Pure-Octave Temperament Error

Did we ever figure this out? The discussion devolved into the old tug-o-war about the relative importance of concordance in music, but I really want to figure out the right way to compute pure-octave rank-1 temperament error, so that I can re-do my subgroup badness rankings. I would really like this project not to get lost in the shuffle.

-Igs

On Sat, Jan 7, 2012 at 7:50 PM, cityoftheasleep <igliashon@...> wrote:
>
> Did we ever figure this out? The discussion devolved into the old tug-o-war about the relative importance of concordance in music, but I really want to figure out the right way to compute pure-octave rank-1 temperament error, so that I can re-do my subgroup badness rankings. I would really like this project not to get lost in the shuffle.

Graham suggested using STD error, and I think it's a good idea.

-Mike

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

> Graham suggested using STD error, and I think it's a good idea.
>
> -Mike

I don't know the math behind it, but what are its conceptual advantages over other methods? Any input from Carl and Gene?

-Igs

My advice is to steer clear of anything called "STD error". -C.

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

> I don't know the math behind it, but what are its conceptual
> advantages over other methods? Any input from Carl and Gene?
>
> -Igs
>

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
>
> > Graham suggested using STD error, and I think it's a good idea.
> >
> > -Mike
>
> I don't know the math behind it, but what are its conceptual advantages over other methods? Any input from Carl and Gene?

It doesn't differ significantly from TE error and tuning, and it is very easily computed. But I thought Graham was the one who complained when I called it "self-recommending", so you'd better ask him.

Igs wrote:

> Did we ever figure this out?

Since you decided on pure octaves, I'm going to implement
max subgroup error with an option to turn Tenney weighting
on or off.

> 2-less Pentads:

Since we're using pure octaves, you get 2 for free. It
means these could all be 6-D subgroups with the 2 tacked
on -- they'd have the same error. Note this is different
than saying

> 3:5:7:11:13 = 2.5/3.7/3.11/3.13/3

which by the way is not true, since in the former the
error of 3:1 matters whereas in the latter it doesn't.

Also, subgroups bases need to be more than pairwise
coprime, I think -- they need to be linearly independent.
I suggest the following:

* getting all the unique (lowest terms) ratios of the
first 15 odd numbers

* finding all 4-combinations of them

* casting out the sets that aren't linearly independent

* calculating the given ET's error for each, *assuming
the best available val is used for each*

To cast out the bases that aren't linearly independent
I think one just reduces them to normal interval lists
and then casts out duplicates

http://xenharmonic.wikispaces.com/Normal+lists#x-Normal%20interval%20lists

So I'll code that up and then I'll give you the tool,
leaving enough time for Gene or someone to say if I
got it wrong.

-Carl

STD error may be easier to calculate and it has the conceptual advantage that it doesn't evoke an optimization that you aren't using. The result is practically identical to TE error.

Graham

------Original message------
From: cityoftheasleep <igliashon@...>
To: <tuning@yahoogroups.com>
Date: Sunday, January 8, 2012 3:11:04 AM GMT-0000
Subject: [tuning] Re: Pure-Octave Temperament Error

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

> Graham suggested using STD error, and I think it's a good idea.
>
> -Mike

I don't know the math behind it, but what are its conceptual advantages over other methods? Any input from Carl and Gene?

-Igs

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

> Also, subgroups bases need to be more than pairwise
> coprime, I think -- they need to be linearly independent.

For example, pairwise coprime would exclude 5.7.15
ordinary coprime would include 3.7.9
linear independence includes the former and excludes the latter
I think. -Carl

Did I inappropriately include or exclude any subgroups in the list I posted?

-Igs

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@> wrote:
>
> > Also, subgroups bases need to be more than pairwise
> > coprime, I think -- they need to be linearly independent.
>
> For example, pairwise coprime would exclude 5.7.15
> ordinary coprime would include 3.7.9
> linear independence includes the former and excludes the latter
> I think. -Carl
>

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

> > 2-less Pentads:
>
> Since we're using pure octaves, you get 2 for free. It
> means these could all be 6-D subgroups with the 2 tacked
> on -- they'd have the same error. Note this is different
> than saying
>
> > 3:5:7:11:13 = 2.5/3.7/3.11/3.13/3
>
> which by the way is not true, since in the former the
> error of 3:1 matters whereas in the latter it doesn't.

I know they're not actually equal, I meant that in octave-containing tunings, the pentad on the left can be found in (at minimum) the subgroup on the right, which is still a 5-D subgroup of the 6-D 13-limit, because it requires only 5 basis intervals to give the pentad (technically, 4 basis-intervals, because the two doesn't show up in the pentad). Of course you'll also find 3:5:7:11:13 pentads in a 13-limit tuning, but there are ETs that give the 5-D subgroup much more accurately than the full 13-limit.

> So I'll code that up and then I'll give you the tool,
> leaving enough time for Gene or someone to say if I
> got it wrong.

Sweet. I'm excited!

-Igs

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
> Since you decided on pure octaves, I'm going to implement
> max subgroup error with an option to turn Tenney weighting
> on or off.

After some pondering, why max subgroup error, rather than average subgroup error? Seems like there may be some ETs with a high max but a low average, or a low max but a high average. Isn't average a better indicator?

-Igs

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
> After some pondering, why max subgroup error, rather than
> average subgroup error? Seems like there may be some ETs
> with a high max but a low average, or a low max but a high
> average. Isn't average a better indicator?

This is only true if you consider all the internal intervals
between subgroup members, and that raises other questions, and
any improvement to be had is tiny. So to get this thing out
the door I've made some decisions. I documented my reasoning
as best I could here... other than that you'll have to trust
me (or not). -Carl

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

> This is only true if you consider all the internal intervals
> between subgroup members, and that raises other questions, and
> any improvement to be had is tiny.

If the final clause is true, then I won't worry about the first two. I will, however, compare the results with TE error, just for giggles.

-Igs

Igs wrote:
> If the final clause is true, then I won't worry about the
> first two. I will, however, compare the results with TE error,
> just for giggles.

It's true. Just be aware that the TE error from Graham's
site will be quite different, since it assumes tempered
octaves. -C.

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> Igs wrote:
> > If the final clause is true, then I won't worry about the
> > first two. I will, however, compare the results with TE error,
> > just for giggles.
>
> It's true. Just be aware that the TE error from Graham's
> site will be quite different, since it assumes tempered
> octaves. -C.
>

Of course. I'm just curious how different it will be in the end rankings, i.e. if it significantly alters the badness scoring or the "Best subgroup for ET".

Also, you never answered my question about whether I had inappropriately included or excluded any subgroups in my master list. I didn't use any calculations to determine if they were linearly-independent, nor did I check against normal interval lists, but I suspect my brute-force intuitive method may have produced the same results. Unfortunately I don't know enough about linear independence or normal interval lists (despite having read the wiki articles) to check my own work.

-Igs

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> Also, you never answered my question about whether I had
> inappropriately included or excluded any subgroups in my master
> list. I didn't use any calculations to determine if they were
> linearly-independent, nor did I check against normal interval
> lists, but I suspect my brute-force intuitive method may have
> produced the same results. Unfortunately I don't know enough
> about linear independence or normal interval lists (despite
> having read the wiki articles) to check my own work.

It's in my queue. -Carl

I'm only like half tuned into this, but when you say linearly independent,
do you literally mean the linear independence of the basis vectors that
you're using? As in, making sure you don't have stuff like 2.3.5.15 in
there?

Sent from my iPhone

On Jan 9, 2012, at 12:16 PM, cityoftheasleep <igliashon@...>
wrote:

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> Igs wrote:
> > If the final clause is true, then I won't worry about the
> > first two. I will, however, compare the results with TE error,
> > just for giggles.
>
> It's true. Just be aware that the TE error from Graham's
> site will be quite different, since it assumes tempered
> octaves. -C.
>

Of course. I'm just curious how different it will be in the end rankings,
i.e. if it significantly alters the badness scoring or the "Best subgroup
for ET".

Also, you never answered my question about whether I had inappropriately
included or excluded any subgroups in my master list. I didn't use any
calculations to determine if they were linearly-independent, nor did I
check against normal interval lists, but I suspect my brute-force intuitive
method may have produced the same results. Unfortunately I don't know
enough about linear independence or normal interval lists (despite having
read the wiki articles) to check my own work.

-Igs

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> I'm only like half tuned into this, but when you say linearly independent,
> do you literally mean the linear independence of the basis vectors that
> you're using? As in, making sure you don't have stuff like 2.3.5.15 in
> there?

Yes, I believe so. IOW making sure that no 5D group can be derived from a group with fewer basis vectors. I'm not 100% on what linear independence means, but it looks like a more precise formulation of how I was deciding which subgroups to include or exclude.

