What's the best way to describe JI's relation to temperaments?

I was giving a high-level overview of regular temperaments on XA,
where I described all temperaments as deriving from JI, which I said
was like "the almighty super-temperament that all mere mortal
temperaments are derived from." I should have thought this was clear
enough, but as you might expect, someone messaged me offlist telling
me that JI isn't a temperament.

Our definitions have typically treated temperaments as abstract
mathematical objects of which JI is itself included. For instance, if
"temperaments" are homomorphisms from some p-limit subset of Q to Z^n,
the non-contorted homomorphism mapping from the 5-limit rationals to
Z^3 is a "temperament."

This definition is implied in other definitions we use. For instance,
"wedgies" are defined as denoting valid "temperaments" if their
coefficients have GCD = 1 and if they satisfy the Plucker relations.
Therefore, the wedgies <1|, <<1||, <<<1|||, <<<<1||||, etc all denote
valid "temperaments."

Is there some agreement that under the definition we've all been
using, JI is itself a "temperament," just a special one which has a
zero-dimensional null space? If so, I'll just say from now on that
this is the definition of "temperament" we've chosen for regular
temperament theory, and that people should note that it differs from
definitions which some authors have used.

-Mike

Usually temperament is defined explicitly to exclude just intonations. There are of course contexts where just intonations end up as special cases of things that loosely get called temperaments.
Note that you might tune a just intonation in a capricious way so that it stops being just and it still belongs to the loose category of temperaments. Note also that Vicentino's second tuning is sometimes called o temperament. Not only does it have all five limit intervals just but it is also contorted so it fails certain definitions of regular temperament two ways.
In general it's best to avoid calling just intonations temperaments. It's also dull to correct somebody who does otherwise and clearly knows what they're doing

Graham

------Original message------
From: Mike Battaglia <battaglia01@...>
To: <tuning@yahoogroups.com>
Date: Saturday, February 11, 2012 1:18:14 PM GMT-0500
Subject: [tuning] What's the best way to describe JI's relation to temperaments?

I was giving a high-level overview of regular temperaments on XA,
where I described all temperaments as deriving from JI, which I said
was like "the almighty super-temperament that all mere mortal
temperaments are derived from." I should have thought this was clear
enough, but as you might expect, someone messaged me offlist telling
me that JI isn't a temperament.

Our definitions have typically treated temperaments as abstract
mathematical objects of which JI is itself included. For instance, if
"temperaments" are homomorphisms from some p-limit subset of Q to Z^n,
the non-contorted homomorphism mapping from the 5-limit rationals to
Z^3 is a "temperament."

This definition is implied in other definitions we use. For instance,
"wedgies" are defined as denoting valid "temperaments" if their
coefficients have GCD = 1 and if they satisfy the Plucker relations.
Therefore, the wedgies <1|, <<1||, <<<1|||, <<<<1||||, etc all denote
valid "temperaments."

Is there some agreement that under the definition we've all been
using, JI is itself a "temperament," just a special one which has a
zero-dimensional null space? If so, I'll just say from now on that
this is the definition of "temperament" we've chosen for regular
temperament theory, and that people should note that it differs from
definitions which some authors have used.

-Mike

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I think it's a bad idea to call JI a "temperament". It would have
confused me when I was first learning this stuff.

Historically, temperaments existed before they were described with
wedgies; even now, if I understand things correctly, any temperament
that doesn't fall within the regular mapping paradigm is not described
by a wedgie. Therefore, it doesn't make sense to call JI a temperament
just because it can be mapped to itself using a special-case wedgie.

You could, if you wanted to, say that those wedgies are the regular
mapping paradigm's identity functions -- JI gets mapped to itself
without any tempering. That subordinates the wedgie to the paradigm,
and doesn't presume that this is the only way of thinking about JI and
temperaments. But calling JI a temperament when there's no tempering
going on really seems to muddy the waters.

One man's opinion.

Regards,
Jake

On 2/11/12, Mike Battaglia <battaglia01@...> wrote:
> I was giving a high-level overview of regular temperaments on XA,
> where I described all temperaments as deriving from JI, which I said
> was like "the almighty super-temperament that all mere mortal
> temperaments are derived from." I should have thought this was clear
> enough, but as you might expect, someone messaged me offlist telling
> me that JI isn't a temperament.
>
> Our definitions have typically treated temperaments as abstract
> mathematical objects of which JI is itself included. For instance, if
> "temperaments" are homomorphisms from some p-limit subset of Q to Z^n,
> the non-contorted homomorphism mapping from the 5-limit rationals to
> Z^3 is a "temperament."
>
> This definition is implied in other definitions we use. For instance,
> "wedgies" are defined as denoting valid "temperaments" if their
> coefficients have GCD = 1 and if they satisfy the Plucker relations.
> Therefore, the wedgies <1|, <<1||, <<<1|||, <<<<1||||, etc all denote
> valid "temperaments."
>
> Is there some agreement that under the definition we've all been
> using, JI is itself a "temperament," just a special one which has a
> zero-dimensional null space? If so, I'll just say from now on that
> this is the definition of "temperament" we've chosen for regular
> temperament theory, and that people should note that it differs from
> definitions which some authors have used.
>
> -Mike
>
>
> ------------------------------------
>
> You can configure your subscription by sending an empty email to one
> of these addresses (from the address at which you receive the list):
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>
>
>
>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> I was giving a high-level overview of regular temperaments on XA,
> where I described all temperaments as deriving from JI, which I said
> was like "the almighty super-temperament that all mere mortal
> temperaments are derived from." I should have thought this was clear
> enough,

You thought that was clear? No wonder we misunderstand
one another all the time. JI is the identity temperament,
and it can be useful to point this out.

> Is there some agreement that under the definition we've all been
> using, JI is itself a "temperament,"

It's a fact... it doesn't much matter if there's agreement
about it. Actually it does matter, because without such
agreement things can be made very much more confusing than
they really are...

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
> JI is the identity temperament,
> and it can be useful to point this out.

By which you mean, the temperament where 1/1 is tempered out?

Whoa...is it even mathematically possible to not temper out 1/1?

-Igs

Can you or Graham give me a 2-3 word buzzword to use instead then? I hate
having to give these lengthy expositions every time I start talking about
this stuff. There's obviously no way newcomers know what wedgies are, so I
can't reference that in my first ever message to them about the subject.

Sent from my iPhone

On Feb 11, 2012, at 2:08 PM, Jake Freivald <jdfreivald@gmail.com> wrote:

I think it's a bad idea to call JI a "temperament". It would have
confused me when I was first learning this stuff.

Historically, temperaments existed before they were described with
wedgies; even now, if I understand things correctly, any temperament
that doesn't fall within the regular mapping paradigm is not described
by a wedgie. Therefore, it doesn't make sense to call JI a temperament
just because it can be mapped to itself using a special-case wedgie.

You could, if you wanted to, say that those wedgies are the regular
mapping paradigm's identity functions -- JI gets mapped to itself
without any tempering. That subordinates the wedgie to the paradigm,
and doesn't presume that this is the only way of thinking about JI and
temperaments. But calling JI a temperament when there's no tempering
going on really seems to muddy the waters.

One man's opinion.

Regards,
Jake

On 2/11/12, Mike Battaglia <battaglia01@...> wrote:
> I was giving a high-level overview of regular temperaments on XA,
> where I described all temperaments as deriving from JI, which I said
> was like "the almighty super-temperament that all mere mortal
> temperaments are derived from." I should have thought this was clear
> enough, but as you might expect, someone messaged me offlist telling
> me that JI isn't a temperament.
>
> Our definitions have typically treated temperaments as abstract
> mathematical objects of which JI is itself included. For instance, if
> "temperaments" are homomorphisms from some p-limit subset of Q to Z^n,
> the non-contorted homomorphism mapping from the 5-limit rationals to
> Z^3 is a "temperament."
>
> This definition is implied in other definitions we use. For instance,
> "wedgies" are defined as denoting valid "temperaments" if their
> coefficients have GCD = 1 and if they satisfy the Plucker relations.
> Therefore, the wedgies <1|, <<1||, <<<1|||, <<<<1||||, etc all denote
> valid "temperaments."
>
> Is there some agreement that under the definition we've all been
> using, JI is itself a "temperament," just a special one which has a
> zero-dimensional null space? If so, I'll just say from now on that
> this is the definition of "temperament" we've chosen for regular
> temperament theory, and that people should note that it differs from
> definitions which some authors have used.
>
> -Mike
>
>
> ------------------------------------
>
> 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
>
>
>
>

--- In tuning@yahoogroups.com, Jake Freivald <jdfreivald@...> wrote:
>
> I think it's a bad idea to call JI a "temperament". It would have
> confused me when I was first learning this stuff.

There's often a disconnect between the way math works and the way common sense works. Is a collection with nothing in it still a collection? If I take all subsets of a set of apples, and also all subsets of a set oranges, should there be a set in common? Common sense says no, math says yes.

On Feb 11, 2012, at 2:38 PM, Carl Lumma <carl@...> wrote:

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> I was giving a high-level overview of regular temperaments on XA,
> where I described all temperaments as deriving from JI, which I said
> was like "the almighty super-temperament that all mere mortal
> temperaments are derived from." I should have thought this was clear
> enough,

You thought that was clear? No wonder we misunderstand
one another all the time. JI is the identity temperament,
and it can be useful to point this out.

You think it'd be clearer, in an intuitive exposition to a newcomer, to say
that JI is "the identity temperament" instead of saying that it's "the
master temperament from which all others are derived?"

> Is there some agreement that under the definition we've all been
> using, JI is itself a "temperament,"

It's a fact... it doesn't much matter if there's agreement
about it. Actually it does matter, because without such
agreement things can be made very much more confusing than
they really are...

-Carl

If we could agree on here on a definition, I'll just use that and leave a
footnote that this is the definition in this specific theory, but that
authors have traditionally used the term to exclude things like JI. Or, if
we don't want JI to be a temperament, then I need a phrase to use instead
("tuning system"?).

If nobody can agree, I'll be bold in my writing and assert JI is a
"special" temperament, and note that this is a deliberate departure from
the historical use of the term.

-Mike

Temperaments are mappings between groups. Specifically, they
are monomorphic (one-way) mappings from subgroups of the rational
numbers. 1 is an identity operator defining the group of the
rational numbers, therefore it cannot be tempered in RMP. It is
possible to map from groups in which 1 is not an identity, but
such groups are exotic and unlikely to be applicable to music
intonation.

A lot of the confusion I referred to comes from thinking one of
the note groups is the temperament and the other JI. This is
emphatically not the case, as the music of some microtonalists
amply shows. The *mapping* is the important thing in RMP,
whether you're trying to define a temperament or just intonation.
That's probably why it's called RMP. :)

-Carl

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@> wrote:
> > JI is the identity temperament,
> > and it can be useful to point this out.
>
> By which you mean, the temperament where 1/1 is tempered out?
> Whoa...is it even mathematically possible to not temper out 1/1?
>
> -Igs

On Feb 11, 2012, at 2:53 PM, cityoftheasleep <igliashon@...>
wrote:

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
> JI is the identity temperament,
> and it can be useful to point this out.

By which you mean, the temperament where 1/1 is tempered out?

The big secret: monzos are column matrices. So 5/4 is this

[-2]
[0]
[1]

This can be written [-2 0 1]', where ' means transpose.

The mapping matrix for meantone is

[1 1 0]
[0 1 4]

Now, multiply the mapping matrix on the left by 5/4 on the right:

[1 1 0]
[0 1 4] * [-2 0 1]'

I wrote the second transposed for ease of formatting but it should be
vertical. Work out the multiplication and you get

[-2]
[4]

Or |-2 4> in tempered period/generator coordinates.

Let's consider the mapping matrix for 5-limit JI and how it behaves in this
situation

<1 0 1|
<0 1 0|
<0 0 1|

The 3x3 "identity matrix" from linear algebra is

[1 0 0]
[0 1 0]
[0 0 1]

Same thing. The identity matrix has the property of spitting back out
whatever you multiply it with. So

[1 0 0]
[0 1 0] * [-2 0 1]'
[0 0 1]

evaluates to [-2 0 1]' in the "tempered coordinate system", which is the
same as the original coordinate system. The identity matrix sends every
monzo to itself in the same coordinates, which is the essence of JI.

Whoa...is it even mathematically possible to not temper out 1/1?

-Igs

Nope.

-Mike

__,

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

> You think it'd be clearer, in an intuitive exposition to a
> newcomer, to say that JI is "the identity temperament" instead
> of saying that it's "the master temperament from which all
> others are derived?"

I think "identity temperament" can be clear to anyone who's
interested. I think "the master temperament from which all
others are derived" can't be clear to anyone, ever.

> Or, if we don't want JI to be a temperament, then I need a
> phrase to use instead ("tuning system"?).

Howabout "mapping"?

> If nobody can agree, I'll be bold in my writing and assert
> JI is a "special" temperament, and note that this is a
> deliberate departure from the historical use of the term.

I think that would be fine, though I'm not sure how much
of a departure it is. That implies the term was used
in one or more consistent ways in the past - that is not
really the case.

-Carl

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

> The big secret: monzos are column matrices.

When I first started out, I was making vals column matricies. Vals and monzos never really caught on until we switched to bra-ket notation.

On Feb 11, 2012, at 3:34 PM, Carl Lumma <carl@...> wrote:

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

> You think it'd be clearer, in an intuitive exposition to a
> newcomer, to say that JI is "the identity temperament" instead
> of saying that it's "the master temperament from which all
> others are derived?"

I think "identity temperament" can be clear to anyone who's
interested. I think "the master temperament from which all
others are derived" can't be clear to anyone, ever.

After taking it into consideration, I disagree and cite Dustin's response
to my explanation, and Igs confusion in response to your term as example
cases. But I think calling JI the "identity temperament" in general is good
though.

But, I note that if we're not arguing about terminology in this group,
we're arguing about pedagogical approaches. If you think I led Dustin in
the wrong direction, feel free to clarify over on XA.

> Or, if we don't want JI to be a temperament, then I need a
> phrase to use instead ("tuning system"?).

Howabout "mapping"?

OK. I still think for "temperament" is easier for beginners though.

> If nobody can agree, I'll be bold in my writing and assert
> JI is a "special" temperament, and note that this is a
> deliberate departure from the historical use of the term.

I think that would be fine, though I'm not sure how much
of a departure it is. That implies the term was used
in one or more consistent ways in the past - that is not
really the case.

Whatever keeps the JI Preservation League at bay.

-Mike

__,_._,__

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

>> I think "identity temperament" can be clear to anyone who's
>> interested. I think "the master temperament from which all
>> others are derived" can't be clear to anyone, ever.
>
> After taking it into consideration, I disagree and cite Dustin's
> response to my explanation,

Who's Dustin?

> and Igs confusion in response to your term as example cases.

I didn't think Igs was confused.

> If you think I led Dustin in the wrong direction, feel free
> to clarify over on XA.

I don't know who Dustin is and I have no reason to think
you've led anyone in the wrong direction. I do think you
should tone down the superlatives.

>> Howabout "mapping"?
>
> OK. I still think for "temperament" is easier for
> beginners though.

Fine by me. I usually write based on what I think the person
already knows and what he wants to do. For most people,
either "mapping" or "temperament" should work.

> Whatever keeps the JI Preservation League at bay.

They are irrelevant now. Crush them!

*cough* I mean, if anyone took a historical term and
changed it, it was them. Just intonation usually referred
to intervals sounding pure. They made it out to apply to
pitches being rational numbers (sometimes of arbitrary
complexity). But pitches being rational numbers is neither
necessary or sufficient for just intonation harmony.

-Carl

On Feb 11, 2012, at 4:23 PM, Carl Lumma <carl@...> wrote:

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

>> I think "identity temperament" can be clear to anyone who's
>> interested. I think "the master temperament from which all
>> others are derived" can't be clear to anyone, ever.
>
> After taking it into consideration, I disagree and cite Dustin's
> response to my explanation,

Who's Dustin?

The guy on XA I was explaining this to.

> If you think I led Dustin in the wrong direction, feel free
> to clarify over on XA.

I don't know who Dustin is and I have no reason to think
you've led anyone in the wrong direction. I do think you
should tone down the superlatives.

"Superlatives?"

> Whatever keeps the JI Preservation League at bay.

They are irrelevant now. Crush them!

*cough* I mean, if anyone took a historical term and
changed it, it was them. Just intonation usually referred
to intervals sounding pure. They made it out to apply to
pitches being rational numbers (sometimes of arbitrary
complexity). But pitches being rational numbers is neither
necessary or sufficient for just intonation harmony.

-Carl

That implies that not every identity matrix is a mapping matrix for JI.

-Mike

In adaptive temperament, each just interval will have more than one tempered equivalent. One equivalent of 1/1 will always be itself but if there's any adaptation you'll also be able to find impure unisons.

Graham

------Original message------
From: cityoftheasleep <igliashon@...>
To: <tuning@yahoogroups.com>
Date: Saturday, February 11, 2012 7:53:15 PM GMT-0000
Subject: [tuning] Re: What's the best way to describe JI's relation to temperaments?

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
> JI is the identity temperament,
> and it can be useful to point this out.

By which you mean, the temperament where 1/1 is tempered out?

Whoa...is it even mathematically possible to not temper out 1/1?

-Igs

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--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>> *cough* I mean, if anyone took a historical term and
>> changed it, it was them. Just intonation usually referred
>> to intervals sounding pure. They made it out to apply to
>> pitches being rational numbers (sometimes of arbitrary
>> complexity). But pitches being rational numbers is neither
>> necessary or sufficient for just intonation harmony.
>
> That implies that not every identity matrix is a mapping
> matrix for JI.
>

Not sure what you mean - you may be assuming regular mapping,
which the strict JI folks often did not use.

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
> But pitches being rational numbers is neither
> necessary or sufficient for just intonation harmony.

Good to have you back, Carl. While we're on the subject, might you be able to elucidate the conditions that *are* necessary and/or sufficient for just intonation harmony?

-Igs

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> Temperaments are mappings between groups.

In RMP, yes. But this isn't really consistent with other uses of the word. The verb "to temper", used in the musical sense, means to mistune a pure interval by some amount, usually a fraction of some comma. Historically, temperaments tended to refer to specific variants of meantone, designated either with a fraction of the syntonic comma, or with some proper name in the case of well-temperaments or other circulating temperaments. A "circular mapping between groups" does not sound like it is the same thing as a circular temperament.

There is often much confusion among new-comers about the difference between tunings and temperaments. Knowing what it means "to temper", it seems that "a temperament" should be a specific tuning arrived at by mistuning some Just scale by a particular amount. The conception of temperaments as these abstract mappings of rationals to irrationals, which can be instantiated as a boundless variety of tunings represents an advancement that occurred in our group and hasn't yet reached widespread use. We should be more sensitive to the fact that we are using the term "temperament" in an unorthodox form peculiar to our community.

> A lot of the confusion I referred to comes from thinking one of
> the note groups is the temperament and the other JI. This is
> emphatically not the case, as the music of some microtonalists
> amply shows. The *mapping* is the important thing in RMP,
> whether you're trying to define a temperament or just intonation.
> That's probably why it's called RMP. :)

How does the mapping define JI?

-Igs

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@> wrote:
> > But pitches being rational numbers is neither
> > necessary or sufficient for just intonation harmony.
>
> Good to have you back, Carl. While we're on the subject, might
> you be able to elucidate the conditions that *are* necessary
> and/or sufficient for just intonation harmony?
>
> -Igs

If we're talking about a scale,
necessary: the scale's diamond contains some just
intonation dyads
sufficient: the scale's diamond contains only just
intonation dyads

If we're talking about music, I reckon
every beat that contains a vertical sonority contains at
least one that is consonant
is both necessary and sufficient

That's off the top of my head and I don't claim it's
perfect. -Carl

That was, er, a rather circular definition. Maybe I worded the question poorly. What's just intonation?

-Igs

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@> wrote:
> >
> > --- In tuning@yahoogroups.com, "Carl Lumma" <carl@> wrote:
> > > But pitches being rational numbers is neither
> > > necessary or sufficient for just intonation harmony.
> >
> > Good to have you back, Carl. While we're on the subject, might
> > you be able to elucidate the conditions that *are* necessary
> > and/or sufficient for just intonation harmony?
> >
> > -Igs
>
> If we're talking about a scale,
> necessary: the scale's diamond contains some just
> intonation dyads
> sufficient: the scale's diamond contains only just
> intonation dyads
>
> If we're talking about music, I reckon
> every beat that contains a vertical sonority contains at
> least one that is consonant
> is both necessary and sufficient
>
> That's off the top of my head and I don't claim it's
> perfect. -Carl
>

On Sat, Feb 11, 2012 at 4:59 PM, Carl Lumma <carl@...> wrote:
>
> Not sure what you mean - you may be assuming regular mapping,
> which the strict JI folks often did not use.

I mean that this matrix

[1 0 0]
[0 1 0]
[0 0 1]

isn't necessarily "JI" under that definition.

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Sat, Feb 11, 2012 at 4:59 PM, Carl Lumma <carl@...> wrote:
> >
> > Not sure what you mean - you may be assuming regular mapping,
> > which the strict JI folks often did not use.
>
> I mean that this matrix
>
> [1 0 0]
> [0 1 0]
> [0 0 1]
>
> isn't necessarily "JI" under that definition.

Not to mention

[1 0 0]
[1 -1 1]
[4 -1 0]

Actually, let's ditch the terminology debate and talk about something
more interesting. Maybe Gene can clear some of this up

On Sat, Feb 11, 2012 at 3:28 PM, Carl Lumma <carl@...> wrote:
>
> Temperaments are mappings between groups. Specifically, they
> are monomorphic (one-way) mappings from subgroups of the rational
> numbers.

Monomorphisms are injective functions, at least according to
wikipedia. Temperaments are not monomorphisms; their entire point is
to map more than one element in the parent domain (the rationals) to
the same domain (Z^n). Here's a picture of a noninjective function
which is surjective

http://en.wikipedia.org/wiki/File:Surjection.svg

Since more than one element in X maps to Y, it's non-injective, as is
the case of 81/80 and 1/1 both mapping to the tempered monzo |0 0>.

> 1 is an identity operator defining the group of the
> rational numbers, therefore it cannot be tempered in RMP. It is
> possible to map from groups in which 1 is not an identity, but
> such groups are exotic and unlikely to be applicable to music
> intonation.

I don't understand. 1/1 has monzo |0 0 0 0 0 0 ...>, which is
trivially in the null space of any mapping matrix. Doesn't "tempering
out" mean "equate with the identity"? 1/1 is trivially also equated
with itself.

> A lot of the confusion I referred to comes from thinking one of
> the note groups is the temperament and the other JI. This is
> emphatically not the case, as the music of some microtonalists
> amply shows. The *mapping* is the important thing in RMP,
> whether you're trying to define a temperament or just intonation.
> That's probably why it's called RMP. :)

I don't get it. You're saying that mappings aren't from JI to other
things, because JI is itself a mapping, but that all mappings are from
Q to Z^n?

-Mike

On Sat, Feb 11, 2012 at 7:17 PM, genewardsmith
<genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> >
> > [1 0 0]
> > [0 1 0]
> > [0 0 1]
> >
> > isn't necessarily "JI" under that definition.
>
> Not to mention
>
> [1 0 0]
> [1 -1 1]
> [4 -1 0]

Yeah, that's true; you'd have to change it to say that it's the
temperament which Hermite reduces to the identity matrix.

But even then, not all identity matrices would be JI under Carl's
definition: if the 3x3 identity matrix represents the
2.3001.5001-limit it wouldn't be JI, for example, but just RI or
something.

That definition would subtly change the way in which I present the
material. Instead of saying that "the identity matrix represents JI,"
I'd say that "the identity matrix represents RI," with the additional
qualification that if the limit is chosen to represent some audible
psychoacoustic effect that it's also JI.

I'd personally be inclined to simplify the definition and call the
whole thing JI in the context of this theory, just like I'd rather
call JI and RI a type of temperament. But then, instead of the JI
Preservation League being on my case about it, it'll be the
Psychoacoustic Integrity Coalition I have to disarm.

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Sat, Feb 11, 2012 at 4:59 PM, Carl Lumma <carl@...> wrote:
> >
> > Not sure what you mean - you may be assuming regular mapping,
> > which the strict JI folks often did not use.
>
> I mean that this matrix
> [1 0 0]
> [0 1 0]
> [0 0 1]
> isn't necessarily "JI" under that definition.

Under what definition? I just told you there is no RMP, and
therefore no matrices, in what you were responding to (which
you clipped for some reason). -Carl

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

> > Temperaments are mappings between groups.
>
> In RMP, yes.

Yes.

> But this isn't really consistent with other uses of the word.

It's as consistent as any definition... like that of glass,
salt, etc I've brought up here in the past. No definition
is all-encompassing.

> The verb "to temper",
> used in the musical sense, means to mistune a pure interval by
> some amount, usually a fraction of some comma.

One can also temper a scale.

> Historically, temperaments tended to refer to specific
> variants of meantone,

Howabout when Helmholtz referred to schismic temperament?
Is that historical? And why does it matter whether it is?

In the Baroque era tempered scales were described by
fractions of the Pythagorean comma. In the previous era,
bearing plans had to do with eliminating the syntonic comma.
Authors of both eras sometimes confused the two, as they
are near in size.

> There is often much confusion among new-comers about the
> difference between tunings and temperaments.

And the situation will be improved by conflating them?

> > A lot of the confusion I referred to comes from thinking one of
> > the note groups is the temperament and the other JI. This is
> > emphatically not the case, as the music of some microtonalists
> > amply shows. The *mapping* is the important thing in RMP,
> > whether you're trying to define a temperament or just intonation.
> > That's probably why it's called RMP. :)
>
> How does the mapping define JI?

It means there will be no comma pumps, for one. Other
definitions (such as saying that anything you play in a "just"
scale will be JI) do not mean this, and in fact JI purists
unknowingly play comma pumps in JI scales all the time.
In one apocryphal story (by way of Daniel Wolf), Erv Wilson
pointed out to Partch that he was trying to transpose the
tonality diamond, and just using the nearest available
chromelodeon pitches as proxies. In another, I found myself
playing marvel-tempered 7th chords on my piano, and when I
realized it I became enlightened and forever gave up the
strict JI dogma I had (to some extent) previously espoused.

On the other side of the coin, doodling in a rank-2 MOS is
not any more likely to generate good music than doodling at
a piano without knowing any scales or chords. In fact it's
less likely if the MOS in question has fewer consonances per
note than 12.

In both cases, you have to use the mapping. So this is not
just an abstract distinction, but one intimately connected
to how scales can be used to make music.

> That was, er, a rather circular definition. Maybe I worded
> the question poorly. What's just intonation?

http://lumma.org/tuning/faq/#whatisJI

-Carl

--- Mike Battaglia <battaglia01@...> wrote:
>
> > Temperaments are mappings between groups. Specifically, they
> > are monomorphic (one-way) mappings from subgroups of the
> > rational numbers.
>
> Monomorphisms are injective functions, at least according to
> wikipedia. Temperaments are not monomorphisms; their entire
> point is to map more than one element in the parent domain (the
> rationals)

Quite right, I believe it's an epimorphism from the rationals,
and a monomorphism to them.

>> 1 is an identity operator defining the group of the
>> rational numbers, therefore it cannot be tempered in RMP. It is
>> possible to map from groups in which 1 is not an identity, but
>> such groups are exotic and unlikely to be applicable to music
>> intonation.
>
> I don't understand. 1/1 has monzo |0 0 0 0 0 0 ...>, which is
> trivially in the null space of any mapping matrix. Doesn't
> "tempering out" mean "equate with the identity"? 1/1 is
> trivially also equated with itself.

Yes, I think so. It's this "triviality" I'm referring to
in my answer to Igs.

> I don't get it. You're saying that mappings aren't from JI to
> other things, because JI is itself a mapping,

Yes, and I thought I was agreeing with you.

-Carl

On Sat, Feb 11, 2012 at 7:39 PM, Carl Lumma <carl@...> wrote:
>
> Under what definition? I just told you there is no RMP, and
> therefore no matrices, in what you were responding to (which
> you clipped for some reason). -Carl

I'm talking about your definition, not theirs. You said this:

>> But pitches being rational numbers is neither
>> necessary or sufficient for just intonation harmony.

I'll assume that you're saying here what you've said before, which is
that to really be considered JI the pitches don't just have to be
rationals in general, but simple rationals. This means that the
statement "JI is the identity temperament" is true, but that the
converse isn't true in general, because it depends on what subgroup
you're working in. If the subgroup is sufficiently complex it won't be
JI under your definition; I presume you'd call it RI instead.

This is the definition of a "val":

"A val "maps" just intonation to a certain number of steps in a chain
of generators; by putting vals together we can define the mapping of a
regular temperament and thereby define the temperament."

For example, if you don't believe that 13/7 by itself is a "just"
interval because it's too high in harmonic entropy, this would mean
that the 2.13/7 covector <10 9| isn't a val, because it isn't mapping
from just intonation.

-Mike

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

> > Under what definition? I just told you there is no RMP, and
> > therefore no matrices, in what you were responding to (which
> > you clipped for some reason). -Carl
>
> I'm talking about your definition, not theirs. You said this:
>
> >> But pitches being rational numbers is neither
> >> necessary or sufficient for just intonation harmony.
>
> I'll assume that you're saying here what you've said before,
> which is that to really be considered JI the pitches don't just
> have to be rationals in general, but simple rationals.

Why would you assume that? I was talking about "their"
definition here!

-Carl

On Sat, Feb 11, 2012 at 8:06 PM, Carl Lumma <carl@...> wrote:
>
> --- Mike Battaglia <battaglia01@...> wrote:
> >
> > Monomorphisms are injective functions, at least according to
> > wikipedia. Temperaments are not monomorphisms; their entire
> > point is to map more than one element in the parent domain (the
> > rationals)
>
> Quite right, I believe it's an epimorphism from the rationals,
> and a monomorphism to them.

This is what the discussion was about when I was adding my "abstract"
summaries to the Wiki math pages; I said something like this and Gene
and Keenan clobbered me.

A temperament isn't a monomorphism to the rationals, because the "map"
from Z^n to the rationals isn't actually a function at all. A function
has to have only one output for any input, but a meantone perfect
fifth has multiple outputs as rationals. See here

http://en.wikipedia.org/wiki/File:Injection_keine_Injektion_1.svg

"This does not represent a function since 2 is the first element in
more than one ordered pair, in particular, (2,B) and (2,C) are both
elements of the set of ordered pairs."

The correct way to say it is that the 5-limit meantone perfect fifth
maps to the entire "coset" of 5-limit rationals of the form 3/2 *
(81/80)^n, all taken as a single object. In general, temperaments map
from elements in Z^n to "cosets" of the subgroup specified by the
kernel, which themselves form a group called a quotient group. This
mapping is an isomorphism, and this whole concept is called the "first
isomorphism" of group theory.

> > I don't get it. You're saying that mappings aren't from JI to
> > other things, because JI is itself a mapping,
>
> Yes, and I thought I was agreeing with you.

OK, so you'd like to define JI itself as a mapping from the rationals
to Z^n then, and not the rationals themselves? I can see why you
didn't like the notion that JI was "the master temperament that others
were derived from" then.

-Mike

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

> > Historically, temperaments tended to refer to specific
> > variants of meantone,
>
> Howabout when Helmholtz referred to schismic temperament?
> Is that historical? And why does it matter whether it is?
>
> In the Baroque era tempered scales were described by
> fractions of the Pythagorean comma. In the previous era,
> bearing plans had to do with eliminating the syntonic comma.
> Authors of both eras sometimes confused the two, as they
> are near in size.

Well, in your FAQ you say:

"In traditional Western keyboard practice, a "temperament" is usually what defines how the keys are tuned,"

That's what I'm talking about. You are already aware that the use of the term "temperament" in microtonal theory is a deviation from (or an advancement of) the traditional Western usage of the term, which specifically eliminates any reference to actually tuning anything in a specific way. In other words, a "temperament" in microtonal theory is definitvely *not* "how the keys are tuned".

> > There is often much confusion among new-comers about the
> > difference between tunings and temperaments.
>
> And the situation will be improved by conflating them?

They're already conflated in the mind of the newcomer, because of the reasons given above. We use "temperament" to refer to something abstract and not related to specific tunings; most non-microtonalists who are familiar with the term "temperament" are familiar with it as designating specific tunings. Or at the very least are familiar with it designating (12-tone) equal temperament.

A temperament, in our sense, is at least another level of abstraction above the traditional sense. What we'd call a tuning, a new-comer might call a temperament. What we'd call a temperament is something most new-comers don't even have a word for. And what they'd call a tuning, we might even call a scale--from your FAQ, a scale is "An ordered list of intervals, which may be applied to a given concert pitch to generate an ordered list of pitches that can be used to tune an instrument"--it sounds like the open strings of a guitar could fit this definition of "scale", so what people call different "tunings" of the open strings of a guitar are different "scales" in our lingo.

I am *not* suggesting that we change anything. I'm simply suggesting that we all remember that we are using words that non-microtonal musicians use, except that we have given them new meanings that need to be explained to anyone before they'll understand. I vaguely recall that I had a bunch of heated discussions with Paul in the early days that only occurred because he was using terms like "tuning", "temperament", and "scale" in a way I wasn't familiar with, without me realizing that he was doing so. Had I known from the get-go what meanings he was operating with, I would have understood him better and not thought he was talking nonsense at times. It took me a long time to get that temperaments have literally *nothing* to do with tunings and only vaguely anything to do with scales, and it was a major epiphany when I finally got it. It should have been "lesson 1".

> > How does the mapping define JI?
>
> It means there will be no comma pumps, for one. Other
> definitions (such as saying that anything you play in a "just"
> scale will be JI) do not mean this, and in fact JI purists
> unknowingly play comma pumps in JI scales all the time.
> In one apocryphal story (by way of Daniel Wolf), Erv Wilson
> pointed out to Partch that he was trying to transpose the
> tonality diamond, and just using the nearest available
> chromelodeon pitches as proxies. In another, I found myself
> playing marvel-tempered 7th chords on my piano, and when I
> realized it I became enlightened and forever gave up the
> strict JI dogma I had (to some extent) previously espoused.

These stories are interesting but don't answer my question. In what way does the mapping define JI?

> On the other side of the coin, doodling in a rank-2 MOS is
> not any more likely to generate good music than doodling at
> a piano without knowing any scales or chords. In fact it's
> less likely if the MOS in question has fewer consonances per
> note than 12.

Why do you mention this? What does this have to do with anything?

> In both cases, you have to use the mapping. So this is not
> just an abstract distinction, but one intimately connected
> to how scales can be used to make music.

What do you mean, "use the mapping"?

> http://lumma.org/tuning/faq/#whatisJI

I still don't feel like my question was answered. How can I tell if a given sonority is JI or not?

-Igs

On Sat, Feb 11, 2012 at 8:15 PM, Carl Lumma <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > > Under what definition? I just told you there is no RMP, and
> > > therefore no matrices, in what you were responding to (which
> > > you clipped for some reason). -Carl
> >
> > I'm talking about your definition, not theirs. You said this:
> >
> > >> But pitches being rational numbers is neither
> > >> necessary or sufficient for just intonation harmony.
> >
> > I'll assume that you're saying here what you've said before,
> > which is that to really be considered JI the pitches don't just
> > have to be rationals in general, but simple rationals.
>
> Why would you assume that? I was talking about "their"
> definition here!

Aren't you saying that -your- definition of JI is "intervals which
sound pure," and that "they" were the ones who fubared the definition
to basically define it to also include things that you'd probably call
RI?

-Mike

--- Mike Battaglia <battaglia01@...> wrote:
> >
> > Quite right, I believe it's an epimorphism from the rationals,
> > and a monomorphism to them.
>
> This is what the discussion was about when I was adding my
> "abstract" summaries to the Wiki math pages; I said something
> like this and Gene and Keenan clobbered me.
> A temperament isn't a monomorphism to the rationals, because
> the "map" from Z^n to the rationals isn't actually a function
> at all. A function has to have only one output for any input,
> but a meantone perfect fifth has multiple outputs as rationals.

There are some subtleties here, and Gene certainly knows
better than I, but I don't believe we need to have a function
to have a morphism in the broadest possible sense (e.g.
category theory).

> > > I don't get it. You're saying that mappings aren't from JI to
> > > other things, because JI is itself a mapping,
> >
> > Yes, and I thought I was agreeing with you.
>
> OK, so you'd like to define JI itself as a mapping from the
> rationals to Z^n then, and not the rationals themselves?
> I can see why you didn't like the notion that JI was "the
> master temperament that others were derived from" then.

Again, I thought that's what you were doing and I was only
chiming in to agree. I didn't like the "master temperament"
phrase because it's ambiguous. For example, I have no idea
why you now think I wouldn't like it.

-Carl

On Sat, Feb 11, 2012 at 8:44 PM, Carl Lumma <carl@...> wrote:
>
> There are some subtleties here, and Gene certainly knows
> better than I, but I don't believe we need to have a function
> to have a morphism in the broadest possible sense (e.g.
> category theory).

Maybe, I haven't studied category theory at all yet.

> > > Yes, and I thought I was agreeing with you.
> >
> > OK, so you'd like to define JI itself as a mapping from the
> > rationals to Z^n then, and not the rationals themselves?
> > I can see why you didn't like the notion that JI was "the
> > master temperament that others were derived from" then.
>
> Again, I thought that's what you were doing and I was only
> chiming in to agree. I didn't like the "master temperament"
> phrase because it's ambiguous. For example, I have no idea
> why you now think I wouldn't like it.

