--share the same independent variable: the relative frequencies of the notes making up the intervals. As you vary these frequencies, the different curves go up or down in different places. The "relative importance" of each curve at a given point is proportional to the level of discordance it predicts at that point: when an interval or chord has high HE, the Sethares curve is irrelevant, and where the interval has high Setharesian dissonance, the HE curve is irrelevant. But because these are curves, that means the relevance of each model varies continuously, so there will be points where it's sort of a crapshoot as to which one is more relevant.
>
> What I want is a unified measure of discordance, one which takes both curves into account and where I don't have to guess at which one is more relevant at which point. I *don't* want to ignore one in favor of the other, because I think that's a musically stupid decision to make. They both matter, but no one has (as of yet) shown me a way to unify them such that we can have a single curve that predicts/models the absolute perceptual discordance of an interval or chord based on the single independent variable of frequency (or frequencies) relative to a fixed "root" tone.
>
> An incomplete measure is of no use to me.
>
> -Igs
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
> >
> > On Thu, Mar 24, 2011 at 1:31 AM, cityoftheasleep
> > <igliashon@> wrote:
> > >
> > > > Setharean dissonance is very important. Do you still feel that the
> > > > chords rank the same way if you use sine waves?
> > >
> > > I don't care about sine waves. Why should I?
> >
> > And this gets us to the crux of the situation.
> >
> > I don't know if this has ever been explained in plain English, so
> > maybe a bit of basic psychoacoustic background will help here. You
> > probably already know some of this but I can't figure out why you
> > point at the two models as though they're interchangeable - they model
> > two different, but interlocking, things. So here's exactly what the
> > "big picture" is, and perhaps this will help you understand how to use
> > these models and how to use them in your book.
> >
> > Sethares models stuff that's going on in the ear, and Erlich models
> > stuff that's going on in the brain. Erlich models how "fused" a chord
> > sounds, and Sethares models how much the cochlea can split the chord
> > into individual "notes" at all - and if it can't, Paul's model doesn't
> > apply. Both are important and you need to understand how they interact
> > to be able to make judgments from them.
> >
> > This applies to many of the other models that are thrown as well:
> > Tenney Height is a really rough rule of thumb to model stuff going on
> > in the brain, and Plomp and Llevelt's curve models stuff going on in
> > the ear. John's formula is an attempt to come up with a rough rule of
> > thumb that models stuff going on in the ear and the brain, although he
> > doesn't seem to like that explanation too much. You can't just, as
> > some have done, compare Plomp and Llevelt's curve with HE. I strongly
> > suspect that some people on here got in a fight early with Carl Lumma
> > and are now hell-bent on "disproving HE's ironclad grasp on the tuning
> > list" by showing how much "better" Sethares' model is in certain
> > cases. But proletariat rebellion aside, they are just two different
> > models. They don't measure the same thing. If you're going to do that
> > you might as well throw the 120dB threshold of pain in there as its
> > own dissonance model and declare it the winner.
> >
> > The two yield "similar looking" curves for various reasons, but in
> > your case, the differences are very meaningful and important. And I
> > think particularly for the kind of music you want to write, Sethares
> > will likely be a better curve for you to use.
> >
> > Firstly,
> >
> > There's the concept of chord "quality." Is it major, is it minor,
> > happy, sad, what? However you resolve the nuances involving tonalness
> > and entropy and whether or not HE applies to melody - all of it has to
> > do with stuff going on in the brain. Why does 5:10:14 sound "sad" and
> > 1:2:3 sound "happy?" Not because of stuff going on in the cochlea, but
> > stuff in the brain. Further downstream, there's also a bunch of stuff
> > that has to do with learning, the kind of stuff Rothenberg's written
> > about, but we're not thinking about that for now.
> >
> > HE is just one simple model that measures one aspect of this stuff
> > (ideally timbral fusion, liberally can perhaps be applied to chord
> > quality in a broader sense). Aside from a few issues with how well it
> > handles different minor chords, it's definitely a step in the right
> > direction - a diminished chord is more dissonant than a major chord, a
> > minor chord is in between, etc. There are a bit of nits to pick about
> > how accurate HE in its current formulation is, but it's at least a
> > handy, decent guide to figure out whether a certain chord or interval
> > will be more appropriate for a church choir or for Slipknot. 4:5:6 is
> > going to be happier than 10:12:15, and 4000:5001:6000 is going to be
> > about as happy as 4:5:6.
> >
> > The fact that some uncertainty exists in pitch perception is a
> > fantastic musical tool. It means that you can have a father-tempered
> > fifth that sounds simultaneously like 3/2 and 8/5. It can sound either
> > rooted or unrooted, and as an artist you can communicate tons of
> > useful information with that. Sevish has a track on golden hour where
> > he's in 22-tet and uses the 650 cent interval as a really flat pelog
> > "fifth"; it sounds like a subdued combination of a fifth and tritone
> > when you hear it. Really beautiful stuff.
> >
> > HOWEVER, many people on here just don't like the sound of
> > higher-entropy intervals - period. Some people hate stuff like I've
> > outlined above, whereas others like you really like high-error
> > temperaments. And this is even despite any issues with beating,
> > because they just don't like the sound of weird "ambiguous" intervals
> > like that. On the other hand, folks like you don't mind them at all,
> > and so you've found interesting ways to use these intervals. So you
> > can use a fifth at like 720 cents which just sounds like a brighter,
> > wider fifth, and five of them hit the octave. And life is good.
> >
> > HOLD RIGHT THERE
> >
> > We never get to any of this beautiful art if the signal never makes it
> > past the cochlea. If you're a masochist and have nothing to do, go
> > back to the periodicity buzz gammatone filter thread and check out
> > what happens to the signal when there's too much roughness -
> > everything goes to hell. AM, FM, all kinds of stuff gets thrown on the
> > signal. And for every significantly detuned interval with a complex
> > timbre, this is happening on -every- otherwise coincident partial. The
> > cochlea wreaks utter havoc on what's going on and makes it difficult
> > to figure anything out.
> >
> > Unfortunately, most of the interesting "in between" intervals up there
> > happen to be the ones that wreak havoc on the signal the most. So what
> > do we do if we want to use 15-tet, but the fifth beats so much that
> > you can't just hear it as a wide fifth and get it overwith? There are
> > a few ways to solve this problem:
> >
> > 1) Be careful with the timbres you use such that the harmonics that
> > would otherwise beat don't end up being strongest
> > 2) Put effects on the signal to smear it and make your ear less
> > sensitive to beating in general
> > 3) Make more use of arpeggiation and less use of concurrent harmonies
> > (assuming my stronger hypothesis)
> > Use specialized, detuned timbres
> > 4) Use a sync-beating or an omni-sync beating (RI) tuning, which is
> > hit or miss in terms of how well theory can predict its crappiness
> > right now. But sometimes it can make a high-error tuning sound less
> > crappy; you fix things in the cochlea so now you can play around
> > better with these higher entropy intervals
> > 5) Use specialized, detuned timbres
> >
> > phew.
> >
> > THE POINT
> >
> > The point is that individual tolerance varies for both of these. Some
> > people can't stand ambiguous, higher entropy intervals, and some
> > people don't mind them. So when we're talking about which model
> > predicts what chords sound "better," we need to figure out what we, as
> > individuals, think "better" means. Grandiose statements about
> > Sethares' curve or HE or Plomp and Llevelt's curve or whatever being
> > "The One True Dissonance Curve" are MEANINGLESS unless you define
> > exactly what type of "dissonant" aural characteristic you're trying to
> > model. Minor chords vs major chords rank equally on Sethares model,
> > but very differently in HE. On the other hand, 720 cents is clearly in
> > the field of attraction for 3/2, but if you're using a timbre that has
> > strong second and third harmonics you're going to hate that interval
> > with a passion because of precisely the kind of thing that Sethares
> > claims to model.
> >
> > Lastly, people often complain that it seems like they're being bullied
> > into trusting the model over their own ears. But none of these are
> > supposed to be more accurate than your ears. They're supposed to be
> > ways for a computer to "listen" to a thousand tunings at once and make
> > heuristic judgments about which ones will be the most musically
> > useful. We're in the phase where we're overwhelmed by the infinity of
> > tunings out there and are trying to find the ones that we think fit
> > the criteria that will be musically useful.
> >
> > So someone who doesn't mind a bit of harmonic ambiguity but hates
> > beating might want to stick more with Sethares' model (perhaps this
> > applies to Igs). On the other hand, someone who knows they're going to
> > go entirely by the harmonic "flavor" of the chords and intervals they
> > want to use, and play with timbres until they manage to make it sound
> > OK, should probably use HE and not pay much attention to Sethares. But
> > as there's clearly some variation in which percept people prioritize
> > for actual music-making, statements about which is "more relevant" are
> > meaningless.
> >
> > -Mike
> >
>