However, I'm on the fence about whether it's worth including the 3D and 4D basis groups that naturally extend to pentads, for instance 2.3.5, 2.3.5.7, 2.3.5.11, and 2.3.5.13 all naturally extend to pentads. I feel like on the one hand, these are pentads, and if we're comparing pentads to pentads that should be fair. On the other hand, I feel like the accuracy of these pentads depends on fewer basis elements than the true 5D sets, giving them somewhat of an unfair advantage--it's easier to find accurate tunings of 3 basis elements than 5 basis elements among the ETs. If we include them, then tunings like 12, 19, and 22 suddenly look a lot better, whereas at least 12 looks pretty bad if we exclude them (since the simplest 5D subgroup is the 11-limit, and 12-TET is not a particularly good 11-limit tuning).

-Igs

On Mon, Jan 9, 2012 at 1:49 PM, cityoftheasleep <igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> >
> > I'm only like half tuned into this, but when you say linearly independent,
> > do you literally mean the linear independence of the basis vectors that
> > you're using? As in, making sure you don't have stuff like 2.3.5.15 in
> > there?
>
> Yes, I believe so. IOW making sure that no 5D group can be derived from a group with fewer basis vectors. I'm not 100% on what linear independence means, but it looks like a more precise formulation of how I was deciding which subgroups to include or exclude.

That's exactly what it means. There's no mystery beyond that. Although
I should note that if you're deliberately looking for something like
2.3.9', where 9' is defined to be different from 9, then that's still
linearly independent.

> However, I'm on the fence about whether it's worth including the 3D and 4D basis groups that naturally extend to pentads, for instance 2.3.5, 2.3.5.7, 2.3.5.11, and 2.3.5.13 all naturally extend to pentads. I feel like on the one hand, these are pentads, and if we're comparing pentads to pentads that should be fair.

What do you mean they naturally extend to pentads? How are they all pentads?

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> > However, I'm on the fence about whether it's worth including the 3D and 4D basis groups that naturally extend to pentads, for instance 2.3.5, 2.3.5.7, 2.3.5.11, and 2.3.5.13 all naturally extend to pentads. I feel like on the one hand, these are pentads, and if we're comparing pentads to pentads that should be fair.
>
> What do you mean they naturally extend to pentads? How are they all pentads?

2.3.5 gives you 1:3:5:9:15 chords. 2.3.5.7 gives you 1:3:5:7:9:15, so that's overkill, and so are the others. You can get *at least* pentads with all of them. (At least I think that's what Igs is saying.)

Keenan

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

> 2.3.5 gives you 1:3:5:9:15 chords. 2.3.5.7 gives you 1:3:5:7:9:15, so that's overkill, and so > are the others. You can get *at least* pentads with all of them. (At least I think that's what > Igs is saying.)

Yep, Keenan's got it (as usual).

-Igs

On Mon, Jan 9, 2012 at 6:33 PM, cityoftheasleep <igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@...> wrote:
>
> > 2.3.5 gives you 1:3:5:9:15 chords. 2.3.5.7 gives you 1:3:5:7:9:15, so that's overkill, and so > are the others. You can get *at least* pentads with all of them. (At least I think that's what > Igs is saying.)
>
> Yep, Keenan's got it (as usual).

You're talking specifically about the cardinality of the most dense
chord that can be formed from a subgroup that fits within the
15-odd-limit?

-Mike

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

> You're talking specifically about the cardinality of the most dense
> chord that can be formed from a subgroup that fits within the
> 15-odd-limit?

Yes.

-igs

On Mon, Jan 9, 2012 at 8:05 PM, cityoftheasleep <igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > You're talking specifically about the cardinality of the most dense
> > chord that can be formed from a subgroup that fits within the
> > 15-odd-limit?
>
> Yes.
>
> -igs

I say throw them in. If a tuning manages to nail a phat 15-limit chord
by doing clever tricks with prime numbers, all the better for it.

-Mike

On Mon, Jan 9, 2012 at 8:07 PM, Mike Battaglia <battaglia01@...> wrote:
> On Mon, Jan 9, 2012 at 8:05 PM, cityoftheasleep <igliashon@...> wrote:
>>
>> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>>
>> > You're talking specifically about the cardinality of the most dense
>> > chord that can be formed from a subgroup that fits within the
>> > 15-odd-limit?
>>
>> Yes.
>>
>> -igs
>
> I say throw them in. If a tuning manages to nail a phat 15-limit chord
> by doing clever tricks with prime numbers, all the better for it.

Also, this problem can be partially attenuated by NOT considering
prime error. For example, if 3 and 5 are both sharp, so that 15/8 is
double sharp, it doesn't have a "good" pentad at all. For a tuning to
really be successful in the 15-odd-limit, 5-prime-limit, it has to
worry about less primes, true - but the accuracy on those primes will
have to be more competitive to compete with subgroups that don't have
composite intervals in them.

Seems to me that it might be best to give up on all this fancy prime
error stuff and get back to basics: compute the intersection of the
15-odd-limit tonality diamond and the subgroup you want, and work out
the error of the average interval when mapped into your chosen
temperament. I think that's the way to go.

-Mike

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

> Seems to me that it might be best to give up on all this fancy prime
> error stuff and get back to basics: compute the intersection of the
> 15-odd-limit tonality diamond and the subgroup you want, and work out
> the error of the average interval when mapped into your chosen
> temperament. I think that's the way to go.

That was my naive idea, but I have no quick easy way to calculate it. Carl wants to go with max error of subgroup basis interval, which the more I think about it, makes more and more sense. What do you think?

-Igs

On Mon, Jan 9, 2012 at 9:06 PM, cityoftheasleep <igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > Seems to me that it might be best to give up on all this fancy prime
> > error stuff and get back to basics: compute the intersection of the
> > 15-odd-limit tonality diamond and the subgroup you want, and work out
> > the error of the average interval when mapped into your chosen
> > temperament. I think that's the way to go.
>
> That was my naive idea, but I have no quick easy way to calculate it. Carl wants to go with max error of subgroup basis interval, which the more I think about it, makes more and more sense. What do you think?
>
> -Igs

This should be extremely easy to calculate. If you give me a list of
subgroups and EDOs I'll do it for you. Might take a day or two for me
to get to it though as I have to head up to NYC tomorrow or the day
after.

Again, I haven't been following at all, but I'll assume that this has
to do with the theorem that Paul mentioned whereby average composite
interval error correlates to max prime error. I'm curious to see if
that still holds for subgroups. Maybe I'll work it out for both.

-Mike

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

> Again, I haven't been following at all, but I'll assume that this
> has to do with the theorem that Paul mentioned whereby average
> composite interval error correlates to max prime error. I'm curious
> to see if that still holds for subgroups. Maybe I'll work it out
> for both.

It does, and it's not much of a theorem, just a simple identity.
And the max weighted basis error is more than just correlated,
it's equal to the max weighted error of all intervals in the
subgroup. -Carl

On Mon, Jan 9, 2012 at 11:26 PM, Carl Lumma <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > Again, I haven't been following at all, but I'll assume that this
> > has to do with the theorem that Paul mentioned whereby average
> > composite interval error correlates to max prime error. I'm curious
> > to see if that still holds for subgroups. Maybe I'll work it out
> > for both.
>
> It does, and it's not much of a theorem, just a simple identity.
> And the max weighted basis error is more than just correlated,
> it's equal to the max weighted error of all intervals in the
> subgroup. -Carl

Do you have a derivation of this, or do you know of one in the
archives somewhere?

-Mike

-- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> Do you have a derivation of this, or do you know of one in the
> archives somewhere?

It's in the Middle Path, in a footnote IIRC. It's just the
fact that, in composite intervals, the weights add up exactly
as fast as the errors.

-Carl

RMS errors are about as easy to calculate in general as for the special case of prime errors. See composite.pdf and find a linear algebra library. You could also look at my old temper.py

Graham

------Original message------
From: cityoftheasleep <igliashon@...>
To: <tuning@yahoogroups.com>
Date: Tuesday, January 10, 2012 2:06:08 AM GMT-0000
Subject: [tuning] Re: Pure-Octave Temperament Error

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

> Seems to me that it might be best to give up on all this fancy prime
> error stuff and get back to basics: compute the intersection of the
> 15-odd-limit tonality diamond and the subgroup you want, and work out
> the error of the average interval when mapped into your chosen
> temperament. I think that's the way to go.

That was my naive idea, but I have no quick easy way to calculate it. Carl wants to go with max error of subgroup basis interval, which the more I think about it, makes more and more sense. What do you think?

-Igs

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--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> This should be extremely easy to calculate. If you give me a list of
> subgroups and EDOs I'll do it for you. Might take a day or two for me
> to get to it though as I have to head up to NYC tomorrow or the day
> after.

ETs: 5 to 36

Subgroups:

2.3.5.11.13
2.3.5.7.11
2.3.5.7.13
2.3.7.11.13
2.5.7.9.11
2.5.7.9.13
2.5.7.11.13
2.5.9.11.13
2.7.9.11.13
2.7.9.11.15
2.7.11.13.15
2.7.9.13.15
2.9.11.13.15
2.5/3.7/3.11/3.13/3
2.5.7/3.11/3.13/3
2.3.7/5.11/5.13/5
2.7/5.9/5.11/5.13/5
2.9/7.11/7.13/7.15/7

You can maybe play with including 2.3.5.9.15, 2.3.5.7.9, 2.3.7.9.11, 2.3.7.9.13, 2.3.7.9.15, and 2.5.7.9.15 (and any other pentads reducible to a 3- or 4-D subgroup). Just keep them separate.