I was just trying to explain it to him on a high-level. The exact quote was

"Regular temperament theory envisions every temperament, more or less,
as distortions of JI, which is like the almighty super-temperament all
mere mortal temperaments are derived from. They distort JI in such a
way that one or more small JI interval, called a comma, vanishes, so
that intervals which differ by it become the same. Another way to
think of it is that regular temperaments are these things which "map"
JI onto some scalar or lattice structure."

So in this case, I assumed that the rationals themselves are JI, which
I suppose is still a correct description up to isomorphism.

-Mike

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

> These stories are interesting but don't answer my question.
> In what way does the mapping define JI?

I guess I don't know how to answer then. Other than to try
re-reading what Mike and I have written today, and to note
that in my FAQ I make the error of equating just intonation
with Q (the thing being mapped) rather than the mapping
itself.

> > On the other side of the coin, doodling in a rank-2 MOS is
> > not any more likely to generate good music than doodling at
> > a piano without knowing any scales or chords. In fact it's
> > less likely if the MOS in question has fewer consonances per
> > note than 12.
>
> Why do you mention this? What does this have to do with
> anything?

It's an example of how, whether we're defining JI or
temperament, scales will get you into all sorts of trouble.

> > In both cases, you have to use the mapping. So this is not
> > just an abstract distinction, but one intimately connected
> > to how scales can be used to make music.
>
> What do you mean, "use the mapping"?

You must know... I mean, really. Take a stab at it.

> > http://lumma.org/tuning/faq/#whatisJI
>
> I still don't feel like my question was answered. How can
> I tell if a given sonority is JI or not?

To say this has been discussed extensively here and elsewhere
is to risk opening a naked singularity in my office from the
understatement. If this hasn't been answered to your
satisfaction by now, it never will be.

-Carl

On Sat, Feb 11, 2012 at 8:51 PM, Carl Lumma <carl@...> wrote:
> >
> > I still don't feel like my question was answered. How can
> > I tell if a given sonority is JI or not?
>
> To say this has been discussed extensively here and elsewhere
> is to risk opening a naked singularity in my office from the
> understatement. If this hasn't been answered to your
> satisfaction by now, it never will be.

Haha, I'm so glad you said this. Please God, let this discussion never
take place on the tuning list ever again.

-Mike

On Sat, Feb 11, 2012 at 8:49 PM, Mike Battaglia <battaglia01@...> wrote:
>
> "Regular temperament theory envisions every temperament, more or less,
> as distortions of JI, which is like the almighty super-temperament all
> mere mortal temperaments are derived from. They distort JI in such a
> way that one or more small JI interval, called a comma, vanishes, so
> that intervals which differ by it become the same. Another way to
> think of it is that regular temperaments are these things which "map"
> JI onto some scalar or lattice structure."
>
> So in this case, I assumed that the rationals themselves are JI, which
> I suppose is still a correct description up to isomorphism.

Actually, it looks like JI really is defined as being the rationals
themselves. That's how the terminology is used on the Wiki

"A just intonation subgroup is a group generated by a finite set of
positive rational numbers via arbitrary multiplications and
divisions."

"A val "maps" just intonation to a certain number of steps in a chain
of generators;"

etc. So if a temperament is a homomorphism from Q to Z^n, and vals are
homomorphisms, and vals map from JI to a certain number of steps in a
chain of generators, that would seem to equate JI and the rationals.

-Mike

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

> Actually, it looks like JI really is defined as being the
> rationals themselves. That's how the terminology is used on
> the Wiki

You can see I did the same thing in my FAQ (circa 2008).
I now think this is wrong, for the reasons stated today.
But I suppose it's not the end of the world.

-Carl

On Sat, Feb 11, 2012 at 9:10 PM, Carl Lumma <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > Actually, it looks like JI really is defined as being the
> > rationals themselves. That's how the terminology is used on
> > the Wiki
>
> You can see I did the same thing in my FAQ (circa 2008).
> I now think this is wrong, for the reasons stated today.
> But I suppose it's not the end of the world.

Now I have no idea what we were talking about at any point in this
conversation. The only reason I saw you mention was this

> A lot of the confusion I referred to comes from thinking one of
> the note groups is the temperament and the other JI. This is
> emphatically not the case, as the music of some microtonalists
> amply shows.

How can the music of some microtonalists amply show that JI is a
homomorphic mapping from Q to Z^n and not Q itself?????? That's pretty
heavy stuff, man.

-Mike

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

> I guess I don't know how to answer then. Other than to try
> re-reading what Mike and I have written today, and to note
> that in my FAQ I make the error of equating just intonation
> with Q (the thing being mapped) rather than the mapping
> itself.

I think you guys are playing fast-and-loose with the term "JI", using it interchangeably with RI.

> > > In both cases, you have to use the mapping. So this is not
> > > just an abstract distinction, but one intimately connected
> > > to how scales can be used to make music.
> >
> > What do you mean, "use the mapping"?
>
> You must know... I mean, really. Take a stab at it.

Well, when you were playing around in 7-limit JI and accidentally discovered those marvel-tempered chords, does that mean you failed at using the 7-limit JI mapping, and that you accidentally the marvel mapping?

We had a huge debate on here recently that maybe would have benefited from your input, about what it means to use an interval "as" another interval. What does it mean to use 400 cents "as" a 5/4? When does a mapping fail to describe a tuning that was derived from it? Can I use any mapping in any tuning? If so, how? If not, why not? We failed to resolve these issues and I gave up trying because I felt like I didn't know what I was talking about. Do you have answers for these questions?

> > > http://lumma.org/tuning/faq/#whatisJI
> >
> > I still don't feel like my question was answered. How can
> > I tell if a given sonority is JI or not?
>
> To say this has been discussed extensively here and elsewhere
> is to risk opening a naked singularity in my office from the
> understatement. If this hasn't been answered to your
> satisfaction by now, it never will be.

That's the thing--it's been discussed to death, but I've never seen a consensus emerge, let alone a rigorous formulation of such a consensus. Since you're the unofficial group historian, I'm asking you if there ever was such a consensus and/or rigorous formulation. I mean, I recently failed to describe to Mike what it is that makes (say) a 5/4 a "5/4", or what would allow an interval to be recognized as being "like" a 5/4. It seems like it should be both simple and obvious but every time I try to put words to it, it's like grasping the wind.

I don't really know what mapping means on a musical level. What is it that is being mapped, in a musical sense, since we already know it's not JI? What does it mean, musically, that some interval "represents" some other interval(s)? I thought I understood all this stuff but there is a very deep level on which I am still utterly bewildered, and I *really* hope you can help me figure it out. I feel like Wile E. Coyote just before he looks down and realizes he's been running on thin air right now.

-Igs

On Sat, Feb 11, 2012 at 9:38 PM, cityoftheasleep
<igliashon@...> wrote:
>
> I think you guys are playing fast-and-loose with the term "JI", using it interchangeably with RI.

Yes, that's how I like to use it when introducing regular
temperaments, for the same reason I like to call JI a type of
"temperament." It's just simpler to define things that way.

> That's the thing--it's been discussed to death, but I've never seen a consensus emerge, let alone a rigorous formulation of such a consensus. Since you're the unofficial group historian, I'm asking you if there ever was such a consensus and/or rigorous formulation. I mean, I recently failed to describe to Mike what it is that makes (say) a 5/4 a "5/4", or what would allow an interval to be recognized as being "like" a 5/4. It seems like it should be both simple and obvious but every time I try to put words to it, it's like grasping the wind.

Or like asking what would allow the wind to be recognized.

-Mike

--- "cityoftheasleep" <igliashon@...> wrote:

> Well, when you were playing around in 7-limit JI and
> accidentally discovered those marvel-tempered chords, does
> that mean you failed at using the 7-limit JI mapping, and
> that you accidentally the marvel mapping?

Yes!

> Do you have answers for these questions?

Nothing's coming to mind.

> I don't really know what mapping means on a musical level. What
> is it that is being mapped, in a musical sense, since we already
> know it's not JI? What does it mean, musically, that some
> interval "represents" some other interval(s)?

Hm... it's the mapping that tells you what represents what.
In order to figure it out by listening to a piece of music,
you need to be able to tell whether two pitches are the
same (regardless of where they appear in the piece) and you
need to be able to recognize chords. The number of chords
you can recognize and your resolution for telling pitches
apart will determine how many mappings you can recognize.

-Carl

--- Mike Battaglia <battaglia01@...> wrote:

> > > Actually, it looks like JI really is defined as being the
> > > rationals themselves. That's how the terminology is used on
> > > the Wiki
> >
> > You can see I did the same thing in my FAQ (circa 2008).
> > I now think this is wrong, for the reasons stated today.
> > But I suppose it's not the end of the world.
>
> Now I have no idea what we were talking about at any point in this
> conversation. The only reason I saw you mention was this
>
> > A lot of the confusion I referred to comes from thinking one of
> > the note groups is the temperament and the other JI. This is
> > emphatically not the case, as the music of some microtonalists
> > amply shows.

Right, it's contra what's in the wiki and what's in my FAQ.

> How can the music of some microtonalists amply show that JI
> is a homomorphic mapping from Q to Z^n and not Q itself??????
> That's pretty heavy stuff, man.

Some microtonalists use rank 2 scales, but they do not make
music that is any kind of consistent image of Q.

-Carl

On Feb 12, 2012, at 4:01 AM, Carl Lumma <carl@...> wrote:

--- Mike Battaglia <battaglia01@...> wrote:

> How can the music of some microtonalists amply show that JI
> is a homomorphic mapping from Q to Z^n and not Q itself??????
> That's pretty heavy stuff, man.

Some microtonalists use rank 2 scales, but they do not make
music that is any kind of consistent image of Q.

-Carl

I'm lost. Can you give an example of this behavior? A rank 2 scale which
doesn't fully map from the rationals to every element in Z^2 isn't a
temperament at all, so I don't see what bearing this has on the definition
of JI.

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Sat, Feb 11, 2012 at 9:38 PM, cityoftheasleep
> <igliashon@...> wrote:
> >
> > I think you guys are playing fast-and-loose with the term "JI", using it interchangeably with RI.
>
> Yes, that's how I like to use it when introducing regular
> temperaments, for the same reason I like to call JI a type of
> "temperament." It's just simpler to define things that way.
>

I do not see any evidence that the fundamental distinction between intonation and tone is made on these lists. Long ago when people thought (insert name of tallest local mountain) was the tallest mountain in the world (so to speak), it was understandable to conflate intonation and tone- the tones were the tones, what else was there? Today we know that there is a lot more to things than any one local tradition has it. The conceptual blunder here was actually made by "JI purists", as Carl pointed out. So, why perpetuate this blunder? Rationals are rationals, they are not Just Intonation unless they are intonations OF tones.

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

> > Well, when you were playing around in 7-limit JI and
> > accidentally discovered those marvel-tempered chords, does
> > that mean you failed at using the 7-limit JI mapping, and
> > that you accidentally the marvel mapping?
>
> Yes!

So basically, you were playing some nominally-non-JI chords that *weren't* marvel-tempered (let's say you were using 225/128 in place of a 7/4, for simplicity's sake). You suddenly realized that 225/128, despite being a distinct interval in your JI tuning, sounded to your ears to be close enough to a 7/4 that it might as well be called a 7/4, and you realized that this meant you were equating 225/128 with 7/4 and thus operating in Marvel temperament, even though you were using a tuning where the two intervals were tuned distinctly.

I think Mike might want to ask you some questions about this.

> > Do you have answers for these questions?
>
> Nothing's coming to mind.

Darn.

> > I don't really know what mapping means on a musical level. What
> > is it that is being mapped, in a musical sense, since we already
> > know it's not JI? What does it mean, musically, that some
> > interval "represents" some other interval(s)?
>
> Hm... it's the mapping that tells you what represents what.
> In order to figure it out by listening to a piece of music,
> you need to be able to tell whether two pitches are the
> same (regardless of where they appear in the piece) and you
> need to be able to recognize chords. The number of chords
> you can recognize and your resolution for telling pitches
> apart will determine how many mappings you can recognize.

That's what I thought you'd say. So it sounds like you need to learn what Q sounds like on its own before you can learn to recognize that something is representing it, which in other words means we have to develop categorical perception based on Q before temperaments will actually make musical sense to us.

Would you agree that if you can't recognize a mapping, that that mapping lacks musical reality for you?

-Igs

I think what you mean to ask, Mike, is "what does it mean to be a consistent image of Q?"

I'll bet Carl would make the claim that even if we're mapping Q to a scale using the identity function, it'll be possible to make music that fails to be a consistent image of Q. Think about it: what if you made a JI scale and played tons of wolf intervals and "shimmering commatic unisons" (i.e. "random dissonances of the scale"), and more-or-less systematically avoided the simple consonances? I'm expecting that Carl might say that such music "isn't JI", and because of that, it's not allowing the tuning to be recognized as an "image of Q". But I might be wrong.

-Igs

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Feb 12, 2012, at 4:01 AM, Carl Lumma <carl@...> wrote:
>
>
>
> --- Mike Battaglia <battaglia01@> wrote:
>
> > How can the music of some microtonalists amply show that JI
> > is a homomorphic mapping from Q to Z^n and not Q itself??????
> > That's pretty heavy stuff, man.
>
> Some microtonalists use rank 2 scales, but they do not make
> music that is any kind of consistent image of Q.
>
> -Carl
>
> I'm lost. Can you give an example of this behavior? A rank 2 scale which
> doesn't fully map from the rationals to every element in Z^2 isn't a
> temperament at all, so I don't see what bearing this has on the definition
> of JI.
>
> -Mike
>

On Sun, Feb 12, 2012 at 11:25 AM, cityoftheasleep
<igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> > > Well, when you were playing around in 7-limit JI and
> > > accidentally discovered those marvel-tempered chords, does
> > > that mean you failed at using the 7-limit JI mapping, and
> > > that you accidentally the marvel mapping?
> >
> > Yes!
>
> So basically, you were playing some nominally-non-JI chords that *weren't* marvel-tempered (let's say you were using 225/128 in place of a 7/4, for simplicity's sake). You suddenly realized that 225/128, despite being a distinct interval in your JI tuning, sounded to your ears to be close enough to a 7/4 that it might as well be called a 7/4, and you realized that this meant you were equating 225/128 with 7/4 and thus operating in Marvel temperament, even though you were using a tuning where the two intervals were tuned distinctly.
>
> I think Mike might want to ask you some questions about this.

No, I have nothing at all to ask Carl on this topic ever again. What I
have to say is below, and then I don't want to say anymore.

Here's something Graham wrote in primerr.pdf which I always remembered

"Before leaping into a quantitative discussion of the errors of
different temperaments, it may be worth thinking about what it means
for a tuning to have an error. Error relative to what, and why should
we care? Without surveying the relevant literature (which is far from
conclusive anyway) I hope we can agree on
the following qualitative properties.

1. Simple ratios have a desirable affect.
2. The closer to a ratio the stronger the affect.
3. Moderate errors stand out more than small ones.
4. Large errors are irrelevant."

Those are the only things you need to assume for every single part of
regular mapping theory to work. That's it. Graham notes that the
literature is far from conclusive, so instead comes up with a basic,
bare minimum set of assumptions which almost everyone would have to
agree on in some fashion, and then goes on to show how we can even use
those simple ideas to create enormously useful models and do cool
stuff. That is the right way to handle this situation.

Sometimes, when you ask these questions to Carl or to the group, it
seems like what you want is a tightening of the bounds made by the
above assumptions. When does "simple" stop being simple? How "close"
do you have to be to a ratio for the affect to be noticeable? How
large does an error have to be before it's "irrelevant?" etc. What,
specifically is the most important "affect" in this set of
assumptions?

And, as Graham said, many of these tough questions don't have
conclusive existing answers. That's my conclusion from debating with
Carl about this for years, talking to Paul about it for years,
watching Carl and Paul sometimes disagree, watching Gene sometimes
disagree with both, reading Parncutt, Cariani, Terhardt, Huron,
Krumhansl, now Benade, Jordan, Shepard, Trehub, Oxenham, and a million
papers from the psychoacoustics literature from people whose names I
forget, etc. I don't see any clear answer to these questions at all,
nor any consensus on anything, nor any big secret "scientific" answer
that I'm aware of which is custom-tailored to the specific needs of
our community. If what you want is some tuning "authority" to
reiterate this, go read the conversation I just had on XA with Paul,
where it's not a big secret that he doesn't claim to have all the
answers either, but that he thinks our model is still a step in the
right direction anyway.

So when you ask the above questions, you're basically asking us the
list to speculate. The resulting situation reminds me of a windup toy
running continuously into a wall, schizophrenically saying robotic
phrases like "it's most scientific to assume that really dark gray is
black" and then "no, it's most scientific to assume that really dark
gray is dark gray" and and so on.

This isn't to say that I don't like discussing music cognition, or
that I don't think it's worthwhile to ask the questions you're asking.
I mean that to ask them under the moniker that there's some existing
well-known answer which is "more scientific" than the rest of the
half-assed guesses is Bad. It is Good, however, to ask these questions
in open-ended fashion, with the awareness that nobody knows what the
answer is yet, so as to try to learn. There's a subtle difference
there.

-Mike

On Sun, Feb 12, 2012 at 11:39 AM, cityoftheasleep
<igliashon@...> wrote:
>
> I think what you mean to ask, Mike, is "what does it mean to be a consistent image of Q?"
>
> I'll bet Carl would make the claim that even if we're mapping Q to a scale using the identity function, it'll be possible to make music that fails to be a consistent image of Q. Think about it: what if you made a JI scale and played tons of wolf intervals and "shimmering commatic unisons" (i.e. "random dissonances of the scale"), and more-or-less systematically avoided the simple consonances? I'm expecting that Carl might say that such music "isn't JI", and because of that, it's not allowing the tuning to be recognized as an "image of Q". But I might be wrong.

Keenan also just came up with a similar notion about using a
temperament "as" a temperament. I could have nitpicked over some
aspects of it, but I opted not to because I spend so many hours
talking with Keenan about this stuff in XA chat that I know he already
understands any nit that I'd pick, and is just simplifying a bit here.

All of these definitions of temperaments "existing" ultimately break
down when you get into the shades of gray involved. In this case, what
Keenan didn't do was assert that his notion of what the smart vs
stupid way to use a temperament is is the "best" or "most scientific"
or whatever. So, I have no problem with it, because it doesn't assert
to a claim about how music cognition works or whatever, but reflects
his high-level compositional paradigm about how to use the
mathematical objects we have. (I still maintain that the augmented
Looney Tunes example is "valid" as augmented under his definition
though, because they deliberately go down three 5/4's to get back to
1/1, which meets his criteria.)

I agree that if you take some temperament, like porcupine[15], and use
it like a 12-EDO muddle, you're not utilizing its full potential at
all. I also agree that if you take 5-limit JI, and wantonly play wolf
fifths to treat the whole thing like it's a 12-EDO well temperament or
something, that that's a stupid way to use JI. What about someone who
has a scale where 5/4 and 81/64 share an interval class, and the
composer just plays major triads indiscriminately and doesn't play the
pure ones more? It always goes back to semantics. Shall we say that
this "is not JI?" Do we want to say that it it's just "a stupid way to
use JI?" I dunno, let's argue over it for a while.

-Mike

On Sun, Feb 12, 2012 at 10:55 AM, lobawad <lobawad@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> >
> > On Sat, Feb 11, 2012 at 9:38 PM, cityoftheasleep
> > <igliashon@...> wrote:
> > >
> > > I think you guys are playing fast-and-loose with the term "JI", using it interchangeably with RI.
> >
> > Yes, that's how I like to use it when introducing regular
> > temperaments, for the same reason I like to call JI a type of
> > "temperament." It's just simpler to define things that way.
> >
>
> I do not see any evidence that the fundamental distinction between intonation and tone is made on these lists.

Didn't we just discuss this topic for something like 3 weeks?

> The conceptual blunder here was actually made by "JI purists", as Carl pointed out. So, why perpetuate this blunder? Rationals are rationals, they are not Just Intonation unless they are intonations OF tones.

The context here is that I'm explaining the subject of regular mapping
for the first time to a newcomer on XA, not talking about music
cognition.

I said that all temperaments are derived from JI, and are defined as
distortions of that so that commas vanish. If I was going to use your
definition, I'd have to say that all temperaments are derived from RI,
and that only the subgroups of RI which have simple ratios are
actually JI, but that there's no hard and strict definition of where
"simple" is.

I think the second definition is more confusing. And, unless somebody
cares enough to get into the science behind it, I want to shield them
from all of these music cog. debates which don't really matter.

In this context, JI is defined as the "temperament" with wedgie <1|,
<<1||, <<<1|||, etc.

-Mike

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

> So when you ask the above questions, you're basically asking us the
> list to speculate. The resulting situation reminds me of a windup toy
> running continuously into a wall, schizophrenically saying robotic
> phrases like "it's most scientific to assume that really dark gray is
> black" and then "no, it's most scientific to assume that really dark
> gray is dark gray" and and so on.

No, I'm not asking for firm boundaries or definite limits. All I'm asking is for people to acknowledge that it's valid to say that some temperaments are irrelevant or absurd, and that for any given listener, some temperaments make more sense as descriptions of tunings than others. I've even proposed a method of quantifying the amount of sense a temperament makes as a description of a tuning.

I don't know why people think they disagree with me, because in practice everyone behaves consistently with what I'm saying. Nobody ever insists that 11-ED2 makes more sense as a Meantone temeprament than an Orgone temperament. In so far as we use tunings as temperaments, we all tend to use mappings that make good sense, if not necessarily maximally-good sense.

-Igs

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Sun, Feb 12, 2012 at 10:55 AM, lobawad <lobawad@...> wrote:
> >
> > --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
> > >
> > > On Sat, Feb 11, 2012 at 9:38 PM, cityoftheasleep
> > > <igliashon@> wrote:
> > > >
> > > > I think you guys are playing fast-and-loose with the term "JI", using it interchangeably with RI.
> > >
> > > Yes, that's how I like to use it when introducing regular
> > > temperaments, for the same reason I like to call JI a type of
> > > "temperament." It's just simpler to define things that way.
> > >
> >
> > I do not see any evidence that the fundamental distinction between intonation and tone is made on these lists.
>
> Didn't we just discuss this topic for something like 3 weeks?

Yes, and we agreed- as any sane person with any concern with broader communication in historical context would. But...
>
> > The conceptual blunder here was actually made by "JI purists", as Carl pointed out. So, why perpetuate this blunder? Rationals are rationals, they are not Just Intonation unless they are intonations OF tones.
>
> The context here is that I'm explaining the subject of regular mapping
> for the first time to a newcomer on XA, not talking about music
> cognition.
>
> I said that all temperaments are derived from JI, and are defined as
> distortions of that so that commas vanish. If I was going to use your
> definition, I'd have to say that all temperaments are derived from RI,
> and that only the subgroups of RI which have simple ratios are
> actually JI, but that there's no hard and strict definition of where
> "simple" is.

... there you go with this "JI" and "RI" stuff! Intonation OF WHAT? Do you mean justly intoning traditional Western tonal intervals? If so, why did you say nothing when Keenan pooh-poohed my simple observation to the effect that if we're talking about the intonation of traditional Western intervals, well, we have to talk about the intonation of traditional Western intervals?

If we are not talking about justly intoning traditional Western intervals, we are NOT talking about Just Intonation, not in a reasonable and historically informed way. Nor or we talking about rational intonation. We're talking about rational pitch structures.

Fokker blocks and Meyers diamonds are not Just Intonation- they are rational pitch structures (or some such appropriate moniker).

>
> I think the second definition is more confusing. And, unless somebody
> cares enough to get into the science behind it, I want to shield them
> from all of these music cog. debates which don't really matter.
>
> In this context, JI is defined as the "temperament" with wedgie <1|,
> <<1||, <<<1|||, etc.
>
> -Mike
>

Like it or not, Just Intonation is already defined, and concepts of it deeply entrenched. The "Just Intonation" subculture took the name but applied it to rational pitch structures. This doesn't really matter for those in the "JI" community who are hopelessly western in their thinking: their rational pitch structures correspond more or less to the Just Intonation of traditional Western intervals anyway.

The "JI" referred to on this list can NOT be said with certainty to correspond to the Just intonation of western intervals, though. Sure, Schoenberg (long before Partch) mapped out the chromatic scale to the 13th partial and claimed that the harmonic partials were the source of our 12-tone scale. Anyone up for quoting THAT as authoritative precedence to what goes on here?

And in no case is it wise to call any kind of "JI" a "temperament". Find some new words, or a very different way to state this. Yes anyone who gets into it can figure out that yeah, we could look at it that way! and see that it makes sense if we adhere to certain definitions of different concepts. But the words that come out in the end are wearing motley.

On Sun, Feb 12, 2012 at 1:23 PM, cityoftheasleep
<igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > So when you ask the above questions, you're basically asking us the
> > list to speculate. The resulting situation reminds me of a windup toy
> > running continuously into a wall, schizophrenically saying robotic
> > phrases like "it's most scientific to assume that really dark gray is
> > black" and then "no, it's most scientific to assume that really dark
> > gray is dark gray" and and so on.
>
> No, I'm not asking for firm boundaries or definite limits. All I'm asking is for people to acknowledge that it's valid to say that some temperaments are irrelevant or absurd, and that for any given listener, some temperaments make more sense as descriptions of tunings than others. I've even proposed a method of quantifying the amount of sense a temperament makes as a description of a tuning.
>
> I don't know why people think they disagree with me, because in practice everyone behaves consistently with what I'm saying. Nobody ever insists that 11-ED2 makes more sense as a Meantone temeprament than an Orgone temperament. In so far as we use tunings as temperaments, we all tend to use mappings that make good sense, if not necessarily maximally-good sense.

My answer to everything you just said is right here

/tuning/topicId_103549.html#103606

-Mike

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

> All of these definitions of temperaments "existing" ultimately break
> down when you get into the shades of gray involved. In this case, what
> Keenan didn't do was assert that his notion of what the smart vs
> stupid way to use a temperament is is the "best" or "most scientific"
> or whatever. So, I have no problem with it, because it doesn't assert
> to a claim about how music cognition works or whatever, but reflects
> his high-level compositional paradigm about how to use the
> mathematical objects we have. (I still maintain that the augmented
> Looney Tunes example is "valid" as augmented under his definition
> though, because they deliberately go down three 5/4's to get back to
> 1/1, which meets his criteria.)

So, because Keenan's notion is outside the realm of falsification, you find it unobjectionable, but because I tried to describe the exact same thing in terms that are subject to experimental falsification, you find it unacceptable? And you're okay with saying things like "this is a smarter way to use x temperament than that", but not "this temperament is a more accurate depiction of what this tuning is, rather than that temperament"?

> I agree that if you take some temperament, like porcupine[15], and use
> it like a 12-EDO muddle, you're not utilizing its full potential at
> all. I also agree that if you take 5-limit JI, and wantonly play wolf
> fifths to treat the whole thing like it's a 12-EDO well temperament or
> something, that that's a stupid way to use JI. What about someone who
> has a scale where 5/4 and 81/64 share an interval class, and the
> composer just plays major triads indiscriminately and doesn't play the
> pure ones more? It always goes back to semantics. Shall we say that
> this "is not JI?" Do we want to say that it it's just "a stupid way to
> use JI?" I dunno, let's argue over it for a while.

I don't want to argue about it, but I would like to stop feeling like we don't actually know what we mean when we talk about things like JI and temperament. I have a disconcerting feeling that we're putting everyone on with this whole paradigm, because we don't actually have the means of describing how the mathematical operations reflect musical reality.

Why is it a better solution, in your eyes, to assert the existence of some vague "desirable affect" of simple ratios than to try to formally describe what those desirable properties are? If we *can't* formally describe them--if such a formal description is impossible--then how can we even meaningfully discuss them? A word without a definition is meaningless. I'd say that if we can't meaningfully discuss a subject, we ought to shut up about it.

-Igs

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

> Why is it a better solution, in your eyes, to assert the existence of some vague "desirable affect" of simple ratios than to try to formally describe what those desirable properties are? If we *can't* formally describe them--if such a formal description is impossible--then how can we even meaningfully discuss them? A word without a definition is meaningless. I'd say that if we can't meaningfully discuss a subject, we ought to shut up about it.
>
> -Igs
>

I have yet to see any convincing argument against the old (and "QED, f*cking obvious") observations that simple ratios are distinguished by the way they melt together, sing together, beat less, etc. etc.

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

> I have yet to see any convincing argument against the old (and "QED, f*cking obvious")
> observations that simple ratios are distinguished by the way they melt together, sing
> together, beat less, etc. etc.

Well, for some reason people are pulling away from that, pulling away from making any firm or concrete statements about what audible properties are necessary for a sonority to be called JI. Maybe because 1) simple ratios *aren't* distinguishable by these criteria, because nearby irrationals also display these properties, 2) no one has yet advanced an hypothesis describing why we'd find the presence of these qualities pleasing and the absence of them displeasing (why is beating/roughness/low tonalness/etc. unpleasant? Or is it?), 3) using a pitch set composed entirely of simple ratios is no guarantee than all harmonies played in the pitch set will display the properties you mentioned (due to wolf intervals, etc.), 4) some irrational or complex-rational pitch sets offer more sonorities that display the properties you mentioned, than would the nearest pitch set composed of simple rationals, or 5) it's possible we haven't exhaustively described the (psycho)acoustic properties associated with Just harmony?

-Igs

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, "lobawad" <lobawad@> wrote:
>
> > I have yet to see any convincing argument against the old (and "QED, f*cking obvious")
> > observations that simple ratios are distinguished by the way they melt together, sing
> > together, beat less, etc. etc.
>
> Well, for some reason people are pulling away from that, pulling >away from making any firm or concrete statements about what audible >properties are necessary for a sonority to be called JI.

Well, "people" isn't "this tuning list and closely related communities".

>Maybe because 1) simple ratios *aren't* distinguishable by these criteria, because nearby irrationals also display these properties,

Out in the real world, no one has problems identifying either Just Intonation or simple rational intevlas. By ear. You hear that melting-together sound, or you don't.

2) no one has yet advanced an hypothesis describing why we'd find the presence of these qualities pleasing and the absence of them displeasing (why is beating/roughness/low tonalness/etc. unpleasant? Or is it?),

Pleasant or not is not important- as I've mentioned many times, my wife immediately recognizes "5-limit" JI and hates it. It's just a thing- some people like how orange and green clash, some don't, and for most people it depends on context. Sane people don't pretend there is no striking visual effect created by the juxtaposition of orange and green, and sane people don't claim this effect is the ultimate answer to all visual art.

3) using a pitch set composed entirely of simple ratios is no guarantee than all harmonies played in the pitch set will display the properties you mentioned (due to wolf intervals, etc.),

The idea of pan-smoothness (or whatever you'd like to call it) is a nutty idea that does NOT come from Just Intonation, but from "JI" theorists who mistake their rational pitch structures for Just intonation: Just Intonation is intonation OF pre-existing intervals, which are understood to be dissonant, consonant, imperfectly consonant, etc.

4) some irrational or complex-rational pitch sets offer more sonorities that display the properties you mentioned, than would the nearest pitch set composed of simple rationals, or

I don't know, what would be examples?

5) it's possible we haven't exhaustively described the (psycho)acoustic properties associated with Just harmony?

That I don't know. I think we have not yet catalogued the combinations of LEAST concordant sonorities, even though it seems like such an obvious thing to do, given that the 20th century has been called the "century of the tritone".

On Sun, Feb 12, 2012 at 2:00 PM, cityoftheasleep
<igliashon@...> wrote:
>
> So, because Keenan's notion is outside the realm of falsification, you find it unobjectionable, but because I tried to describe the exact same thing in terms that are subject to experimental falsification, you find it unacceptable?

What did you say that's subject to experimental falsification?

> And you're okay with saying things like "this is a smarter way to use x temperament than that", but not "this temperament is a more accurate depiction of what this tuning is, rather than that temperament"?

Keenan's point, as I understood it, was that if you play in something
like porcupine, but you don't assume there's any new patterns or
structure to learn and just use the same mental approach that you do
when you play 12, then you're not unlocking the full musical potential
of the tuning. I have no problem with that because this is his
opinion. It's also an opinion I happen to agree with. The statement
"if you do the same thing you always do in a new environment then you
miss the new things you can do in the new environment" is A-OK with
me.

In contrast, during our conversation, you seemed to make some concrete
assertions about music and the brain and how it works. The conclusion
that you ultimately arrived at was that dicot temperament doesn't
truly exist in a musically relevant sense. It seemed to me at the time
that you weren't asserting this as your opinion, but as an objectively
scientific fact. I didn't think I agreed with that statement, because
it seemed to depend on assumptions that I wasn't comfortable making
and which didn't adequately explain things I'd experienced in the
past. Before I leveled any criticism against it I tried to make sure I
knew precisely what you were saying, but then our communication broke
down.

> I don't want to argue about it, but I would like to stop feeling like we don't actually know what we mean when we talk about things like JI and temperament.
> I have a disconcerting feeling that we're putting everyone on with this whole paradigm, because we don't actually have the means of describing how the mathematical operations reflect musical reality.

It's not true as a blanket statement that we "don't know what we
mean," in general, when we talk about things like JI and temperament.
Everyone internally knows what they mean, and our internal meanings
all differ from one another. There are a number of meanings which all
seem "sensible," and which are mutually contradictory, and we have
almost no evidence at all right now to conclusively pick the "right"
one.

Even if we did, wtf would it mean? Even if we knew everything, there'd
still be more than one way to use this model to model stuff. It
associates things in Q with things in Z^n, and we know that things in
Q have more than one effect. What if we get real creative one day and
decide that we really care about periodicity buzz, which is more
fragile than virtual pitch integration, and also tends to work for
higher-limit isoharmonic chords? Then we might be working with a
different set of parameters. In fact, I'd like to actually do that
sometime.

But even besides this, we don't need to know everything in order to do
build a nice theory around what we do know. There are a few things
most of us agree on, all centered around the idea that simple ratios
can create all of these aural effects which a lot of people think
sound really cool. So, Gene and Paul and Graham and others came up
with a simple model to associate elements in Q with elements in Z^n.
This lets us find all the tunings which have as many simple ratios
tuned as accurately as possible. Now we have a ton of new material
with which to make musical compositions that can exploit these
effects. Woo hoo!

So I disagree we're "putting anyone on" with the theory. It's a good
framework to figure out some awesome sounds that you can use to write
music and base compositions on, and it's based on some very very
simple assumptions. There's nothing false about that, nothing that
puts anyone on. If someone says "11-EDO is dissonant and atonal blah
blah blah," anyone can link to something like this

http://www.youtube.com/watch?v=AhPjsCoMy-Q

or write a little throwaway demo that starts off first with it
sounding stupid, and then demonstrates how to make it sound less
atonal afterward

http://soundcloud.com/mikebattagliamusic/tonality-patterns-in-11-edo

and say that these sounds come from playing 4:7:9:11 in 11-EDO, which
it supports with abc cents of error. Then, if they're like oh hey,
looks like 11-EDO isn't dissonant after all, you gave them something
musically useful. How is that putting anyone on?

However, it DOES get into the realm of "putting people on" if you try
to bullshit some additional, fully formed scientific conjecture that
explains all of the unknown things that we don't know, and then assert
that this is how all the hip cool science kids like to guess at what
they don't know. Then it gets into the realm of putting people on.
Figuring out the "full extent of how the mathematical operations
reflect musical reality" is for composers to figure out, with maybe
some clues from a well-designed experiment or two.

> Why is it a better solution, in your eyes, to assert the existence of some vague "desirable affect" of simple ratios than to try to formally describe what those desirable properties are? If we *can't* formally describe them--if such a formal description is impossible--then how can we even meaningfully discuss them? A word without a definition is meaningless. I'd say that if we can't meaningfully discuss a subject, we ought to shut up about it.

Igs, I'd love to formally describe what those properties are. It's an
impediment to doing so if we don't admit exactly what we don't know at
the current point in time.

-Mike

On Sun, Feb 12, 2012 at 1:57 PM, lobawad <lobawad@...> wrote:
>
> ... there you go with this "JI" and "RI" stuff! Intonation OF WHAT? Do you mean justly intoning traditional Western tonal intervals? If so, why did you say nothing when Keenan pooh-poohed my simple observation to the effect that if we're talking about the intonation of traditional Western intervals, well, we have to talk about the intonation of traditional Western intervals?

What?

> If we are not talking about justly intoning traditional Western intervals, we are NOT talking about Just Intonation, not in a reasonable and historically informed way. Nor or we talking about rational intonation. We're talking about rational pitch structures.

We can define "just intonation" however we want. It's a string of
characters that serves as a placeholder for an idea. We can define it
to mean "toothpaste" if we want.

In the context of this mathematical theory, I think it makes the most
sense to define it as the "temperament" with wedgie <1|, or <<1||, or
<<<1|||, etc. Which just means a "temperament" which "tempers out"
nothing but 1/1. And sometimes I also think it makes the most sense to
define it as the domain of the mapping, which is the rationals, to
which this "temperament" is isomorphic.

You might think that this includes certain things which defeat the
purpose of JI, like really complex ratios. OK, whatever. But, I think
it's less confusing and that people are smart enough to figure it out,
just like that they're smart enough to figure out what I mean when I
say that in the theory, JI is treated as a special type of temperament
with zero tuning error. I'm not worried that if I just say the entire
thing under the moniker of JI that they're all going to start using
2.34923.1201329-limit temperaments or what have you, if that's the
objection.