On Thu, Mar 24, 2011 at 1:18 PM, cityoftheasleep
<igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > You should try either max(Sethares, HE) or, more elegantly, Sethares *
> > HE, that'll probably do the trick. That'll give you a resulting curve
> > that's only low in dissonance when both HE and Sethares are low, and
> > high when either one spikes.
>
> Right, you've said this before and I've said I'd like to do this but I don't have any idea how. I don't even know how either of the curves are mathematically defined, let alone how to take the product of the two of them.
>
> -Igs

Well, we already have HE down solid. If you can obtain a copy of
Sethares' curve in tabular form, I'll be happy to run it in MATLAB and
multiply the two together for you. You might be able to email Bill for
it, or I'm sure it was posted here at one point.

-Mike

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:

> An incomplete measure is of no use to me.

I suspect a complete measure is impossible and probably meaningless. If so, what then?

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:
>
>    In 32TET I can stack 1/1 7/6 3/2 = 6:7:9 triads and 1/1 9/7 3/2 (14:18:21) triads to form a 7 tone scale with 5 triads in the form of such-above triads.  What's the formal name for this scale?

I have no idea but because we have no 32edo article at present on the xenwiki (http://xenharmonic.wikispaces.com/edo) I'll look at this.

>   And boy does that scale sound jazz/bluesy...and loaded with near-perfect 5ths.   Only problem is...there are two tiny clustered dyads...so it acts more like a 5-tone scale melodically.

Care to create any musical examples?

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
> > An incomplete measure is of no use to me.
>
> I suspect a complete measure is impossible and probably meaningless. If so, what then?
>

Then I am exactly where I am now: armed with my ears and my ears alone.

-Igs