Thanks for your help!

-Igs

So, I did some preliminary comparisons of "average subgroup diamond" error (the average error of all intervals in the subgroup tonality diamond) vs. error of worst basis interval, and found them not to be proportionate. I believe I'd prefer to go with average subgroup diamond error for the sake of the ET badness scoring, rather than error of worst basis element. I'm hoping Mike will come through with those calculations, unless Carl wants to modify his code.

-Igs

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> -- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
> >
> > Do you have a derivation of this, or do you know of one in the
> > archives somewhere?
>
> It's in the Middle Path, in a footnote IIRC. It's just the
> fact that, in composite intervals, the weights add up exactly
> as fast as the errors.
>
> -Carl
>

You have to use weighted error, not unweighted.

I'm trying to do it, but needed to ask a question on tuning-math about
algorithmically finding out the best val to use. But if you have specific
vals you want me to check, I can do that much faster.

-Mike

On Jan 11, 2012, at 4:55 PM, "cityoftheasleep" <igliashon@...>
wrote:

So, I did some preliminary comparisons of "average subgroup diamond" error
(the average error of all intervals in the subgroup tonality diamond) vs.
error of worst basis interval, and found them not to be proportionate. I
believe I'd prefer to go with average subgroup diamond error for the sake
of the ET badness scoring, rather than error of worst basis element. I'm
hoping Mike will come through with those calculations, unless Carl wants to
modify his code.

-Igs

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> -- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
> >
> > Do you have a derivation of this, or do you know of one in the
> > archives somewhere?
>
> It's in the Middle Path, in a footnote IIRC. It's just the
> fact that, in composite intervals, the weights add up exactly
> as fast as the errors.
>
> -Carl
>

Also, I can now confirm that ET stretching can drastically alter the "best subgroup for ET" scoring. 15-ET, for example, is best on the 2.3.5.11.13 group **when stretched** (or compressed, rather, down to about 78 cents, aka Carlos Alpha), but when 2/1 is kept pure, it's much better with the 11-limit than 2.3.5.11.13. So I'm gonna throw out all my previous results.

-Igs

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> So, I did some preliminary comparisons of "average subgroup diamond" error (the average error of all intervals in the subgroup tonality diamond) vs. error of worst basis interval, and found them not to be proportionate. I believe I'd prefer to go with average subgroup diamond error for the sake of the ET badness scoring, rather than error of worst basis element. I'm hoping Mike will come through with those calculations, unless Carl wants to modify his code.
>
> -Igs
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@> wrote:
> >
> > -- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
> > >
> > > Do you have a derivation of this, or do you know of one in the
> > > archives somewhere?
> >
> > It's in the Middle Path, in a footnote IIRC. It's just the
> > fact that, in composite intervals, the weights add up exactly
> > as fast as the errors.
> >
> > -Carl
> >
>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> You have to use weighted error, not unweighted.

You mean when comparing [worst basis interval error] with [average subgroup diamond error]? Do I have to weight both? Why do I have to weight?

> I'm trying to do it, but needed to ask a question on tuning-math about
> algorithmically finding out the best val to use. But if you have specific
> vals you want me to check, I can do that much faster.

Hmmm...I'd have to bang them out by hand, which for 18 subgroups, 31 ETs, and god knows how many potential vals (let's assume 3 per tuning), that's...1,674 vals to look at. Better off doing the algorithmic approach.

-Igs

On Jan 11, 2012, at 5:08 PM, "cityoftheasleep" <igliashon@...>
wrote:

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> You have to use weighted error, not unweighted.

You mean when comparing [worst basis interval error] with [average subgroup
diamond error]? Do I have to weight both? Why do I have to weight?

Because we want the purity of 15/14 to count less than that of 3/2, right?

-Mike

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> So, I did some preliminary comparisons of "average subgroup
> diamond" error (the average error of all intervals in the
> subgroup tonality diamond) vs. error of worst basis interval,
> and found them not to be proportionate.

Did you weight the errors? Include 0 in your basis
calculations?

-Carl

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

> Because we want the purity of 15/14 to count less than that of 3/2, right?

I dunno, do we? Is there a reason why it's better to include the weighting in the error calculation, rather than apply the weighting/"discordance penalty" after the error calculation? I'd kind of like to see both weighted and unweighted results so I can compare by ear myself and see which I prefer. I slightly suspect that people who desire near-JI are more apt to embrace or dismiss a tuning according to unweighted error ("that 13/11 is 20 cents sharp! Unacceptable!"), since a lot of people believe that the "identity" (if not the concordance) of more complex ratios is more easily destroyed by small mistunings than are the identities of simpler ratios. Tenney Weighting reflects a certain prejudice that may not be held by everyone; only an unweighted result is "neutral".

-Igs

No, I didn't weight the error; I'm not convinced that weighted error is the way to go for what I'm trying to compare here. What do you mean by "include 0"?

-Igs

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@> wrote:
> >
> > So, I did some preliminary comparisons of "average subgroup
> > diamond" error (the average error of all intervals in the
> > subgroup tonality diamond) vs. error of worst basis interval,
> > and found them not to be proportionate.
>
> Did you weight the errors? Include 0 in your basis
> calculations?
>
> -Carl
>

Igs & Mike wrote:

--- Mike Battaglia <battaglia01@...> wrote:
>
>> You have to use weighted error, not unweighted.
>
>You mean when comparing [worst basis interval error] with
>[average subgroup diamond error]? Do I have to weight both?
>Why do I have to weight?

If you compare max errors for basis vs tonality diamond,
you DON'T have to weight. You just have to use (max - min)
error of the basis, respecting signs. That'll give you the
max tonality diamond error, weighted or not. To get max
error over ALL intervals, you need to weight.

> > Because we want the purity of 15/14 to count less than that
> > of 3/2, right?
>
> I dunno, do we?

Yes. This is well-established. 15/14 isn't even consonant
by itself.

> Is there a reason why it's better to include the weighting
> in the error calculation, rather than apply the weighting/
> "discordance penalty" after the error calculation?

Maybe not, which is why I said from the outset that
weighting will be optional.

-Carl

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

> What do you mean by "include 0"?

When you find the (max - min), you need to salt the list
of errors with 0, in case they're all positive. For ETs
like you decided you wanted, this is the same as including
2 in the subgroup, which you should do.

-Carl

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

> If you compare max errors for basis vs tonality diamond,
> you DON'T have to weight. You just have to use (max - min)
> error of the basis, respecting signs. That'll give you the
> max tonality diamond error, weighted or not. To get max
> error over ALL intervals, you need to weight.

When you say "respecting signs", do you mean if (say) the max error is on 3 and it's 28 cents flat (-28 c) and the min error is on, say, 5, and it's 13 cents flat (-13 c), then (max - min) would be -28 - (-13) = -28 + 13 = -15 cents?

Why don't you have to weight for basis vs. tonality diamond?

> Yes. This is well-established. 15/14 isn't even consonant
> by itself.

Why does error need to reflect consonance?

> Maybe not, which is why I said from the outset that
> weighting will be optional.

Right. Mike was the one saying he wanted to do weighting (well, first he didn't, then he did, and now I don't know).

Let me know if I have you correctly: max error of basis intervals will be equal or proportional (which is it?) to average weighted error over all intervals, while (max - min) with signs respected will be equal to unweighted tonality diamond error?

If this is the case, then why would you have an option to turn weighting on, if your code is measuring max error?

-Igs

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> "cityoftheasleep" <igliashon@> wrote:
>
> > What do you mean by "include 0"?
>
> When you find the (max - min), you need to salt the list
> of errors with 0, in case they're all positive. For ETs
> like you decided you wanted, this is the same as including
> 2 in the subgroup, which you should do.

Oh, well in that case then yes, I did include the zeros (for 1/1 which = 2/1 under octave equivalence).

-Igs

Also, when I averaged the errors, I used absolute values of the errors across the tonality diamond, if that makes a difference to you. Also if it makes a difference, my test case was 15-TET, comparing its performance on two different subgroups (2.3.5.11.13 vs 2.3.5.7.11). I'll try it again with (max - min) with signs respected.

-Igs

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@> wrote:
> >
> > "cityoftheasleep" <igliashon@> wrote:
> >
> > > What do you mean by "include 0"?
> >
> > When you find the (max - min), you need to salt the list
> > of errors with 0, in case they're all positive. For ETs
> > like you decided you wanted, this is the same as including
> > 2 in the subgroup, which you should do.
>
> Oh, well in that case then yes, I did include the zeros (for 1/1 which = 2/1 under octave equivalence).
>
> -Igs
>

Igs wrote:

> > If you compare max errors for basis vs tonality diamond,
> > you DON'T have to weight. You just have to use (max - min)
> > error of the basis, respecting signs. That'll give you the
> > max tonality diamond error, weighted or not. To get max
> > error over ALL intervals, you need to weight.
>
> When you say "respecting signs", do you mean if (say) the max
> error is on 3 and it's 28 cents flat (-28 c) and the min error
> is on, say, 5, and it's 13 cents flat (-13 c), then (max - min)
> would be -28 - (-13) = -28 + 13 = -15 cents?