> Like it or not, Just Intonation is already defined, and concepts of it deeply entrenched. The "Just Intonation" subculture took the name but applied it to rational pitch structures. This doesn't really matter for those in the "JI" community who are hopelessly western in their thinking: their rational pitch structures correspond more or less to the Just Intonation of traditional Western intervals anyway.
>
> The "JI" referred to on this list can NOT be said with certainty to correspond to the Just intonation of western intervals, though. Sure, Schoenberg (long before Partch) mapped out the chromatic scale to the 13th partial and claimed that the harmonic partials were the source of our 12-tone scale. Anyone up for quoting THAT as authoritative precedence to what goes on here?

I hate the definition of JI where it refers to common practice music
being intoned with simple ratios. I'm never going to use that. I've
also heard it only refer to 5-limit JI and I'm never going to use that
either. I don't care who used it like that, I hate it.

> And in no case is it wise to call any kind of "JI" a "temperament". Find some new words, or a very different way to state this. Yes anyone who gets into it can figure out that yeah, we could look at it that way! and see that it makes sense if we adhere to certain definitions of different concepts. But the words that come out in the end are wearing motley.

There are only a few times when I think debates over semantics are
useful: to simplify definitions to make them less cumbersome, and to
make it easier and simpler to teach stuff. The aesthetic value of the
words chosen is like a tertiary consideration after those two things
for me.

In this case, I think both of the first two desiderata are satisfied
most strongly by defining JI exactly the way I said, just for the
purposes of this theory. We just say that we model JI as a perfect
temperament with zero error, and we don't even mention at all the
debate on where JI ends and RI begins. I think that's perfect.

For clarity's sake, if this were a book I was writing, I'd have a
footnote saying that some authors use the word "temperament"
specifically to exclude things like JI, so that it's not a temperament
at all, not even a "special temperament with 0 error." And, I'd also
include a footnote saying that some authors define JI only to mean the
use of relatively simple ratios, and that they'd call the thing I'm
calling just intonation "rational intonation" instead. I can't imagine
anyone being confused by that.

The goal is for the newcomer to understand what's going on. But, if
you think there's a simpler way to define things above, I'm all for
it. After trying to explain this in a lot of different ways, I've
concluded that this is the most elegant way to do it, but I'm open to
something better. But if it's just a matter of pedagogical preference,
then you use yours, and I'll use mine.

I'm still holding out for Carl's explanation though of why it's better
to say that the isomorphism is JI and not the rationals though. I've
been using the term for both.

-Mike

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

> What did you say that's subject to experimental falsification?

Any statement as regards the impossibility of perceiving a certain temperament in music is easily falsifiable by finding an example where the temperament's mapping succeeds in describing someone's perception of music. If I told you that meantone doesn't exist, you could prove me wrong by showing me someone who, on hearing a meantone-tempered 4:5:6 triad, says "that sounds like a 4:5:6 triad". If even one person succeeds in recognizing the image of Q in Z^n, then the mapping is legit and the temperament exists.

If we fail to falsify the statement, of course, this doesn't mean it's true. Scientifically-speaking, we cannot verify, we can only falsify or fail to falsify. When reasonable efforts fail to falsify something, we tentatively adopt it with whatever confidence level is appropriate for the effort we put in to falsify it (which is never 100%). And we keep looking for more and more rigorous ways to try to falsify it.

Compare this to saying a temperament is stupid. How can this statement be falsified? It can't.

> Keenan's point, as I understood it, was that if you play in something
> like porcupine, but you don't assume there's any new patterns or
> structure to learn and just use the same mental approach that you do
> when you play 12, then you're not unlocking the full musical potential
> of the tuning. I have no problem with that because this is his
> opinion. It's also an opinion I happen to agree with. The statement
> "if you do the same thing you always do in a new environment then you
> miss the new things you can do in the new environment" is A-OK with
> me.

Why is it stupid to not unlock the full musical potential of the tuning?

> In contrast, during our conversation, you seemed to make some concrete
> assertions about music and the brain and how it works.

If I did, then they're assertions I took directly from the explanations of various psychoacoustic principles given to me by you, Paul, and Carl.

> The conclusion
> that you ultimately arrived at was that dicot temperament doesn't
> truly exist in a musically relevant sense.

Well, here we go again.

There were multiple points I was attempting to make. Point 1: let's say I play you a piece of music composed of a bunch of neutral triads, and I ask you whether this music is demonstrating dicot temperament, 2.3.11 243/242 temperament, 2.3.13 512/507, all of the above, none of the above, or some combination of the above. Let's imagine you want to say that it's not all of the above; then there has to be some way you (or even *someone*) could figure it out, based on the music. Who cares what that could be, the fact that a distinction is possible is good enough, even if it's based on some totally random idea of what ratios "sound like". The point is, if you can give a definite answer, single out a given temperament mapping as being "the right (or least-wrong) answer" to the question of what temperament the music is in--even if other people would disagree, even if there's no consensus--then we have learned something about your perception of musical reality, and we can say "given these intervals in this musical context, Mike perceives this temperament". And we can now definitively say that whatever temperament you selected is real, to at least you.

If it *is* all of the above, then we have to conclude that all of these temperaments are actually the same thing, and that tempering 25/24 out of the 5-limit is the *same thing* as tempering 243/242 out of the 2.3.11-limit (etc.), which, y'know, I'm cool with that as well.

Point 2: the adaptive JI problem. How the hell can one tune dicot in 5-limit adaptive JI? It is impossible to determine whether a given dicot triad is a 4:5:6 or a 10:12:15, because every chord is both, but in order for the music to sound like 5-limit JI, every triad has to be one or the other. The only way to come up with an adaptive JI algorithm for dicot temperament would be to allow randomness to decide a given chord's tuning. What this means is that there is effectively no way to "use" the dicot mapping, at least in the sense that I understand how one can "use" a mapping at all.

> It's not true as a blanket statement that we "don't know what we
> mean," in general, when we talk about things like JI and temperament.
> Everyone internally knows what they mean, and our internal meanings
> all differ from one another. There are a number of meanings which all
> seem "sensible," and which are mutually contradictory, and we have
> almost no evidence at all right now to conclusively pick the "right"
> one.

Right--"we" as a collective entity, "the group", do not have agreed-upon definitions for these words. Nor does there seem to be significant understanding between us about what definitions a given group-member is operating with.

> Even if we did, wtf would it mean? Even if we knew everything, there'd
> still be more than one way to use this model to model stuff. It
> associates things in Q with things in Z^n, and we know that things in
> Q have more than one effect. What if we get real creative one day and
> decide that we really care about periodicity buzz, which is more
> fragile than virtual pitch integration, and also tends to work for
> higher-limit isoharmonic chords? Then we might be working with a
> different set of parameters. In fact, I'd like to actually do that
> sometime.

Sure, but we'd also have some understanding about when different uses of these models apply and when they don't. That's a long way off.

> But even besides this, we don't need to know everything in order to do
> build a nice theory around what we do know. There are a few things
> most of us agree on, all centered around the idea that simple ratios
> can create all of these aural effects which a lot of people think
> sound really cool. So, Gene and Paul and Graham and others came up
> with a simple model to associate elements in Q with elements in Z^n.
> This lets us find all the tunings which have as many simple ratios
> tuned as accurately as possible. Now we have a ton of new material
> with which to make musical compositions that can exploit these
> effects. Woo hoo!

RMP is about much more than mapping; it would be utterly useless in helping us find tunings without badness and without the various optimization methods. But even with these, RMP is only as successful as the person wielding it is knowledgeable. It has no built-in guarantee that it will lead to tunings that display the aural effects associated with simple ratios, because it's based on user-supplied targets and user-supplied error thresholds, as well as error-based optimization. Some effects of simple ratios, like synchronous beating, won't come out of any of our current optimization methods, because error does not correlate with synchronicity of beat frequencies. Furthermore, some high-error temperaments succeed in producing the effects of simple ratios just fine, because they're actually equivalent to low-error temperaments of different target intervals. It currently takes a sharp eye to recognize the temperaments where this is the case--and is the area of the field where I've spent the most time.

> So I disagree we're "putting anyone on" with the theory. It's a good
> framework to figure out some awesome sounds that you can use to write
> music and base compositions on, and it's based on some very very
> simple assumptions. There's nothing false about that, nothing that
> puts anyone on.

I beg to differ. There are some huge and complex assumptions that go into badness rankings and optimization procedures, and these assumptions are based on incomplete knowledge of music cognition. It's possible to get total nonsense out of RMP and we don't currently have anything but our instincts to let us discern what's nonsense and what's not. And my best efforts to codify some methodology for separating the nonsense from the sense lead to you telling me I'm assuming too much--when all I'm assuming is that in fact some mappings are nonsense.

> However, it DOES get into the realm of "putting people on" if you try
> to bullshit some additional, fully formed scientific conjecture that
> explains all of the unknown things that we don't know, and then assert
> that this is how all the hip cool science kids like to guess at what
> they don't know. Then it gets into the realm of putting people on.

Who's doing that??

> Igs, I'd love to formally describe what those properties are. It's an
> impediment to doing so if we don't admit exactly what we don't know at
> the current point in time.

It's also an impediment if we don't admit what we DO know!

-Igs

On Sun, Feb 12, 2012 at 7:00 PM, cityoftheasleep
<igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > What did you say that's subject to experimental falsification?
>
> Any statement as regards the impossibility of perceiving a certain temperament in music is easily falsifiable by finding an example where the temperament's mapping succeeds in describing someone's perception of music. If I told you that meantone doesn't exist, you could prove me wrong by showing me someone who, on hearing a meantone-tempered 4:5:6 triad, says "that sounds like a 4:5:6 triad". If even one person succeeds in recognizing the image of Q in Z^n, then the mapping is legit and the temperament exists.

So, under your scheme, all we need to do to establish the "existence"
of a temperament -

- which is the most loaded possible term you could use to denote a
rather simple and ordinary concept -

is to find a person who's like, "yeah, I think that sounds enough like
4:5:6 for me to give it the thumbs up?"

And we'll just leave it totally subjective like that, leaving them
open to interpret the meaning of a ratio in their own way and however
they want?

Please confirm.

Also, what tuning do I use for the temperament when I do this test?

> If we fail to falsify the statement, of course, this doesn't mean it's true. Scientifically-speaking, we cannot verify, we can only falsify or fail to falsify. When reasonable efforts fail to falsify something, we tentatively adopt it with whatever confidence level is appropriate for the effort we put in to falsify it (which is never 100%). And we keep looking for more and more rigorous ways to try to falsify it.

Fine, let's use your paradigm. What do you think the appropriate
"confidence level" is to establish perceptual impossiblity for a brand
new field of study that's a few years old with no literature and which
is solely centered around the goal of finding new things that are
perceptually possible and in which we know almost nothing?

> Compare this to saying a temperament is stupid. How can this statement be falsified? It can't.

It isn't a scientific statement. Keenan's just saying he thinks it's
stupid. There's nothing inherent in his argument that requires me to
make silly assumptions about "the brain" and however the hell it
works, so why would I have a problem with it?

Why am I supposed to apply the scientific method to someone's
subjective value judgments? The whole point is that I don't want to do
that.

> Why is it stupid to not unlock the full musical potential of the tuning?

It's not objectively stupid, but Keenan's opinion was that it was.
I'll assume that it's because he likes when full musical potentials
are unlocked.

> There were multiple points I was attempting to make. Point 1: let's say I play you a piece of music composed of a bunch of neutral triads, and I ask you whether this music is demonstrating dicot temperament, 2.3.11 243/242 temperament, 2.3.13 512/507, all of the above, none of the above, or some combination of the above. Let's imagine you want to say that it's not all of the above; then there has to be some way you (or even *someone*) could figure it out, based on the music. Who cares what that could be, the fact that a distinction is possible is good enough, even if it's based on some totally random idea of what ratios "sound like". The point is, if you can give a definite answer, single out a given temperament mapping as being "the right (or least-wrong) answer" to the question of what temperament the music is in--even if other people would disagree, even if there's no consensus--then we have learned something about your perception of musical reality

Yes, you've learned about the way I make either/or and same/different
judgments. This is worthwhile to know, sure.

> and we can say, <for no other reason than that I like the use of these words for purely aesthetic reasons> "given these intervals in this musical context, <loaded phrase here>". And we can now definitively say that whatever temperament you selected is <loaded term>, to at least you.

And this is where I have to hop off the train.

> If it *is* all of the above, then we have to conclude that all of these temperaments are actually the same thing, and that tempering 25/24 out of the 5-limit is the *same thing* as tempering 243/242 out of the 2.3.11-limit (etc.), which, y'know, I'm cool with that as well.

We don't have to conclude that they "are the same thing" at all. We
can say that they sound the same. I don't know what that isn't enough
for you.

We can have a much more intelligent understanding of it than that.
These two temperaments have the same scalar structure but have
different POTE tunings and would have different adaptive tunings and
would have different everything else.

> Point 2: the adaptive JI problem. How the hell can one tune dicot in 5-limit adaptive JI? It is impossible to determine whether a given dicot triad is a 4:5:6 or a 10:12:15, because every chord is both, but in order for the music to sound like 5-limit JI, every triad has to be one or the other. The only way to come up with an adaptive JI algorithm for dicot temperament would be to allow randomness to decide a given chord's tuning. What this means is that there is effectively no way to "use" the dicot mapping, at least in the sense that I understand how one can "use" a mapping at all.

Every single thing you said I disagree with. I disagree that being
able to distinguish 4:5:6 and 10:12:15 is sufficient to say music
"sounds like 5-limit JI," and I disagree that being able to
distinguish them is necessary to say music "sounds like the 5-limit"
in general, and I disagree that the only decent adaptive-JI algorithm
you could have for dicot is to map things randomly, and I disagree
that there's no way to "use" the dicot mapping. This paragraph was a
perfect no-hitter for me.

> > So I disagree we're "putting anyone on" with the theory. It's a good
> > framework to figure out some awesome sounds that you can use to write
> > music and base compositions on, and it's based on some very very
> > simple assumptions. There's nothing false about that, nothing that
> > puts anyone on.
>
> I beg to differ. There are some huge and complex assumptions that go into badness rankings and optimization procedures, and these assumptions are based on incomplete knowledge of music cognition.

They're neither huge nor complex. Simple ratios sound a certain way,
it seems to be fairly universal that people hear this sound, and at
least some people like that sound. That's all that you need, you don't
need to make any further assumptions about music cognition other than
that. And if someone out there doesn't like the sound of simple
ratios, then they shouldn't use this theory.

> It's possible to get total nonsense out of RMP and we don't currently have anything but our instincts to let us discern what's nonsense and what's not. And my best efforts to codify some methodology for separating the nonsense from the sense lead to you telling me I'm assuming too much--when all I'm assuming is that in fact some mappings are nonsense.

Correct. Mappings are abstract mathematical objects with lots of uses.
We don't even know what all of the uses for them are yet. To write one
off as "being nonsense" is like this crazy nonsensical statement in
and of itself.

I can't imagine why you're not happy with the phrase "I can't conceive
of any possible use for that temperament."

Unless, of course, you just informally mean that some mappings are
nonsense in the sense that Keenan thinks that some temperaments are
stupid. In which case, I agree, the temperament eliminating 3/2 is
stupid, meaning I'll never use it because I can't conceive of any
possible use for that temperament, nor any mental benefit conferred to
my understanding of a tuning system by mapping things that way.

> > Igs, I'd love to formally describe what those properties are. It's an
> > impediment to doing so if we don't admit exactly what we don't know at
> > the current point in time.
>
> It's also an impediment if we don't admit what we DO know!

I think I'm pretty clear, internally, on what I do and don't know.

-Mike

Look, man--we don't disagree about anything except for a bit of epistemology. You don't want to dismiss anything even if neither you nor anyone you know can conceive of any possible use for it. I want to dismiss everything unless *somebody* I know finds it useful. We're clearly never going to reconcile that difference. So let's let it stand as a known point of philosophical contention.

We agree that there's a limit to the number of temperaments a person can recognize, as long as I don't try to appeal to science to explain why this is. I mean, I don't have a scientific explanation for it, but I believe that there could be one and would like to work toward it. Why is that problematic for you? Why are you okay recognizing that everyone you know will think of certain temperaments as useless, but not okay with the possibility of there existing a scientific explanation for this state of affairs?

Also, please explain how if three temperaments can sound the same, that they can be musically different. Also, please explain how to adaptively tune dicot temperament in 5-limit JI.

-Igs

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Sun, Feb 12, 2012 at 7:00 PM, cityoftheasleep
> <igliashon@...> wrote:
> >
> > --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
> >
> > > What did you say that's subject to experimental falsification?
> >
> > Any statement as regards the impossibility of perceiving a certain temperament in music is easily falsifiable by finding an example where the temperament's mapping succeeds in describing someone's perception of music. If I told you that meantone doesn't exist, you could prove me wrong by showing me someone who, on hearing a meantone-tempered 4:5:6 triad, says "that sounds like a 4:5:6 triad". If even one person succeeds in recognizing the image of Q in Z^n, then the mapping is legit and the temperament exists.
>
> So, under your scheme, all we need to do to establish the "existence"
> of a temperament -
>
> - which is the most loaded possible term you could use to denote a
> rather simple and ordinary concept -
>
> is to find a person who's like, "yeah, I think that sounds enough like
> 4:5:6 for me to give it the thumbs up?"
>
> And we'll just leave it totally subjective like that, leaving them
> open to interpret the meaning of a ratio in their own way and however
> they want?
>
> Please confirm.
>
> Also, what tuning do I use for the temperament when I do this test?
>
> > If we fail to falsify the statement, of course, this doesn't mean it's true. Scientifically-speaking, we cannot verify, we can only falsify or fail to falsify. When reasonable efforts fail to falsify something, we tentatively adopt it with whatever confidence level is appropriate for the effort we put in to falsify it (which is never 100%). And we keep looking for more and more rigorous ways to try to falsify it.
>
> Fine, let's use your paradigm. What do you think the appropriate
> "confidence level" is to establish perceptual impossiblity for a brand
> new field of study that's a few years old with no literature and which
> is solely centered around the goal of finding new things that are
> perceptually possible and in which we know almost nothing?
>
> > Compare this to saying a temperament is stupid. How can this statement be falsified? It can't.
>
> It isn't a scientific statement. Keenan's just saying he thinks it's
> stupid. There's nothing inherent in his argument that requires me to
> make silly assumptions about "the brain" and however the hell it
> works, so why would I have a problem with it?
>
> Why am I supposed to apply the scientific method to someone's
> subjective value judgments? The whole point is that I don't want to do
> that.
>
> > Why is it stupid to not unlock the full musical potential of the tuning?
>
> It's not objectively stupid, but Keenan's opinion was that it was.
> I'll assume that it's because he likes when full musical potentials
> are unlocked.
>
> > There were multiple points I was attempting to make. Point 1: let's say I play you a piece of music composed of a bunch of neutral triads, and I ask you whether this music is demonstrating dicot temperament, 2.3.11 243/242 temperament, 2.3.13 512/507, all of the above, none of the above, or some combination of the above. Let's imagine you want to say that it's not all of the above; then there has to be some way you (or even *someone*) could figure it out, based on the music. Who cares what that could be, the fact that a distinction is possible is good enough, even if it's based on some totally random idea of what ratios "sound like". The point is, if you can give a definite answer, single out a given temperament mapping as being "the right (or least-wrong) answer" to the question of what temperament the music is in--even if other people would disagree, even if there's no consensus--then we have learned something about your perception of musical reality
>
> Yes, you've learned about the way I make either/or and same/different
> judgments. This is worthwhile to know, sure.
>
> > and we can say, <for no other reason than that I like the use of these words for purely aesthetic reasons> "given these intervals in this musical context, <loaded phrase here>". And we can now definitively say that whatever temperament you selected is <loaded term>, to at least you.
>
> And this is where I have to hop off the train.
>
> > If it *is* all of the above, then we have to conclude that all of these temperaments are actually the same thing, and that tempering 25/24 out of the 5-limit is the *same thing* as tempering 243/242 out of the 2.3.11-limit (etc.), which, y'know, I'm cool with that as well.
>
> We don't have to conclude that they "are the same thing" at all. We
> can say that they sound the same. I don't know what that isn't enough
> for you.
>
> We can have a much more intelligent understanding of it than that.
> These two temperaments have the same scalar structure but have
> different POTE tunings and would have different adaptive tunings and
> would have different everything else.
>
> > Point 2: the adaptive JI problem. How the hell can one tune dicot in 5-limit adaptive JI? It is impossible to determine whether a given dicot triad is a 4:5:6 or a 10:12:15, because every chord is both, but in order for the music to sound like 5-limit JI, every triad has to be one or the other. The only way to come up with an adaptive JI algorithm for dicot temperament would be to allow randomness to decide a given chord's tuning. What this means is that there is effectively no way to "use" the dicot mapping, at least in the sense that I understand how one can "use" a mapping at all.
>
> Every single thing you said I disagree with. I disagree that being
> able to distinguish 4:5:6 and 10:12:15 is sufficient to say music
> "sounds like 5-limit JI," and I disagree that being able to
> distinguish them is necessary to say music "sounds like the 5-limit"
> in general, and I disagree that the only decent adaptive-JI algorithm
> you could have for dicot is to map things randomly, and I disagree
> that there's no way to "use" the dicot mapping. This paragraph was a
> perfect no-hitter for me.
>
> > > So I disagree we're "putting anyone on" with the theory. It's a good
> > > framework to figure out some awesome sounds that you can use to write
> > > music and base compositions on, and it's based on some very very
> > > simple assumptions. There's nothing false about that, nothing that
> > > puts anyone on.
> >
> > I beg to differ. There are some huge and complex assumptions that go into badness rankings and optimization procedures, and these assumptions are based on incomplete knowledge of music cognition.
>
> They're neither huge nor complex. Simple ratios sound a certain way,
> it seems to be fairly universal that people hear this sound, and at
> least some people like that sound. That's all that you need, you don't
> need to make any further assumptions about music cognition other than
> that. And if someone out there doesn't like the sound of simple
> ratios, then they shouldn't use this theory.
>
> > It's possible to get total nonsense out of RMP and we don't currently have anything but our instincts to let us discern what's nonsense and what's not. And my best efforts to codify some methodology for separating the nonsense from the sense lead to you telling me I'm assuming too much--when all I'm assuming is that in fact some mappings are nonsense.
>
> Correct. Mappings are abstract mathematical objects with lots of uses.
> We don't even know what all of the uses for them are yet. To write one
> off as "being nonsense" is like this crazy nonsensical statement in
> and of itself.
>
> I can't imagine why you're not happy with the phrase "I can't conceive
> of any possible use for that temperament."
>
> Unless, of course, you just informally mean that some mappings are
> nonsense in the sense that Keenan thinks that some temperaments are
> stupid. In which case, I agree, the temperament eliminating 3/2 is
> stupid, meaning I'll never use it because I can't conceive of any
> possible use for that temperament, nor any mental benefit conferred to
> my understanding of a tuning system by mapping things that way.
>
> > > Igs, I'd love to formally describe what those properties are. It's an
> > > impediment to doing so if we don't admit exactly what we don't know at
> > > the current point in time.
> >
> > It's also an impediment if we don't admit what we DO know!
>
> I think I'm pretty clear, internally, on what I do and don't know.
>
> -Mike
>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Sun, Feb 12, 2012 at 1:57 PM, lobawad <lobawad@...> wrote:
> >
> > ... there you go with this "JI" and "RI" stuff! Intonation OF WHAT? Do you mean justly intoning traditional Western tonal intervals? If so, why did you say nothing when Keenan pooh-poohed my simple observation to the effect that if we're talking about the intonation of traditional Western intervals, well, we have to talk about the intonation of traditional Western intervals?
>
> What?

You missed it. Don't worry, all this has happened and will happen again.

>
> We can define "just intonation" however we want. It's a string of
> characters that serves as a placeholder for an idea. We can define it
> to mean "toothpaste" if we want.

Out here in real life, that doesn't fly.

>
> In the context of this mathematical theory, I think it makes the >most
> sense to define it as the "temperament" with wedgie <1|, or <<1||, >or
> <<<1|||, etc. Which just means a "temperament" which "tempers out"
> nothing but 1/1.
And sometimes I also think it makes the most sense to
> define it as the domain of the mapping, which is the rationals, to
> which this "temperament" is isomorphic.

Why not say something like: Rational intervallic space is the zero temperament?

>
> I hate the definition of JI where it refers to common practice music
> being intoned with simple ratios. I'm never going to use that. I've
> also heard it only refer to 5-limit JI and I'm never going to use that
> either. I don't care who used it like that, I hate it.

Not "used", but "uses". I don't like it either. For one thing, in my experience the effect of rationally tuned intervals is not so curtly limited. And the ethnocentric uses are bunk. But I prefer to use different words rather than try to change firmly entrenched existing words.

>
> > And in no case is it wise to call any kind of "JI" a "temperament". Find some new words, or a very different way to state this. Yes anyone who gets into it can figure out that yeah, we could look at it that way! and see that it makes sense if we adhere to certain definitions of different concepts. But the words that come out in the end are wearing motley.
>
> There are only a few times when I think debates over semantics are
> useful: to simplify definitions to make them less cumbersome, and to
> make it easier and simpler to teach stuff. The aesthetic value of the
> words chosen is like a tertiary consideration after those two things
> for me.
>
> In this case, I think both of the first two desiderata are satisfied
> most strongly by defining JI exactly the way I said, just for the
> purposes of this theory. We just say that we model JI as a perfect
> temperament with zero error, and we don't even mention at all the
> debate on where JI ends and RI begins. I think that's perfect.

Just or Rational intonation OF WHAT? THAT is the problem. Unless you want to deliberately isolate yourself from a wide musical community, intonation is always intonation OF.

This is not about semantics or aesthetics, it's about understanding. What is meant on this list by "JI" is rational intervallic structures. Why in the name of all that is not Babel not just say that instead of incorrectly lading an older term which is already burdened by all manner of stank baggage?

On Mon, Feb 13, 2012 at 12:42 AM, lobawad <lobawad@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> >
> > We can define "just intonation" however we want. It's a string of
> > characters that serves as a placeholder for an idea. We can define it
> > to mean "toothpaste" if we want.
>
> Out here in real life, that doesn't fly.

It flies, baby, yeeeeeah!

> > In the context of this mathematical theory, I think it makes the >most
> > sense to define it as the "temperament" with wedgie <1|, or <<1||, >or
> > <<<1|||, etc. Which just means a "temperament" which "tempers out"
> > nothing but 1/1.
> And sometimes I also think it makes the most sense to
> > define it as the domain of the mapping, which is the rationals, to
> > which this "temperament" is isomorphic.
>
> Why not say something like: Rational intervallic space is the zero temperament?

I'd call it the "identity temperament" instead of the zero
temperament. But, also, I think that's more confusing for newcomers.

> > I hate the definition of JI where it refers to common practice music
> > being intoned with simple ratios. I'm never going to use that. I've
> > also heard it only refer to 5-limit JI and I'm never going to use that
> > either. I don't care who used it like that, I hate it.
>
> Not "used", but "uses". I don't like it either. For one thing, in my experience the effect of rationally tuned intervals is not so curtly limited. And the ethnocentric uses are bunk. But I prefer to use different words rather than try to change firmly entrenched existing words.

There's lots of people who already don't use it that way, and I'm
happy to join the crowd.

> > In this case, I think both of the first two desiderata are satisfied
> > most strongly by defining JI exactly the way I said, just for the
> > purposes of this theory. We just say that we model JI as a perfect
> > temperament with zero error, and we don't even mention at all the
> > debate on where JI ends and RI begins. I think that's perfect.
>
> Just or Rational intonation OF WHAT? THAT is the problem. Unless you want to deliberately isolate yourself from a wide musical community, intonation is always intonation OF.
>
> This is not about semantics or aesthetics, it's about understanding. What is meant on this list by "JI" is rational intervallic structures. Why in the name of all that is not Babel not just say that instead of incorrectly lading an older term which is already burdened by all manner of stank baggage?

It seems like people are already using it this way, and I think it's a
handy definition. Although Carl's now proposed a slightly altered
definition I find intriguing but still don't really get.

But there's no real problem with understanding. I think we all
understand this plenty. It's not really about semantics either. It's
about pedagogy and definitions.

If you really want a simple, one-line answer to your question -
intonation OF WHAT - 5-limit just intonation is intonation of the
rank-3 lattice with generators of 1200, 1902, and 2786 cents. One
might assume that a listener who spends some time in this lattice will
adapt and form new categorical structures towards the intervals in it.

I'm still open to something better if you can give me something you
feel is more effective though.

-Mike

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
> Point 2: the adaptive JI problem. How the hell can one tune dicot in 5-limit adaptive JI? It is impossible to determine whether a given dicot triad is a 4:5:6 or a 10:12:15, because every chord is both, but in order for the music to sound like 5-limit JI, every triad has to be one or the other. The only way to come up with an adaptive JI algorithm for dicot temperament would be to allow randomness to decide a given chord's tuning. What this means is that there is effectively no way to "use" the dicot mapping, at least in the sense that I understand how one can "use" a mapping at all.

This exact argument also applies to meantone. How can you tune meantone in 5-limit adaptive JI if it's impossible to determine whether a given "C D E"-type triad is 8:9:10 or its inverse? Does this mean every adaptive JI algorithm for meantone has to involve randomness? Is this a problem at all?

I'm not trying to make a particular point by saying this, just pointing out something interesting.

Keenan

On Sun, Feb 12, 2012 at 11:59 PM, cityoftheasleep
<igliashon@...> wrote:
>
> Look, man--we don't disagree about anything except for a bit of epistemology. You don't want to dismiss anything even if neither you nor anyone you know can conceive of any possible use for it. I want to dismiss everything unless *somebody* I know finds it useful. We're clearly never going to reconcile that difference. So let's let it stand as a known point of philosophical contention.

Correct. Everything I could possibly want to say is said in this
Wikipedia article:

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

I would like to avoid this fallacy, because I think it will lead to
clearer, more precise discourse, and that it will also lead to the
discoveries of things that we haven't found a possible use for "yet."

I should also say that pragmatically speaking, to avoid being
strawmanned, I have no problem with the notion that there are
temperaments that are ridiculous, like ones which temper out 3/2 or
whatever. It's an informal, compositional-level distinction, but if
that's all you were saying, I wouldn't be pedantic about it, although
I'd still probably try to use fair-minded terms to convey that
concept. But that's not what we end up talking about. These
conversations always go into the shades of gray, with things like
dicot or whatever, so that we always discuss the things in that
precise region where our knowledge ends.

Your question is always whether things in this gray area "exist" or
"not," and I feel that the theory already solves that problem
adequately by treating your concept of "existence" as a scalar instead
of a Boolean value. Every temperament has a scalar value representing
the degree of its "existence," instead of a quantized binary
"exists/not exists" value as you suggest. Except instead of
"existence," we just call it "error," or rather the inverse of it. I
think it's elegant and the perfect solution to this problem, and I
wish more people felt the same way. I don't know why it doesn't
satisfy you.

> We agree that there's a limit to the number of temperaments a person can recognize, as long as I don't try to appeal to science to explain why this is. I mean, I don't have a scientific explanation for it, but I believe that there could be one and would like to work toward it. Why is that problematic for you? Why are you okay recognizing that everyone you know will think of certain temperaments as useless, but not okay with the possibility of there existing a scientific explanation for this state of affairs?

I don't have a problem at all with you trying to work towards that.
I'd love for us all to work towards that. In the absence of an
existing, convincing scientific explanation, what I'm not okay with is
any "scientific" explanation that substitutes your heuristic judgments
of ontological likelihood for actual scientific knowledge of the
truth.

But mostly what I have a problem with is that all of these discussions
end up boiling down to semantics, and I'm not the one who keeps
starting the semantic debates. Every conversation goes something like
this: "Let's say someone hears 3L4s and says it sounds like 4:5:6.
Thus, we can say that this person is perceiving dicot. Thus, we can
say that only dicot exists for this person. Thus, we can say that for
this person, mohajira doesn't exist." But what you're really saying
is, "I propose that, given this observation, we define mohajira as
'not existing' for this person."

This is a purely semantic discussion and it makes no sense to me why
you'd want to define that term that way.

> Also, please explain how if three temperaments can sound the same, that they can be musically different.

Find ways to make them not sound the same.

> Also, please explain how to adaptively tune dicot temperament in 5-limit JI.

Sure. Here's a musical composition in adaptive dicot temperament:

http://soundcloud.com/mikebattagliamusic/the-adaptive-ji-song

This is also in adaptive meantone, adaptive schismatic, adaptive
mavila, adaptive porcupine, adaptive blackwood, adaptive father,
adaptive bug, the adaptive tuning of the temperament where 9/8
vanishes, and so on.

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> Your question is always whether things in this gray area "exist" or
> "not," and I feel that the theory already solves that problem
> adequately by treating your concept of "existence" as a scalar instead
> of a Boolean value. Every temperament has a scalar value representing
> the degree of its "existence," instead of a quantized binary
> "exists/not exists" value as you suggest. Except instead of
> "existence," we just call it "error," or rather the inverse of it. I
> think it's elegant and the perfect solution to this problem, and I
> wish more people felt the same way. I don't know why it doesn't
> satisfy you.

You had better use some kind of badness, for example Graham's parametric badness with some reasonble parameter for humans, rather than simply error. Otherwise you're saying that temperaments like this one:

http://x31eq.com/cgi-bin/rt.cgi?ets=8269_26966&limit=13

are totally "existant", but I think Igs would beg to differ. If being so inaccurate that it's unclear how to relate it back to JI makes something "non-existant", then being so complex that it's impossible to actually use any of the commas must also make something "non-existant".

Is there a flaw in my thinking?

Keenan

On Mon, Feb 13, 2012 at 2:35 AM, Keenan Pepper <keenanpepper@...> wrote:
>
> You had better use some kind of badness, for example Graham's parametric badness with some reasonble parameter for humans, rather than simply error. Otherwise you're saying that temperaments like this one:
>
> http://x31eq.com/cgi-bin/rt.cgi?ets=8269_26966&limit=13
>
> are totally "existant", but I think Igs would beg to differ. If being so inaccurate that it's unclear how to relate it back to JI makes something "non-existant", then being so complex that it's impossible to actually use any of the commas must also make something "non-existant".
>
> Is there a flaw in my thinking?

Yes, because it's not impossible to use the commas. For instance, one
of the commas is

[-6, 6, -2, -1, -1, 2> (123201:123200)

if we drop octaves, we get

[*, 6, -2, -1, -1, 2>

Now let's say we build a chord progression to pump this comma, and we
only move by 3/*, 5/*, 7/*, 11/*, and 13/* - nothing like 5/3 or 7/6
allowed. So it'll take 6+2+1+1+2 = 12 chords to get back to 1/1 again.
If you do 1 chord per bar, that's a 12 bar chord progression right
there. If you allow for motion by things like 5/3, it'll be even less.
My calculations tell me that ends up being 5 chords if you allow for
any motion by 13-odd-limit consonance, including 9/8.

Let's go for something more adventurous. The most complex comma listed
by Graham is

[6, 7, -1, 6, -7, -2> (16467095232:16466659495)

This will take 7+1+6+7+2 = 23 chords to get back to 1/1 if you only
allow root movement by primes. This is the same amount of time as the
above - just change the harmonic rhythm so that you have two chords
per bar instead of one, and make the last bar have double the rhythm
as everything else. If you allow for motion by 13-odd-limit
consonance, including 9/8, my calculations are saying it takes 10
chords to traverse this comma pump, which could easily be done in 4
bars.

This is why I don't think it makes sense to be like, "right now as of
2012 I can't figure out how to use this stuff, so I'm going to say it
doesn't exist."

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Mon, Feb 13, 2012 at 12:42 AM, lobawad <lobawad@...> wrote:
> >
> > --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
> > >
> > > We can define "just intonation" however we want. It's a string of
> > > characters that serves as a placeholder for an idea. We can define it
> > > to mean "toothpaste" if we want.
> >
> > Out here in real life, that doesn't fly.
>
> It flies, baby, yeeeeeah!
>
> > > In the context of this mathematical theory, I think it makes the >most
> > > sense to define it as the "temperament" with wedgie <1|, or <<1||, >or
> > > <<<1|||, etc. Which just means a "temperament" which "tempers out"
> > > nothing but 1/1.
> > And sometimes I also think it makes the most sense to
> > > define it as the domain of the mapping, which is the rationals, to
> > > which this "temperament" is isomorphic.
> >
> > Why not say something like: Rational intervallic space is the zero temperament?
>
> I'd call it the "identity temperament" instead of the zero
> temperament. But, also, I think that's more confusing for newcomers.
>
> > > I hate the definition of JI where it refers to common practice music
> > > being intoned with simple ratios. I'm never going to use that. I've
> > > also heard it only refer to 5-limit JI and I'm never going to use that
> > > either. I don't care who used it like that, I hate it.
> >
> > Not "used", but "uses". I don't like it either. For one thing, in my experience the effect of rationally tuned intervals is not so curtly limited. And the ethnocentric uses are bunk. But I prefer to use different words rather than try to change firmly entrenched existing words.
>
> There's lots of people who already don't use it that way, and I'm
> happy to join the crowd.

The English-language Wikipedia articles are dominated by eccentrics (an observation, not necessarily a value judgement), but on the German page,

http://de.wikipedia.org/wiki/Reine_Stimmung

even if you do not read German, from the pictures you can figure out what "Just Intonation" means in mainstream understanding. Notice that in German, 11:8 is referred to as Alphorn-Fa, and the natural 7th is, in keeping with common practice tradition, considered as an element in natural horns, jazz and blues, and "tuning" music (Lamonte Young): the idea that is has a place in European art-music can be succinctily described as eccentric-but-respected, i.e. the situation hasn't really changed over the last four centuries, the latest champion being Vogel in Bonn.