Which is bigger, -28 or -13? :)

Here the max error, respecting signs, is -13 and the
min is -28, giving -13 - (-28) = 15.

Except 0 > -13 so it's 0 - (-28) = 28.

> Why don't you have to weight for basis vs. tonality diamond?

Because the tonality diamond is just a listing of the
intervals between the basis intervals (and their octave
inversions). And the max-min procedure finds the maximum
error among the intervals between the basis intervals.

> > Yes. This is well-established. 15/14 isn't even consonant
> > by itself.
>
> Why does error need to reflect consonance?

What else would you be measuring the error of?

> Let me know if I have you correctly: max error of basis
> intervals will be equal or proportional (which is it?) to
> average weighted error over all intervals, while (max - min)
> with signs respected will be equal to unweighted tonality
> diamond error?

Nope, (max-min) of the basis is always equal to the max
of the tonality diamond (both weighted or both unweighted).
The average error of the tonality diamond will be related
but different.

-Carl

On Fri, Jan 13, 2012 at 6:49 PM, cityoftheasleep
<igliashon@...> wrote:
>
> > Maybe not, which is why I said from the outset that
> > weighting will be optional.
>
> Right. Mike was the one saying he wanted to do weighting (well, first he didn't, then he did, and now I don't know).

I was going to Tenney-weight everything. How would you like me to do it?

-Mike

And am I assuming pure octaves?

-Mike

On Sat, Jan 14, 2012 at 1:27 AM, Mike Battaglia <battaglia01@...> wrote:
> On Fri, Jan 13, 2012 at 6:49 PM, cityoftheasleep
> <igliashon@...> wrote:
>>
>> > Maybe not, which is why I said from the outset that
>> > weighting will be optional.
>>
>> Right. Mike was the one saying he wanted to do weighting (well, first he didn't, then he did, and now I don't know).
>
> I was going to Tenney-weight everything. How would you like me to do it?
>
> -Mike

Are these weighted? If not you should include 9 in the harmonics. Maybe 15 as well.

Graham

------Original message------
From: cityoftheasleep <igliashon@...>
To: <tuning@yahoogroups.com>
Date: Friday, January 13, 2012 11:54:14 PM GMT-0000
Subject: [tuning] Re: Pure-Octave Temperament Error

Also, when I averaged the errors, I used absolute values of the errors across the tonality diamond, if that makes a difference to you. Also if it makes a difference, my test case was 15-TET, comparing its performance on two different subgroups (2.3.5.11.13 vs 2.3.5.7.11). I'll try it again with (max - min) with signs respected.

-Igs

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@> wrote:
> >
> > "cityoftheasleep" <igliashon@> wrote:
> >
> > > What do you mean by "include 0"?
> >
> > When you find the (max - min), you need to salt the list
> > of errors with 0, in case they're all positive. For ETs
> > like you decided you wanted, this is the same as including
> > 2 in the subgroup, which you should do.
>
> Oh, well in that case then yes, I did include the zeros (for 1/1 which = 2/1 under octave equivalence).
>
> -Igs
>

------------------------------------

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--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> Which is bigger, -28 or -13? :)

But...are you saying that being 13 cents flat is a bigger error than being 28 cents flat???

> Here the max error, respecting signs, is -13 and the
> min is -28, giving -13 - (-28) = 15.
>
> Except 0 > -13 so it's 0 - (-28) = 28.

Still confused...did you mean (sharpest - flattest) error, rather than (biggest error - smallest error)??

> Because the tonality diamond is just a listing of the
> intervals between the basis intervals (and their octave
> inversions). And the max-min procedure finds the maximum
> error among the intervals between the basis intervals.

Oh. Brilliant.

> What else would you be measuring the error of?

Some people like to make claims about "identity" or "character" of rational intervals, such that higher-limit intervals more easily lose this "character" than lower-limit intervals. Such people might say that 3/2 flattened by 10 cents still sounds like a 3/2, but a 13/8 flattened by 10 cents sounds like a mistuned 8/5 and not a 13/8. Or they might even say it's a 21/13 if they include ratios of 21 in their world view. To these sorts of people, it seems ass-backwards to allow MORE mistuning of complex ratios than of simple ones. I know you don't think this way, and probably think it's silly, but I'd like the option to be able to humor such people. It makes my life easier than trying to talk people out of their beliefs about music.

> Nope, (max-min) of the basis is always equal to the max
> of the tonality diamond (both weighted or both unweighted).
> The average error of the tonality diamond will be related
> but different.

By "related", do you mean proportional?

-Igs

No Tenney-weighting, plz. We can Tenney-weight the error after the fact, can't we?

-Igs

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Fri, Jan 13, 2012 at 6:49 PM, cityoftheasleep
> <igliashon@...> wrote:
> >
> > > Maybe not, which is why I said from the outset that
> > > weighting will be optional.
> >
> > Right. Mike was the one saying he wanted to do weighting (well, first he didn't, then he did, and now I don't know).
>
> I was going to Tenney-weight everything. How would you like me to do it?
>
> -Mike
>

--- In tuning@yahoogroups.com, "gbreed@..." <gbreed@...> wrote:
>
> Are these weighted? If not you should include 9 in the harmonics. Maybe 15 as well.

No weighting, and I deliberately excluded those harmonics because I only wanted to look at the error of the intervals forming a pentad (a 5D tonality diamond, IOW).

The unweighted error of the 2.3.5.11.13 group will be very different than that of the 2.3.5.9.11.13.15 group, and people seeing a low error on the former may mistakenly think the latter will also have low error, when in fact it does not. I should make it explicit that the 2.3.5.11.13 group does not include the products of the basis harmonics.

-Igs

> ------Original message------
> From: cityoftheasleep <igliashon@...>
> To: <tuning@yahoogroups.com>
> Date: Friday, January 13, 2012 11:54:14 PM GMT-0000
> Subject: [tuning] Re: Pure-Octave Temperament Error
>
> Also, when I averaged the errors, I used absolute values of the errors across the tonality diamond, if that makes a difference to you. Also if it makes a difference, my test case was 15-TET, comparing its performance on two different subgroups (2.3.5.11.13 vs 2.3.5.7.11). I'll try it again with (max - min) with signs respected.
>
> -Igs
>
> --- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@> wrote:
> >
> > --- In tuning@yahoogroups.com, "Carl Lumma" <carl@> wrote:
> > >
> > > "cityoftheasleep" <igliashon@> wrote:
> > >
> > > > What do you mean by "include 0"?
> > >
> > > When you find the (max - min), you need to salt the list
> > > of errors with 0, in case they're all positive. For ETs
> > > like you decided you wanted, this is the same as including
> > > 2 in the subgroup, which you should do.
> >
> > Oh, well in that case then yes, I did include the zeros (for 1/1 which = 2/1 under octave equivalence).
> >
> > -Igs
> >
>
>
>
>
> ------------------------------------
>
> You can configure your subscription by sending an empty email to one
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>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> And am I assuming pure octaves?
>
> -Mike

Absolutely.

-Igs

Igs wrote:

> > Which is bigger, -28 or -13? :)
>
> But...are you saying that being 13 cents flat is a bigger
> error than being 28 cents flat???

I'm saying -13 is bigger than -28.

> > Here the max error, respecting signs, is -13 and the
> > min is -28, giving -13 - (-28) = 15.
> >
> > Except 0 > -13 so it's 0 - (-28) = 28.
>
> Still confused...did you mean (sharpest - flattest) error,
> rather than (biggest error - smallest error)??

All of the above, *respecting signs*. When you say "biggest
error" I think you are thinking of absolute values.

> > What else would you be measuring the error of?
>
> Some people like to make claims about "identity" or
> "character" of rational intervals, such that higher-limit
> intervals more easily lose this "character" than lower-limit
> intervals. Such people might say that 3/2 flattened by 10
> cents still sounds like a 3/2, but a 13/8 flattened by
> 10 cents sounds like a mistuned 8/5 and not a 13/8.

The fields of attraction are narrower for higher-limit
consonances, but the increase in dissonance per cent
detuning is far less than for simple ratios. 15/14 doesn't
even have a field of attraction outside of lab conditions.
15/7 sometimes does, and 4:7:15 or 7:14:15 usually will.
This 15 vs 7 thing gets its identity more from musical
context than from its size. By the time you get to 81/64,
there's no field of attraction at all.

I forget what we were talking about here... oh yeah, what
error is. Whatever it is, it must have units of dissonance
increase per cent of interval size change. That's why
weighted error is better than unweighted error, at least
for dyads. You'll also note I've gone back to using
"dissonance" to mean discordance, because it's easier to
type and pronounce and it should be bloody obvious what
I mean. And as long as some JI chords appear in a piece,
I have a hard time believing they're completely unrelated.