> But there's no real problem with understanding. I think we all
> understand this plenty. It's not really about semantics either. It's
> about pedagogy and definitions.

>
> If you really want a simple, one-line answer to your question -
> intonation OF WHAT - 5-limit just intonation is intonation of the
> rank-3 lattice with generators of 1200, 1902, and 2786 cents.

Ah- a rational intervallic structure. I'll keep things simple and call rational intervallic structures rational intervallic structures.

--- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@...> wrote:

> Is there a flaw in my thinking?

Yes. You've not explained why, if 8269&26966 if doesn't "exist", it's also not true that 13-limit just intonation doesn't "exist". Also, if you were to discuss 13-limit JI, it might be useful in some contexts to temper out the chalmerisma. After all, tempering out the atom seems to be a useful plan in discussing 12-note 5-limit circulating temperaments, and that's about the same size as the chalmerisma.

Trying to understand Cameron's point here.

Mike (I think) said:
> > If you really want a simple, one-line answer to your question -
> > intonation OF WHAT - 5-limit just intonation is intonation of the
> > rank-3 lattice with generators of 1200, 1902, and 2786 cents.

Lobawad replied:
> Ah- a rational intervallic structure. I'll keep things simple and call
> rational intervallic structures rational intervallic structures.

From the way that you're speaking, I'm inferring that you would consider
"just intonation" to be pure intonation of any interval. So, for example,
pi or phi or e or 2^(1/2) could all be examples of JI that don't involve
rational intervallic structures. (I guess pi and phi could be considered
"rational" in the sense that they're ratios, but they don't involve
rational numbers.)

If that's the case, then rational intervallic structures are just special
cases, albeit the most common cases, of just intonation.

Is that what you meant?

I think I like that. These values exist in some Platonic sense, and just
intervals are theoretically perfect instantiations of them. There are two
ways our actual instantiations of them deviate from just intervals: One is
accidental, in which case we're simply out of tune; The other is through
temperament, in which we deliberately deviate from the just interval to
achieve some purpose.

Regards,
Jake

--- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@...> wrote:

> This exact argument also applies to meantone. How can you tune meantone in 5-limit adaptive JI if it's impossible to determine whether a given "C D E"-type triad is 8:9:10 or its inverse? Does this mean every adaptive JI algorithm for meantone has to involve randomness? Is this a problem at all?
>
> I'm not trying to make a particular point by saying this, just pointing out something interesting.
>

Under what circumstance would 1/(8:9:10) ever make more sense?

-Igs

--- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@...> wrote:

> You had better use some kind of badness, for example Graham's parametric badness with some reasonble parameter for humans, rather than simply error. Otherwise you're saying that temperaments like this one:
>
> http://x31eq.com/cgi-bin/rt.cgi?ets=8269_26966&limit=13
>
> are totally "existant", but I think Igs would beg to differ. If being so inaccurate that it's unclear how to relate it back to JI makes something "non-existant", then being so complex that it's impossible to actually use any of the commas must also make something "non-existant".
>
> Is there a flaw in my thinking?

It's a good point. If a temperament has a huge complexity like this, odds are that as you stack generators on your way to the target intervals, you'll hit acceptable approximations before you've used the whole mapping. Compare the above temperament to this:
http://x31eq.com/cgi-bin/rt.cgi?ets=26%2C+29&limit=13

On the other hand, who says you have to use an MOS of the temperament? Couldn't you just use a selection of pitches from the lattice of the super-complex temperament? Man, I just don't even know. I'm beginning to think that we really don't know what it means to "use" a temperament, despite that recent discussion.

-Igs

--- In tuning@yahoogroups.com, Jake Freivald <jdfreivald@...> wrote:
>
> Trying to understand Cameron's point here.
>
> Mike (I think) said:
> > > If you really want a simple, one-line answer to your question -
> > > intonation OF WHAT - 5-limit just intonation is intonation of the
> > > rank-3 lattice with generators of 1200, 1902, and 2786 cents.
>
> Lobawad replied:
> > Ah- a rational intervallic structure. I'll keep things simple and call
> > rational intervallic structures rational intervallic structures.
>
> From the way that you're speaking, I'm inferring that you would consider
> "just intonation" to be pure intonation of any interval. So, for example,
> pi or phi or e or 2^(1/2) could all be examples of JI that don't involve
> rational intervallic structures. (I guess pi and phi could be considered
> "rational" in the sense that they're ratios, but they don't involve
> rational numbers.)
>
> If that's the case, then rational intervallic structures are just special
> cases, albeit the most common cases, of just intonation.
>
> Is that what you meant?
>
> I think I like that. These values exist in some Platonic sense, and just
> intervals are theoretically perfect instantiations of them. There are two
> ways our actual instantiations of them deviate from just intervals: One is
> accidental, in which case we're simply out of tune; The other is through
> temperament, in which we deliberately deviate from the just interval to
> achieve some purpose.
>
> Regards,
> Jake
>

Traditionally (and today, for the most part) "just" means "pure" which in turn simply means "beatless".

The ancient Greek concept of intervals, as far as I can make out, seems to have been precisely in keeping with their concepts in the visual arts, poetry, etc. We could call it "ideal proportions". I'm all for that. Dividing a string length in half, taking one of the many means they used (the "golden mean" being just one), and so on. Nice ways to get intervals (and rational structures).

But it would be just as eccentric calling that "Just Intonation" as calling JI a temperament. I think we should just use the clearest names we can for things.

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@> wrote:
>
> > This exact argument also applies to meantone. How can you tune meantone in 5-limit adaptive JI if it's impossible to determine whether a given "C D E"-type triad is 8:9:10 or its inverse? Does this mean every adaptive JI algorithm for meantone has to involve randomness? Is this a problem at all?
> >
> > I'm not trying to make a particular point by saying this, just pointing out something interesting.
> >
>
> Under what circumstance would 1/(8:9:10) ever make more sense?
>
> -Igs
>

I assume Keenan is pointing out once again that Re might be 10:9 or 9:8 in "5-limit JI", and he's correct of course (the very name of meantone indicates its distinction from JI right at this spot). But
I don't know where the bit about "random" is coming in: in traditional JI, the kind that's called "5-limit" around here, the intonational nature of Re isn't random, but determined by context.

Some people like a dominant seventh to be tuned with a 9/5. Add a ninth to that and you have a 1/(8:9:10).

Graham

------Original message------
From: cityoftheasleep <igliashon@...>
To: <tuning@yahoogroups.com>
Date: Monday, February 13, 2012 5:03:50 PM GMT-0000
Subject: [tuning] Re: What's the best way to describe JI's relation to temperaments?

--- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@...> wrote:

> This exact argument also applies to meantone. How can you tune meantone in 5-limit adaptive JI if it's impossible to determine whether a given "C D E"-type triad is 8:9:10 or its inverse? Does this mean every adaptive JI algorithm for meantone has to involve randomness? Is this a problem at all?
>
> I'm not trying to make a particular point by saying this, just pointing out something interesting.
>

Under what circumstance would 1/(8:9:10) ever make more sense?

-Igs

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

> Correct. Everything I could possibly want to say is said in this
> Wikipedia article:
>
> http://en.wikipedia.org/wiki/Argument_from_ignorance
>
> I would like to avoid this fallacy, because I think it will lead to
> clearer, more precise discourse, and that it will also lead to the
> discoveries of things that we haven't found a possible use for "yet."

Interesting, because everything *I* could possibly want to say is also said, in the very same article:

"The fallaciousness of arguments from ignorance does not mean that one can never possess good reasons for thinking that something does not exist, an idea captured by philosopher Bertrand Russell's teapot, a hypothetical china teapot revolving about the sun between Earth and Mars; however this would fall more duly under the arena of pragmatism, wherein a position must be demonstrated or proven in order to be upheld, and therefore the burden of proof is on the argument's proponent."

Essentially what I'm saying is that some temperaments are like Russell's teapot. Based on my experience and my admittedly-incomplete knowledge of music cognition, I believe I have good reason to believe that some temperaments don't exist.

> I should also say that pragmatically speaking, to avoid being
> strawmanned, I have no problem with the notion that there are
> temperaments that are ridiculous, like ones which temper out 3/2 or
> whatever. It's an informal, compositional-level distinction, but if
> that's all you were saying, I wouldn't be pedantic about it, although
> I'd still probably try to use fair-minded terms to convey that
> concept. But that's not what we end up talking about. These
> conversations always go into the shades of gray, with things like
> dicot or whatever, so that we always discuss the things in that
> precise region where our knowledge ends.

Now wait just a minute--what makes something a shade of gray? In my estimation, temperaments like dicot and father are not shades of gray. Mavila, beep, blackwood--those are shades of gray.

Let me ask you: what evidence could I provide that would be sufficient for you to accept my claims?

> Your question is always whether things in this gray area "exist" or
> "not," and I feel that the theory already solves that problem
> adequately by treating your concept of "existence" as a scalar instead
> of a Boolean value. Every temperament has a scalar value representing
> the degree of its "existence," instead of a quantized binary
> "exists/not exists" value as you suggest. Except instead of
> "existence," we just call it "error," or rather the inverse of it. I
> think it's elegant and the perfect solution to this problem, and I
> wish more people felt the same way. I don't know why it doesn't
> satisfy you.

It doesn't satisfy me because it doesn't model my experience. There exist mappings that I simply can't hear, and I haven't yet met a sane reasonable person who claims to be able to hear or use every possible mapping. And in point of fact, if it was possible for any of us to hear every possible mapping, then we'd be able to hear any tuning as any temperament. Or in other words, we'd perceive an infinity of Q's in any single Z^n. That we can't do this is, to me, sufficient reason to believe some temperaments are unhearable.

Even Graham claims that large errors are irrelevant: "Finally, I'm simply observing that if a mistuning gets stupidly large, an interval won't be heard as an approximation of the ratio you're measuring it relative to. As an extreme example, calling a semitone an approximation to 3:2 is meaningless. Saying that a whole tone has a smaller error as a 3:2 is also meaningless. It's better to say that neither of them will sound at all like a 3:2." Clearly there are some cases that are not gray areas. I'm okay with there being gray areas, but we ought to have at least some idea of where the gray areas end and begin, and some idea of what it *means* to be in a gray area.

The point I tried to make a while ago is that regardless of whatever method someone uses to recognize intervals "as" intervals--be it a cultural thing, a training thing, an inborn/physiological thing, a purely psychoacoustic thing--all of our current understanding of music cognition suggests that the threshold of recognizability of an interval has to end somewhere. Maybe we haven't proven that it's impossible to hear a 9/8 as a 3/2, but if it *did* turn out to be possible, it would be inconsistent with everything we currently understand and would necessitate a massive paradigm shift requiring us to abandon everything we currently think we understand. Until that happens, we have good reason to believe it *won't* happen--namely, because it's inconsistent with our current understanding.

> I don't have a problem at all with you trying to work towards that.
> I'd love for us all to work towards that. In the absence of an
> existing, convincing scientific explanation, what I'm not okay with is
> any "scientific" explanation that substitutes your heuristic judgments
> of ontological likelihood for actual scientific knowledge of the
> truth.

All work has to start somewhere. What, in your estimation, would constitute "actual scientific knowledge of the truth" in this matter? What would it take to prove that a given temperament is objectively absurd on a musical level? Is our current understanding of musical cognition really so deficient that we can't ascertain whether Father temperament is objectively absurd on a musical level or not?

> But mostly what I have a problem with is that all of these discussions
> end up boiling down to semantics, and I'm not the one who keeps
> starting the semantic debates. Every conversation goes something like
> this: "Let's say someone hears 3L4s and says it sounds like 4:5:6.
> Thus, we can say that this person is perceiving dicot. Thus, we can
> say that only dicot exists for this person. Thus, we can say that for
> this person, mohajira doesn't exist." But what you're really saying
> is, "I propose that, given this observation, we define mohajira as
> 'not existing' for this person."
>
> This is a purely semantic discussion and it makes no sense to me why
> you'd want to define that term that way.

Define which term? Existence?

> > Also, please explain how if three temperaments can sound the same, that they can be > > musically different.
>
> Find ways to make them not sound the same.

Okay. What if there are no ways to make them not sound the same?

> > Also, please explain how to adaptively tune dicot temperament in 5-limit JI.
>
> Sure. Here's a musical composition in adaptive dicot temperament:
>
> http://soundcloud.com/mikebattagliamusic/the-adaptive-ji-song
>
> This is also in adaptive meantone, adaptive schismatic, adaptive
> mavila, adaptive porcupine, adaptive blackwood, adaptive father,
> adaptive bug, the adaptive tuning of the temperament where 9/8
> vanishes, and so on.

Funny, but also wrong. It's not an adaptive tuning of any temperament.

-Igs

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@> wrote:
>
> > This exact argument also applies to meantone. How can you tune meantone in 5-limit adaptive JI if it's impossible to determine whether a given "C D E"-type triad is 8:9:10 or its inverse? Does this mean every adaptive JI algorithm for meantone has to involve randomness? Is this a problem at all?
> >
> > I'm not trying to make a particular point by saying this, just pointing out something interesting.
> >
>
> Under what circumstance would 1/(8:9:10) ever make more sense?

You could just as easily say that 4:5:6 always makes more sense than 1/(4:5:6). If you really internalize the temperament what happens is it seems like a very picky, subtle distinction, so you're like "Well of course this one is the right one - but why does it make a difference anyway? They're just different flavors of the same thing."

That's what you're saying right now with meantone, but a porcupine from Mizar would be like "Meantone temperament makes no sense - how can you tell if C D E is supposed to be 8:9:10 (major step, minor step), or 1/(8:9:10) (minor step, major step)? This temperament doesn't really exist because I always hear it as being one or the other but in meantone they're the same." For a Mizarian porcupine 200 cents is right on a category boundary, so they're especially sensitive to differences straddling that boundary. For us, 350 cents is a category boundary, so we're especially sensitive to the differences in adaptive dicot.

I think some of Elaine Walker's 10edo songs are actually pretty well described as adaptive dicot temperament. She's often playing the root and fifth and singing the third slightly sharp of 10edo to make it clearly major. But then she goes up to the chord based on the third, and that can be major too. Check out "Love is the Catalyst" around 2:35. That's adaptive dicot right there. Major triad, minor triad, neutral triad... who cares?

Keenan

On Mon, Feb 13, 2012 at 2:56 PM, cityoftheasleep
<igliashon@...> wrote:
>
> Essentially what I'm saying is that some temperaments are like Russell's teapot. Based on my experience and my admittedly-incomplete knowledge of music cognition, I believe I have good reason to believe that some temperaments don't exist.

Temperaments are mathematical objects, and mathematical objects exist
unless they're logically self-contradictory.

> Now wait just a minute--what makes something a shade of gray? In my estimation, temperaments like dicot and father are not shades of gray. Mavila, beep, blackwood--those are shades of gray.
>
> Let me ask you: what evidence could I provide that would be sufficient for you to accept my claims?

Which claims, specifically?

> It doesn't satisfy me because it doesn't model my experience. There exist mappings that I simply can't hear, and I haven't yet met a sane reasonable person who claims to be able to hear or use every possible mapping. And in point of fact, if it was possible for any of us to hear every possible mapping, then we'd be able to hear any tuning as any temperament. Or in other words, we'd perceive an infinity of Q's in any single Z^n. That we can't do this is, to me, sufficient reason to believe some temperaments are unhearable.

Again, to "hear a mapping" to you means to perceive any resemblance at
all between the thing that's being played and the thing that's being
mapped?

> Clearly there are some cases that are not gray areas. I'm okay with there being gray areas, but we ought to have at least some idea of where the gray areas end and begin, and some idea of what it *means* to be in a gray area.

OK, but we don't. So now what? You're going to make an arbitrary rule
that doesn't work for all of the conceivable ways in which we could
use temperaments?

> The point I tried to make a while ago is that regardless of whatever method someone uses to recognize intervals "as" intervals--be it a cultural thing, a training thing, an inborn/physiological thing, a purely psychoacoustic thing--all of our current understanding of music cognition suggests that the threshold of recognizability of an interval has to end somewhere. Maybe we haven't proven that it's impossible to hear a 9/8 as a 3/2, but if it *did* turn out to be possible, it would be inconsistent with everything we currently understand and would necessitate a massive paradigm shift requiring us to abandon everything we currently think we understand. Until that happens, we have good reason to believe it *won't* happen--namely, because it's inconsistent with our current understanding.

Igs, if all you were saying is that calling 100 cents a 3/2 is silly,
I wouldn't even argue it at this point. I still think that your choice
of language and overall paradigm about treating the "recognizability"
of a stimulus as an "objective" is crude and coarse, but I'd have long
given up on the pedantry by now. Also, no part of my paradigm involves
or requires making any hard and fast assumptions at all about when 3/2
stops being "heard as a 3/2," because it treats almost every notion of
"heard as" that I can think of as a scalar value and not a boolean,
which is also what HE says if you'd like to cite that. And, I think
that the fact that leaving it open is something that would require you
to experience a massive paradigm shift would seem to indicate that
your paradigm isn't as solid as mine, because it's built on
unnecessary assumptions. But, if the crux of this argument was, it's
stupid to say that 204 cents is 3/2, I'd have long given up on any
pedantry over this point.

> > I don't have a problem at all with you trying to work towards that.
> > I'd love for us all to work towards that. In the absence of an
> > existing, convincing scientific explanation, what I'm not okay with is
> > any "scientific" explanation that substitutes your heuristic judgments
> > of ontological likelihood for actual scientific knowledge of the
> > truth.
>
> All work has to start somewhere. What, in your estimation, would constitute "actual scientific knowledge of the truth" in this matter?

What's the specific claim that we're testing?

> What would it take to prove that a given temperament is objectively absurd on a musical level? Is our current understanding of musical cognition really so deficient that we can't ascertain whether Father temperament is objectively absurd on a musical level or not?

What does "objectively absurd" mean? You keep DEFINING these words as
the outcomes of certain experiments. If Alice thinks this sounds more
like stimulus a then b, "then we can say that for her, mapping b is
absurd." What scientific evidence do you need to define that term?

> > This is a purely semantic discussion and it makes no sense to me why
> > you'd want to define that term that way.
>
> Define which term? Existence?

Yes.

> > > Also, please explain how if three temperaments can sound the same, that they can be > > musically different.
> >
> > Find ways to make them not sound the same.
>
> Okay. What if there are no ways to make them not sound the same?

I can think of several trivial ways to make dicot and mohajira sound
the same. Tune dicot to 13-EDO, where the 5/4's are 369 cents, and the
3/2's are 738 cents. I "perceive a resemblance" between 369 cents and
a JI 5/4, and I also "perceive a resemblance" between 738 cents and a
JI 3/2, which meets your criteria for "hearing a temperament." I can
tell that two of the things that I perceive as resembling 5/4 make up
one of the things that I perceive as resembling 3/2. Now what?

> > Sure. Here's a musical composition in adaptive dicot temperament:
> >
> > http://soundcloud.com/mikebattagliamusic/the-adaptive-ji-song
> >
> > This is also in adaptive meantone, adaptive schismatic, adaptive
> > mavila, adaptive porcupine, adaptive blackwood, adaptive father,
> > adaptive bug, the adaptive tuning of the temperament where 9/8
> > vanishes, and so on.
>
> Funny, but also wrong. It's not an adaptive tuning of any temperament.

Goalposts moved! What about this composition? Just the main theme. Is
this not in 12-EDO?

http://www.youtube.com/watch?v=IizWc4cJwbw

-Mike

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
> It's a good point. If a temperament has a huge complexity like this, odds are that as you stack generators on your way to the target intervals, you'll hit acceptable approximations before you've used the whole mapping. Compare the above temperament to this:
> http://x31eq.com/cgi-bin/rt.cgi?ets=26%2C+29&limit=13
>
> On the other hand, who says you have to use an MOS of the temperament? Couldn't you just use a selection of pitches from the lattice of the super-complex temperament? Man, I just don't even know. I'm beginning to think that we really don't know what it means to "use" a temperament, despite that recent discussion.

You could do that, of course, but if you're just picking and choosing specific notes, and not using the vanishing of any commas, you're not really using the temperament at all. Everything you'd be doing would work equally well in JI, so why temper at all?

Mike's point about a complex (actually moderate-length) comma pump is a good one though. My only rebuttal is that it's impossible to "interalize" such a comma pump, which is admittedly ill-defined and weak.

Keenan

--- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@...> wrote:
> You could do that, of course, but if you're just picking and choosing specific notes, and not
> using the vanishing of any commas, you're not really using the temperament at all.
> Everything you'd be doing would work equally well in JI, so why temper at all?

That's not necessarily true...it's not any different than using a MODMOS, right? Or using an MOS that's got too few notes to traverse the comma? For instance, you can't pump the orgonisma with orgone[7] if you're using 8:11:14 and 1/(8:11:14) triads. Is a MODMOS of helmholtz[7] not helmholtz temperament?

-Igs

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@> wrote:
> > You could do that, of course, but if you're just picking and choosing specific notes, and not
> > using the vanishing of any commas, you're not really using the temperament at all.
> > Everything you'd be doing would work equally well in JI, so why temper at all?
>
> That's not necessarily true...it's not any different than using a MODMOS, right? Or using an MOS that's got too few notes to traverse the comma? For instance, you can't pump the orgonisma with orgone[7] if you're using 8:11:14 and 1/(8:11:14) triads. Is a MODMOS of helmholtz[7] not helmholtz temperament?

If I use the scale 1/1 9/8 7/6 5/4 21/16 4/3 3/2 5/3 7/4 15/8 2/1 but ennealimmal tempered, am I really using ennealimmal temperament?

Keenan

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

> Temperaments are mathematical objects, and mathematical objects exist
> unless they're logically self-contradictory.

If temperaments were just mathematical objects, we'd have no interest in them. They're musical objects too, and are thus subject to musical cognition.

> > Let me ask you: what evidence could I provide that would be sufficient for you to
> > accept my claims?
>
> Which claims, specifically?

The claims that certain temperaments are imperceptible or unintelligible given a sane human with a normal auditory apparatus.

> Again, to "hear a mapping" to you means to perceive any resemblance at
> all between the thing that's being played and the thing that's being
> mapped?

I don't want to define it any more rigorously than that. So yes, full stop.

> OK, but we don't. So now what? You're going to make an arbitrary rule
> that doesn't work for all of the conceivable ways in which we could
> use temperaments?

No, dammit! I'm just trying to explore this, I don't have the friggin' answers yet. I'm interested in hypothesizing, speculating, and trying to find some logically-consistent possibilities based on what little we do know.

> Igs, if all you were saying is that calling 100 cents a 3/2 is silly,
> I wouldn't even argue it at this point. I still think that your choice
> of language and overall paradigm about treating the "recognizability"
> of a stimulus as an "objective" is crude and coarse, but I'd have long
> given up on the pedantry by now. Also, no part of my paradigm involves
> or requires making any hard and fast assumptions at all about when 3/2
> stops being "heard as a 3/2," because it treats almost every notion of
> "heard as" that I can think of as a scalar value and not a boolean,
> which is also what HE says if you'd like to cite that.

Even if the probability of hearing something as a 3/2 is never 0, there's still a point where it becomes less likely than some other interval.

Specifically, though, I'm trying to explore into some of the gray areas and see if they actually are gray, and why. What is it that makes Sentry temperament a more sensible interpretation of 8-ED2 than Father? In what circumstances would Father be sensible? Can those circumstances exist in music? From where I stand, I can't conceive of how Father would ever be sensible, but I'm not just dogmatically asserting that. I'm trying to figure out a way to determine what makes a temperament "sensible" to me, rather than just make naive value judgments about them, because I think it would be useful to know what temperaments will be sensible to me and which won't. And because I believe that I'm not a "special case" of human beings, I have reason to believe that a concept of sensibility for me might be useful to others, even if they have slightly different criteria or constraints on what they find sensible.

> And, I think
> that the fact that leaving it open is something that would require you
> to experience a massive paradigm shift would seem to indicate that
> your paradigm isn't as solid as mine, because it's built on
> unnecessary assumptions. But, if the crux of this argument was, it's
> stupid to say that 204 cents is 3/2, I'd have long given up on any
> pedantry over this point.

Why? I'm trying to figure out *why* it's stupid to say that 204 cents is a 3/2, why is that so objectionable?

> > All work has to start somewhere. What, in your estimation, would constitute "actual
> > scientific knowledge of the truth" in this matter?
>
> What's the specific claim that we're testing?

The claim that any temperament cannot possibly be musically evoked.

> What does "objectively absurd" mean?

Let's say "incompatible with known mechanisms of human music cognition."

> > > This is a purely semantic discussion and it makes no sense to me why
> > > you'd want to define that term that way.
> >
> > Define which term? Existence?
>
> Yes.

What's wrong with it?

> > Okay. What if there are no ways to make them not sound the same?
>
> I can think of several trivial ways to make dicot and mohajira sound
> the same. Tune dicot to 13-EDO, where the 5/4's are 369 cents, and the
> 3/2's are 738 cents. I "perceive a resemblance" between 369 cents and
> a JI 5/4, and I also "perceive a resemblance" between 738 cents and a
> JI 3/2, which meets your criteria for "hearing a temperament." I can
> tell that two of the things that I perceive as resembling 5/4 make up
> one of the things that I perceive as resembling 3/2. Now what?

Well, now you've proven that dicot was a bad example on my part. Congratulations! But hey, what if we force you to use optimal dicot? How easy is it now? This ties back into what I was saying about the assumptions behind optimization and badness. I think exotemperaments like bug, father, and dicot, are great examples where the lowest-error tuning is not the one that best preserves the "recognizability" of the mapping.

> Goalposts moved! What about this composition? Just the main theme. Is
> this not in 12-EDO?
>
> http://www.youtube.com/watch?v=IizWc4cJwbw
>

I'll get back to you on that.

-Igs

--- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@...> wrote:

> > That's not necessarily true...it's not any different than using a MODMOS, right? Or using an MOS that's got too few notes to traverse the comma? For instance, you can't pump the orgonisma with orgone[7] if you're using 8:11:14 and 1/(8:11:14) triads. Is a MODMOS of helmholtz[7] not helmholtz temperament?
>
> If I use the scale 1/1 9/8 7/6 5/4 21/16 4/3 3/2 5/3 7/4 15/8 2/1 but ennealimmal
> tempered, am I really using ennealimmal temperament?

Damn good question. I think we need to answer it, or else there's a big hole in our paradigm. Problem is, I really don't know.

-Igs

On Mon, Feb 13, 2012 at 6:13 PM, cityoftheasleep
<igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > Temperaments are mathematical objects, and mathematical objects exist
> > unless they're logically self-contradictory.
>
> If temperaments were just mathematical objects, we'd have no interest in them. They're musical objects too, and are thus subject to musical cognition.

A temperament is a mathematical object. How you'd like to use that
mathematical object for musical purposes is up to you. To say that
temperaments with really high error "don't exist" is wrong. If you
want to say that they don't accurately model perception or something,
just say that.

> > > Let me ask you: what evidence could I provide that would be sufficient for you to
> > > accept my claims?
> >
> > Which claims, specifically?
>
> The claims that certain temperaments are imperceptible or unintelligible given a sane human with a normal auditory apparatus.
//snip
> > Again, to "hear a mapping" to you means to perceive any resemblance at
> > all between the thing that's being played and the thing that's being
> > mapped?
>
> I don't want to define it any more rigorously than that. So yes, full stop.

Part of the problem is that you don't seem to be acknowledging that a
"temperament" doesn't imply the POTE version or even a fixed-pitch
example at all, and also that since your definition "imperceptible"
doesn't take into account any differences between ratios and
categorical perception and all that, things like warped diatonic
scales let us hear "resemblances to 5/4" in all kinds of goofy and f'd
up places. If we allow for that, meaning we don't care if people
confuse categorical perception and scalar effects and anything else
with ratios, then there are lots of "warped diatonic" scales which
make absurdly high-error temperaments meaningful, like ones that let
you hear resemblances of perfect fifth, which you might think means
3/2, in all kinds of goofy places. Like hedgehog[8], in which it's
easy to sometimes think 600 cents is a fifth. Then 9/8 vanishes.

> > OK, but we don't. So now what? You're going to make an arbitrary rule
> > that doesn't work for all of the conceivable ways in which we could
> > use temperaments?
>
> No, dammit! I'm just trying to explore this, I don't have the friggin' answers yet. I'm interested in hypothesizing, speculating, and trying to find some logically-consistent possibilities based on what little we do know.

OK. Well, good! I disagree with the speculative assessments I've heard
so far, but as long as we're all happy to admit they're just
speculative and not pretending they're scientific because of things
like Russell's teapot, I'm happy. Except my speculative answer to this
conundrum is that the best model for this behavior is to say exactly
what it is, which is that as an interval is detuned the probability of
"hearing it as" itself decreases, for almost any definition of
"hearing it as" that I can think of, never quite hitting zero but
getting arbitrarily close to the point where the likelihood of
"hearing it as" the original becomes so small as to be practically
absurd. That's fine with me, speculatively speaking, although I'm
perfectly OK with new information changing that picture.

> > Igs, if all you were saying is that calling 100 cents a 3/2 is silly,
> > I wouldn't even argue it at this point. I still think that your choice
> > of language and overall paradigm about treating the "recognizability"
> > of a stimulus as an "objective" is crude and coarse, but I'd have long
> > given up on the pedantry by now. Also, no part of my paradigm involves
> > or requires making any hard and fast assumptions at all about when 3/2
> > stops being "heard as a 3/2," because it treats almost every notion of
> > "heard as" that I can think of as a scalar value and not a boolean,
> > which is also what HE says if you'd like to cite that.
>
> Even if the probability of hearing something as a 3/2 is never 0, there's still a point where it becomes less likely than some other interval.

We're talking about probabilities. If something has an improbable
chance of happening, then it has a chance of happening.

> Specifically, though, I'm trying to explore into some of the gray areas and see if they actually are gray, and why. What is it that makes Sentry temperament a more sensible interpretation of 8-ED2 than Father? In what circumstances would Father be sensible?

They're just ideals you want to work towards. The TE tunings for each
will be different. Adaptive tunings for each would be different.
They're different things you can do with each scale.

> Can those circumstances exist in music? From where I stand, I can't conceive of how Father would ever be sensible, but I'm not just dogmatically asserting that.

Well, 750 cents "sounds kinda like 3/2" to me, and 450 cents "sounds
kinda like 5/4," so I'm happy.

> I'm trying to figure out a way to determine what makes a temperament "sensible" to me, rather than just make naive value judgments about them, because I think it would be useful to know what temperaments will be sensible to me and which won't. And because I believe that I'm not a "special case" of human beings, I have reason to believe that a concept of sensibility for me might be useful to others, even if they have slightly different criteria or constraints on what they find sensible.

You are a special case of human being. Everyone alive is unique in
their own special way. We all have our own unique fingerprints, DNA,
and way of using temperament mappings. What's sensible for you might
not be sensible for someone who's using it all differently.

> > And, I think
> > that the fact that leaving it open is something that would require you
> > to experience a massive paradigm shift would seem to indicate that
> > your paradigm isn't as solid as mine, because it's built on
> > unnecessary assumptions. But, if the crux of this argument was, it's
> > stupid to say that 204 cents is 3/2, I'd have long given up on any
> > pedantry over this point.
>
> Why? I'm trying to figure out *why* it's stupid to say that 204 cents is a 3/2, why is that so objectionable?

I'm saying that that notion, by itself, isn't something I'd be arguing
with. I do think that the whole "x is heard as y" paradigm itself,
where we pretend subjective things are objective, is totally crude and
coarse and a loaded way of putting it, but if that's all you were
saying, I wouldn't be pedantic about it. But, we're talking about
dicot.

> > > All work has to start somewhere. What, in your estimation, would constitute "actual
> > > scientific knowledge of the truth" in this matter?
> >
> > What's the specific claim that we're testing?
>
> The claim that any temperament cannot possibly be musically evoked.

Musically evoked means what, someone hears it and says "that sounds
like 5/4?" I'm pretty sure I could play some stuff in 12-EDO that
would leave most people unable to tell me the chord quality of some
arbitrary chord in a trippy sequence of chords, so that most
effectively wouldn't be able to tell me if a chord was major or minor
or "sounds like 4:5:6" or "sounds like 10:12:15" or whatever. Then
they won't be able to actively able to compare with some prior,
remembered stimulus, thus failing by this definition.

> > What does "objectively absurd" mean?
>
> Let's say "incompatible with known mechanisms of human music cognition."

Can you give an example of such a mechanism and a limitation it would provide?

> > > Define which term? Existence?
> >
> > Yes.
>
> What's wrong with it?

It's ridiculous! First off, again, temperaments imply NO TUNING AT
ALL. You can tune them however. You don't even need to use fixed pitch
instruments. We haven't even finished inventing all of the clever ways
to use mappings. But we're going to use the word "existence" to
describe an abstract regular temperament which doesn't seem musically
useful under all of the circumstances that we've thought of so far?
That seems like this crazy statement to make.

If you want to make a statement about a specific TUNING, and
"perceiving" some ratio within the tuning, just make that statement.
Temperaments are DEFINED as existing iff they're homomorphisms from
the rationals to Z^n, so it just doesn't make sense to me to use that
term; it's about as confusing as you could possibly get. If you want
to talk about perception I don't see why you don't just talk about
that directly.

> > I can think of several trivial ways to make dicot and mohajira sound
> > the same. Tune dicot to 13-EDO, where the 5/4's are 369 cents, and the
> > 3/2's are 738 cents. I "perceive a resemblance" between 369 cents and
> > a JI 5/4, and I also "perceive a resemblance" between 738 cents and a
> > JI 3/2, which meets your criteria for "hearing a temperament." I can
> > tell that two of the things that I perceive as resembling 5/4 make up
> > one of the things that I perceive as resembling 3/2. Now what?
>
> Well, now you've proven that dicot was a bad example on my part. Congratulations!

OK, but the salient point here is that you were about to write off the
entire "existence" of a temperament, and all it took was for me to
write a paragraph telling you to tune it differently to completely
change your mind about it. Same with the "absurdly complex"
temperament Keenan just came up with which is associated with a unique
~4 or 5 bar chord progression that only it can do.

You keep talking about how you don't want to assume that these crazy
novel musical circumstances could exist unless you have evidence for
them. Well, is the above example not sufficient evidence for the
existence of musical circumstances that you of I or nobody is
currently thinking of? I'm sure if I'm clever enough I could even
figure out a way to make the temperament eliminating 9/8 work. Would
that convince you that it's bad to write things off at this point in
time?

Why is it not better to admit that we haven't thought of all the
clever and offbeat ways we could use these temperaments, rather than
assuming we currently have the capability to declare various
mathematical objects as being musically useless?

> But hey, what if we force you to use optimal dicot? How easy is it now?

It's still easy. If in dicot I play a bunch of 2:3:4:6:8:9:10:12
chords, I can easily hear "a resemblance" between the dicot-tempered
version and the JI version of that chord. It basically sounds to me
like exactly what dicot says it sounds like, which is a really high
error version of that chord. This is, of course, me turning all of my
knowledge of categories vs psychoacoustics and all that off, and just
telling you on an intuitive level exactly what it sounds like. In
contrast, if you're using mohajira, just play lots of 11-limit harmony
everywhere, I dunno.

I mean, I hear a resemblance to 5-limit harmony all over this album -
http://split-notes.com/004/

This could be me hearing 12-based categories, right? But of course, we
don't really know the full story there, and you just mentioned to
"hear a resemblance" and so on.

> This ties back into what I was saying about the assumptions behind optimization and badness. I think exotemperaments like bug, father, and dicot, are great examples where the lowest-error tuning is not the one that best preserves the "recognizability" of the mapping.

Or don't use a fixed pitch tuning at all. The whole point of a
"mapping," which is also called an "abstract regular temperament," is
that it's larger than any single tuning.

-Mike

On 2/13/2012 6:13 PM, cityoftheasleep wrote:

> Specifically, though, I'm trying to explore into some of the gray
> areas and see if they actually are gray, and why. What is it that
> makes Sentry temperament a more sensible interpretation of 8-ED2 than
> Father? In what circumstances would Father be sensible? Can those
> circumstances exist in music? From where I stand, I can't conceive
> of how Father would ever be sensible, but I'm not just dogmatically
> asserting that. I'm trying to figure out a way to determine what
> makes a temperament "sensible" to me, rather than just make naive
> value judgments about them, because I think it would be useful to
> know what temperaments will be sensible to me and which won't. And
> because I believe that I'm not a "special case" of human beings, I
> have reason to believe that a concept of sensibility for me might be
> useful to others, even if they have slightly different criteria or
> constraints on what they find sensible.

I think father started making sense as a temperament while I was writing "Yulegu Island" (which originally used a more harmonic timbre before I did the current version with inharmonic timbres). I won't say it was totally convincing, but I think it's enough to leave the possibility open. Beep is another marginal temperament, and at times I've been convinced it doesn't exist as a temperament, but with the right tuning it might be usable.

The really questionable temperaments are ones like sharptone. A sharptone tetrad sounds like an added sixth chord (at best) no matter how you tune it.

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

> A temperament is a mathematical object. How you'd like to use that
> mathematical object for musical purposes is up to you. To say that
> temperaments with really high error "don't exist" is wrong. If you
> want to say that they don't accurately model perception or something,
> just say that.

I think defining temperaments as mathematical objects is stupid. As mappings or homomorphisms, sure, they're pure math. But "temperament" implies music, music implies perception, perception implies reality, and in reality, things either exist or they don't.

> Part of the problem is that you don't seem to be acknowledging that a
> "temperament" doesn't imply the POTE version or even a fixed-pitch
> example at all,

Not true. I suggest that for some temperaments, there are no tunings that will allow the temperament to be perceived, and that we can possibly deduce what these are based on an understanding of the limits of interval recognizability.