> Or they might even say it's a 21/13 if they include ratios
> of 21 in their world view. To these sorts of people, it
> seems ass-backwards to allow MORE mistuning of complex ratios
> than of simple ones. I know you don't think this way, and
> probably think it's silly, but I'd like the option to be
> able to humor such people. It makes my life easier than
> trying to talk people out of their beliefs about music.

Those people are probably using 21 in chords, because 21/16
sounds like a mistuned 4/3. Not only doesn't it have a
field of attraction, it's inside the field of attraction of
another ratio! The higher you go in the harmonic series,
the more dependent on musical context things get and the
less any general analysis like TOP damage will reflect the
situation on the ground.

> > Nope, (max-min) of the basis is always equal to the max
> > of the tonality diamond (both weighted or both unweighted).
> > The average error of the tonality diamond will be related
> > but different.
>
> By "related", do you mean proportional?

No.

-Carl
> -Igs
>

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

> > But...are you saying that being 13 cents flat is a bigger
> > error than being 28 cents flat???
>
> I'm saying -13 is bigger than -28.

Right, but that's not how we usually deal with error. But I understand you now.

> All of the above, *respecting signs*. When you say "biggest
> error" I think you are thinking of absolute values.

Yes, I must be. If I think in terms of (sharpest - flattest) it all makes sense, so I'll think of it that way.

> The fields of attraction are narrower for higher-limit
> consonances, but the increase in dissonance per cent
> detuning is far less than for simple ratios. 15/14 doesn't
> even have a field of attraction outside of lab conditions.
> 15/7 sometimes does, and 4:7:15 or 7:14:15 usually will.
> This 15 vs 7 thing gets its identity more from musical
> context than from its size. By the time you get to 81/64,
> there's no field of attraction at all.

Well, I don't buy the whole "field of attraction" thing, that's all learning and conditioning. But other people do buy it and I hate debating it, so I won't.

> I forget what we were talking about here... oh yeah, what
> error is. Whatever it is, it must have units of dissonance
> increase per cent of interval size change.

Why?

> Those people are probably using 21 in chords, because 21/16
> sounds like a mistuned 4/3. Not only doesn't it have a
> field of attraction, it's inside the field of attraction of
> another ratio! The higher you go in the harmonic series,
> the more dependent on musical context things get and the
> less any general analysis like TOP damage will reflect the
> situation on the ground.

I don't want to assume anything about consonance and dissonance, nor fields of attraction. I want to assume as little as possible. Fields of attraction are debatable. Consonance and dissonance are debatable. There are about a dozen HE curves that I've seen, with none of them being clearly universally-superior and several of them conflicting with each other. See the XA facebook group photos section. However, the absolute distance of a tempered interval from a rational interval is not debatable. I want to measure how close each ET gets to the various subgroup tonality diamonds, and then other people can debate what those measurements mean as far as consonance/dissonance and intervallic identities. This way if someone asks "which subgroup is most accurately represented in 15-TET?", I can say "2.a.b.c.d" and not have to worry about what the weighting did or did not do to the error calculations.

> > > Nope, (max-min) of the basis is always equal to the max
> > > of the tonality diamond (both weighted or both unweighted).
> > > The average error of the tonality diamond will be related
> > > but different.
> >
> > By "related", do you mean proportional?
>
> No.

Then related in what way?

-Igs

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

> > The fields of attraction are narrower for higher-limit
> > consonances, but the increase in dissonance per cent
> > detuning is far less than for simple ratios. 15/14 doesn't
> > even have a field of attraction outside of lab conditions.
> > 15/7 sometimes does, and 4:7:15 or 7:14:15 usually will.
> > This 15 vs 7 thing gets its identity more from musical
> > context than from its size. By the time you get to 81/64,
> > there's no field of attraction at all.
>
> Well, I don't buy the whole "field of attraction" thing, that's
> all learning and conditioning.

Actually it's not. And it can't be conditioned, at least
not by any means anyone can do while leading a normal life.

> But other people do buy it and I hate debating it, so I won't.

Other people buy it because it's a fact of the universe
around us.

> > > > Nope, (max-min) of the basis is always equal to the max
> > > > of the tonality diamond (both weighted or both unweighted).
> > > > The average error of the tonality diamond will be related
> > > > but different.
> > >
> > > By "related", do you mean proportional?
> >
> > No.
>
> Then related in what way?

Generally when comparing RMS and max, you're comparing a
dodecahedron to a sphere. I don't recall the shape of the
unit ball for the arithmetic mean but it might be on
wikipedia http://en.wikipedia.org/wiki/Unit_ball

-Carl

On Jan 14, 2012, at 6:55 PM, "Carl Lumma" <carl@...> wrote:

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

> > The fields of attraction are narrower for higher-limit
> > consonances, but the increase in dissonance per cent
> > detuning is far less than for simple ratios. 15/14 doesn't
> > even have a field of attraction outside of lab conditions.
> > 15/7 sometimes does, and 4:7:15 or 7:14:15 usually will.
> > This 15 vs 7 thing gets its identity more from musical
> > context than from its size. By the time you get to 81/64,
> > there's no field of attraction at all.
>
> Well, I don't buy the whole "field of attraction" thing, that's
> all learning and conditioning.

Actually it's not. And it can't be conditioned, at least
not by any means anyone can do while leading a normal life.

How do you know that categorical effects can't pick up the slack where raw
concordance fails?

-Mike

On Jan 14, 2012, at 6:55 PM, Carl Lumma <carl@...> wrote:

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

> > The fields of attraction are narrower for higher-limit
> > consonances, but the increase in dissonance per cent
> > detuning is far less than for simple ratios. 15/14 doesn't
> > even have a field of attraction outside of lab conditions.
> > 15/7 sometimes does, and 4:7:15 or 7:14:15 usually will.
> > This 15 vs 7 thing gets its identity more from musical
> > context than from its size. By the time you get to 81/64,
> > there's no field of attraction at all.
>
> Well, I don't buy the whole "field of attraction" thing, that's
> all learning and conditioning.

Actually it's not. And it can't be conditioned, at least
not by any means anyone can do while leading a normal life.

And, even besides categorical effects, where is the evidence that complex
pitch perception itself doesn't change in response to training?

-Mike

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

> Actually it's not. And it can't be conditioned, at least
> not by any means anyone can do while leading a normal life.

Well, like I said, I disagree (at least as far as I understand what you mean by "field of attraction") but I have no desire to debate it. I'll leave that to Mike. I've seen where it goes in the past and I have no desire to go there now.

In any case, I hope you understand where I'm coming from, the way I laid it out in my prior post. I'll say it again just to be sure: regardless of your opinion, consonance/dissonance and "fields of attraction" are debated by many and not clearly resolved or defined.

Compare these images:
https://fbcdn-sphotos-a.akamaihd.net/hphotos-ak-ash4/299419_10150332447604367_766299366_7828048_72739404_n.jpg
https://fbcdn-sphotos-a.akamaihd.net/hphotos-ak-snc7/318670_10150327423814367_766299366_7800615_1178130122_n.jpg
https://fbcdn-sphotos-a.akamaihd.net/hphotos-ak-snc7/305278_10150327283689367_766299366_7800075_1184789201_n.jpg
https://fbcdn-sphotos-a.akamaihd.net/hphotos-ak-ash4/398538_10150515896264367_766299366_8543136_961317604_n.jpg
https://fbcdn-sphotos-a.akamaihd.net/hphotos-ak-ash4/395988_10150514147259367_766299366_8540259_1683411426_n.jpg
https://fbcdn-sphotos-a.akamaihd.net/hphotos-ak-ash4/375261_10150515902929367_766299366_8543161_109214662_n.jpg

These are some of the possible dyadic HE curves, straight from Paul himself. Depending on which one we decide is correct, we will end up with a different hierarchy of consonance and dissonance, as well as a different model of the "fields of attraction". We don't currently have sufficient evidence to single any one of these curves out as the universally-correct one, and some of them are wildly at variance with the others. There are free variables within the theory of HE, including s, octave equivalence, type of probability distribution, weighting method, and type of seed series. There are points they all share in common, such as 3/2 being the most concordant interval between 1/1 and 2/1 or 81/64 failing to be a local minimum. However, in for instance the last curve, we do in fact see 15/14 emerge as a local minimum, whereas in others we might not even see 11/7 emerge as a local minimum. As regards the consonance or attractiveness of the ratios of 11 to maybe 19 or 21, the jury is still out--especially for intervals wider than a 2/1. I don't have a horse in the race (anymore) and I'm content to allow there to be debate and ambiguity. Paul has suggested to me on numerous occasions that s is *necessarily* a free parameter, as it varies from subject to subject. People do, after all, vary from "utterly tone-deaf" (can't even sing a unison) to "surgically precise" (the best singers of barbershop music, for instance--able to reliably sing 9-limit harmonies accurately on command).

Which is why I want to have access to unweighted error measures.