> and also that since your definition "imperceptible"
> doesn't take into account any differences between ratios and
> categorical perception and all that, things like warped diatonic
> scales let us hear "resemblances to 5/4" in all kinds of goofy and f'd
> up places. If we allow for that, meaning we don't care if people
> confuse categorical perception and scalar effects and anything else
> with ratios, then there are lots of "warped diatonic" scales which
> make absurdly high-error temperaments meaningful, like ones that let
> you hear resemblances of perfect fifth, which you might think means
> 3/2, in all kinds of goofy places. Like hedgehog[8], in which it's
> easy to sometimes think 600 cents is a fifth. Then 9/8 vanishes.

And I'm fine with that. I'd love to have a more nuanced view of temperament where we allow that it's not the mathematical structure alone that defines the temperament, but also the effects of musical context on intervallic perception. As an aside, you're not correct that the hedgehog[8] example demonstrates 9/8 vanishing. We'd have to hear 500 cents as a 3/2 for that. Hearing 600 cents as a 3/2 might be 15/14 vanishing or something, depending on what you want to say 600 cents is.

> OK. Well, good! I disagree with the speculative assessments I've heard
> so far, but as long as we're all happy to admit they're just
> speculative and not pretending they're scientific because of things
> like Russell's teapot, I'm happy.

WHY did it take so long for you to realize that I'm just speculating and trying to work things out logically, rather than asserting that I've got it all figured out and here's the truth? Well anyway, I'm glad we've finally got there.

> Except my speculative answer to this
> conundrum is that the best model for this behavior is to say exactly
> what it is, which is that as an interval is detuned the probability of
> "hearing it as" itself decreases, for almost any definition of
> "hearing it as" that I can think of, never quite hitting zero but
> getting arbitrarily close to the point where the likelihood of
> "hearing it as" the original becomes so small as to be practically
> absurd. That's fine with me, speculatively speaking, although I'm
> perfectly OK with new information changing that picture.

As am I! Just because I don't believe something exists now, doesn't mean I'm going to maintain that belief dogmatically when I suddenly find myself staring it in the face.

> We're talking about probabilities. If something has an improbable
> chance of happening, then it has a chance of happening.

Sure, anything's possible! There's a non-zero probability that I'll turn into a bowl of petunias in 30 seconds, or that I'll suddenly gain the ability to fly, or that the TARDIS will materialize in my bedroom.

> They're just ideals you want to work towards. The TE tunings for each
> will be different.

How's that relevant? Temperaments aren't tied to specific tunings, remember?

> Adaptive tunings for each would be different.

What about non-adaptive tunings?

> They're different things you can do with each scale.

Say you're in 8-ED2. How are they different things you can do with 8-ED2?

> Well, 750 cents "sounds kinda like 3/2" to me, and 450 cents "sounds
> kinda like 5/4," so I'm happy.

That's not father temperament. 750 cents has to sound kinda like 3/2 and kinda like 8/5. I don't think it sounds like either, I think it sounds like a flat 11/7. 450 cents has to sound like 5/4 and 4/3, but I don't think it sounds like either, I think it sounds like a sharp 9/7. More importantly, 0-450-750 has to sound like a 4:5:6 and a 15:20:24 and a 9:12:16 and a 16:20:25. I don't think it sounds like any of those, I think it sounds like an out-of-tune 7:9:11. It's possible that you could fool me into thinking those intervals sound like out-of-tune 5-limit intervals, and if you could, I'd say "great job, you've shown me how to 'activate' my father temperament perception. Okay, how did you do it? Great, now we've learned something! Now let's apply this new knowledge and beef up our theories about music cognition."

> You are a special case of human being. Everyone alive is unique in
> their own special way. We all have our own unique fingerprints, DNA,
> and way of using temperament mappings. What's sensible for you might
> not be sensible for someone who's using it all differently.

And yet, we are all enough alike that the field of biology is possible, that the field of medicine is possible, that the field of psychology is possible, that the field of psychoacoustics is possible...my individual idiosyncrasies are not so great that I can't make any generalizations from my experience to the experience of others.

> I'm saying that that notion, by itself, isn't something I'd be arguing
> with. I do think that the whole "x is heard as y" paradigm itself,
> where we pretend subjective things are objective, is totally crude and
> coarse and a loaded way of putting it, but if that's all you were
> saying, I wouldn't be pedantic about it. But, we're talking about
> dicot.

Then stop being pedantic about it!

> Musically evoked means what, someone hears it and says "that sounds
> like 5/4?" I'm pretty sure I could play some stuff in 12-EDO that
> would leave most people unable to tell me the chord quality of some
> arbitrary chord in a trippy sequence of chords, so that most
> effectively wouldn't be able to tell me if a chord was major or minor
> or "sounds like 4:5:6" or "sounds like 10:12:15" or whatever. Then
> they won't be able to actively able to compare with some prior,
> remembered stimulus, thus failing by this definition.

Right. And in doing so, you would have "broken" their sense of temperament, they wouldn't be perceiving any image of Q in Z^n, so the mapping would break and the temperament would cease to exist in that moment.

> > > What does "objectively absurd" mean?
> >
> > Let's say "incompatible with known mechanisms of human music cognition."
>
> Can you give an example of such a mechanism and a limitation it would provide?

You know more about the mechanisms of human music cognition than I do...why don't you tell me? Maybe I have a totally warped view of how music cognition works, I never studied this stuff, everything I know I got from you, Paul, and Carl!

> It's ridiculous! First off, again, temperaments imply NO TUNING AT
> ALL. You can tune them however. You don't even need to use fixed pitch
> instruments. We haven't even finished inventing all of the clever ways
> to use mappings. But we're going to use the word "existence" to
> describe an abstract regular temperament which doesn't seem musically
> useful under all of the circumstances that we've thought of so far?
> That seems like this crazy statement to make.

Tell me, Mike...does a song exist before it's written? Does a picture exist before it's painted?

> If you want to make a statement about a specific TUNING, and
> "perceiving" some ratio within the tuning, just make that statement.
> Temperaments are DEFINED as existing iff they're homomorphisms from
> the rationals to Z^n, so it just doesn't make sense to me to use that
> term; it's about as confusing as you could possibly get. If you want
> to talk about perception I don't see why you don't just talk about
> that directly.

Again, I think that's a short-sighted and misleading definition of temperaments. The mathematical objects can be defined without any identification with musical intervals, and I would argue that they are only temperaments if they can be identified with musical intervals. That means that you need to be able to do more than mathematically define a temperament to assert its reality--you have to be able to connect it to music in some meaningful way.

> OK, but the salient point here is that you were about to write off the
> entire "existence" of a temperament, and all it took was for me to
> write a paragraph telling you to tune it differently to completely
> change your mind about it. Same with the "absurdly complex"
> temperament Keenan just came up with which is associated with a unique
> ~4 or 5 bar chord progression that only it can do.

Yep. Hypothesize, test, conclude, modify. You just saw it happen. I posited that dicot temperament doesn't exist, you showed me a case where it does, thereby falsifying my hypothesis, and my hypothesis was rejected.

> You keep talking about how you don't want to assume that these crazy
> novel musical circumstances could exist unless you have evidence for
> them. Well, is the above example not sufficient evidence for the
> existence of musical circumstances that you of I or nobody is
> currently thinking of? I'm sure if I'm clever enough I could even
> figure out a way to make the temperament eliminating 9/8 work. Would
> that convince you that it's bad to write things off at this point in
> time?

No. Why should it?

> Why is it not better to admit that we haven't thought of all the
> clever and offbeat ways we could use these temperaments, rather than
> assuming we currently have the capability to declare various
> mathematical objects as being musically useless?

Because *everything* is useless until a use is found for it!

> > But hey, what if we force you to use optimal dicot? How easy is it now?
>
> It's still easy. If in dicot I play a bunch of 2:3:4:6:8:9:10:12
> chords, I can easily hear "a resemblance" between the dicot-tempered
> version and the JI version of that chord. It basically sounds to me
> like exactly what dicot says it sounds like, which is a really high
> error version of that chord. This is, of course, me turning all of my
> knowledge of categories vs psychoacoustics and all that off, and just
> telling you on an intuitive level exactly what it sounds like. In
> contrast, if you're using mohajira, just play lots of 11-limit harmony
> everywhere, I dunno.

Well, there we have it--context. You determine whether it's dicot vs. mohajira according to the nearest JI chord that a given tempered chord sounds like. So if I'm playing around in 24-ED2, playing a bunch of 0-700-1200-1900-2400-2600-2750-3100 chords, you're going to go "oh, dicot, totally"; but if I should happen to drop in a 0-700-1200-1400-1750 chord, you'll go "oh, that's a 4:6:8:9:11 chord, this is mohajira". It's only dicot so long as the chords are sounding to you like what the mapping says. As soon as you hear a chord that doesn't fit the mapping, your perception switches over to a mapping that fits the chord.

So if I were to load up a .scl file of POTE dicot[7]...

! regular.scl
!
7 note scale from some Dicot temperament.
! 7 & 3 Fokker block.
! Generated by http://x31eq.com/temper/
7
!
194.377
348.594
542.971
697.189
891.566
1045.783
1200.000

...and play a bunch of 0-542.971-697.189 triads, you'd have to say "that's mohajira, not dicot." Right?

This is a big problem in our paradigm right now, in that we really haven't pinned down what it means to "use" a temperament. It's not enough to just load up the POTE or TOP or TE scala file of some scale derived from the temperament. You have to do specific things with the music to "activate" perception of the mapping--you have to create the image of Q with Z^n--or you're just using Z^n, no mapping is taking place, and no temperament is being invoked.

> Or don't use a fixed pitch tuning at all. The whole point of a
> "mapping," which is also called an "abstract regular temperament," is
> that it's larger than any single tuning.

And yet, a temperament is only usable in the form of some tuning. Pretending we can leave tuning out of it altogether is a grievous error.

-Igs

On Mon, Feb 13, 2012 at 10:28 PM, cityoftheasleep
<igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > A temperament is a mathematical object. How you'd like to use that
> > mathematical object for musical purposes is up to you. To say that
> > temperaments with really high error "don't exist" is wrong. If you
> > want to say that they don't accurately model perception or something,
> > just say that.
>
> I think defining temperaments as mathematical objects is stupid. As mappings or homomorphisms, sure, they're pure math. But "temperament" implies music, music implies perception, perception implies reality, and in reality, things either exist or they don't.

OK, so you below agreed that we don't know what's going on, that our
paradigm is still embryonic and/or "broken," and that you don't have
any scientific answer, and that you want to start finding one. Woo
hoo. So I'll move on from this and get into that, because this is
like, new research on the list, for once.

What I suggest is to think hard about how to handle the phrase
"[perceptual] things either exist or they don't" in this field. While
this statement is very obviously true, I've found that it can be a
very limiting factor in studying this stuff. This is because we're
dealing with something as tenuous as the perception of a single person
- actually, we're dealing with the perceptions of large groups of
people. So while it's obvious that things either exist or they don't,
it's very difficult - actually in some cases, I might believe it's
mathematically impossible, for the same sorts of reasons that Turing's
famous "halting problem" is impossible - to know when they do or
don't.

What I've found to be a freeing paradigm is to think instead in terms
of the -probability- that something will exist. We need not talk about
the actual existence of things now, but the likelihood that they
-will- exist when performed. This allows us to completely sidestep all
of the above problems. Furthermore, once you start thinking entirely
in terms of probabilities, you allow yourself to plug into what is
probably the coolest branch of mathematics I know of, and that's
information theory. In this field, "information" is defined as the
outcome of a random variable. Thinking in these terms allows us to
stop worrying about what's being transmitted through these discrete
random variables - what the "meaning" of the information is - and
allows us to start thinking about things like how much information, of
whatever "meaning," is transmitted at all (the Shannon entropy of the
signal), how "clear" the channel is vs how noisy (the mutual
information of the channel), and how clear the channel COULD BE if you
carefully custom-tailor the information you send to avoid "noise" (the
channel capacity), how difficult it is to "guess" at the information
in a noisy channel (the Renyi entropy) and so on.

The above isn't even a fraction of the useful concepts floating around
this field, which was initially designed to handle things like
electrical communication channels despite that the engineers working
on this stuff will ever know what information is being transmitted. In
that case, the quantum leap in thought was to not worrying about what
actual information ("meaning") was being transmitted, but to think
about the overall characteristics of the signal and the channels for
which this meaning is transmitted at all. I think the same leap
applies here, and even though this paradigm isn't going to give you
the hard and fast answer you may be looking for, it's powerful enough
to make a lot of good, real progress with minimal assumptions, which
is good. We can model the "clarity" of scales as the mutual
information of an information channel, the "clarity" of a ratio as a
type of Shannon entropy, the "intelligibility" of a category as a type
of min-entropy, and a ton of other stuff.

I can't say I understand all of the implications of the above paradigm
- I'm still looking for the single unifying theme that ties it al
together. All I can say is it's worth not adopting a philosophy that
rules these sorts of ideas out. (Plus, information theory is easier to
learn and more awesome than exterior algebra anyway.)

> > Part of the problem is that you don't seem to be acknowledging that a
> > "temperament" doesn't imply the POTE version or even a fixed-pitch
> > example at all,
>
> Not true. I suggest that for some temperaments, there are no tunings that will allow the temperament to be perceived, and that we can possibly deduce what these are based on an understanding of the limits of interval recognizability.

The only ones I can think of involve tempering out actual consonances
in the chord that's being played. So tempering out 6/5, for instance -
unless you intone one ratio two ways at the same time. Anything else I
can think of some dumb adaptive scheme that would trivially satisfy
that it has some dumb musical use, even though it's dumb. Even dumb
things like tempering out 9/8 have some dumb use.

But since you, below, said you don't mind including categorical
perception in this - I assure you that it's almost impossible to find
anything that's truly impossible to be perceived. Categorical
perception is nuts, especially for someone like me who has AP and has
categorized the pitch spectrum itself. I hear 12-EDO in everything.

> And I'm fine with that. I'd love to have a more nuanced view of temperament where we allow that it's not the mathematical structure alone that defines the temperament, but also the effects of musical context on intervallic perception. As an aside, you're not correct that the hedgehog[8] example demonstrates 9/8 vanishing. We'd have to hear 500 cents as a 3/2 for that. Hearing 600 cents as a 3/2 might be 15/14 vanishing or something, depending on what you want to say 600 cents is.

If we hear 600 cents as 3/2, then 2*600 is 1200 = 2/1 = 9/4 = 9/8 vanishes.

> As am I! Just because I don't believe something exists now, doesn't mean I'm going to maintain that belief dogmatically when I suddenly find myself staring it in the face.

Ok, but my point is that I don't think it's a good idea to assume that
things don't exist right now, in 2012.

> > We're talking about probabilities. If something has an improbable
> > chance of happening, then it has a chance of happening.
>
> Sure, anything's possible! There's a non-zero probability that I'll turn into a bowl of petunias in 30 seconds, or that I'll suddenly gain the ability to fly, or that the TARDIS will materialize in my bedroom.

Yeah, that seems right to me. Possible, but not likely.

> > They're just ideals you want to work towards. The TE tunings for each
> > will be different.
>
> How's that relevant? Temperaments aren't tied to specific tunings, remember?

My point is that different mappings imply different ideals for the
same scale, and this is partly reflected in that they have different
TE tunings.

> > They're different things you can do with each scale.
>
> Say you're in 8-ED2. How are they different things you can do with 8-ED2?

Consider 6-EDO in the 2.9 subgroup. Now consider it in the 2.5.7.9.11
subgroup. Tune the latter so that the 11/4 is pure. How are these
different things you can do with 6-EDO?

> > Well, 750 cents "sounds kinda like 3/2" to me, and 450 cents "sounds
> > kinda like 5/4," so I'm happy.
>
> That's not father temperament. 750 cents has to sound kinda like 3/2 and kinda like 8/5. I don't think it sounds like either, I think it sounds like a flat 11/7.

To me it sort of sounds like all three of those things, assuming I
ignore everything I've learned about music in the past year and
equivocate between ratios and categories.

450 cents has to sound like 5/4 and 4/3, but I don't think it sounds
like either, I think it sounds like a sharp 9/7.

To me it sort of sounds like all three of those things, assuming I
ignore everything I've learned about music in the past year and
equivocate between ratios and categories.

> More importantly, 0-450-750 has to sound like a 4:5:6 and a 15:20:24 and a 9:12:16 and a 16:20:25. I don't think it sounds like any of those, I think it sounds like an out-of-tune 7:9:11.

It's vaguely recognizable as 4:5:6, I'd say, assuming I ignore
everything I've learned about music in the past year and equivocate
between ratios and categories.

> It's possible that you could fool me into thinking those intervals sound like out-of-tune 5-limit intervals, and if you could, I'd say "great job, you've shown me how to 'activate' my father temperament perception. Okay, how did you do it? Great, now we've learned something! Now let's apply this new knowledge and beef up our theories about music cognition."

You should join XA chat, where we've been talking about this stuff for
months now. (I wish we were documenting it). For starters, I'd say:
play slendroid in 16-EDO, 3 3 1 3 3 3. Just play the first 5 notes
over and over. That makes the 450 cents to me sound like a 5/4, except
I'm actually wantonly equivocating it with "major third" here because
of your totally subjective definition and now I need to go take a
shower to cleanse myself.

> > You are a special case of human being. Everyone alive is unique in
> > their own special way. We all have our own unique fingerprints, DNA,
> > and way of using temperament mappings. What's sensible for you might
> > not be sensible for someone who's using it all differently.
>
> And yet, we are all enough alike that the field of biology is possible, that the field of medicine is possible, that the field of psychology is possible, that the field of psychoacoustics is possible...my individual idiosyncrasies are not so great that I can't make any generalizations from my experience to the experience of others.

OK, but we're all using temperaments differently and so your
conclusions will only extrapolate to your own personal interpretation.

> > I'm saying that that notion, by itself, isn't something I'd be arguing
> > with. I do think that the whole "x is heard as y" paradigm itself,
> > where we pretend subjective things are objective, is totally crude and
> > coarse and a loaded way of putting it, but if that's all you were
> > saying, I wouldn't be pedantic about it. But, we're talking about
> > dicot.
>
> Then stop being pedantic about it!

I'm not. We're talking about dicot.

> > Musically evoked means what, someone hears it and says "that sounds
> > like 5/4?" I'm pretty sure I could play some stuff in 12-EDO that
> > would leave most people unable to tell me the chord quality of some
> > arbitrary chord in a trippy sequence of chords, so that most
> > effectively wouldn't be able to tell me if a chord was major or minor
> > or "sounds like 4:5:6" or "sounds like 10:12:15" or whatever. Then
> > they won't be able to actively able to compare with some prior,
> > remembered stimulus, thus failing by this definition.
>
> Right. And in doing so, you would have "broken" their sense of temperament, they wouldn't be perceiving any image of Q in Z^n, so the mapping would break and the temperament would cease to exist in that moment.

My mom can't figure out what the hell's going on when I play music at
all, but she likes it; this is no different from that.

> > > > What does "objectively absurd" mean?
> > >
> > > Let's say "incompatible with known mechanisms of human music cognition."
> >
> > Can you give an example of such a mechanism and a limitation it would provide?
>
> You know more about the mechanisms of human music cognition than I do...why don't you tell me? Maybe I have a totally warped view of how music cognition works, I never studied this stuff, everything I know I got from you, Paul, and Carl!

What I know is that this whole notion of "perceiving a ratio as
______" is actually not related to psychoacoustics or music cognition
at all, but just normal, regular, boring old cognition. If I'm exposed
to a stimulus long enough, I'll remember it and be able to gauge how
much other things are the same and different from it. If an interval
has certain defining features which are associated with it being tuned
a certain way, like the usual small-integer ratio features, I'll tend
to remember those things about it.

It doesn't seem to me like you're trying to put a cap on the bounds of
music cognition but on -cognition-. You're now talking about totally
subjective measures of when an interval "resembles" another. In the
sense you're talking now, I don't think that these basic entities
which are being resembled have anything to do with small-integer
ratios. And lastly, as far as resemblances are concerned, what I know
is that the mind is a really, really weird place.

> > It's ridiculous! First off, again, temperaments imply NO TUNING AT
> > ALL. You can tune them however. You don't even need to use fixed pitch
> > instruments. We haven't even finished inventing all of the clever ways
> > to use mappings. But we're going to use the word "existence" to
> > describe an abstract regular temperament which doesn't seem musically
> > useful under all of the circumstances that we've thought of so far?
> > That seems like this crazy statement to make.
>
> Tell me, Mike...does a song exist before it's written? Does a picture exist before it's painted?

No, but a temperament exists before you write music in it, because
that's how Gene defined everything, and I happen to like it.

> Again, I think that's a short-sighted and misleading definition of temperaments. The mathematical objects can be defined without any identification with musical intervals, and I would argue that they are only temperaments if they can be identified with musical intervals. That means that you need to be able to do more than mathematically define a temperament to assert its reality--you have to be able to connect it to music in some meaningful way.

The mathematical objects are always defined with respect to musical
intervals; that's what the Z^n business is all about. Temperaments are
ideals for how to to intone Z^n.

> Yep. Hypothesize, test, conclude, modify. You just saw it happen. I posited that dicot temperament doesn't exist, you showed me a case where it does, thereby falsifying my hypothesis, and my hypothesis was rejected.

I'm not going to be able to falsify all of your hypotheses just
because I'm not infinitely creative. This seems obvious to me and I
don't see why you or anyone else would pretend that I'm the arbiter of
good or bad temperaments. You should have more of a healthy self-doubt
about writing stuff off.

> > You keep talking about how you don't want to assume that these crazy
> > novel musical circumstances could exist unless you have evidence for
> > them. Well, is the above example not sufficient evidence for the
> > existence of musical circumstances that you of I or nobody is
> > currently thinking of? I'm sure if I'm clever enough I could even
> > figure out a way to make the temperament eliminating 9/8 work. Would
> > that convince you that it's bad to write things off at this point in
> > time?
>
> No. Why should it?

Because you missed something once and you might miss something else?

> > Why is it not better to admit that we haven't thought of all the
> > clever and offbeat ways we could use these temperaments, rather than
> > assuming we currently have the capability to declare various
> > mathematical objects as being musically useless?
>
> Because *everything* is useless until a use is found for it!

I disagree.

> Well, there we have it--context. You determine whether it's dicot vs. mohajira according to the nearest JI chord that a given tempered chord sounds like. So if I'm playing around in 24-ED2, playing a bunch of 0-700-1200-1900-2400-2600-2750-3100 chords, you're going to go "oh, dicot, totally"; but if I should happen to drop in a 0-700-1200-1400-1750 chord, you'll go "oh, that's a 4:6:8:9:11 chord, this is mohajira". It's only dicot so long as the chords are sounding to you like what the mapping says. As soon as you hear a chord that doesn't fit the mapping, your perception switches over to a mapping that fits the chord.

Under your scheme, which I hate. I think that dicot is something more
abstract than any mode of perception and refers to a certain tuning
ideal for a scalar structure.

> ...and play a bunch of 0-542.971-697.189 triads, you'd have to say "that's mohajira, not dicot." Right?

I'd probably say that just for the sake of communication, sure. Or an
11-limit higher extension of dicot.

> This is a big problem in our paradigm right now, in that we really haven't pinned down what it means to "use" a temperament. It's not enough to just load up the POTE or TOP or TE scala file of some scale derived from the temperament. You have to do specific things with the music to "activate" perception of the mapping--you have to create the image of Q with Z^n--or you're just using Z^n, no mapping is taking place, and no temperament is being invoked.

Look, it's not a big problem for me, because I went through this
little crisis already. Yes, the paradigm is incomplete. Temperaments
aren't everything they should be. You're right, we can't go claim how
great and complete and scientific and perfect and finished the theory
is. But, they're still useful as conceptual tools, and I'm happy to
know exactly what their limitations are and use the theory anyway.

> > Or don't use a fixed pitch tuning at all. The whole point of a
> > "mapping," which is also called an "abstract regular temperament," is
> > that it's larger than any single tuning.
>
> And yet, a temperament is only usable in the form of some tuning. Pretending we can leave tuning out of it altogether is a grievous error.

Then it makes even less sense to invalidate a temperament before it's
been given a tuning.

-Mike

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

> What I suggest is to think hard about how to handle the phrase
> "[perceptual] things either exist or they don't" in this field. While
> this statement is very obviously true, I've found that it can be a
> very limiting factor in studying this stuff. This is because we're
> dealing with something as tenuous as the perception of a single person
> - actually, we're dealing with the perceptions of large groups of
> people. So while it's obvious that things either exist or they don't,
> it's very difficult - actually in some cases, I might believe it's
> mathematically impossible, for the same sorts of reasons that Turing's
> famous "halting problem" is impossible - to know when they do or
> don't.

You may be right.

> I can't say I understand all of the implications of the above paradigm
> - I'm still looking for the single unifying theme that ties it al
> together. All I can say is it's worth not adopting a philosophy that
> rules these sorts of ideas out. (Plus, information theory is easier to
> learn and more awesome than exterior algebra anyway.)

Well, you're probably on to something here. So, in these terms, what do you think of a temperament that maps an element of Q to an element of Z^n that has a very low probability of being interpreted as that element of Q? Or am I still missing the point of the above?

> The only ones I can think of involve tempering out actual consonances
> in the chord that's being played. So tempering out 6/5, for instance -
> unless you intone one ratio two ways at the same time. Anything else I
> can think of some dumb adaptive scheme that would trivially satisfy
> that it has some dumb musical use, even though it's dumb. Even dumb
> things like tempering out 9/8 have some dumb use.

Fair enough--perhaps I'm going about it all backwards. It seems like the more restrictions we have to follow, compositionally-speaking, to successfully invoke recognition of a temperament, the less useful that temperament will be. So we can at least say that a temperament that's only useful in a very specific circumstance is less useful than one that's useful in a wider set of circumstances. But yeah, tempering out consonances (or, say, tempering out any ratio where n*d<70) is probably going to be entirely useless under any normal musical circumstances.

> But since you, below, said you don't mind including categorical
> perception in this - I assure you that it's almost impossible to find
> anything that's truly impossible to be perceived. Categorical
> perception is nuts, especially for someone like me who has AP and has
> categorized the pitch spectrum itself. I hear 12-EDO in everything.

Yeah, as I mentioned over on XA, I wonder if people like you, highly trained in 12-TET, don't actually hear JI as some kind of tempering of 12-TET. If you think about it, if we can say 12-TET tempers out 81/80, 64/63, and 128/125, then we can also look at JI as being an inconsistent temperament of 12-TET, where there's multiple mappings of 400 cents, multiple mappings of 1000 cents, multiple mappings of 200 cents, etc. By which I mean, 400 cents might be 5/4, 400' cents might be 81/64, 400'' might be 9/7, etc.

> If we hear 600 cents as 3/2, then 2*600 is 1200 = 2/1 = 9/4 = 9/8 vanishes.

Herp derp!! Got it.

> Ok, but my point is that I don't think it's a good idea to assume that
> things don't exist right now, in 2012.

I don't see how, in your world view, it'd ever be possible to assume that anything doesn't exist.

> My point is that different mappings imply different ideals for the
> same scale, and this is partly reflected in that they have different
> TE tunings.

But isn't the implication of different ideals only relevant if we assume that temperaments are going to be tuned as close to the ideals as possible?

> > > They're different things you can do with each scale.
> >
> > Say you're in 8-ED2. How are they different things you can do with 8-ED2?
>
> Consider 6-EDO in the 2.9 subgroup. Now consider it in the 2.5.7.9.11
> subgroup. Tune the latter so that the 11/4 is pure. How are these
> different things you can do with 6-EDO?

I'm enforcing pure octaves.

> > That's not father temperament. 750 cents has to sound kinda like 3/2 and kinda like
> > 8/5. I don't think it sounds like either, I think it sounds like a flat 11/7.
>
> To me it sort of sounds like all three of those things, assuming I
> ignore everything I've learned about music in the past year and
> equivocate between ratios and categories.

Is there ever a case where it only sounds like 2 of those things?

> > More importantly, 0-450-750 has to sound like a 4:5:6 and a 15:20:24 and a 9:12:16 > > and a 16:20:25. I don't think it sounds like any of those, I think it sounds like an out-> > of-tune 7:9:11.
>
> It's vaguely recognizable as 4:5:6, I'd say, assuming I ignore
> everything I've learned about music in the past year and equivocate
> between ratios and categories.

Unless it's also vaguely recognizable as 9:12:16 and 16:20:25 and 15:20:24, doesn't that mean the mapping's not working?

> You should join XA chat, where we've been talking about this stuff for
> months now. (I wish we were documenting it). For starters, I'd say:
> play slendroid in 16-EDO, 3 3 1 3 3 3. Just play the first 5 notes
> over and over. That makes the 450 cents to me sound like a 5/4, except
> I'm actually wantonly equivocating it with "major third" here because
> of your totally subjective definition and now I need to go take a
> shower to cleanse myself.

Does it work if you play that over a drone? I might suggest that, because JI is only a type of harmony (and not melody), that temperaments also require harmony to be perceived. What do you think of that?

> > And yet, we are all enough alike that the field of biology is possible, that the field of
> >medicine is possible, that the field of psychology is possible, that the field of
> >psychoacoustics is possible...my individual idiosyncrasies are not so great that I can't
> > make any generalizations from my experience to the experience of others.
>
> OK, but we're all using temperaments differently and so your
> conclusions will only extrapolate to your own personal interpretation.

Are we, though? I think my experience with other people is more supportive of the conclusion that we're all mostly using temperaments the same way, at least insofar as we're all "using" temperaments (which, who knows to what extent we're all doing that, since we don't really know what it means to "use" a temperament).

> > > Musically evoked means what, someone hears it and says "that sounds
> > > like 5/4?" I'm pretty sure I could play some stuff in 12-EDO that
> > > would leave most people unable to tell me the chord quality of some
> > > arbitrary chord in a trippy sequence of chords, so that most
> > > effectively wouldn't be able to tell me if a chord was major or minor
> > > or "sounds like 4:5:6" or "sounds like 10:12:15" or whatever. Then
> > > they won't be able to actively able to compare with some prior,
> > > remembered stimulus, thus failing by this definition.
> >
> > Right. And in doing so, you would have "broken" their sense of temperament, they
> > wouldn't be perceiving any image of Q in Z^n, so the mapping would break and the
> > temperament would cease to exist in that moment.
>
> My mom can't figure out what the hell's going on when I play music at
> all, but she likes it; this is no different from that.

How is it not different? How is your mom's enjoyment of music a refutation of my above assertion about "breaking" someone's sense of temperament by playing a confusing progression?

> What I know is that this whole notion of "perceiving a ratio as
> ______" is actually not related to psychoacoustics or music cognition
> at all, but just normal, regular, boring old cognition. If I'm exposed
> to a stimulus long enough, I'll remember it and be able to gauge how
> much other things are the same and different from it. If an interval
> has certain defining features which are associated with it being tuned
> a certain way, like the usual small-integer ratio features, I'll tend
> to remember those things about it.

Well, this is reassuring. I know more about regular cognition than I do about music-specific cognition.

> It doesn't seem to me like you're trying to put a cap on the bounds of
> music cognition but on -cognition-. You're now talking about totally
> subjective measures of when an interval "resembles" another. In the
> sense you're talking now, I don't think that these basic entities
> which are being resembled have anything to do with small-integer
> ratios. And lastly, as far as resemblances are concerned, what I know
> is that the mind is a really, really weird place.

Would you agree with this: it doesn't make sense to use temperaments unless you have learned to categorically perceive whatever-limit JI that you're trying to temper? And that you can't recognize a temperament of some n-limit JI unless you can categorically-perceive n-limit JI?

> No, but a temperament exists before you write music in it, because
> that's how Gene defined everything, and I happen to like it.

I don't like it at all, I think it's the root of all misunderstandings and the reason that no one can figure out what it means to "use" a temperament. The mappings exist, but I think we'd be able to make much more sense of this paradigm if we defined temperaments as not existing meaningfully outside of music.

> The mathematical objects are always defined with respect to musical
> intervals; that's what the Z^n business is all about. Temperaments are
> ideals for how to to intone Z^n.

How are the mathematical objects define with respect to musical intervals? What makes a number a musical interval? Can musical intervals be described soundlessly? What would 386 cents mean to a deaf person?

> I'm not going to be able to falsify all of your hypotheses just
> because I'm not infinitely creative. This seems obvious to me and I
> don't see why you or anyone else would pretend that I'm the arbiter of
> good or bad temperaments. You should have more of a healthy self-doubt
> about writing stuff off.

Okay, I get it. When I say something "doesn't exist" what I mean is that it is outside the sphere of my experience of reality, but this actually describes two classes of things: 1) things that cannot possibly enter my experience, 2) things that can possibly enter my experience, but haven't yet. At any given point in time, it is impossible for me to distinguish whether something outside of my experience is in one class or the other, though I can speculate, and also use logic to rule some things out as "logically impossible" (though even that isn't 100%, because my reasoning isn't 100% reliable). Only through experience do I discover what was possible and what wasn't, and I'll never discover all of what is possible. But sometimes I have to make a leap of faith based on my speculation, just as in order to find my way around a room in the dark, I have to occasionally just take a step and hope that I'm not gonna step on a lego or something.

What I think is that our understanding of what temperaments *are* is being held back by our refusal to rule some things out. There, I said it. I think that in order to progress, we need to make some more assumptions, not fewer. And of course we'll have to test those assumptions. But isn't this normally how a field progresses? You start with a vague and general model, and then progressively refine it until it makes predictions of greater and greater specificity? Is that not a direction we should move in?

> Look, it's not a big problem for me, because I went through this
> little crisis already. Yes, the paradigm is incomplete. Temperaments
> aren't everything they should be. You're right, we can't go claim how
> great and complete and scientific and perfect and finished the theory
> is. But, they're still useful as conceptual tools, and I'm happy to
> know exactly what their limitations are and use the theory anyway.

Since when were you content to rest on your laurels with this stuff? Just because everyone else (Graham, Carl, Gene, and maybe even Paul) have put in their time, paid their dues, and consider their work on developing the theory pretty much done, does that mean we shouldn't keep pushing forward, asking tough questions, and trying to refine more?

-Igs

On Tue, Feb 14, 2012 at 12:53 PM, cityoftheasleep
<igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > I can't say I understand all of the implications of the above paradigm
> > - I'm still looking for the single unifying theme that ties it al
> > together. All I can say is it's worth not adopting a philosophy that
> > rules these sorts of ideas out. (Plus, information theory is easier to
> > learn and more awesome than exterior algebra anyway.)
>
> Well, you're probably on to something here. So, in these terms, what do you think of a temperament that maps an element of Q to an element of Z^n that has a very low probability of being interpreted as that element of Q? Or am I still missing the point of the above?

Right, so first I'd say that again, a "mapping" doesn't imply any
tuning. If you want to consider these sorts of scenarios you have to
imply a tuning, probably a fixed-pitch one, or else I can think of
arbitrary ways in which low-accuracy temperaments might become useful.
They even already have names:

http://xenharmonic.wikispaces.com/Very+low+accuracy+temperaments

So with regards to your question, what do I think of it? I think it
has a low probability of being musically useful. But the math is made
simpler by just assuming that we're mapping to definite things rather
than indefinite ones, so that's why we do that.

> > But since you, below, said you don't mind including categorical
> > perception in this - I assure you that it's almost impossible to find
> > anything that's truly impossible to be perceived. Categorical
> > perception is nuts, especially for someone like me who has AP and has
> > categorized the pitch spectrum itself. I hear 12-EDO in everything.
>
> Yeah, as I mentioned over on XA, I wonder if people like you, highly trained in 12-TET, don't actually hear JI as some kind of tempering of 12-TET. If you think about it, if we can say 12-TET tempers out 81/80, 64/63, and 128/125, then we can also look at JI as being an inconsistent temperament of 12-TET, where there's multiple mappings of 400 cents, multiple mappings of 1000 cents, multiple mappings of 200 cents, etc. By which I mean, 400 cents might be 5/4, 400' cents might be 81/64, 400'' might be 9/7, etc.

Correct. I feel like I posted some huge rant about this concept to the
tuning list before (that someone used to meantone and moving to JI is
like someone used to JI and moving to inconsistent JI), but now I
can't find it.

> > Ok, but my point is that I don't think it's a good idea to assume that
> > things don't exist right now, in 2012.
>
> I don't see how, in your world view, it'd ever be possible to assume that anything doesn't exist.

I don't ever have a burning need to assume things don't exist. If
something has a really really really low probability of existing, I'm
totally comfortable with that.

If we're talking about some sort of model, and it simplifies
everything to assume that as an approximation things underneath a
certain cutoff don't exist, and that this still gives good results in
the model, I'm also fine with that. Most of my "models" for everyday
life include some assumption that really unlikely things, like pigs
flying in the sky, are so unlikely that I can just treat them as
definite non-possibilities. And in music theory, if I'm computing HE,
I can get a speedup if I leave out target ratios from the calculation
which are below a certain amount of probability, and the curve looks
almost the same.

If you were trying to model something in this case, and it involved
throwing some small probabilities away, I'd say go for it. HE itself
throws a ton of stuff away and smooths over a lot of pertinent things
for the sake of having something simple that sort of works. But,
mathematics itself is on a higher level than all that; it's always
clear what's being modeled, what the behaviors in question are, and
what approximations you're making. And it seems like you're trying to
make a mathematical statement.

> > My point is that different mappings imply different ideals for the
> > same scale, and this is partly reflected in that they have different
> > TE tunings.
>
> But isn't the implication of different ideals only relevant if we assume that temperaments are going to be tuned as close to the ideals as possible?

We don't need to assume that temperaments are going to have any one
tuning. A temperament could be adaptive, or it could change tunings
inside a piece, or someone could choose an irregular circulating
tuning for it. And no, there are plenty of reasons why we wouldn't
tune a temperament to the TE tuning or what not - like that 12-EDO
supports meantone.

> > > > They're different things you can do with each scale.
> > >
> > > Say you're in 8-ED2. How are they different things you can do with 8-ED2?
> >
> > Consider 6-EDO in the 2.9 subgroup. Now consider it in the 2.5.7.9.11
> > subgroup. Tune the latter so that the 11/4 is pure. How are these
> > different things you can do with 6-EDO?
>
> I'm enforcing pure octaves.

Then you're placing restrictions on how well I can answer your question.

> > > That's not father temperament. 750 cents has to sound kinda like 3/2 and kinda like
> > > 8/5. I don't think it sounds like either, I think it sounds like a flat 11/7.
> >
> > To me it sort of sounds like all three of those things, assuming I
> > ignore everything I've learned about music in the past year and
> > equivocate between ratios and categories.
>
> Is there ever a case where it only sounds like 2 of those things?

Sure, different contextual factors might even only make it sound like
one of those things, assuming I ignore everything I've learned about
music in the past year and equivocate between ratios and categories.

> > > More importantly, 0-450-750 has to sound like a 4:5:6 and a 15:20:24 and a 9:12:16 > > and a 16:20:25. I don't think it sounds like any of those, I think it sounds like an out-> > of-tune 7:9:11.
>
> >
> > It's vaguely recognizable as 4:5:6, I'd say, assuming I ignore
> > everything I've learned about music in the past year and equivocate
> > between ratios and categories.
>
> Unless it's also vaguely recognizable as 9:12:16 and 16:20:25 and 15:20:24, doesn't that mean the mapping's not working?

It doesn't inherently mean that, because "the mapping's not working"
is an arbitrary phrase with no meaning that you just threw in there.
If you'd like to define "the mapping's not working" as the result of
this outcome, then sure. It's pretty vaguely recognizable as a minor
chord in second inversion too, which is 15:20:24. 9:12:16 and 16:20:25
aren't right above; that'd be for 0-450-900.

> > You should join XA chat, where we've been talking about this stuff for
> > months now. (I wish we were documenting it). For starters, I'd say:
> > play slendroid in 16-EDO, 3 3 1 3 3 3. Just play the first 5 notes
> > over and over. That makes the 450 cents to me sound like a 5/4, except
> > I'm actually wantonly equivocating it with "major third" here because
> > of your totally subjective definition and now I need to go take a
> > shower to cleanse myself.
>
> Does it work if you play that over a drone? I might suggest that, because JI is only a type of harmony (and not melody), that temperaments also require harmony to be perceived. What do you think of that?

Yeah, it works if I play it over a drone.

> > OK, but we're all using temperaments differently and so your
> > conclusions will only extrapolate to your own personal interpretation.
>
> Are we, though? I think my experience with other people is more supportive of the conclusion that we're all mostly using temperaments the same way, at least insofar as we're all "using" temperaments (which, who knows to what extent we're all doing that, since we don't really know what it means to "use" a temperament).

There are lots of people who probably are just going with subjective
resemblances. But, there are also people like me, who are trying to
separate subjective resemblance from actual "essence of ratio," and so
I use temperament differently. Sometimes I don't use temperaments
consistently at all.

This doesn't bother me, because I've come to the conclusion that "a
temperament" is an imperfect vehicle for describing all my current
understanding of all of the things going into how music, and I'm not
going to try and pigeonhole it into a role I don't think it's designed
for. This is why I keep objecting to your current notion of "hearing a
mapping" as anything other than an informality, because it seems like
that you are trying to pigeonhole it into that role.

However, I do think temperaments get the job done at least in part,
and I think they're useful conceptual tools for understanding music
anyway. I think the stuff we're talking about is separate. If a new
mathematical object comes along that seems more useful, I'm all for
using that instead. But so far, despite my personal, current
understanding of what's going on, the current mathematical objects are
useful enough to have some musical use anyway, despite their
limitations.

> > My mom can't figure out what the hell's going on when I play music at
> > all, but she likes it; this is no different from that.
>
> How is it not different? How is your mom's enjoyment of music a refutation of my above assertion about "breaking" someone's sense of temperament by playing a confusing progression?

Because every single piece of music I ever play "breaks" her
non-existent sense of temperament, so for her, nothing is in 12-EDO or
in anything at all.

> > What I know is that this whole notion of "perceiving a ratio as
> > ______" is actually not related to psychoacoustics or music cognition
> > at all, but just normal, regular, boring old cognition. If I'm exposed
> > to a stimulus long enough, I'll remember it and be able to gauge how
> > much other things are the same and different from it. If an interval
> > has certain defining features which are associated with it being tuned
> > a certain way, like the usual small-integer ratio features, I'll tend
> > to remember those things about it.
>
> Well, this is reassuring. I know more about regular cognition than I do about music-specific cognition.

I don't think there's a lot of groundbreaking research out there on
music-specific cognition at all, to be honest. There are a few good
things, but they're embryonic. Infants like ratios and also unequal
scales (they prefer orgone[7] to 7-edo apparently), and also there's
categorical perception for trained musicians etc, but it's not like
there's a clear picture of what's out there, despite that some earlier
researchers (e.g. Parncutt) seem to think they had one.

> Would you agree with this: it doesn't make sense to use temperaments unless you have learned to categorically perceive whatever-limit JI that you're trying to temper? And that you can't recognize a temperament of some n-limit JI unless you can categorically-perceive n-limit JI?

This is your definition of temperament, which had to do with
subjective resemblances. So under your definition, then yes,
obviously, in order to perceive a subjective resemblance, you need to
be able to remember something schematically to compare with the
current stimulus. I don't know about "categorically" perceive, which
implies something like a discontinuous interval spectrum, but that's
the basic gist of it.

But that's not the only way to use temperaments; you could assume that
interval "identities" come from somewhere else, and treat ratios as
ways to intone those things and make these identities nice and crunchy
sounding. This is the "regular temperament as distortion pedal"
paradigm.

> > No, but a temperament exists before you write music in it, because
> > that's how Gene defined everything, and I happen to like it.
>
> I don't like it at all, I think it's the root of all misunderstandings and the reason that no one can figure out what it means to "use" a temperament. The mappings exist, but I think we'd be able to make much more sense of this paradigm if we defined temperaments as not existing meaningfully outside of music.

But this is how temperaments have always been defined. They've always
been mathematical objects independent of any composition. I feel again
like you're trying to pigeonhole these things into something they're
not. The concept you're talking about has to do with music cognition
and not mathematics, and for those of us who have been studying the
mathematics of this subject, it's very confusing when you say these
kinds of things. So I wish you'd just coin new terms of your own for
the effects you care about.

> > The mathematical objects are always defined with respect to musical
> > intervals; that's what the Z^n business is all about. Temperaments are
> > ideals for how to to intone Z^n.
>
> How are the mathematical objects define with respect to musical intervals? What makes a number a musical interval? Can musical intervals be described soundlessly? What would 386 cents mean to a deaf person?

Z^n is supposed to reflect a point in a lattice, or a linear
combination of some set of n basis generators. We're taking this
unmapped, "melodic," "scalar," maybe "categorical," etc lattice, and
we're associating each point with a set of ratios. That's the basic
quantum leap here. Once we do that, we can treat this association in a
number of useful ways, such as an optimal intonation for the intervals
in this lattice to make everything as beatless and crunchy as
possible.

> What I think is that our understanding of what temperaments *are* is being held back by our refusal to rule some things out. There, I said it. I think that in order to progress, we need to make some more assumptions, not fewer. And of course we'll have to test those assumptions. But isn't this normally how a field progresses? You start with a vague and general model, and then progressively refine it until it makes predictions of greater and greater specificity? Is that not a direction we should move in?

I agree that we need more assumptions, and that we may also need to
throw some existing assumptions out. But to know what assumptions to
make, you need to be completely open to experiencing new things, which
means in this case being cautious before ever ruling things out.

But again, for the sake of modeling things, if you come up with a
model that improves on our understanding that requires ruling out
certain some notion of temperaments that are really really bad, I
think it'll be useful enough for everyone to be happy. That's kind of
what "limits" are: I really wish everything was mapped into the
infinite limit, because I think a lot of this confusion would go away
and it might be more elegant in modeling perception. But it makes the
math so easy to just assume that primes beyond a certain limit don't
exist that that's the approach that's won out.

This doesn't say that infinite limits are bad or pointless; I'd still
like to keep working on them. But it does mean that it's OK to
deliberately rule things out if you think it'll be useful and if
you're clear about what's being ruled out.

> > Look, it's not a big problem for me, because I went through this
> > little crisis already. Yes, the paradigm is incomplete. Temperaments
> > aren't everything they should be. You're right, we can't go claim how
> > great and complete and scientific and perfect and finished the theory
> > is. But, they're still useful as conceptual tools, and I'm happy to
> > know exactly what their limitations are and use the theory anyway.
>
> Since when were you content to rest on your laurels with this stuff? Just because everyone else (Graham, Carl, Gene, and maybe even Paul) have put in their time, paid their dues, and consider their work on developing the theory pretty much done, does that mean we shouldn't keep pushing forward, asking tough questions, and trying to refine more?

I'm not at all content to rest on my laurels with any of this. I'm
content to rest on the current mathematical theory as being of
sufficient integrity to be musically useful and worth promoting. I
don't think that the theory itself requires any of these really tough
assumptions, and that when you talk about "our paradigm" you're not
talking about the theory itself. I also think that many of the things
that I want to model may don't have to do with ratios at all. But it's
useful for me to not try and stuff the existing paradigm into
something it wasn't meant to handle. I'd rather get a good grasp on
what's going on so far that the paradigm is missing, then model that,
and then see if reintegration with temperaments in their current form
is possible, or if not, treat these new things as separate things to
model in their own right.

-Mike

On Tue, Feb 14, 2012 at 1:54 PM, Mike Battaglia <battaglia01@...> wrote:
> I'm not at all content to rest on my laurels with any of this. I'm
> content to rest on the current mathematical theory as being of
> sufficient integrity to be musically useful and worth promoting. I
> don't think that the theory itself requires any of these really tough
> assumptions, and that when you talk about "our paradigm" you're not
> talking about the theory itself. I also think that many of the things
> that I want to model may don't have to do with ratios at all. But it's
> useful for me to not try and stuff the existing paradigm into
> something it wasn't meant to handle. I'd rather get a good grasp on
> what's going on so far that the paradigm is missing, then model that,
> and then see if reintegration with temperaments in their current form
> is possible, or if not, treat these new things as separate things to
> model in their own right.

Or, if this wasn't clear and forceful enough, I'm saying that I've
concluded that temperaments themselves are not useful vehicles to
describe the sorts of ultramodern things that we're now talking about,
because half of the thing you keep calling "our paradigm" is built on
unsound principles that aren't well-defined (like "hearing a mapping,"
"hearing a ratio," whatever) and which break down when you dig at
them. And the only reason that I ever thought they were well-defined
is that certain people kept telling me to read the archives, and
making it seem like they were well defined, and that there was some
golden age in which this was all figured out and that we've all fallen
from grace. And my conclusion after reading a solid majority of the
archives and asking the purported experts who supposedly have it all
figured out, that that isn't true at all, that it's time to move on,
but that temperaments are useful anyway for all of the stuff prior to
this new chapter we're opening.

-Mike

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

> And my conclusion after reading a solid majority of the
> archives and asking the purported experts who supposedly have it all
> figured out, that that isn't true at all, that it's time to move on,
> but that temperaments are useful anyway for all of the stuff prior to
> this new chapter we're opening.

To actually open a new chapter in music to have to do something other than talk philosophy.

On Tue, Feb 14, 2012 at 2:28 PM, genewardsmith
<genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > And my conclusion after reading a solid majority of the
> > archives and asking the purported experts who supposedly have it all
> > figured out, that that isn't true at all, that it's time to move on,
> > but that temperaments are useful anyway for all of the stuff prior to
> > this new chapter we're opening.
>
> To actually open a new chapter in music to have to do something other than talk philosophy.

I hate philosophy. But in this case, because Igs raised the point for
3-4 weeks in a row, I thought it was a good idea to suck it up and
explain the wavelength I'm on, since I was asking the same questions
not too long ago and in many ways I still am.

I'm sorry to say that I don't have a nice model of how everything
works, but I think the notion of not cramming every single new
realization that comes along into the regular mapping paradigm is a
good one, even if you consider it to be purely philosophical.

-Mike

To respond to the thread title, "What's the best way to describe JI's relation to temperaments?" is very simple.

The melting together of harmonic intervals and flow of melodic intervals (there being no hard line between the horizontal and the vertical) is the sine qua non of Just Intonation. The same and similar effects can also happen in various rational intervallic structures.

When these effects remain audible in a tempered structure, we have a temperament in a traditional, and mainstream, sense.

If these effects are not audible, whether because of tempering more than the audible effect will bear or because of tempering a rational structure which has little or no such perceivable effects in the first place, then such a structure created by tempering rationals is no longer a temperament in a traditional, and mainstream, sense. There is nothing to gained by calling such a structure a temperament, other than obfuscation. On the other hand, because such structures are nevertheless created tempering rationals, it would be wrong to leave "temperament" off their birth certificates altogether. I would suggest "abstract temperaments", or "xenotemperaments" or something along those lines.

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Tue, Feb 14, 2012 at 1:54 PM, Mike Battaglia <battaglia01@...> wrote:
> > I'm not at all content to rest on my laurels with any of this. I'm
> > content to rest on the current mathematical theory as being of
> > sufficient integrity to be musically useful and worth promoting. I
> > don't think that the theory itself requires any of these really tough
> > assumptions, and that when you talk about "our paradigm" you're not
> > talking about the theory itself. I also think that many of the things
> > that I want to model may don't have to do with ratios at all. But it's
> > useful for me to not try and stuff the existing paradigm into
> > something it wasn't meant to handle. I'd rather get a good grasp on
> > what's going on so far that the paradigm is missing, then model that,
> > and then see if reintegration with temperaments in their current form
> > is possible, or if not, treat these new things as separate things to
> > model in their own right.
>
> Or, if this wasn't clear and forceful enough, I'm saying that I've
> concluded that temperaments themselves are not useful vehicles to
> describe the sorts of ultramodern things that we're now talking about,
> because half of the thing you keep calling "our paradigm" is built on
> unsound principles that aren't well-defined (like "hearing a mapping,"
> "hearing a ratio," whatever) and which break down when you dig at
> them. And the only reason that I ever thought they were well-defined
> is that certain people kept telling me to read the archives, and
> making it seem like they were well defined, and that there was some
> golden age in which this was all figured out and that we've all fallen
> from grace. And my conclusion after reading a solid majority of the
> archives and asking the purported experts who supposedly have it all
> figured out, that that isn't true at all, that it's time to move on,
> but that temperaments are useful anyway for all of the stuff prior to
> this new chapter we're opening.
>
> -Mike
>

>
> --- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@> wrote:
> I'm beginning to think that we really don't know what it means to >"use" a temperament, despite that recent discussion.

I know exactly what it means to use a temperament: to take advantage of the features offered by its deviations from the rational structure from which it is derived, while retaining as much as possible the audible effects of that rational structure.

--- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:
>
> To respond to the thread title, "What's the best way to describe JI's relation to temperaments?" is very simple.
>
> The melting together of harmonic intervals and flow of melodic intervals (there being no hard line between the horizontal and the vertical) is the sine qua non of Just Intonation. The same and similar effects can also happen in various rational intervallic structures.
>
> When these effects remain audible in a tempered structure, we have a temperament in a traditional, and mainstream, sense.
>
> If these effects are not audible, whether because of tempering more >than the audible effect will bear or because of tempering a rational >structure which has little or no such perceivable effects in the >first place, then such a structure created by tempering rationals is >no longer a temperament in a traditional, and mainstream, sense. >There is nothing to gained by calling such a structure a temperament, >other than obfuscation. On the other hand, because such structures >are nevertheless created tempering rationals, it would be wrong to >leave "temperament" off their birth certificates altogether. I would >suggest "abstract temperaments", or "xenotemperaments" or something >along those lines.

"Exotemperaments". Already in use here, great word. It is vital in my opinion to distinguish between temperaments in a tradtional sense and the temperaments here which do not have the audible features associated with temperament, yet are undeniably temperaments as they are created by tempering rational intervals.

On Feb 15, 2012, at 4:30 AM, lobawad <lobawad@...> wrote:

--- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:
>
> To respond to the thread title, "What's the best way to describe JI's
relation to temperaments?" is very simple.
>
> The melting together of harmonic intervals and flow of melodic intervals
(there being no hard line between the horizontal and the vertical) is the
sine qua non of Just Intonation. The same and similar effects can also
happen in various rational intervallic structures.
>
> When these effects remain audible in a tempered structure, we have a
temperament in a traditional, and mainstream, sense.
>
> If these effects are not audible, whether because of tempering more >than
the audible effect will bear or because of tempering a rational >structure
which has little or no such perceivable effects in the >first place, then
such a structure created by tempering rationals is >no longer a temperament
in a traditional, and mainstream, sense. >There is nothing to gained by
calling such a structure a temperament, >other than obfuscation. On the
other hand, because such structures >are nevertheless created tempering
rationals, it would be wrong to >leave "temperament" off their birth
certificates altogether. I would >suggest "abstract temperaments", or
"xenotemperaments" or something >along those lines.

"Exotemperaments". Already in use here, great word. It is vital in my
opinion to distinguish between temperaments in a tradtional sense and the
temperaments here which do not have the audible features associated with
temperament, yet are undeniably temperaments as they are created by
tempering rational intervals.

You can call something an exotemperament if you want, but the problem lies
with when you try to come up with a hard and fast rule to delineate between
the two.

This is why I think the perfect solution is what we're already doing.
Rather than associating each temperament with a boolean representing its
"existence," associate it with a scalar doing the same thing. The higher
this scalar gets, the less it exists. Elegant, simple, avoids making any
assumptions about psychoacoustics.

You also have to keep in mind that adaptive tunings can cause a great deal
many more temperaments to be musically useful.

-Mike

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

>
> You can call something an exotemperament if you want, but the >problem lies with when you try to come up with a hard and fast rule >to delineate between the two.

The hard and fast rule has been in place for centuries. When the rational intervals tempered remain perceptible, we have a temperament in a traditional (and still mainstream) sense. It is very instructive to read tuning/tempering guides from centuries ago: "flatten the fifth as much as is tolerable..."

Of course, as temperament really exists, or exists most importantly, in human perception, there will be fuzzy zones between what is beyond reasonable doubt temperament and what is exotemperament (or whatever you want to call it). So? Fuzzy zones happen in music.

On Wed, Feb 15, 2012 at 12:59 PM, lobawad <lobawad@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > You can call something an exotemperament if you want, but the >problem lies with when you try to come up with a hard and fast rule >to delineate between the two.
>
> The hard and fast rule has been in place for centuries. When the rational intervals tempered remain perceptible, we have a temperament in a traditional (and still mainstream) sense. It is very instructive to read tuning/tempering guides from centuries ago: "flatten the fifth as much as is tolerable..."

This is not a hard and fast rule. This isn't even a soft and slow
rule. There has to be a "person" for anything at all to "remain
perceptible." It is not possible given our current knowledge of
anything to state exactly when some stimulus "becomes imperceptible"
for an arbitrary person, and thus it's especially impossible to state
such hard cutoffs for every person in the entire world. This is why
the best thing to do is to not have hard lines at all, to treat
everything as asymptotically approaching "imperceptible," and give
every temperament a scalar reflecting its distance to the asymptote.

> Of course, as temperament really exists, or exists most importantly, in human perception, there will be fuzzy zones between what is beyond reasonable doubt temperament and what is exotemperament (or whatever you want to call it). So? Fuzzy zones happen in music.

So what the hell was all the song and dance about above?

-Mike

--- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:
> If these effects are not audible, whether because of tempering more than the audible
> effect will bear or because of tempering a rational structure which has little or no such
> perceivable effects in the first place, then such a structure created by tempering
> rationals is no longer a temperament in a traditional, and mainstream, sense. There is
> nothing to gained by calling such a structure a temperament, other than obfuscation. On
> the other hand, because such structures are nevertheless created tempering rationals, it
> would be wrong to leave "temperament" off their birth certificates altogether. I would
> suggest "abstract temperaments", or "xenotemperaments" or something along those
> lines.

Well, we already have the term "exotemperament", coined by Paul, which would probably do...but where's the line between "temperament" and "exotemperament"? Paul referred to dicot and father as exotemperaments, but is mavila an exotemperament? How about blackwood? Diminished? What about temperaments of higher-limit subgroups, where you need large chords to get the effects of JI (like, say, a 2.11.13.15.17 subgroup temperament)? Consider this temperament:

http://x31eq.com/cgi-bin/rt.cgi?ets=13_11&limit=2_11_13_15_17

Is this a temperament only under the special circumstance of playing full 8:11:13:15:17 chords, and is it not a temperament if you write a two-part invention in it?

Or perhaps more ambiguously, how about this temperament:

http://x31eq.com/cgi-bin/rt.cgi?ets=12_38&limit=2_3_5_17_19

It's not so easy, Mr. "This Is How It Works In the Real World".

-Igs

>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
> >
> > On Tue, Feb 14, 2012 at 1:54 PM, Mike Battaglia <battaglia01@> wrote:
> > > I'm not at all content to rest on my laurels with any of this. I'm
> > > content to rest on the current mathematical theory as being of
> > > sufficient integrity to be musically useful and worth promoting. I
> > > don't think that the theory itself requires any of these really tough
> > > assumptions, and that when you talk about "our paradigm" you're not
> > > talking about the theory itself. I also think that many of the things
> > > that I want to model may don't have to do with ratios at all. But it's
> > > useful for me to not try and stuff the existing paradigm into
> > > something it wasn't meant to handle. I'd rather get a good grasp on
> > > what's going on so far that the paradigm is missing, then model that,
> > > and then see if reintegration with temperaments in their current form
> > > is possible, or if not, treat these new things as separate things to
> > > model in their own right.
> >
> > Or, if this wasn't clear and forceful enough, I'm saying that I've
> > concluded that temperaments themselves are not useful vehicles to
> > describe the sorts of ultramodern things that we're now talking about,
> > because half of the thing you keep calling "our paradigm" is built on
> > unsound principles that aren't well-defined (like "hearing a mapping,"
> > "hearing a ratio," whatever) and which break down when you dig at
> > them. And the only reason that I ever thought they were well-defined
> > is that certain people kept telling me to read the archives, and
> > making it seem like they were well defined, and that there was some
> > golden age in which this was all figured out and that we've all fallen
> > from grace. And my conclusion after reading a solid majority of the
> > archives and asking the purported experts who supposedly have it all
> > figured out, that that isn't true at all, that it's time to move on,
> > but that temperaments are useful anyway for all of the stuff prior to
> > this new chapter we're opening.
> >
> > -Mike
> >
>

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

> I know exactly what it means to use a temperament: to take advantage of the features
> offered by its deviations from the rational structure from which it is derived, while retaining > as much as possible the audible effects of that rational structure.

Well, what does it mean to take advantage of those features, and how often do I have to do it to claim that I'm using a temperament? How much of the audible effects must be retained? Can I use meantone in 12-TET? How about 26? 45? 55? If I wrote a whole suite of music in the same tuning of a temperament, and only "took advantage" of the features of the deviation from the rational structure in one bar of the last movement of the suite, could I claim the whole suite was in the temperament suggested by that one bar?

-Igs

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, "lobawad" <lobawad@> wrote:
> > If these effects are not audible, whether because of tempering more than the audible
> > effect will bear or because of tempering a rational structure which has little or no such
> > perceivable effects in the first place, then such a structure created by tempering
> > rationals is no longer a temperament in a traditional, and mainstream, sense. There is
> > nothing to gained by calling such a structure a temperament, other than obfuscation. On
> > the other hand, because such structures are nevertheless created tempering rationals, it
> > would be wrong to leave "temperament" off their birth certificates altogether. I would
> > suggest "abstract temperaments", or "xenotemperaments" or something along those
> > lines.
>
> Well, we already have the term "exotemperament", coined by Paul, which would probably do...but where's the line between "temperament" and "exotemperament"? Paul referred to dicot and father as exotemperaments, but is mavila an exotemperament? How about blackwood? Diminished? What about temperaments of higher-limit subgroups, where you need large chords to get the effects of JI (like, say, a 2.11.13.15.17 subgroup temperament)? Consider this temperament:
>
> http://x31eq.com/cgi-bin/rt.cgi?ets=13_11&limit=2_11_13_15_17
>
> Is this a temperament only under the special circumstance of playing full 8:11:13:15:17 chords, and is it not a temperament if you write a two-part invention in it?
>
> Or perhaps more ambiguously, how about this temperament:
>
> http://x31eq.com/cgi-bin/rt.cgi?ets=12_38&limit=2_3_5_17_19
>
> It's not so easy, Mr. "This Is How It Works In the Real World".
>
> -Igs

Who said everything must be easy? The basic stuff is easy- there is no need to complicate the basic idea of temperament. That we do not know where what is clearly temperament ends and exotemperament begins, that this would be a field of contention, debate, evolving conceptions, is beautiful. Like the real world.

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, "lobawad" <lobawad@> wrote:
>
> > I know exactly what it means to use a temperament: to take advantage of the features
> > offered by its deviations from the rational structure from which it is derived, while retaining > as much as possible the audible effects of that rational structure.
>
> Well, what does it mean to take advantage of those features, and how often do I have to do it to claim that I'm using a temperament? How much of the audible effects must be retained? Can I use meantone in 12-TET? How about 26? 45? 55? If I wrote a whole suite of music in the same tuning of a temperament, and only "took advantage" of the features of the deviation from the rational structure in one bar of the last movement of the suite, could I claim the whole suite was in the temperament suggested by that one bar?
>
> -Igs
>

Would you dictate these things? I would rather let them evolve and acknowledge things like "general agreement, excepting the school of X..."

On Wed, Feb 15, 2012 at 1:28 PM, lobawad <lobawad@...> wrote:
>
> Who said everything must be easy? The basic stuff is easy- there is no need to complicate the basic idea of temperament. That we do not know where what is clearly temperament ends and exotemperament begins, that this would be a field of contention, debate, evolving conceptions, is beautiful. Like the real world.

It's about as beautiful as arguing over when a really small number becomes zero.

> Would you dictate these things? I would rather let them evolve and acknowledge things like "general agreement, excepting the school of X..."

If you're going to try and launch a social campaign to promote there
being some sort of consensus agreement about this, I wish you'd at
least talk about specific tunings for temperaments, rather than the
temperaments themselves. Temperaments can be given any tuning, and can
even be tuned adaptively, and there might be even more clever things
you can do with them.

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Wed, Feb 15, 2012 at 1:28 PM, lobawad <lobawad@...> wrote:
> >
> > Who said everything must be easy? The basic stuff is easy- there is no need to complicate the basic idea of temperament. That we do not know where what is clearly temperament ends and exotemperament begins, that this would be a field of contention, debate, evolving conceptions, is beautiful. Like the real world.
>
> It's about as beautiful as arguing over when a really small number becomes zero.

No, more like arguing whether an ambiguous piece is really in C or G, or whether you hear a tonic in a piece of "atonal" music.

>
> > Would you dictate these things? I would rather let them evolve and acknowledge things like "general agreement, excepting the school of X..."
>
> If you're going to try and launch a social campaign to promote there
> being some sort of consensus agreement about this, I wish you'd at
> least talk about specific tunings for temperaments, rather than the
> temperaments themselves. Temperaments can be given any tuning, and >can
> even be tuned adaptively, and there might be even more clever things
> you can do with them.
>
> -Mike
>

Quarter-comma meantone can be given any tuning? 12-tET can be given any tuning? No. Temperament "types" or "classes" (or something to that effect) can be tuned to different specific tunings.

On Wed, Feb 15, 2012 at 5:52 PM, lobawad <lobawad@...> wrote:
>
> Quarter-comma meantone can be given any tuning? 12-tET can be given any tuning? No. Temperament "types" or "classes" (or something to that effect) can be tuned to different specific tunings.

Under the definition we've all been using, quarter-comma meantone and
third-comma meantone and so on are all tunings for the same
temperament, the thing you might call a "temperament class," and that
thing is "meantone." That's what Igs has been talking about. If you
want to start talking about the perceptual relevance of specific
tunings of temperaments, then maybe this conversation wouldn't be so
absurd.

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Wed, Feb 15, 2012 at 5:52 PM, lobawad <lobawad@...> wrote:
> >
> > Quarter-comma meantone can be given any tuning? 12-tET can be given any tuning? No. Temperament "types" or "classes" (or something to that effect) can be tuned to different specific tunings.
>
> Under the definition we've all been using, quarter-comma meantone and
> third-comma meantone and so on are all tunings for the same
> temperament, the thing you might call a "temperament class," andthat
> thing is "meantone."

Obviously I know how the word is misused here- misuse of the word is precisely what I am criticizing!

There is simply no need to create confusion between the idea of "temperament" as historically understood and that which is called "temperament" on this list.

This is what is going to happen: someone is going to take the whole body of work that has been done here, slap a catchy moniker on it, use "scientific" descriptors rather than fanciful names for the structures generated, not make the idiotic mistake of calling every damn thing under the sun a "temperament", and pass it off as their own, to acclaim.

Maybe neither you nor anyone else cares, though.

>That's what Igs has been talking about. If you
> want to start talking about the perceptual relevance of specific
> tunings of temperaments, then maybe this conversation wouldn't be so
> absurd.

What is absurd is your failure to recognize that the reason your extensive reading of the archives turned up no solid and vigorous machine to wield in music understanding and creation is that the whole enterprise, for all the great stuff within it, is built on foggy usage of words, and the reason the usage is foggy is because the understanding is foggy.

Perhaps you don't really care about this either. Or maybe you *want* the concepts here to remain eccentric.

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

> Maybe neither you nor anyone else cares, though.

I'm a mathematician. I care about precise definitions, which is why when I want to define "abstract regular temperaments" I give one. Other people can do what they like, but I think in the end the mathematical methodology of defining your terms will be seen to work best.

On Thu, Feb 16, 2012 at 1:17 AM, lobawad <lobawad@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> >
> > Under the definition we've all been using, quarter-comma meantone and
> > third-comma meantone and so on are all tunings for the same
> > temperament, the thing you might call a "temperament class," andthat
> > thing is "meantone."
>
> Obviously I know how the word is misused here- misuse of the word is precisely what I am criticizing!
>
> There is simply no need to create confusion between the idea of "temperament" as historically understood and that which is called "temperament" on this list.

You might prefer Graham's terminology then; he calls this sort of
thing a "temperament class." Gene calls it an "abstract regular
temperament." And so now that we're done quibbling over definitions,
my point is that I think it's silly to write off entire abstract
regular temperament/classes, except for ones which are really, really
stupid, in that they temper out 3/2 and so on. In fact, maybe even not
those - who knows what crazy things people will come up with to make
musical sense of these mathematical objects?

> This is what is going to happen: someone is going to take the whole body of work that has been done here, slap a catchy moniker on it, use "scientific" descriptors rather than fanciful names for the structures generated, not make the idiotic mistake of calling every damn thing under the sun a "temperament", and pass it off as their own, to acclaim.
>
> Maybe neither you nor anyone else cares, though.

First off, hasn't the phrase "meantone temperament" has meant the
tuning system in general, outside of any specific 1/4-comma or
1/3-comma or whatever tuning, for quite a while?

Second off, you really think that the entirety of the reason this
hasn't jumped over to academia is because we call things
"temperaments" instead of "temperament classes?" We're not pretending
every "temperament" is musically useful, but rather -defining- the
word within the context of this theory to be the mathematical
correlate of a usual thing called "temperament." The way we defined it
is flexible, robust, simple, etc, all of the things that a good
mathematical definition should be. I don't think academia has a
problem understanding clear definitions. I'd rather expect that the
thing holding us back is that the sum of the world's knowledge on
regular temperaments is either on a Yahoo mailing list or hosted on
wikispaces.org.

> > That's what Igs has been talking about. If you
> > want to start talking about the perceptual relevance of specific
> > tunings of temperaments, then maybe this conversation wouldn't be so
> > absurd.
>
> What is absurd is your failure to recognize that the reason your extensive reading of the archives turned up no solid and vigorous machine to wield in music understanding and creation is that the whole enterprise, for all the great stuff within it, is built on foggy usage of words, and the reason the usage is foggy is because the understanding is foggy.
>
> Perhaps you don't really care about this either. Or maybe you *want* the concepts here to remain eccentric.

I agree that much of this enterprise is built on foggy concepts. Or
rather, I think that it's built on a few limited insights that go a
long long way (like that ratios sound cool), but which aren't fully
"complete" insights into the nature of how music works. Right now,
temperaments (or "temperament classes" or whatever you'd like) are
multivectors in the exterior algebra of the dual space of Tenney
interval space. They end up associating things in Q with things in
Z^n. I think it's a brilliant insight on Gene's part to put all of
that together. I don't think this construct is an adequate vehicle for
modeling things that don't have to do with ratios. They model the
intonation, but not the thing that the intonation is "of," as you keep
saying. If we're interested in modeling that, the best we can do with
this scheme is to assume that the lattice we're projecting intonations
on is its own intended categorical structure, or will become one with
enough exposure.

There's no part of my understanding of the above which isn't crystal
clear to me, although there may be things I'm not aware of or that I
don't know. I know what the limitations of the regular mapping
paradigm are, and I know what its strengths are. But, even though it's
not perfect, I think that it's good to get us started and does a lot,
provided one keeps an open mind about how to use this stuff. For us to
expand and move onto something new, we'll need another new paradigm
shift. I would love, with all me little 'eart, for nothing more than
this paradigm shift to happen, and for us to stop talking about
temperaments and ratios, and to instead start talking about what needs
to be modeled and brainstorm about how to model it. This discussion
will never happen as long as we're trying to force fit temperaments
into a role that they're not currently designed to handle.

A good way to do this force fitting is to ask questions like "when are
we 'hearing' a temperament?" and "what does it mean to 'use' a
temperament?" and "what does it mean for a temperament to 'exist?'" We
can toss around nice pedagogical definitions to help students
understand what "the point" is, but in reality it doesn't mean a god
damn thing, because a "temperament" is a mathematical abstraction
that's supposed to serve as a useful vehicle for music making. We're
asking these ultra-low-level perceptual questions about mathematical
abstractions that aren't meant to model any ultra-low-level perceptual
things except for ratios, and of those they're not even really
modeling anything specific, but allowing the composer to model all
sorts of ratio-associated things. And it doesn't do anything outside
of that and isn't supposed to.

All of us want to try and go to the next level with this stuff. You
and Igs keep telling me what I need to do to start moving to that
level. I think that it's impossible to ever move to the next level
without accepting that the currrent paradigm just isn't designed to
handle it. And from my perspective, it's you and Igs that are foggying
it up by trying to cram more stuff into this temperament business than
it's supposed to handle.

-Mike

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

> You might prefer Graham's terminology then; he calls this sort of
> thing a "temperament class." Gene calls it an "abstract regular
> temperament."

It corresponds to the "temperament class", but I don't call it that because it isn't a class. Moreover, so far as I know no precise definition of "temperament class" has even been proposed.

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "lobawad" <lobawad@> wrote:
>
> > Maybe neither you nor anyone else cares, though.
>
> I'm a mathematician. I care about precise definitions, which is why when I want to define "abstract regular temperaments" I give one. Other people can do what they like, but I think in the end the mathematical methodology of defining your terms will be seen to work best.
>
You make no bones about your definitions being mathematical, how can anyone argue with that? The problem is rambling application of these terms and concepts.

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Thu, Feb 16, 2012 at 1:17 AM, lobawad <lobawad@...> wrote:
> >
> > --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
> > >
> > > Under the definition we've all been using, quarter-comma meantone and
> > > third-comma meantone and so on are all tunings for the same
> > > temperament, the thing you might call a "temperament class," andthat
> > > thing is "meantone."
> >
> > Obviously I know how the word is misused here- misuse of the word is precisely what I am criticizing!
> >
> > There is simply no need to create confusion between the idea of "temperament" as historically understood and that which is called "temperament" on this list.
>
> You might prefer Graham's terminology then; he calls this sort of
> thing a "temperament class." Gene calls it an "abstract regular
> temperament." And so now that we're done quibbling over definitions,
> my point is that I think it's silly to write off entire abstract
> regular temperament/classes, except for ones which are really, really
> stupid, in that they temper out 3/2 and so on. In fact, maybe even not
> those - who knows what crazy things people will come up with to make
> musical sense of these mathematical objects?

Each time we address a fundamental concept, both you and Igs seem to think it's about "semantics" or nit-picking about words, LOL. Okay.

I'll use "abstract regular temperament". A lot of recent goings-around would not have gone around had we all been consistent in making this distinction.
>
> > This is what is going to happen: someone is going to take the whole body of work that has been done here, slap a catchy moniker on it, use "scientific" descriptors rather than fanciful names for the structures generated, not make the idiotic mistake of calling every damn thing under the sun a "temperament", and pass it off as their own, to acclaim.
> >
> > Maybe neither you nor anyone else cares, though.
>
> First off, hasn't the phrase "meantone temperament" has meant the
> tuning system in general, outside of any specific 1/4-comma or
> 1/3-comma or whatever tuning, for quite a while?