> > > > By "related", do you mean proportional?
> > >
> > > No.
> >
> > Then related in what way?
>
> Generally when comparing RMS and max, you're comparing a
> dodecahedron to a sphere. I don't recall the shape of the
> unit ball for the arithmetic mean but it might be on
> wikipedia http://en.wikipedia.org/wiki/Unit_ball

Yeesh. Can't make heads or tails of that.

-Igs

On Jan 14, 2012, at 7:57 PM, "cityoftheasleep" <igliashon@...>
wrote:

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

//snip
Which is why I want to have access to unweighted error measures.

I agree with everything you wrote, but I don't think you need to make any
assumptions about the futility of training on the perception of
concordance, whatever that word means today, for weighted error to be
useful. But aren't you telling me to weight things anyway, at the end?

-Mike

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

> I agree with everything you wrote, but I don't think you need to make any
> assumptions about the futility of training on the perception of
> concordance, whatever that word means today, for weighted error to be
> useful. But aren't you telling me to weight things anyway, at the end?

No, I'm not. What's the use of weighting that's not concordance-related?

-Igs

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
> > Generally when comparing RMS and max, you're comparing a
> > dodecahedron to a sphere. I don't recall the shape of the
> > unit ball for the arithmetic mean but it might be on
> > wikipedia http://en.wikipedia.org/wiki/Unit_ball
>
> Yeesh. Can't make heads or tails of that.

Consider x and y coordinates on a plane. The set of all (x,y) points such that the RMS value of x and y is less than some constant is a circle. The set of all (x,y) points such that the maximum of x and y is less than some constant is, instead, a square. Because the maximum thing reduces to a bunch of linear equations (rather than quadratic equations), you always get something with straight/flat sides, i.e. a polytope.

For 5-limit TOP error, the shape of all tunings under a certain TOP error is a hexagon. For 7-limit, it is a rhombic dodecahedron (not a regular dodecahedron). For higher dimensions you get other kinds of highly symmetric polytopes.

Keenan

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

> Consider x and y coordinates on a plane. The set of all (x,y) points such that the RMS value of x and y is less than some constant is a circle. The set of all (x,y) points such that the maximum of x and y is less than some constant is, instead, a square. Because the maximum thing reduces to a bunch of linear equations (rather than quadratic equations), you always get something with straight/flat sides, i.e. a polytope.
>
> For 5-limit TOP error, the shape of all tunings under a certain TOP error is a hexagon. For 7-limit, it is a rhombic dodecahedron (not a regular dodecahedron). For higher dimensions you get other kinds of highly symmetric polytopes.
>
> Keenan
>

Thanks, Keenan. That makes a lot more sense. Would the square be circumscribed in the circle, or vice-versa?

-Igs

On Sat, Jan 14, 2012 at 9:41 PM, cityoftheasleep
<igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > I agree with everything you wrote, but I don't think you need to make any
> > assumptions about the futility of training on the perception of
> > concordance, whatever that word means today, for weighted error to be
> > useful. But aren't you telling me to weight things anyway, at the end?
>
> No, I'm not. What's the use of weighting that's not concordance-related?

Again, I don't know what you mean by concordance. I wish we could
speak in terms of specific, well-defined psychoacoustic processes.

I view the point of all of this theory as being nothing more than
telling you how nicely intervals are intoned. That's it. The intervals
are the things that have their own "identities" to me, and not the
intonations. I don't view things like 3/2 or 5/4 as having any
"identity" unless you deliberately construct one around those
intervals.

As you keep pointing out yourself, there are a million aspects to
"what people will like" other than intonation, some of which are
probably very straightforward and haven't yet been worked out or
discovered all the way. So why should we try to lump any of them in
here, making a ton of assumptions in the process that probably aren't
right? This is why that as far as intonation is concerned, I only care
about modeling concrete psychoacoustic processes that happen when you
intone intervals, and why I don't care at all about making further
assumptions about "what people will like" after that.

To that effect, as a good first pass, Tenney-weighting accurately
reflects the strength of a number of purely psychoacoustic dyadic
phenomena which occur when you hear intervals. There are plenty of
effects I can think of that don't have to do with VFs that would cause
15/14 to take on as much importance as 3/2, but all of the ones I can
think of either have to do with categorical perception and some
learned system of logic, and none of them are relevant to its
intonation, which is the only thing that we're actually modeling. If
we're interested in modeling other things, then we should just treat
them as separate things and not fit them in here.

And if you don't want to weight things, then why are we limiting our
search to some odd-limit? You're already weighting things by giving
every interval within that limit an equal weight and everything
outside of it a weight of 0.

-Mike

On Sun, Jan 15, 2012 at 12:26 AM, cityoftheasleep
<igliashon@...> wrote:
>
> Thanks, Keenan. That makes a lot more sense. Would the square be circumscribed in the circle, or vice-versa?
>
> -Igs

Assuming you're asking about the Linfty unit circle vs the L2 unit
circle, then vice versa.

-Mike

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

> I view the point of all of this theory as being nothing more than
> telling you how nicely intervals are intoned. That's it. The intervals
> are the things that have their own "identities" to me, and not the
> intonations. I don't view things like 3/2 or 5/4 as having any
> "identity" unless you deliberately construct one around those
> intervals.

I am agnostic about interval identities and the source thereof. But in any case, the above is just, like, your opinion, man. Other people can and do disagree. Lots of microtonalists believe that JI intervals have unique identities and "fields of attraction". I may or may not be one of them, but I'm trying to keep out of as many debates as possible. I just want to make some goddamn measurements and see what I think after that.

> As you keep pointing out yourself, there are a million aspects to
> "what people will like" other than intonation, some of which are
> probably very straightforward and haven't yet been worked out or
> discovered all the way. So why should we try to lump any of them in
> here, making a ton of assumptions in the process that probably aren't
> right? This is why that as far as intonation is concerned, I only care
> about modeling concrete psychoacoustic processes that happen when you
> intone intervals, and why I don't care at all about making further
> assumptions about "what people will like" after that.

I'm not trying to model anything. I'm just trying to measure. Measure the abstract numbers. Psychoacoustics is out of the equation for the moment. Other people are free to model later. Heck, we can even weight the error later too, and see how much difference it makes in the ranking (I'm curious about that, aren't you?).

> And if you don't want to weight things, then why are we limiting our
> search to some odd-limit? You're already weighting things by giving
> every interval within that limit an equal weight and everything
> outside of it a weight of 0.

I'm aware of this. In fact, that's the whole reason I don't want to do any further weighting. There is lots of debate over which intervals in the 15-limit are suitably consonant or not, and in what context. What there isn't debate over is the consonance of 15-odd-limit pentads. We can all agree that any five harmonics between 2 and 15 played together are consonant. So let's see which ETs get closest to which five harmonics. I don't see any need to complicate it further. At least in this form of weighting, I know an error of 8 cents means 8 bloody cents, not actually 31.2551247648681 cents divided by log(15) or however you do the dang Tenney weighting.

-Igs

On Sun, Jan 15, 2012 at 1:33 AM, cityoftheasleep
<igliashon@...> wrote:
>
> > And if you don't want to weight things, then why are we limiting our
> > search to some odd-limit? You're already weighting things by giving
> > every interval within that limit an equal weight and everything
> > outside of it a weight of 0.
>
> I'm aware of this. In fact, that's the whole reason I don't want to do any further weighting. There is lots of debate over which intervals in the 15-limit are suitably consonant or not, and in what context. What there isn't debate over is the consonance of 15-odd-limit pentads. We can all agree that any five harmonics between 2 and 15 played together are consonant. So let's see which ETs get closest to which five harmonics. I don't see any need to complicate it further. At least in this form of weighting, I know an error of 8 cents means 8 bloody cents, not actually 31.2551247648681 cents divided by log(15) or however you do the dang Tenney weighting.

Alright, what do you want me to do? Just get the average unweighted
error of all intervals in the intersection of the 15-limit tonality
diamond and the chosen subgroup?

-Mike

On Sun, Jan 15, 2012 at 1:42 AM, Mike Battaglia <battaglia01@...> wrote:
>
> Alright, what do you want me to do? Just get the average unweighted
> error of all intervals in the intersection of the 15-limit tonality
> diamond and the chosen subgroup?

Or was it the maximum error?

Also, if the average, what type of average? Arithmetic mean, RMS, ???

-Mike

Igs wrote:

> Well, like I said, I disagree (at least as far as I understand
> what you mean by "field of attraction") but I have no desire to
> debate it.

Me neither. Every time we do, you seem to agree or disappear
only to reappear later asserting the same old diatribe.

> In any case, I hope you understand where I'm coming from,

I think I do - I think you like disbelieving things.

> Compare these images:

The all show both features I mentioned: that for simple
ratios, fields of attraction are wider and dissonance
increases more rapidly per cent of detuning -- features
also described by Werckmeister and Partch.

> the jury is still out

The jurors are at home watching the cable TV movie version
of the trial.