"Meantone temperament" without further qualification is understood to mean 1/4-comma, check printed references. "Meantone temperaments" refers to 1/3 comma and so on, yes, but not to 12-tET. The observation that 12-tET can be viewed or treated as belonging to meantone as an abstract regular temperament is a good one. It is a good observation that will be lost in freewheeling eccentric use of the word "temperament".

>
> Second off, you really think that the entirety of the reason this
> hasn't jumped over to academia is because we call things
> "temperaments" instead of "temperament classes?"

Entirety of the reason? Of course not, that's just silly.

> I'd rather expect that the
> thing holding us back is that the sum of the world's knowledge on
> regular temperaments is either on a Yahoo mailing list or hosted on
> wikispaces.org.

Regular temperament has been studied for centuries. A university library is a good place to spend a lot of time- and they will have access to JSTOR. Gene's valuable contribution to that history gets buried in the local jive, that's one problem I see.

> I agree that much of this enterprise is built on foggy concepts. Or
> rather, I think that it's built on a few limited insights that go a
> long long way (like that ratios sound cool), but which aren't fully
> "complete" insights into the nature of how music works. Right now,
> temperaments (or "temperament classes" or whatever you'd like) are
> multivectors in the exterior algebra of the dual space of Tenney
> interval space. They end up associating things in Q with things in
> Z^n. I think it's a brilliant insight on Gene's part to put all of
> that together. I don't think this construct is an adequate vehicle for
> modeling things that don't have to do with ratios. They model the
> intonation, but not the thing that the intonation is "of," as you keep
> saying. If we're interested in modeling that, the best we can do with
> this scheme is to assume that the lattice we're projecting intonations
> on is its own intended categorical structure, or will become one with
> enough exposure.

I actually have a lot to say about this, as I have a structural system which any specific intonational scheme is an intonation "of". But that would be many topics, and frankly I'm loathe to bring it up here, as I perceive that a general conception of musical structure as chord progression dominates here to point of making any other approach downright unwanted.

>
> There's no part of my understanding of the above which isn't crystal
> clear to me, although there may be things I'm not aware of or that I
> don't know. I know what the limitations of the regular mapping
> paradigm are, and I know what its strengths are. But, even though it's
> not perfect, I think that it's good to get us started and does a >lot,
> provided one keeps an open mind about how to use this stuff. For us to
> expand and move onto something new, we'll need another new paradigm
> shift. I would love, with all me little 'eart, for nothing more than
> this paradigm shift to happen, and for us to stop talking about
> temperaments and ratios, and to instead start talking about what needs
> to be modeled and brainstorm about how to model it. This discussion
> will never happen as long as we're trying to force fit temperaments
> into a role that they're not currently designed to handle.
>
> A good way to do this force fitting is to ask questions like "when are
> we 'hearing' a temperament?" and "what does it mean to 'use' a
> temperament?" and "what does it mean for a temperament to 'exist?'" We
> can toss around nice pedagogical definitions to help students
> understand what "the point" is, but in reality it doesn't mean a god
> damn thing, because a "temperament" is a mathematical abstraction
> that's supposed to serve as a useful vehicle for music making. We're
> asking these ultra-low-level perceptual questions about mathematical
> abstractions that aren't meant to model any ultra-low-level perceptual
> things except for ratios, and of those they're not even really
> modeling anything specific, but allowing the composer to model all
> sorts of ratio-associated things. And it doesn't do anything outside
> of that and isn't supposed to.
>
> All of us want to try and go to the next level with this stuff. You
> and Igs keep telling me what I need to do to start moving to that
> level. I think that it's impossible to ever move to the next level
> without accepting that the currrent paradigm just isn't designed to
> handle it. And from my perspective, it's you and Igs that are foggying
> it up by trying to cram more stuff into this temperament business than
> it's supposed to handle.

I can't speak for Igs, but (as seems perfectly clear to at least some others watching on), I am simplifying and clarifying. Try this: make a whole lot of music using a temperament in which the audible effects of the ratios in the rational structure remain clearly audible after tempering. All will fall into place.

And a bit of advice: if you are interested in widening this community and its work, avoid assuming some grandiose future. When we Clear the planet, when the Rapture happens... see what I mean?

On Thu, Feb 16, 2012 at 4:35 AM, lobawad <lobawad@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > You might prefer Graham's terminology then; he calls this sort of
> > thing a "temperament class." Gene calls it an "abstract regular
> > temperament." And so now that we're done quibbling over definitions,
> > my point is that I think it's silly to write off entire abstract
> > regular temperament/classes, except for ones which are really, really
> > stupid, in that they temper out 3/2 and so on. In fact, maybe even not
> > those - who knows what crazy things people will come up with to make
> > musical sense of these mathematical objects?
>
> Each time we address a fundamental concept, both you and Igs seem to think it's about "semantics" or nit-picking about words, LOL. Okay.
>
> I'll use "abstract regular temperament". A lot of recent goings-around would not have gone around had we all been consistent in making this distinction.

What was the fundamental concept here? That this definition conflicts
with the definition of some earlier authors?

> > First off, hasn't the phrase "meantone temperament" has meant the
> > tuning system in general, outside of any specific 1/4-comma or
> > 1/3-comma or whatever tuning, for quite a while?
>
> "Meantone temperament" without further qualification is understood to mean 1/4-comma, check printed references.

Not anymo-ho-hore, check "A Middle Path," published in the fine
journal of Xenharmonikon

> "Meantone temperaments" refers to 1/3 comma and so on, yes, but not to 12-tET. The observation that 12-tET can be viewed or treated as belonging to meantone as an abstract regular temperament is a good one. It is a good observation that will be lost in freewheeling eccentric use of the word "temperament".

I get what you're saying, but how can you tell me that there's some
"fundamental concept" we're addressing when this is the conversation?
What is the fundamental concept here? That people in the past used
these words very slightly differently? I'm not convinced the word
"temperament" was ever used with 100% consistency at any point in its
history. And, if we're worried about making sure this "catches on" in
academia, then a paragraph at the beginning of a paper about this
stuff going over the definitions of these words and some notes about
earlier definitions would suffice for anyone reading.

> > I'd rather expect that the
> > thing holding us back is that the sum of the world's knowledge on
> > regular temperaments is either on a Yahoo mailing list or hosted on
> > wikispaces.org.
>
> Regular temperament has been studied for centuries. A university library is a good place to spend a lot of time- and they will have access to JSTOR. Gene's valuable contribution to that history gets buried in the local jive, that's one problem I see.

It hasn't been studied like it has been here. And if you're so
concerned about respecting the terminology of people who have done
work in this field, then Gene et al have done more work in mapping out
all of the infinite varieties of regular temperaments than any human
beings who have ever existed, and their terminology deserves respect
too. So I could play that card if I wanted.

As for what's getting lost in the local jive - the wiki is far too
obtuse, I agree. That's a matter of time and organization.

> I actually have a lot to say about this, as I have a structural system which any specific intonational scheme is an intonation "of". But that would be many topics, and frankly I'm loathe to bring it up here, as I perceive that a general conception of musical structure as chord progression dominates here to point of making any other approach downright unwanted.

Why don't you just bring it up? I'd rather talk about that than the
many infinite varieties of the word "temperament."

> > All of us want to try and go to the next level with this stuff. You
> > and Igs keep telling me what I need to do to start moving to that
> > level. I think that it's impossible to ever move to the next level
> > without accepting that the currrent paradigm just isn't designed to
> > handle it. And from my perspective, it's you and Igs that are foggying
> > it up by trying to cram more stuff into this temperament business than
> > it's supposed to handle.
>
> I can't speak for Igs, but (as seems perfectly clear to at least some others watching on), I am simplifying and clarifying. Try this: make a whole lot of music using a temperament in which the audible effects of the ratios in the rational structure remain clearly audible after tempering. All will fall into place.

I tend to play in 22-EDO for multiple hours per day at this point.
I've figured out a few interesting things, de-mystified a few other
formerly scientific things, and I haven't found the meaning of life
yet. The best I've come up with is the mystery phrase "music
information theory."

> And a bit of advice: if you are interested in widening this community and its work, avoid assuming some grandiose future. When we Clear the planet, when the Rapture happens... see what I mean?

The only grandiose future I assume is that some point in the not too
distant future, kids at a music festival will say "hey, wanna jam
before seeing Phish?" and then one will ask "which tuning?" and then
they'll play in Blackwood in 15-EDO for about 20 minutes, and then get
a beer and go see Phish. If Phish isn't touring, it'll be a Phish
cover and/or spinoff band. I hope that's not too grandiose.

-Mike

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

> The only grandiose future I assume is that some point in the not too
> distant future, kids at a music festival will say "hey, wanna jam
> before seeing Phish?" and then one will ask "which tuning?" and then
> they'll play in Blackwood in 15-EDO for about 20 minutes, and then get
> a beer and go see Phish. If Phish isn't touring, it'll be a Phish
> cover and/or spinoff band. I hope that's not too grandiose.

Since seeing Andrew Heathwaite's Orwell on an Isomorphic Keyboard, I've been having grandiose visions of a future involving lots of isomorphic keyboards.

http://xenharmonic.wikispaces.com/Orwell+on+an+Isomorphic+Keyboard

At this point I think it would be best to pick up this conversation in a few years.

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Thu, Feb 16, 2012 at 4:35 AM, lobawad <lobawad@...> wrote:
> >
> > --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
> >
> > > You might prefer Graham's terminology then; he calls this sort of
> > > thing a "temperament class." Gene calls it an "abstract regular
> > > temperament." And so now that we're done quibbling over definitions,
> > > my point is that I think it's silly to write off entire abstract
> > > regular temperament/classes, except for ones which are really, really
> > > stupid, in that they temper out 3/2 and so on. In fact, maybe even not
> > > those - who knows what crazy things people will come up with to make
> > > musical sense of these mathematical objects?
> >
> > Each time we address a fundamental concept, both you and Igs seem to think it's about "semantics" or nit-picking about words, LOL. Okay.
> >
> > I'll use "abstract regular temperament". A lot of recent goings-around would not have gone around had we all been consistent in making this distinction.
>
> What was the fundamental concept here? That this definition conflicts
> with the definition of some earlier authors?
>
>
> > > First off, hasn't the phrase "meantone temperament" has meant the
> > > tuning system in general, outside of any specific 1/4-comma or
> > > 1/3-comma or whatever tuning, for quite a while?
> >
> > "Meantone temperament" without further qualification is understood to mean 1/4-comma, check printed references.
>
> Not anymo-ho-hore, check "A Middle Path," published in the fine
> journal of Xenharmonikon
>
> > "Meantone temperaments" refers to 1/3 comma and so on, yes, but not to 12-tET. The observation that 12-tET can be viewed or treated as belonging to meantone as an abstract regular temperament is a good one. It is a good observation that will be lost in freewheeling eccentric use of the word "temperament".
>
> I get what you're saying, but how can you tell me that there's some
> "fundamental concept" we're addressing when this is the conversation?
> What is the fundamental concept here? That people in the past used
> these words very slightly differently? I'm not convinced the word
> "temperament" was ever used with 100% consistency at any point in its
> history. And, if we're worried about making sure this "catches on" in
> academia, then a paragraph at the beginning of a paper about this
> stuff going over the definitions of these words and some notes about
> earlier definitions would suffice for anyone reading.
>
> > > I'd rather expect that the
> > > thing holding us back is that the sum of the world's knowledge on
> > > regular temperaments is either on a Yahoo mailing list or hosted on
> > > wikispaces.org.
> >
> > Regular temperament has been studied for centuries. A university library is a good place to spend a lot of time- and they will have access to JSTOR. Gene's valuable contribution to that history gets buried in the local jive, that's one problem I see.
>
> It hasn't been studied like it has been here. And if you're so
> concerned about respecting the terminology of people who have done
> work in this field, then Gene et al have done more work in mapping out
> all of the infinite varieties of regular temperaments than any human
> beings who have ever existed, and their terminology deserves respect
> too. So I could play that card if I wanted.
>
> As for what's getting lost in the local jive - the wiki is far too
> obtuse, I agree. That's a matter of time and organization.
>
> > I actually have a lot to say about this, as I have a structural system which any specific intonational scheme is an intonation "of". But that would be many topics, and frankly I'm loathe to bring it up here, as I perceive that a general conception of musical structure as chord progression dominates here to point of making any other approach downright unwanted.
>
> Why don't you just bring it up? I'd rather talk about that than the
> many infinite varieties of the word "temperament."
>
> > > All of us want to try and go to the next level with this stuff. You
> > > and Igs keep telling me what I need to do to start moving to that
> > > level. I think that it's impossible to ever move to the next level
> > > without accepting that the currrent paradigm just isn't designed to
> > > handle it. And from my perspective, it's you and Igs that are foggying
> > > it up by trying to cram more stuff into this temperament business than
> > > it's supposed to handle.
> >
> > I can't speak for Igs, but (as seems perfectly clear to at least some others watching on), I am simplifying and clarifying. Try this: make a whole lot of music using a temperament in which the audible effects of the ratios in the rational structure remain clearly audible after tempering. All will fall into place.
>
> I tend to play in 22-EDO for multiple hours per day at this point.
> I've figured out a few interesting things, de-mystified a few other
> formerly scientific things, and I haven't found the meaning of life
> yet. The best I've come up with is the mystery phrase "music
> information theory."
>
> > And a bit of advice: if you are interested in widening this community and its work, avoid assuming some grandiose future. When we Clear the planet, when the Rapture happens... see what I mean?
>
> The only grandiose future I assume is that some point in the not too
> distant future, kids at a music festival will say "hey, wanna jam
> before seeing Phish?" and then one will ask "which tuning?" and then
> they'll play in Blackwood in 15-EDO for about 20 minutes, and then get
> a beer and go see Phish. If Phish isn't touring, it'll be a Phish
> cover and/or spinoff band. I hope that's not too grandiose.
>
> -Mike
>

On Thu, Feb 16, 2012 at 11:46 AM, genewardsmith
<genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > The only grandiose future I assume is that some point in the not too
> > distant future, kids at a music festival will say "hey, wanna jam
> > before seeing Phish?" and then one will ask "which tuning?" and then
> > they'll play in Blackwood in 15-EDO for about 20 minutes, and then get
> > a beer and go see Phish. If Phish isn't touring, it'll be a Phish
> > cover and/or spinoff band. I hope that's not too grandiose.
>
> Since seeing Andrew Heathwaite's Orwell on an Isomorphic Keyboard, I've been having grandiose visions of a future involving lots of isomorphic keyboards.
>
> http://xenharmonic.wikispaces.com/Orwell+on+an+Isomorphic+Keyboard

They'll have to be involved for sure. I think that the generalized
keyboard layout that'll catch on most is something like a generalized
version of this:

http://www.h-pi.com/images/eopimages/keyboards/u288.jpg

So like, a generalized Bosanquet layout, but for other MOS's than
meantone as well, set up so that the octaves end up being on the same
line. This sort of thing lets you actually play melodies, unlike many
of the other layouts I've seen. (Is there a name for this sort of
layout? I can't be the only one who actually uses it.)

The problem with this layout, however, it it takes up a lot of real
estate on the keyboard, and doesn't let you switch too easily between
layouts - if you have a keyboard built around porcupine (1L6s), then
you're going to be SOL when you switch to Orwell (4L5s), because
nothing's going to line up anymore. The best contender I've seen for
these sorts of problems is the Wicki-Hayden layout, which is John
Moriarty's goto layout for everything. It lets you fit more real
estate onto the keyboard, but is pretty harsh for things like
chromatic playing, which are important for melodies. Maybe somewhere
between that and this will turn out to be best.

This is why generalized keyboards can be maddening. Sometimes I have
nightmares where I'm locked in a padded cell, except instead of
padding on the walls and ceiling it's just hexagonal buttons
everywhere.

-Mike

On Thu, Feb 16, 2012 at 2:45 PM, lobawad <lobawad@...> wrote:
>
> At this point I think it would be best to pick up this conversation in a few years.

What's there to pick up? You entered into this conversation nitpicking
over terminology, but I put up with your claims that your nitpicking
was really some kind of fundamental paradigmatic misunderstanding on
my part that needed to be addressed (they weren't), so I could see
what you'd end up saying when we got past that discussion. After
sticking through to the end, all you had to say was basically "when
you're a great composer like I am, you'll understand."

Out here in real life, "great composers" don't say those sorts of
things, so I assume that you had nothing of substance to say, other
than that you don't like our word choice for certain definitions.
Maybe in a few years you'll be able to take your great composer
insights, and communicate them in plain English for the rest of us
non-great composers to learn from, like the actual great composers I
know.

-Mike

I don't know where you get these bizarre interpretations, LOL. This has nothing to do with "you" or "me", it's about how the concept of temperament exists in mainstream usage. If you want to make it personal, then, personally, I think that mainstream conceptions of all kinds of musical things are loaded to the gills with horseshit and worse. But I am not going to change things by insisting on remaining ignorant of the status quo.

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Thu, Feb 16, 2012 at 2:45 PM, lobawad <lobawad@...> wrote:
> >
> > At this point I think it would be best to pick up this conversation in a few years.
>
> What's there to pick up? You entered into this conversation nitpicking
> over terminology, but I put up with your claims that your nitpicking
> was really some kind of fundamental paradigmatic misunderstanding on
> my part that needed to be addressed (they weren't), so I could see
> what you'd end up saying when we got past that discussion. After
> sticking through to the end, all you had to say was basically "when
> you're a great composer like I am, you'll understand."
>
> Out here in real life, "great composers" don't say those sorts of
> things, so I assume that you had nothing of substance to say, other
> than that you don't like our word choice for certain definitions.
> Maybe in a few years you'll be able to take your great composer
> insights, and communicate them in plain English for the rest of us
> non-great composers to learn from, like the actual great composers I
> know.
>
> -Mike
>

On Feb 16, 2012, at 4:09 PM, lobawad <lobawad@...> wrote:

I don't know where you get these bizarre interpretations, LOL. This has
nothing to do with "you" or "me", it's about how the concept of temperament
exists in mainstream usage. If you want to make it personal, then,
personally, I think that mainstream conceptions of all kinds of musical
things are loaded to the gills with horseshit and worse. But I am not going
to change things by insisting on remaining ignorant of the status quo.

I'm obviously not "ignorant" of it, since we're here talking about it. I
think that nobody here was ignorant of it either. I think that the mindful
decision to use a very slightly more abstract definition of "temperament"
for our purposes is ok, as long as it's mindful, and it's clearly stated in
introductional texts what the definition is and how it diverges from
previous ones. Maybe in the context of this conversation it wasn't clear.

Now that we're on the same page about what's being said, does anyone know
how does music works?

-Mike

> I think father started making sense as a temperament while I was writing
> "Yulegu Island" (which originally used a more harmonic timbre before I
> did the current version with inharmonic timbres). I won't say it was
> totally convincing, but I think it's enough to leave the possibility
> open. Beep is another marginal temperament, and at times I've been
> convinced it doesn't exist as a temperament, but with the right tuning
> it might be usable.

Concerning Beep, check out the chord progression I play here:
http://www.youtube.com/watch?feature=player_detailpage&v=aIdWYl2e0es#t=176s

I definitely hear five limit harmony exactly as beep describes it in that passage, and it's a comma pump to boot! Beep is one of my absolute favorite temperaments, second to hanson probably. I find it dead easy to hear, so count me as one data point for "exists".

Do you hear it that way?

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

> Concerning Beep, check out the chord progression I play here:
> http://www.youtube.com/watch?feature=player_detailpage&v=aIdWYl2e0es#t=176s
>
> Do you hear it that way?

Nope. Sounds like supermajors and subminors to me. Does superpyth[7] sound 5-limit to you, too? If no, why not? If so, what do you think that means about your ability to perceive 7-limit harmony?

-Igs

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

> I definitely hear five limit harmony exactly as beep describes it in that passage, and it's a comma pump to boot!

I don't hear 5-limit harmony at all.

On Feb 17, 2012, at 3:13 AM, cityoftheasleep <igliashon@...>
wrote:

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

> Concerning Beep, check out the chord progression I play here:
>
http://www.youtube.com/watch?feature=player_detailpage&v=aIdWYl2e0es#t=176s
>
> Do you hear it that way?

Nope. Sounds like supermajors and subminors to me.

I hear Bm | Dmaj | Gmaj | Bbmaj=Amaj | Cmaj.

Does superpyth[7] sound 5-limit to you, too? If no, why not? If so, what do
you think that means about your ability to perceive 7-limit harmony?

Supermajor chords themselves sound kind of like major chords to me, but
also different when I get used to them.

-Mike

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

> --- In tuning@yahoogroups.com, "jlmoriart" <JlMoriart@> wrote:
>
> > Concerning Beep, check out the chord progression I play here:
> >
> http://www.youtube.com/watch?feature=player_detailpage&v=aIdWYl2e0es#t=176s
> >
> > Do you hear it that way?
>
> Nope. Sounds like supermajors and subminors to me.
>
> I hear Bm | Dmaj | Gmaj | Bbmaj=Amaj | Cmaj.
>
> Does superpyth[7] sound 5-limit to you, too? If no, why not? If so, what do
> you think that means about your ability to perceive 7-limit harmony?
>
> Supermajor chords themselves sound kind of like major chords to me, but
> also different when I get used to them.

I wonder if we took John's progression and retuned it to barbados[9] (~250-cent generator) if you two would still hear it as 5-limit? Or maybe this just means that supermajor and subminor chords aren't really "septimal" harmonies to you guys?

-Igs

On Fri, Feb 17, 2012 at 2:57 PM, cityoftheasleep
<igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > --- In tuning@yahoogroups.com, "jlmoriart" <JlMoriart@> wrote:
> >
> > > Concerning Beep, check out the chord progression I play here:
> > >
> > http://www.youtube.com/watch?feature=player_detailpage&v=aIdWYl2e0es#t=176s
> > >
> > > Do you hear it that way?
> >
> > Nope. Sounds like supermajors and subminors to me.
> >
> > I hear Bm | Dmaj | Gmaj | Bbmaj=Amaj | Cmaj.
> >
> > Does superpyth[7] sound 5-limit to you, too? If no, why not? If so, what do
> > you think that means about your ability to perceive 7-limit harmony?
> >
> > Supermajor chords themselves sound kind of like major chords to me, but
> > also different when I get used to them.
>
> I wonder if we took John's progression and retuned it to barbados[9] (~250-cent generator) if you two would still hear it as 5-limit? Or maybe this just means that supermajor and subminor chords aren't really "septimal" harmonies to you guys?
>
> -Igs

I completely reject this question and line of reasoning on the grounds
that it's like the zen koan "does a dog have Buddha nature?"

-Mike

On Fri, Feb 17, 2012 at 3:07 PM, Mike Battaglia <battaglia01@...> wrote:
> On Fri, Feb 17, 2012 at 2:57 PM, cityoftheasleep
> <igliashon@...> wrote:
>>
>> I wonder if we took John's progression and retuned it to barbados[9] (~250-cent generator) if you two would still hear it as 5-limit? Or maybe this just means that supermajor and subminor chords aren't really "septimal" harmonies to you guys?
>>
>> -Igs
>
> I completely reject this question and line of reasoning on the grounds
> that it's like the zen koan "does a dog have Buddha nature?"

If you take out the loaded jargon from this question, I think that
it's like asking if 300 cents in 12-EDO is "quintal" or "septimal." Is
it "septimal" in C-E-G-Bb? Is it "quintal" in C-E-G?

If we're going by my own categories, I'd probably hear it more like a
supermajor/subminor thing if you did this experiment in 14-EDO.
Whether or not I hear subminor chords "as septimal" in 14-EDO is a
question that to me makes no sense. What does it mean to hear even a
JI 6:7:9 "as septimal?" If I hear the root as 6 or 3, is that hearing
it as septimal? If I hear it as 4 or 1, is that septimal?

-Mike

> Nope. Sounds like supermajors and subminors to me. Does superpyth[7] sound 5-limit to you, too? If no, why not? If so, what do you think that means about your ability to perceive 7-limit harmony?

You've probably hit the nail on the head right there Igs. I'm not completely sure I've zoned in on 7-limit stuff, let alone 11 or 13. I mean, I can hear the awesomeness of 4:5:6:7, but I certainly haven't gained a feel of what most 7-limit intervals sound like like you probably have. It may even be because when I'm playing intervals that would fit better into 7-limit categorization with normal timbres, I'm playing warped timbres where there was still no beating between, say, the fifth and the fourth partial, and so instead of hearing a 9/7, I still hear a 5/4.

Does the fact that I may have conditioned myself to hear 5-limit everywhere (and probably nothing else) void the idea that someone can hear 5-limit harmony in bug? (or 11-edo hanson?) I think obviously not. It should show the opposite. One CAN hear those things. It just takes conditioning, the same way I could say you are conditioned *not* to hear extremely inaccurate 5-limit because of your use of harmonic timbres.

-John

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

> I hear Bm | Dmaj | Gmaj | Bbmaj=Amaj | Cmaj.

That's exactly it Mike. Of course without AP I think about it as

Cm | Ebmaj | Abmaj | Bbmaj | Db maj

On Fri, Feb 17, 2012 at 3:40 PM, jlmoriart <JlMoriart@...> wrote:
>
> > Nope. Sounds like supermajors and subminors to me. Does superpyth[7] sound 5-limit to you, too? If no, why not? If so, what do you think that means about your ability to perceive 7-limit harmony?
>
> You've probably hit the nail on the head right there Igs. I'm not completely sure I've zoned in on 7-limit stuff, let alone 11 or 13. I mean, I can hear the awesomeness of 4:5:6:7, but I certainly haven't gained a feel of what most 7-limit intervals sound like like you probably have. It may even be because when I'm playing intervals that would fit better into 7-limit categorization with normal timbres, I'm playing warped timbres where there was still no beating between, say, the fifth and the fourth partial, and so instead of hearing a 9/7, I still hear a 5/4.
>
> Does the fact that I may have conditioned myself to hear 5-limit everywhere (and probably nothing else) void the idea that someone can hear 5-limit harmony in bug? (or 11-edo hanson?) I think obviously not. It should show the opposite. One CAN hear those things. It just takes conditioning, the same way I could say you are conditioned *not* to hear extremely inaccurate 5-limit because of your use of harmonic timbres.

If you guys want to adopt this definition of "hearing a ratio," that's
totally fine, but just understand that you're not talking about some
sort of automatic, inborn auditory system response to ratios anymore,
thus removing the raison d'etre from much of the other things that
have been said. We're now talking about some sort of conscious
partitioning of the interval spectrum into different regions built
around different target intervals.

The sort of thing that we're talking about here is subject to the
particular illusion of there being "warped diatonic scales," where
intervals very far from their usual tuning resemble the usually tuned
ones because of some cleverly designed scale or musical context making
you hear them that way. This doesn't apply to the usual low-level
auditory system features we typically associate with ratios, meaning
things like periodicity buzz or virtual fundamentals or what not.

Beyond that, I think I'm going to retire from this discussion at this
point. I don't feel like anything I'm saying is getting through to
Igs, which makes me think that this is surely how Carl must have felt
to me when I was asking these sorts of questions to him back in the
day :)

(This is more a post to Igs rather than John, since I talk to John
about this stuff offlist pretty frequently.)

-Mike

--- In tuning@yahoogroups.com, "jlmoriart" <JlMoriart@...> wrote:
> Does the fact that I may have conditioned myself to hear 5-limit everywhere (and probably > nothing else) void the idea that someone can hear 5-limit harmony in bug? (or 11-edo
> hanson?) I think obviously not. It should show the opposite. One CAN hear those things. It
> just takes conditioning, the same way I could say you are conditioned *not* to hear
> extremely inaccurate 5-limit because of your use of harmonic timbres.

Well, I'm only concerned with figuring out under what conditions people hear certain things certain ways; my point wasn't necessarily that Bug doesn't exist, just that there's no way to distinguish it from Semaphore (and further, that it may be impossible to distinguish Semaphore from Barbados), and that depending on whether your hearing is aimed at the 7-limit, 5-limit, or 13-limit, you're necessarily going to interpret all those temperaments as being "the same", because there's no way to tune them so that they're distinct. But after Mike spent the last few months raking me over the coals for making snap judgments, I'm rescinding my use of the words "existence" and "impossible", and am instead just asking the open-ended question of "under what conditions will I hear a tuning as bug, vs. hearing it as beep, vs. hearing it as semaphore, vs. hearing it as barbados?" I am *quite* certain that insofar as it is possible for me to hear the difference between these temperaments, it may require more than tuning changes.

For instance, I'm pretty sure that no matter how you tune these temperaments (as long as the generator is between 266.67 cents and 240 cents), if you use approximate major/minor triads with normal harmonic timbres, I'm always going to hear beep or semaphore, never bug, never barbados. Well, maybe as you approach 240 cents, I'll start hearing the triads as 8:9:12 and 12:16:18, i.e. as 3-limit Blackwood. But maybe using different harmonies beyond those major and minor triads will allow me to hear different identities in different tunings, and maybe using different timbres will allow me to activate my bug hearing.

Really, what I'm interested in exploring is what it takes to activate the perception of temperaments. And you, John, are an excellent case-study.

-Igs

On 2/17/2012 2:56 AM, jlmoriart wrote:
>> I think father started making sense as a temperament while I was writing
>> "Yulegu Island" (which originally used a more harmonic timbre before I
>> did the current version with inharmonic timbres). I won't say it was
>> totally convincing, but I think it's enough to leave the possibility
>> open. Beep is another marginal temperament, and at times I've been
>> convinced it doesn't exist as a temperament, but with the right tuning
>> it might be usable.
>
> Concerning Beep, check out the chord progression I play here:
> http://www.youtube.com/watch?feature=player_detailpage&v=aIdWYl2e0es#t=176s
>
> I definitely hear five limit harmony exactly as beep describes it in that passage, and it's a comma pump to boot! Beep is one of my absolute favorite temperaments, second to hanson probably. I find it dead easy to hear, so count me as one data point for "exists".
>
> Do you hear it that way?

Bug is useful as a 5-limit temperament, but beep is a 7-limit extension that's somewhat marginal.

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Fri, Feb 17, 2012 at 3:07 PM, Mike Battaglia <battaglia01@...> wrote:
> > On Fri, Feb 17, 2012 at 2:57 PM, cityoftheasleep
> > <igliashon@...> wrote:
> >>
> >> I wonder if we took John's progression and retuned it to barbados[9] (~250-cent generator) if you two would still hear it as 5-limit? Or maybe this just means that supermajor and subminor chords aren't really "septimal" harmonies to you guys?
> >>
> >> -Igs
> >
> > I completely reject this question and line of reasoning on the grounds
> > that it's like the zen koan "does a dog have Buddha nature?"
>
> If you take out the loaded jargon from this question, I think that
> it's like asking if 300 cents in 12-EDO is "quintal" or "septimal." Is
> it "septimal" in C-E-G-Bb? Is it "quintal" in C-E-G?
>
> If we're going by my own categories, I'd probably hear it more like a
> supermajor/subminor thing if you did this experiment in 14-EDO.
> Whether or not I hear subminor chords "as septimal" in 14-EDO is a
> question that to me makes no sense. What does it mean to hear even a
> JI 6:7:9 "as septimal?" If I hear the root as 6 or 3, is that hearing
> it as septimal? If I hear it as 4 or 1, is that septimal?
>
> -Mike
>

What can "septimal" as a category in the realm of perception mean other than coincidence of partials at the seventh partial(s)?

6:7:9 certainly sounds "septimal" to me. Coincidences at the seventh partial(s) have a particular character. To paint with overly broad strokes, or describe in terms of general associations, I would say that septimal harmonies have either a bluesy/jazzy or ultra-romantic sounding quality to them.

Does this effect exist with "sine waves"? I doubt that there is much if any of this effect perceptible with septimal intervals in such tests. So what? I am not talking about ratios as abstract or magical entities, but as proportions between tones, in physical reality. Here, they create recognizable effects.

The perceived root of a chord doesn't affect whether there are coincidences at the seventh partial(s) or not.

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

> If we're going by my own categories, I'd probably hear it more like a
> supermajor/subminor thing if you did this experiment in 14-EDO.
> Whether or not I hear subminor chords "as septimal" in 14-EDO is a
> question that to me makes no sense. What does it mean to hear even a
> JI 6:7:9 "as septimal?" If I hear the root as 6 or 3, is that hearing
> it as septimal? If I hear it as 4 or 1, is that septimal?

You tell me! I'm trying to figure out why I have a tendency to want to call these chords 7-limit sonorities, while John wants to call them 5-limit. Personally, I use "subminor" to mean "septimal minor", because when I was introduced to those kinds of chords, they were explained to me as being 6:7:9 (or at least, 1/1-7/6-3/2). So I just equate "subminor" with "some chord similar in tuning to 6:7:9". I presume there's something about the 7th partial, like what Cameron was saying, like I can recognize (with harmonic timbres) that 6:7:9 is the name of a significant sonority with strong periodicity buzz and low sensory dissonance that can be accessed by flattening a minor 3rd a significant amount. I should whole-heartedly admit that this is categorical perception that I've learned--I've learned to categorize based on sonorities that display certain acoustic phenomena, into categories that are named after ratios.

But this begs a wholly different question: what makes a partial "the 7th partial"? If we use a remapped timbre where the 5th and 6th partials are now where the 6th and 7th partials used to be, John's experience seems to suggest that that leads to hearing subminor chords as simply "minor", like he lacks the category of subminor because of his experience with these warped timbres. If he moves along the generator spectrum of various temperaments, the partials move with him, leading to progressively less-harmonic timbres but never changing the sensory dissonance aspects. So what would be "subminor" for me is just a "more bell-like minor" for him. But at the same time, in these remapped timbres, if the overtone structure is stretched so that the 6th partial is where a normal 7th partial would be, why should that sound different? It's the same pitch as the old 7th partial, and I doubt the brain is registering the ordinality of the partials. I really wonder what's going on here!

-Igs

On Sat, Feb 18, 2012 at 2:08 AM, lobawad <lobawad@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> >
> > If we're going by my own categories, I'd probably hear it more like a
> > supermajor/subminor thing if you did this experiment in 14-EDO.
> > Whether or not I hear subminor chords "as septimal" in 14-EDO is a
> > question that to me makes no sense. What does it mean to hear even a
> > JI 6:7:9 "as septimal?" If I hear the root as 6 or 3, is that hearing
> > it as septimal? If I hear it as 4 or 1, is that septimal?
>
> What can "septimal" as a category in the realm of perception mean other than coincidence of partials at the seventh partial(s)?
>
> 6:7:9 certainly sounds "septimal" to me. Coincidences at the seventh partial(s) have a particular character. To paint with overly broad strokes, or describe in terms of general associations, I would say that septimal harmonies have either a bluesy/jazzy or ultra-romantic sounding quality to them.
>
> Does this effect exist with "sine waves"? I doubt that there is much if any of this effect perceptible with septimal intervals in such tests. So what? I am not talking about ratios as abstract or magical entities, but as proportions between tones, in physical reality. Here, they create recognizable effects.
>
> The perceived root of a chord doesn't affect whether there are coincidences at the seventh partial(s) or not.

There are a few things I could say here, since there are a lot of
psychoacoustic effects that could happen other than just with partials
coinciding, but this definition rules out more than just sine waves -
this also means that 4:6:7 when played with a square wave, or a
clarinet, isn't septimal, for instance. But even with sines, you can
get an effect - something like 6:7:9:11:13 is strong enough for me to
hear a VF, and also I hear periodicity buzz, and so on.

Also, what does it mean to hear partials "coinciding?" That the volume
of the harmonic that they have in common gets louder, so you hear it
sticking out?

-Mike

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

>
> There are a few things I could say here, since there are a lot of
> psychoacoustic effects that could happen other than just with partials
> coinciding, but this definition rules out more than just sine waves -
> this also means that 4:6:7 when played with a square wave, or a
> clarinet, isn't septimal, for instance. But even with sines, you can
> get an effect - something like 6:7:9:11:13 is strong enough for me to
> hear a VF, and also I hear periodicity buzz, and so on.

Certainly there is more going on than only coincidence of partials. I don't think we know how deep perception of frequency ratios really goes- and I think such things probably vary greatly among individuals, and perhaps variations are due not only to conditioning.

But coincidence of partials is something solid we can measure, predict, demonstrate, and has a long history as an accepted effect in musical perception.

And, it is possible by altering timbre, a la Sethares, to demonstrate that coincidence of partials is indeed a strong effect even in conflict with rational proportions of fundamental partials. I think that Sethares' work also demonstrates that coincidence of partials is NOT all there is to rational pitch structures, and that frequency ratios and/or other effects or catagories of perception also have power independent of spectra, else examples based on his work would be perfectly convincing, and I would say that they are definitely not perfectly convincing.

In short, coincidence of partials- the melting together of sounds that people have been raving about since days of yore- is not the only thing going on, but it is a big thing, and something about as concrete as can be when it comes to music.

It is true that there are gaps in coincidence in such spectra as presented by clarinet ensembles, but this can be used to demonstrate the strength of partial coincidence as well. A 5:3 with clarinets is quite striking.

>
> Also, what does it mean to hear partials "coinciding?" That the volume
> of the harmonic that they have in common gets louder, so you hear it
> sticking out?

That is part of it, I am sure. There are those who propose that perception of tonality in atonality in music can be attributed to the implications of partial coincidence in the whole of the piece seem to be, though. Spectral analysis does indicate that consistent spectral patterns can amass in the course of a piece, this is something you can easily verify yourself. But like anything else in music, I would say this is "a" thing, not "the" thing (there being no one "the" thing".