-Carl

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

>
> The all show both features I mentioned: that for simple
> ratios, fields of attraction are wider and dissonance
> increases more rapidly per cent of detuning -- features
> also described by Werckmeister and Partch.

Quarter-comma meantone, with 3:2 audibly flat and pure 5:4, demonstrates that this observation does not constitute a valid foundational principle for musical tuning.

>Me neither. Every time we do, you seem to agree or disappear
>only to reappear later asserting the same old diatribe.

I've never seen a "bitter, sharply abusive denunciation, attack, or criticism" from Igliashon.

Quarter-comma meantone is the minimax tuning for a range of weightings. It proves very little.

Graham

------Original message------
From: lobawad <lobawad@...>
To: <tuning@yahoogroups.com>
Date: Sunday, January 15, 2012 10:13:29 AM GMT-0000
Subject: [tuning] Re: Pure-Octave Temperament Error

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

>
> The all show both features I mentioned: that for simple
> ratios, fields of attraction are wider and dissonance
> increases more rapidly per cent of detuning -- features
> also described by Werckmeister and Partch.

Quarter-comma meantone, with 3:2 audibly flat and pure 5:4, demonstrates that this observation does not constitute a valid foundational principle for musical tuning.

>Me neither. Every time we do, you seem to agree or disappear
>only to reappear later asserting the same old diatribe.

I've never seen a "bitter, sharply abusive denunciation, attack, or criticism" from Igliashon.

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

> Alright, what do you want me to do? Just get the average unweighted
> error of all intervals in the intersection of the 15-limit tonality
> diamond and the chosen subgroup?

That's a good place to start, yes.

-Igs

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Sun, Jan 15, 2012 at 1:42 AM, Mike Battaglia <battaglia01@...> wrote:
> >
> > Alright, what do you want me to do? Just get the average unweighted
> > error of all intervals in the intersection of the 15-limit tonality
> > diamond and the chosen subgroup?
>
> Or was it the maximum error?
>
> Also, if the average, what type of average? Arithmetic mean, RMS, ???

Let's go with RMS. Max would be good to know if it's easy to compute; if it's a PITA, don't worry about it.

-Igs

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

> Me neither. Every time we do, you seem to agree or disappear
> only to reappear later asserting the same old diatribe.

Yep. Because you seem to think there is no ambiguity about the absolute dissonance of dyads of the 11-limit and up, despite a lack of sufficient evidence to convince, well, anyone. I'm quite sure you're the only person here who considers the matter settled. Even Paul was flabbergasted at your insistence that a Tenney Height above 70 was an automatic disqualifier for consonance (he puts the Tenney Height at *least* around 100, FWIW, and has noted in himself the ability to tune up to a 17/13 by eliminating beats).

> > In any case, I hope you understand where I'm coming from,
>
> I think I do - I think you like disbelieving things.

It's true. Like most philosophers, I try like hell to disprove as many of my beliefs as I have the resources to disprove, and only an overwhelming failure to succeed at this disproof is sufficient grounds to let the belief stand. In recent times, you've given me evidence to reject my previous beliefs on nuclear power, the economy, the NDAA, and many things espoused by the Occupy movement, and I have immediately modified my beliefs in accordance with the compelling evidence or arguments you presented. My love of discordant EDOs emerged from a similar test of my (previously-held) belief that only maximally-consonant tunings are worth composing with. I still have some correspondence between Paul and me where *he* was trying to convince *me* that 720 cents could work as an approximate 3/2. At the time I refused to even call 720 cents a "fifth".

In the case of the question of consonance and fields of attraction, I think your usual ability to produce robust and convincing evidence (which tends to obviate any debate) has come up very short, again and again and again, yet your conviction never wavers. The fact that the vast majority of people in this community are also not convinced by you, and that this "debate" comes up again and again, should give you pause about either a) the evidence for your beliefs or b) your ability to articulate your beliefs and your evidence for them. I won't say you're wrong, just that you haven't given me enough reason to agree with you.

> > Compare these images:
>
> The all show both features I mentioned: that for simple
> ratios, fields of attraction are wider and dissonance
> increases more rapidly per cent of detuning -- features
> also described by Werckmeister and Partch.

And I acknowledged this. But the question of how wide the fields of attraction are, which ratios have them, and how fast the dissonance increases with detuning, are decidedly not answered. Some of the Vos-curve models show fields of attraction for intervals up to 21/11, for instance. Of course they are not deep or wide, and of course the 5-limit is mostly more concordant than the 7-limit, which is mostly more concordant than the 9-limit, which is mostly more concordant than the 11-limit (etc.).

If the goal of weighting is to reflect discordance, I don't see how one single weighting algorithm (Tenney weighting) can accurately reflect all of the possible discordance curves. I am not ready to commit to a curve, so I'm not ready to commit to a weighting. Is that reasoning so nonsensical?

-Igs

--- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:
> Quarter-comma meantone, with 3:2 audibly flat and pure 5:4, demonstrates that this
> observation does not constitute a valid foundational principle for musical tuning.

Not really; there's more going into the optimization than those two ratios. The set of the ratios of 5 is greater than the set of the ratios of 3 (excluding the ratios of 2) (consider 3:2 and 4:3, vs. 5:4, 8:5, 5:3, 6:5), and this gives the ratios of 5 more weight collectively, even if they're all given less weight individually (if I understand correctly).

> >Me neither. Every time we do, you seem to agree or disappear
> >only to reappear later asserting the same old diatribe.
>
> I've never seen a "bitter, sharply abusive denunciation, attack, or criticism" from Igliashon.

LOL, you missed my feud with Robert Thomas Martin on the Facebook XA group, then!

-Igs

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

> Quarter-comma meantone, with 3:2 audibly flat and pure 5:4,
> demonstrates that this observation does not constitute a
> valid foundational principle for musical tuning.

Incorrect, since you can get quarter-comma meantone tuning
out of optimizations based on the two features I mentioned.

-Carl

On Sun, Jan 15, 2012 at 11:48 AM, cityoftheasleep
<igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> > Me neither. Every time we do, you seem to agree or disappear
> > only to reappear later asserting the same old diatribe.
>
> Yep. Because you seem to think there is no ambiguity about the absolute dissonance of dyads of the 11-limit and up, despite a lack of sufficient evidence to convince, well, anyone. I'm quite sure you're the only person here who considers the matter settled. Even Paul was flabbergasted at your insistence that a Tenney Height above 70 was an automatic disqualifier for consonance (he puts the Tenney Height at *least* around 100, FWIW, and has noted in himself the ability to tune up to a 17/13 by eliminating beats).
>
//snip
>
> In the case of the question of consonance and fields of attraction, I think your usual ability to produce robust and convincing evidence (which tends to obviate any debate) has come up very short, again and again and again, yet your conviction never wavers. The fact that the vast majority of people in this community are also not convinced by you, and that this "debate" comes up again and again, should give you pause about either a) the evidence for your beliefs or b) your ability to articulate your beliefs and your evidence for them. I won't say you're wrong, just that you haven't given me enough reason to agree with you.

I'd like to say "hear hear," but I'm still not sure exactly what Carl
is saying. I wish he'd clarify by responding to my two questions.

I do agree that in a purely low-level, psychoacoustic sense, there are
a number of psychoacoustic effects that 3/2 generates more than 15/14.
I also agree that if our goal is to write music that predominantly
makes use of those effects, we may want to maximize the extent to
which they occur. But it's only in this very limited, low-level sense
in which I agree with everything Carl wrote. And it's never entirely
clear if that's the level he's talking on.

-Mike

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

> > Me neither. Every time we do, you seem to agree or disappear
> > only to reappear later asserting the same old diatribe.
>
> Yep. Because you seem to think there is no ambiguity about
> the absolute dissonance of dyads of the 11-limit and up,

I haven't said that.

> despite a lack of sufficient evidence to convince, well, anyone.

What I *have* said came out of years of traveling the
country playing extended JI intervals for/with people, and
in fact represented the consensus on this list for years,
until nihilism took over. Not only do you express concern-
troll "doubts" about any concrete idea anyone suggests, you
put forward no concrete ideas in return. It's argument for
the sake of argument and it's a big waste of your time and
everyone else's.

> Even Paul was flabbergasted at your insistence that a Tenney
> Height above 70 was an automatic disqualifier for consonance
> (he puts the Tenney Height at *least* around 100, FWIW, and
> has noted in himself the ability to tune up to a 17/13 by
> eliminating beats).

Sounds like you misrepresented my views to him, as it's
clear you've misrepresented his statements about POTE error
etc. here recently.

> > The all show both features I mentioned: that for simple
> > ratios, fields of attraction are wider and dissonance
> > increases more rapidly per cent of detuning -- features
> > also described by Werckmeister and Partch.
>
> And I acknowledged this.

You didn't. You concern-trolled that the matter was
"far from settled" and that "we" lack enough evidence
and and and... a bunch of other crap. Then you linked to
ten graphs that directly contradicted what you were saying.