Another factor is the kind of "negative positive" quality of concordance that has been proposed by others- even if the partials in coincidence do not create a louder entity (there may be great phase cancellation for example), they present a pattern of non-discordance, so to speak. In acoustic practice intervals usually take a bit of time to settle in to concordance, and wobble in and out, drawing attention to both blending and "non-discordance", regardless of whether the blending pumps up the volume of the partials in question.

On Sat, Feb 18, 2012 at 12:17 PM, cityoftheasleep
<igliashon@...> wrote:
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > If we're going by my own categories, I'd probably hear it more like a
> > supermajor/subminor thing if you did this experiment in 14-EDO.
> > Whether or not I hear subminor chords "as septimal" in 14-EDO is a
> > question that to me makes no sense. What does it mean to hear even a
> > JI 6:7:9 "as septimal?" If I hear the root as 6 or 3, is that hearing
> > it as septimal? If I hear it as 4 or 1, is that septimal?
>
> You tell me!

NO YOU TELL ME AHHHHHHHHHHH

> I'm trying to figure out why I have a tendency to want to call these chords 7-limit sonorities, while John wants to call them 5-limit.

Here's a question: 267 cents. Did you always know that if you played
two tones that are 267 cents apart, that they'd sound the way they do?

-Mike

On Sat, Feb 18, 2012 at 5:20 PM, lobawad <lobawad@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > There are a few things I could say here, since there are a lot of
> > psychoacoustic effects that could happen other than just with partials
> > coinciding, but this definition rules out more than just sine waves -
> > this also means that 4:6:7 when played with a square wave, or a
> > clarinet, isn't septimal, for instance. But even with sines, you can
> > get an effect - something like 6:7:9:11:13 is strong enough for me to
> > hear a VF, and also I hear periodicity buzz, and so on.
>
> Certainly there is more going on than only coincidence of partials. I don't think we know how deep perception of frequency ratios really goes- and I think such things probably vary greatly among individuals, and perhaps variations are due not only to conditioning.

Right.

> But coincidence of partials is something solid we can measure, predict, demonstrate, and has a long history as an accepted effect in musical perception.

You're talking, again, about the volume of some common overtone being
raised? I'm not sure I perceive that for dyads as being anything but a
minor, secondary effect, about as strong as VFs are.

> In short, coincidence of partials- the melting together of sounds that people have been raving about since days of yore- is not the only thing going on, but it is a big thing, and something about as concrete as can be when it comes to music.

What do you mean when you say "melting together of sounds?" That sort
of thing sounds like you're talking about timbral fusion to me, which
has more to do with complex pitch perception than the volume of a
random harmonic being made louder...

> It is true that there are gaps in coincidence in such spectra as presented by clarinet ensembles, but this can be used to demonstrate the strength of partial coincidence as well. A 5:3 with clarinets is quite striking.

You know, part of the magic of this effect, which is basically the
same as beatlessness could also be that it's very fragile.

> Another factor is the kind of "negative positive" quality of concordance that has been proposed by others- even if the partials in coincidence do not create a louder entity (there may be great phase cancellation for example), they present a pattern of non-discordance, so to speak. In acoustic practice intervals usually take a bit of time to settle in to concordance, and wobble in and out, drawing attention to both blending and "non-discordance", regardless of whether the blending pumps up the volume of the partials in question.

Right; this wobble what I meant by fragile above. It still doesn't
answer to me the million dollar question though, which is to figure
out what aspect of all of this remains when you play music with sine
waves, like Aaron Johnson's melancholic:
http://www.akjmusic.com/audio/melancholic.mp3

This might just be close to pure tones though, and not actual pure
tones. It definitely seems like I'm hearing a few VFs pop in and out,
but even that's crazy to dump all of this on, because you can
arpeggiate chords and there will still be an effect.

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Sat, Feb 18, 2012 at 12:17 PM, cityoftheasleep
> <igliashon@...> wrote:
> > --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
> >
> > > If we're going by my own categories, I'd probably hear it more like a
> > > supermajor/subminor thing if you did this experiment in 14-EDO.
> > > Whether or not I hear subminor chords "as septimal" in 14-EDO is a
> > > question that to me makes no sense. What does it mean to hear even a
> > > JI 6:7:9 "as septimal?" If I hear the root as 6 or 3, is that hearing
> > > it as septimal? If I hear it as 4 or 1, is that septimal?
> >
> > You tell me!
>
> NO YOU TELL ME AHHHHHHHHHHH

You're the one who finds problems with however I try to define things; I don't know WTF I'm talking about, so why don't *you* propose something? We have all these words we use all the time to describe things, like "7-limit", "subminor", etc.--what do they mean?

> > I'm trying to figure out why I have a tendency to want to call these chords 7-limit
> > sonorities, while John wants to call them 5-limit.
>
> Here's a question: 267 cents. Did you always know that if you played
> two tones that are 267 cents apart, that they'd sound the way they do?

No, absolutely not. How could anyone know what something would sound like before they hear it?

-Igs

On Sun, Feb 19, 2012 at 6:17 PM, cityoftheasleep
<igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > > --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
> > >
> > > > If we're going by my own categories, I'd probably hear it more like a
> > > > supermajor/subminor thing if you did this experiment in 14-EDO.
> > > > Whether or not I hear subminor chords "as septimal" in 14-EDO is a
> > > > question that to me makes no sense. What does it mean to hear even a
> > > > JI 6:7:9 "as septimal?" If I hear the root as 6 or 3, is that hearing
> > > > it as septimal? If I hear it as 4 or 1, is that septimal?
> > >
> > > You tell me!
> >
> > NO YOU TELL ME AHHHHHHHHHHH
>
> You're the one who finds problems with however I try to define things; I don't know WTF I'm talking about, so why don't *you* propose something? We have all these words we use all the time to describe things, like "7-limit", "subminor", etc.--what do they mean?

It's not that I have a problem with your definitions dude, it's that I
don't know what they are... 7-limit refers to a ratio being tuned such
that its greatest odd-factor is 7, subminor means in the minor
category but flatter than usual...

> > > I'm trying to figure out why I have a tendency to want to call these chords 7-limit
> > > sonorities, while John wants to call them 5-limit.
> >
> > Here's a question: 267 cents. Did you always know that if you played
> > two tones that are 267 cents apart, that they'd sound the way they do?
>
> No, absolutely not. How could anyone know what something would sound like before they hear it?

So it seems to me that you've learned, after hearing it, that the
dyads in the 9-EDO chord, like 267 cents, are part of this larger
intervallic structure you might call "the 7-limit." John's envisioning
them as fitting into a larger intervallic structure that you might
call "the 5-limit." I mean, he's even saying that - right?

-Mike

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

> It's not that I have a problem with your definitions dude, it's that I
> don't know what they are...

...because I can never define them to your satisfaction, because they're a bit vague and nebulous even to me. All I can say is that something sounds "septimal" to me when it's tuned close to a 7-limit ratio.

> So it seems to me that you've learned, after hearing it, that the
> dyads in the 9-EDO chord, like 267 cents, are part of this larger
> intervallic structure you might call "the 7-limit." John's envisioning
> them as fitting into a larger intervallic structure that you might
> call "the 5-limit." I mean, he's even saying that - right?

Yeah, sounds like it. So, why's it a 5-limit interval to him and a 7-limit interval to me?

-Igs

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Sat, Feb 18, 2012 at 5:20 PM, lobawad <lobawad@...> wrote:
> >
> > --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
> >
> > > There are a few things I could say here, since there are a lot of
> > > psychoacoustic effects that could happen other than just with partials
> > > coinciding, but this definition rules out more than just sine waves -
> > > this also means that 4:6:7 when played with a square wave, or a
> > > clarinet, isn't septimal, for instance. But even with sines, you can
> > > get an effect - something like 6:7:9:11:13 is strong enough for me to
> > > hear a VF, and also I hear periodicity buzz, and so on.
> >
> > Certainly there is more going on than only coincidence of partials. I don't think we know how deep perception of frequency ratios really goes- and I think such things probably vary greatly among individuals, and perhaps variations are due not only to conditioning.
>
> Right.
>
> > But coincidence of partials is something solid we can measure, predict, demonstrate, and has a long history as an accepted effect in musical perception.
>
> You're talking, again, about the volume of some common overtone being
> raised? I'm not sure I perceive that for dyads as being anything but a
> minor, secondary effect, about as strong as VFs are.
>
> > In short, coincidence of partials- the melting together of sounds that people have been raving about since days of yore- is not the only thing going on, but it is a big thing, and something about as concrete as can be when it comes to music.
>
> What do you mean when you say "melting together of sounds?" That sort
> of thing sounds like you're talking about timbral fusion to me, which
> has more to do with complex pitch perception than the volume of a
> random harmonic being made louder...
>
> > It is true that there are gaps in coincidence in such spectra as presented by clarinet ensembles, but this can be used to demonstrate the strength of partial coincidence as well. A 5:3 with clarinets is quite striking.
>
> You know, part of the magic of this effect, which is basically the
> same as beatlessness could also be that it's very fragile.
>
> > Another factor is the kind of "negative positive" quality of concordance that has been proposed by others- even if the partials in coincidence do not create a louder entity (there may be great phase cancellation for example), they present a pattern of non-discordance, so to speak. In acoustic practice intervals usually take a bit of time to settle in to concordance, and wobble in and out, drawing attention to both blending and "non-discordance", regardless of whether the blending pumps up the volume of the partials in question.
>
> Right; this wobble what I meant by fragile above. It still doesn't
> answer to me the million dollar question though, which is to figure
> out what aspect of all of this remains when you play music with sine
> waves, like Aaron Johnson's melancholic:
> http://www.akjmusic.com/audio/melancholic.mp3
>
> This might just be close to pure tones though, and not actual pure
> tones. It definitely seems like I'm hearing a few VFs pop in and out,
> but even that's crazy to dump all of this on, because you can
> arpeggiate chords and there will still be an effect.
>
> -Mike
>

First of all, sound perception is surely not conducted in infinitely narrow successive discrete "bins". Where vertical begins and horizontal ends is extremely fuzzy, even for robot ears. Is monody in a cathedral monody? Only on paper. Does air start and stop vibrating instantly? No. For human ears, windows of perception are not only wide, but vary immensely. So it is to be expected that theoretically vertical effects will carry to the horizontal, and vice versa.

In response to the rest of what you are saying, you are insisting on addressing increase in amplitude of coinciding partials even after I specifically said that that can only be a possible effect and certainly cannot be all there is to it, as partial coincidence, by virtue of phase cancellation, can conceivably lower volume of partials in question.

"Whatever" it is about the coinciding of partials, they do coincide. "Whatever" causes musical tones in simple frequency ratios to be distinct from tones in complex ratios, they are distinct.

Do you have no way of describing "that sound", without using "scientific words"? I find it hard to believe that you do not perceive the "melting together"- this would make you the first musician I've come across who does not, immediately or shortly thereafter, recognize the effect in question. Some hate it, by the way- an Austrian singer called it "stiff and unmoving", and after thinking about it for a while, I was able to hear what she meant.

On Mon, Feb 20, 2012 at 1:02 AM, cityoftheasleep <igliashon@...>
wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > It's not that I have a problem with your definitions dude, it's that I
> > don't know what they are...
>
> ...because I can never define them to your satisfaction, because they're a
> bit vague and nebulous even to me. All I can say is that something sounds
> "septimal" to me when it's tuned close to a 7-limit ratio.

Odd-limit? Prime-limit? Are 7/5 and 10/7 septimal?

> > So it seems to me that you've learned, after hearing it, that the
> > dyads in the 9-EDO chord, like 267 cents, are part of this larger
> > intervallic structure you might call "the 7-limit." John's envisioning
> > them as fitting into a larger intervallic structure that you might
> > call "the 5-limit." I mean, he's even saying that - right?
>
> Yeah, sounds like it. So, why's it a 5-limit interval to him and a 7-limit
> interval to me?

Well if you agree with that, why isn't that all there is to it? He's
relating to the chord differently than you are, because when he hears
the dyads in that chord, he doesn't intuitively know that the minor
third "is 7/6" and "can do" all of the things that 7/6 "can do" (like
be on top of a 4:5:6:7 chord and sound just and otonal and so on) and
all that.

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Mon, Feb 20, 2012 at 1:02 AM, cityoftheasleep <igliashon@...>
> wrote:

> > ...because I can never define them to your satisfaction, because they're a
> > bit vague and nebulous even to me. All I can say is that something sounds
> > "septimal" to me when it's tuned close to a 7-limit ratio.
>
> Odd-limit? Prime-limit? Are 7/5 and 10/7 septimal?

I guess odd-limit? And yeah, I think 7/5 and 10/7 are septimal...why wouldn't I?

> > Yeah, sounds like it. So, why's it a 5-limit interval to him and a 7-limit
> > interval to me?
>
> Well if you agree with that, why isn't that all there is to it? He's
> relating to the chord differently than you are, because when he hears
> the dyads in that chord, he doesn't intuitively know that the minor
> third "is 7/6" and "can do" all of the things that 7/6 "can do" (like
> be on top of a 4:5:6:7 chord and sound just and otonal and so on) and
> all that.

Well, I'm asking *why* he relates to the chord differently than I do. What factors in his life and learning (or in mine) have led us to disagree about whether a chord represents some ratio or some other ratio?

If it's because he's just never learned to recognize 7-limit JI, then it's consistent with what I was postulating long ago--that what temperaments you can or cannot recognize depend on what kind of JI you can or cannot recognize. However, if he normally could recognize subminor chords as being distinct from minor chords and as being closer to 6:7:9 than 10:12:15, *but* he still hears this bug progression as being in a 5-limit temperament, then I'd have to say "aw, fiddlesticks, that means something is going on here that's not consistent with my current understanding, so it's back to the drawing-board for me!".

-Igs

On Mon, Feb 20, 2012 at 4:27 PM, cityoftheasleep <igliashon@...>
wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> >
> > On Mon, Feb 20, 2012 at 1:02 AM, cityoftheasleep <igliashon@...>
> > wrote:
>
> > > ...because I can never define them to your satisfaction, because
> > > they're a
> > > bit vague and nebulous even to me. All I can say is that something
> > > sounds
> > > "septimal" to me when it's tuned close to a 7-limit ratio.
> >
> > Odd-limit? Prime-limit? Are 7/5 and 10/7 septimal?
>
> I guess odd-limit? And yeah, I think 7/5 and 10/7 are septimal...why
> wouldn't I?

Is 600 cents in 12-EDO septimal?

> > Well if you agree with that, why isn't that all there is to it? He's
> > relating to the chord differently than you are, because when he hears
> > the dyads in that chord, he doesn't intuitively know that the minor
> > third "is 7/6" and "can do" all of the things that 7/6 "can do" (like
> > be on top of a 4:5:6:7 chord and sound just and otonal and so on) and
> > all that.
>
> Well, I'm asking *why* he relates to the chord differently than I do. What
> factors in his life and learning (or in mine) have led us to disagree about
> whether a chord represents some ratio or some other ratio?

Probably just that you've spent more time playing 7-limit harmony than
he has. I think there's a lot more that goes into the perception of a
chord than how easily it fuses into a single virtual pitch or what
have you.

> If it's because he's just never learned to recognize 7-limit JI, then it's
> consistent with what I was postulating long ago--that what temperaments you
> can or cannot recognize depend on what kind of JI you can or cannot
> recognize. However, if he normally could recognize subminor chords as being
> distinct from minor chords and as being closer to 6:7:9 than 10:12:15, *but*
> he still hears this bug progression as being in a 5-limit temperament, then
> I'd have to say "aw, fiddlesticks, that means something is going on here
> that's not consistent with my current understanding, so it's back to the
> drawing-board for me!".

Am I correct that the point of the paragraph above is that you want to
advance this definition of "recognize a temperament," which in turn
implies another perceptually-oriented definition of temperament,
because you think that it leads to a more sensible interpretation of
regular temperament theory? Or have I misunderstood the above?

-Mike

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

> > > Odd-limit? Prime-limit? Are 7/5 and 10/7 septimal?
> >
> > I guess odd-limit? And yeah, I think 7/5 and 10/7 are septimal...why
> > wouldn't I?
>
> Is 600 cents in 12-EDO septimal?

It's an irrational interval, so strictly-speaking, no; but as a naked dyad devoid of context, I'd say that now that I know what 7/5 sounds like, I hear 600 cents as strongly resembling 7/5, and thus giving off a moderate septimal flavor. But that's just me. With sufficient training I might be able to say it's more of septendecimal interval (17-limit? Did I say that right?), owing to its great proximity to 17/12. But I don't have much in the way of 17-limit categories, so for now I'll go with septimal.

> > > Well if you agree with that, why isn't that all there is to it? He's
> > > relating to the chord differently than you are, because when he hears
> > > the dyads in that chord, he doesn't intuitively know that the minor
> > > third "is 7/6" and "can do" all of the things that 7/6 "can do" (like
> > > be on top of a 4:5:6:7 chord and sound just and otonal and so on) and
> > > all that.
> >
> > Well, I'm asking *why* he relates to the chord differently than I do. What
> > factors in his life and learning (or in mine) have led us to disagree about
> > whether a chord represents some ratio or some other ratio?
>
> Probably just that you've spent more time playing 7-limit harmony than
> he has. I think there's a lot more that goes into the perception of a
> chord than how easily it fuses into a single virtual pitch or what
> have you.

I completely agree.

> Am I correct that the point of the paragraph above is that you want to
> advance this definition of "recognize a temperament," which in turn
> implies another perceptually-oriented definition of temperament,
> because you think that it leads to a more sensible interpretation of
> regular temperament theory? Or have I misunderstood the above?

Pretty much. I just think temperament theory is incomplete if we leave perception out of it. Or rather, I think temperament *music* theory is incomplete if we leave perception out of it; the math part is a polished gem of elegance. I just think it's fascinating that two people who have studied JI can interpret the same sound in such different ways.

Another thing I'm really curious about is whether John thinks the tempered chords sound out-of-tune? I wonder what the relevance of rational identities might be to someone who uses spectrally-mapped timbres....

-Igs

On Mon, Feb 20, 2012 at 5:01 PM, cityoftheasleep <igliashon@...>
wrote:
>
> It's an irrational interval, so strictly-speaking, no; but as a naked dyad
> devoid of context, I'd say that now that I know what 7/5 sounds like, I hear
> 600 cents as strongly resembling 7/5, and thus giving off a moderate
> septimal flavor. But that's just me. With sufficient training I might be
> able to say it's more of septendecimal interval (17-limit? Did I say that
> right?), owing to its great proximity to 17/12. But I don't have much in the
> way of 17-limit categories, so for now I'll go with septimal.

Does this means that you're used to how it fits into larger 7-limit
chords or something? And not 17-limit ones?

> > Am I correct that the point of the paragraph above is that you want to
> > advance this definition of "recognize a temperament," which in turn
> > implies another perceptually-oriented definition of temperament,
> > because you think that it leads to a more sensible interpretation of
> > regular temperament theory? Or have I misunderstood the above?
>
> Pretty much. I just think temperament theory is incomplete if we leave
> perception out of it. Or rather, I think temperament *music* theory is
> incomplete if we leave perception out of it; the math part is a polished gem
> of elegance. I just think it's fascinating that two people who have studied
> JI can interpret the same sound in such different ways.
>
> Another thing I'm really curious about is whether John thinks the tempered
> chords sound out-of-tune? I wonder what the relevance of rational identities
> might be to someone who uses spectrally-mapped timbres....

OK, so then the point of this conversation, and prior ones, is that
you want to redefine the word "temperament." So nobody call me a
terminology nazi then, or act like I'm nitpicking things or whatever,
because that's the entire point of the discussion.

I think this might be a useful concept, but it might be better if you
gave this concept a different name than "temperament," which already
has an agreed-upon mathematical definition.

I like this sort of thinking. However, is there anything in this
definition which would require the reference objects to be limited to
JI?

-Mike

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

> Does this means that you're used to how it fits into larger 7-limit
> chords or something? And not 17-limit ones?

Nah, just that 600 cents sounds like this 7/5 thing...or maybe 7/5 is like this 600 cents thing but without beating. But that's just the naked dyad.

> OK, so then the point of this conversation, and prior ones, is that
> you want to redefine the word "temperament." So nobody call me a
> terminology nazi then, or act like I'm nitpicking things or whatever,
> because that's the entire point of the discussion.

I suppose...I was thinking of it more as an "expansion" or "elaboration" of the definition.

> I think this might be a useful concept, but it might be better if you
> gave this concept a different name than "temperament," which already
> has an agreed-upon mathematical definition.

I can see that. Trouble is, I think "temperament" fits what I'm talking about better than it fits the mathematical side of things, so I can't think of a good word to use instead.

> I like this sort of thinking. However, is there anything in this
> definition which would require the reference objects to be limited to
> JI?

I don't think so--observations of people hearing JI as "out of tune" relative to 12-TET suggest anything could be a reference point.

-Igs

On Mon, Feb 20, 2012 at 7:25 PM, cityoftheasleep <igliashon@...>
wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > OK, so then the point of this conversation, and prior ones, is that
> > you want to redefine the word "temperament." So nobody call me a
> > terminology nazi then, or act like I'm nitpicking things or whatever,
> > because that's the entire point of the discussion.
>
> I suppose...I was thinking of it more as an "expansion" or "elaboration"
> of the definition.

The reason it's not is that temperaments are defined as mathematical
objects; they describe the intonational structure of tuning systems.
They're not supposed to describe the nuances of musical perception,
except for whichever ones have to do with ratios.

We might assume that exposure to a tuning system might lead someone to
tailor their perception to it in certain ways, for example, but the
temperament always exists as the thing that they're tailoring it to,
even if they haven't finished tailoring yet.

> > I like this sort of thinking. However, is there anything in this
> > definition which would require the reference objects to be limited to
> > JI?
>
> I don't think so--observations of people hearing JI as "out of tune"
> relative to 12-TET suggest anything could be a reference point.

In psychology, a term which is very relevant to the fundamental thing
that you're talking about - ones mental representation for an interval
- is the term "schema." Read here

http://en.wikipedia.org/wiki/Schema_(psychology)

This actually seems to be quite accurate in describing the sort of
phenomenon we're talking about, so I'm going to coin that term from
now on. This is basically the same thing as what I've called an
interval "category," except categorical perception involves an
additional notion of perceptual warping in which stimuli are "snapped"
into the nearest existing schema and in which all intervals within a
schema are harder to tell apart than inter-schema intervals.
Schemata can exist without categorical perception.

All of the questions I've been asking you have been equivalent, in
some form, to: do you believe that people have to form schemata for JI
intervals, or do you believe that the auditory system somehow comes
with pre-activated ones?

I don't believe the latter at all, and you seem to agree. However, I
do think that there are various phenomena that JI intervals can cause
which you can "assimilate" into an existing schema. This is what I
currently believe the "correct paradigm" is.

This leads to another question that I've been trying to get at in
these discussions. Which aspect of reality are regular temperaments
supposed to model?

1) Noumenal reality(?), or at least mathematical reality, in which we
just deal with frequencies and ratios
2) Phenomenal reality, independent of any listener's cognization of
the phenomena that are occurring, in which we just deal with things
like periodicity buzz and beatlessness and virtual pitch integration
3) Symbolic/schematic reality, in which we only deal with what the
listener thinks is happening and their associations with those things

You seem to think either #2 or #3, but there's no right answer,
because regular temperaments are simply too primitive in their current
form to distinguish between any of these things at all. They can model
any aspect of any of these things which end up mathematically reducing
to an association from things in Q to things in Z^n. Which is also
part of their strength: they can model the extent to which
psychoacoustic phenomena occur, or they can model the extent to
someone's internal and symbolic universe is intelligible, or they can
just be mathematical objects for any composer to interpret any way
they deem to be musically useful.

I don't think you can pick any number from the list of three that I
gave which will cause all of the statements made about regular
temperaments to make sense with one another, and that coming to a full
understanding of the above is the correct way to think about all of
this stuff. You might also want to question if it's reasonable to
expect some confusion between #2 and #3 on a mailing list that's
typically spent years learning how to schematically represent
intervals with various phenomenal qualities.

-Mike

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

> I can see that. Trouble is, I think "temperament" fits what I'm talking about better than it fits the mathematical side of things, so I can't think of a good word to use instead.

That sounds interesting, but I don't know what you guys are talking about.

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

> The reason it's not is that temperaments are defined as mathematical
> objects; they describe the intonational structure of tuning systems.
> They're not supposed to describe the nuances of musical perception,
> except for whichever ones have to do with ratios.
>
> We might assume that exposure to a tuning system might lead someone to
> tailor their perception to it in certain ways, for example, but the
> temperament always exists as the thing that they're tailoring it to,
> even if they haven't finished tailoring yet.

I guess that's a good point. I think what I'm talking about is more how we can use temperaments to describe or model perception, so defining "temperament" in the mathematical sense is probably best.

> This actually seems to be quite accurate in describing the sort of
> phenomenon we're talking about, so I'm going to coin that term from
> now on. This is basically the same thing as what I've called an
> interval "category," except categorical perception involves an
> additional notion of perceptual warping in which stimuli are "snapped"
> into the nearest existing schema and in which all intervals within a
> schema are harder to tell apart than inter-schema intervals.
> Schemata can exist without categorical perception.

Interesting. I like where this is going.

> All of the questions I've been asking you have been equivalent, in
> some form, to: do you believe that people have to form schemata for JI
> intervals, or do you believe that the auditory system somehow comes
> with pre-activated ones?
>
> I don't believe the latter at all, and you seem to agree. However, I
> do think that there are various phenomena that JI intervals can cause
> which you can "assimilate" into an existing schema. This is what I
> currently believe the "correct paradigm" is.

Thank heavens we're finally on the same page! The phenomena of JI intervals are in some sense objective, but the schemata associated with them are not. One's ability to assimilate these phenomena into schemata is directly proprotional to one's ability to perceive these phenomena.

> This leads to another question that I've been trying to get at in
> these discussions. Which aspect of reality are regular temperaments
> supposed to model?

Indeed! Or perhaps, what happens when we try to use regular temperaments to model different aspects of reality?

> I don't think you can pick any number from the list of three that I
> gave which will cause all of the statements made about regular
> temperaments to make sense with one another, and that coming to a full
> understanding of the above is the correct way to think about all of
> this stuff. You might also want to question if it's reasonable to
> expect some confusion between #2 and #3 on a mailing list that's
> typically spent years learning how to schematically represent
> intervals with various phenomenal qualities.

Right-o. We finally understand each other. Now, onward! Or rather, backward, to the question of how these schemata are formed, what phenomena we rely on (or don't) in order to form them, and how some of us come to from different schemata based on similar stimuli (which is what I'm trying to figure out about me and John).

-Igs

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
> The phenomena of JI intervals are in some sense objective, but the >schemata associated with them are not.

Yes!

Now, to Mike: if you agree with this, can you now see that it is not "semantics" when I insist on Just Intonation being intonation "of" something, but a matter of fundamental understanding? Calling any rational pitch structure "JI" is to conflate something which marks "phenomena in some sense objective" with "schemata associated with these phenomena".

>One's ability to assimilate these phenomena into schemata is >directly proprotional to one's ability to perceive these phenomena.

I don't know about "directly", but this seems sensible. Have to think about it.

On Mon, Feb 20, 2012 at 8:22 PM, cityoftheasleep <igliashon@...>
wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > I don't believe the latter at all, and you seem to agree. However, I
> > do think that there are various phenomena that JI intervals can cause
> > which you can "assimilate" into an existing schema. This is what I
> > currently believe the "correct paradigm" is.
>
> Thank heavens we're finally on the same page! The phenomena of JI
> intervals are in some sense objective, but the schemata associated with them
> are not. One's ability to assimilate these phenomena into schemata is
> directly proprotional to one's ability to perceive these phenomena.

I don't know what you mean by "objective." I think they're objective
in the same sense that being able to deadlift 400 pounds is objective.
There's lots of adaptations which take place with response to musical
training, many of which preattentive, neurological, and even cochlear
(!). Aside from the now infamous "Frere Jacques" study

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2565400/

There are things like otoacoustic emissions in the cochlea, which is
sound generated in the inner ear. These things are still poorly
understood, but are shown to improve things like pitch discrimination.
Notably, for people who are hearing impaired, these things don't turn
up as much. This is why if you go to an audiologist and get your
hearing tested, they're going to play sine waves in your ear and
literally measure the amplitude of the most prominent combination tone
(or "DPOAE") which results. Even more notably, cochlear adaptations
related to otoacoustic emissions have been shown to occur with respect
to musical training as well. For example, these studies indicate that
it does

http://www.ncbi.nlm.nih.gov/pubmed/12204350 - shows that pitch
discrimination is improved near SOAE frequencies
http://www.ncbi.nlm.nih.gov/pubmed/8128847 - shows that in the
presence of SOAE's, pitch distances seem to be exagerrated
http://www.ncbi.nlm.nih.gov/pubmed/14552425 - indicated that TOAE's
are suppressed more for musicians than nonmusicians

More notable is this study, which demonstrates

http://web.ics.purdue.edu/~gbidelma/Bidelman%20et%20al%20(2011)%20-%20Enhanced%20brainstem%20encoding%20predicts%20musicians%20perceptual%20advantages%20with%20pitch.pdf

Which sums up much of the above, goes into additional research showing
how OAE's are controlled centrally by the brain, and then measures
pre-attentive aspects of music perception which change in response to
training, showing even pre-attentive neural correlates for things like
categorical perception (!). This paragraph says it all

"The close correspondence between brainstem responses and
discrimination performance supports the idea that enhanced
representation of perceptually salient aspects of musical pitch may be
rooted subcortically at a sensory stage of processing. Traditionally
neglected in discussions of the neurobiology of music, we find that the
brainstem plays an active role in not only the neural encoding of
musically relevant sound but probably influences later processes
governing music perception. Our findings further show that musical
expertise modulates pitch encoding mechanisms that are not under
direct attentional control (cf. Tervaniemi et al., 2005)."

So no, I don't think even what I called "phenomena" are all that objective.

> > This leads to another question that I've been trying to get at in
> > these discussions. Which aspect of reality are regular temperaments
> > supposed to model?
>
> Indeed! Or perhaps, what happens when we try to use regular temperaments
> to model different aspects of reality?

We bulldoze all over that stuff and replace it with ratios.

-Mike

Whoops, sent too soon. The last part:

On Mon, Feb 20, 2012 at 8:22 PM, cityoftheasleep
<igliashon@...> wrote:
>
> Right-o. We finally understand each other. Now, onward! Or rather,
> backward, to the question of how these schemata are formed, what phenomena
> we rely on (or don't) in order to form them, and how some of us come to from
> different schemata based on similar stimuli (which is what I'm trying to
> figure out about me and John).

I don't know about relying on phenomena, but "how to use it" sounds
like a good schematic criterion for an interval to me.

For instance, consider 1050 cents in 16-EDO. Is it a "neutral
seventh?" Now try playing something like (in Armodue notation)
1-5-9b-3b' -> 1-5-8b-1' -> 1-4b-6-1'. It's like bVII -> IV -> I or
something. If you want to hear it, it's the chord progression I'm
doing at the end of the main phrase in this video

http://www.youtube.com/watch?v=y8MXbFtw4rM&feature=related

Also the 9-EDO version here (do these sound like "7-limit" chords to you?)

http://www.youtube.com/watch?v=KV_MzdtU2WQ&feature=related

So now, to me, 1050 cents sounds something like "IV/IV" when used that
way. Whether that means 16/9 or 4/3 of 4/3 or what have you, I don't
know. I do know that 1050 cents is also a "major seventh," which you
can readily hear by playing 1-4b-6-9b. It's also a "neutral seventh,"
which you can probably do something useful with too. It also fits into
lots of nice new xenharmonic chords because it's also 11/6, so you can
probably construct something useful out of this. Most importantly,
14\16 can be any of these things or maybe many of them at the same
time.

Internalizing harmonic relationships like this, which might be
considered a non-JI obsessed form of Boomsliter and Creel's "extended
reference," totally change the perception of intervals for me. An even
more dramatic case for mavila was 5/2, which is both a "major tenth"
in one diatonic sense, and a "minor tenth" in another (IV/IV/IV). If
you can really hear the latter sense it's crazy, because it's not just
a really flat major tenth, it's also a really sharp minor tenth made
up of really sharp fourths.

Keenan's described having similar experiences with pelog; he's stated
that learning that there were "empats" everywhere (3/2's) changed his
perception of it from C E F^ G Bv C to something a bit more
harmonically connected by 3/2. For instance, C-F^ is supposed to be
4/3, and Bv-E is also supposed to be 4/3.

This sort of thing has also factored prominently into my perception of
complex dyads like 9/7; once I learned that they sound great as part
of 4:7:9, that colors the perception of 436 itself to be more
"abstract" in an interesting way, as though it's hinting at something
(or multiple things) rather than just being this sharp nonsense
interval. I always imagine 9/7 in this new way now. This has in turn
affected my perception of things like 245/243-tempered 1/1-9/7-5/3
chords.

I assume this is the same sort of thing that Cameron was talking about
when he mentioned how 81/64 is two 9/8's; he'd just learned that
relationship just like someone learns any of the above.

Sometimes this breaks down though, as just happened with Gene's
example, where he could hear all of these larger chords being implied
by the triads he was playing but where many of the rest of us just
heard random stuff going on, without the benefit of that mental
backdrop.

Anyways, seems to me that this effect - "part of the schematic
representation of an interval is its musical context" - is what's
differing between you and John. You've learned this "7-limit" context
for the intervals being played, maybe just the 7/6 or something, and
have some understanding of how they're these distorted versions of
things used in larger 7-limit chords, and that the chord is itself a
distorted version of some 7-limit chord, and John doesn't have that.

-Mike

On Mon, Feb 20, 2012 at 11:34 PM, lobawad <lobawad@...> wrote:
>
> --- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
> > The phenomena of JI intervals are in some sense objective, but the
> > >schemata associated with them are not.
>
> Yes!
>
> Now, to Mike: if you agree with this, can you now see that it is not
> "semantics" when I insist on Just Intonation being intonation "of"
> something, but a matter of fundamental understanding? Calling any rational
> pitch structure "JI" is to conflate something which marks "phenomena in some
> sense objective" with "schemata associated with these phenomena".

Yes, and I always knew that's what you were saying, but I'm not sure
that the term JI was used consistently in the sense you describe. Lots
of people don't seem to have distinguished between these two things,
and others just describe it in a noumenal or mathematiacl sense.

> >One's ability to assimilate these phenomena into schemata is >directly
> > proprotional to one's ability to perceive these phenomena.
>
> I don't know about "directly", but this seems sensible. Have to think
> about it.

If context is part of a schema, it's pretty easy to perceive lots of phenomena.

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Mon, Feb 20, 2012 at 11:34 PM, lobawad <lobawad@...> wrote:
> >
> > --- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@> wrote:
> > > The phenomena of JI intervals are in some sense objective, but the
> > > >schemata associated with them are not.
> >
> > Yes!
> >
> > Now, to Mike: if you agree with this, can you now see that it is not
> > "semantics" when I insist on Just Intonation being intonation "of"
> > something, but a matter of fundamental understanding? Calling any rational
> > pitch structure "JI" is to conflate something which marks "phenomena in some
> > sense objective" with "schemata associated with these phenomena".
>
> Yes, and I always knew that's what you were saying, but I'm not sure
> that the term JI was used consistently in the sense you describe.

The older references in the university library here have recently been removed and new books brought in, but a good load of reading here and in a neighboring country, in three languages, has convinced
me that "just intonation" was so conceived. It is working with and talking to other musicians from various countries that has convinced me that this remains the mainstream conception.

>Lots
> of people don't seem to have distinguished between these two things,
> and others just describe it in a noumenal or mathematiacl sense.

"Noumenal", LOL. Good description. I'd say "reified". Yes, it is true that it may be too late to correct the gross blunder of the "JI school" in this matter.

On Tue, Feb 21, 2012 at 2:01 AM, lobawad <lobawad@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> >
> > On Mon, Feb 20, 2012 at 11:34 PM, lobawad <lobawad@...> wrote:
>
> > > Now, to Mike: if you agree with this, can you now see that it is not
> > > "semantics" when I insist on Just Intonation being intonation "of"
> > > something, but a matter of fundamental understanding? Calling any
> > > rational
> > > pitch structure "JI" is to conflate something which marks "phenomena
> > > in some
> > > sense objective" with "schemata associated with these phenomena".
> >
> > Yes, and I always knew that's what you were saying, but I'm not sure
> > that the term JI was used consistently in the sense you describe.
>
> The older references in the university library here have recently been
> removed and new books brought in, but a good load of reading here and in a
> neighboring country, in three languages, has convinced
> me that "just intonation" was so conceived. It is working with and talking
> to other musicians from various countries that has convinced me that this
> remains the mainstream conception.

OK, but it's also noteworthy that the "mainstream" conception often
typically treat things as though the usual 12-based or meantone-based
schemata are the only ones which exist at all. The only people that I
know of considering other possible schemata are microtonalists (or
ethnomusicologists, or people playing both western and gamelan music,
etc).

For instance, native Balinese listeners tend to hear 5:6:7:8:9:10 in
terms of being "slendro," in the same way that we might hear
8:9:10:11:12:13:15:16 as being "the diatonic scale." This is
exemplified in the tradition of genggong, which Keenan has two good
examples of here

http://soundcloud.com/keenanpepper

and also a good video here

http://www.youtube.com/watch?v=8Dj2O9DxYuM

you kind of have to listen to how the harmonics from the genggong line
up with the melody on the flute to hear the effect.

Is this JI, even though it's a 7-limit tuning being used to intone
slendro now instead of the diatonic scale? I don't think that the
mainstream conception has any opinion at all on that question.

-Mike