-Carl

On Jan 15, 2012, at 2:54 PM, Carl Lumma <carl@...> wrote:

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

> Quarter-comma meantone, with 3:2 audibly flat and pure 5:4,
> demonstrates that this observation does not constitute a
> valid foundational principle for musical tuning.

Incorrect, since you can get quarter-comma meantone tuning
out of optimizations based on the two features I mentioned.

-Carl

For the third time now, you're failing to communicate your point clearly.
Now you're arguing with Cameron, and he thinks you're saying something very
different than you said. It sounds like you're saying things that
invalidate the role of learning in the net perception of consonance,
instead of invalidating the role of learning in the perception of
"concordance" specifically.

This theme has been played out dozens of times since I've joined the list.
It's stupid that these flamewars continually erupt without any party
checking to see if they understand what the other is saying.

-Mike

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

> > Yep. Because you seem to think there is no ambiguity about
> > the absolute dissonance of dyads of the 11-limit and up,
>
> I haven't said that.

You've certainly given the impression that that is the view you hold; if you go back to the time Ozan left the list, you were making much ado about the fact that quarter-tone intervals over a drone do not imply 11-limit intervals, because you claim 11-limit dyads are too discordant to possess a field of attraction.

> > despite a lack of sufficient evidence to convince, well, anyone.
>
> What I *have* said came out of years of traveling the
> country playing extended JI intervals for/with people,

I take it you're of the mind that anecdotal evidence is sufficient in any scientific study, then?

> and
> in fact represented the consensus on this list for years,
> until nihilism took over. Not only do you express concern-
> troll "doubts" about any concrete idea anyone suggests, you
> put forward no concrete ideas in return. It's argument for
> the sake of argument and it's a big waste of your time and
> everyone else's.

This is always where debates end up with you, Carl. Name-calling. "Concern-troll"? "Until nihilism took over"? Jesus, man. Gimme a break! What are these concrete ideas that I'm doubting? Why can't you do anything more than call names, cry "nihilism!" and make vague hand-waving gestures against what I say? When did it become concern-trolling to practice skepticism?

Honestly, man--anytime Mike or I press you on this matter, you just get all huffy and tell us we're full of shit, instead of offering *even the slightest bit* of evidence or argument. You know goddamn well that I am more than happy to modify my views in the face of compelling argument or evidence, and I just pointed out numerous occasions where you provided such and I duly modified my views. I *will* modify my views on this matter if you can give me sufficient reason to! Why is that so much to ask? You'll happily give me links and lengthy expositions on the economy, but when it comes to music theory all I get from you is "bullshit bullshit nihilism bullshit I'm right you're a troll bullshit nihilism read the archives trolling trolling bullshit". I know you archive all the significant stuff you write, I know you obsessively collect links and resources that support your views, so make with the good stuff already! Or admit it doesn't exist!

> > Even Paul was flabbergasted at your insistence that a Tenney
> > Height above 70 was an automatic disqualifier for consonance
> > (he puts the Tenney Height at *least* around 100, FWIW, and
> > has noted in himself the ability to tune up to a 17/13 by
> > eliminating beats).
>
> Sounds like you misrepresented my views to him, as it's
> clear you've misrepresented his statements about POTE error
> etc. here recently.

Sounds like you can't actually explain what you think I misrepresented. And if you don't believe my representation of Paul's views, ask Paul yourself. Or Mike, he was there too. I mean, it's not that hard to actually send a quick e-mail to someone and say "hey, Igs said that you said this, but that sounds wrong. What did you actually say?".

And did you or did you not express the belief that a Tenney Height of 70 is the cut-off for JI? There was much ado made over that number a while ago, I can't find the quote now but maybe someone else remembers.

> > > The all show both features I mentioned: that for simple
> > > ratios, fields of attraction are wider and dissonance
> > > increases more rapidly per cent of detuning -- features
> > > also described by Werckmeister and Partch.
> >
> > And I acknowledged this.
>
> You didn't.

In message #102845, I wrote:

"There are points they all share in common, such as 3/2 being the most concordant interval between 1/1 and 2/1 or 81/64 failing to be a local minimum."

Yes, they all have *some* commonalities. Although the Farey series curve has an overall downward slope, such that intervals like 15/1 or 17/1 might actually be equally-concordant with or even more concordant than intervals like 3/2. In fact, the Farey series curve might directly contradict your statement. But feel free to ignore that or dismiss the potential validity of that curve without any evidence, since you'll probably do that anyway. Also, the Vos-curve looks to me like it might violate the "for simple ratios, dissonance increases more rapidly per cent of detuning"--the slopes around the various minima look pretty similar. Of course, a look at the first or second derivative of that curve would settle it.

Also, really--you need to e-mail Paul and ask him if Harmonic Entropy has anything to do with "fields of attraction". I've gotten the impression from him that he doesn't believe that it does, that it's got nothing to do with "interval identities" and is nothing more than discordance. I can recall occasions where he's said that interval identity is tied to categorical perception, which is a result of conditioning and is not related to concordance. But I don't want to open myself up to charges of misrepresentation any more, so e-mail him yourself if you don't want to take my word for it. And make sure you actually do it, instead of just going on assuming you know what he's talking about, or there's no way I'm going to believe any arguments you make that are based on harmonic entropy.

> You concern-trolled that the matter was
> "far from settled" and that "we" lack enough evidence
> and and and... a bunch of other crap. Then you linked to
> ten graphs that directly contradicted what you were saying.

If you can tell me how those graphs contradicted what I'm saying (which is that the consonance and field of attraction of intervals of the 11-limit and up have not been definitively quantified), rather than just wave your hands around and call me names, you might actually come out of this looking like a civil and intelligent human being, instead of an arrogant jerk who has no evidence to back up his claims. You want to settle the matter? Point me to some evidence, or start making some compelling arguments. We've been over this before. You can't just call me names and tell me what I wrote was bullshit and expect the matter to be resolved.

-Igs

Igs,

it blows my mind that I went through the trouble of digging up a relevant
example of polyphonic rock music that I can't get a response to on here or
on FB where I had also posted it before deleting it out of embarrassment of
being ignored on your wall.

If you'd rather waste your time wrestling with Carl over, from as far as I
can see, insignificant minutia I guess its your business.

But you don't make anymore sense than the complaints you are saying about
Carl.

Chris

On Sun, Jan 15, 2012 at 6:07 PM, cityoftheasleep <igliashon@...>wrote:

> **
>
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> > > Yep. Because you seem to think there is no ambiguity about
> > > the absolute dissonance of dyads of the 11-limit and up,
> >
> > I haven't said that.
>
> You've certainly given the impression that that is the view you hold; if
> you go back to the time Ozan left the list, you were making much ado about
> the fact that quarter-tone intervals over a drone do not imply 11-limit
> intervals, because you claim 11-limit dyads are too discordant to possess a
> field of attraction.
>
>
> > > despite a lack of sufficient evidence to convince, well, anyone.
> >
> > What I *have* said came out of years of traveling the
> > country playing extended JI intervals for/with people,
>
> I take it you're of the mind that anecdotal evidence is sufficient in any
> scientific study, then?
>
>
> > and
> > in fact represented the consensus on this list for years,
> > until nihilism took over. Not only do you express concern-
> > troll "doubts" about any concrete idea anyone suggests, you
> > put forward no concrete ideas in return. It's argument for
> > the sake of argument and it's a big waste of your time and
> > everyone else's.
>
> This is always where debates end up with you, Carl. Name-calling.
> "Concern-troll"? "Until nihilism took over"? Jesus, man. Gimme a break!
> What are these concrete ideas that I'm doubting? Why can't you do anything
> more than call names, cry "nihilism!" and make vague hand-waving gestures
> against what I say? When did it become concern-trolling to practice
> skepticism?
>
> Honestly, man--anytime Mike or I press you on this matter, you just get
> all huffy and tell us we're full of shit, instead of offering *even the
> slightest bit* of evidence or argument. You know goddamn well that I am
> more than happy to modify my views in the face of compelling argument or
> evidence, and I just pointed out numerous occasions where you provided such
> and I duly modified my views. I *will* modify my views on this matter if
> you can give me sufficient reason to! Why is that so much to ask? You'll
> happily give me links and lengthy expositions on the economy, but when it
> comes to music theory all I get from you is "bullshit bullshit nihilism
> bullshit I'm right you're a troll bullshit nihilism read the archives
> trolling trolling bullshit". I know you archive all the significant stuff
> you write, I know you obsessively collect links and resources that support
> your views, so make with the good stuff already! Or admit it doesn't exist!
>
>
> > > Even Paul was flabbergasted at your insistence that a Tenney
> > > Height above 70 was an automatic disqualifier for consonance
> > > (he puts the Tenney Height at *least* around 100, FWIW, and
> > > has noted in himself the ability to tune up to a 17/13 by
> > > eliminating beats).
> >
> > Sounds like you misrepresented my views to him, as it's
> > clear you've misrepresented his statements about POTE error
> > etc. here recently.
>
> Sounds like you can't actually explain what you think I misrepresented.
> And if you don't believe my representation of Paul's views, ask Paul
> yourself. Or Mike, he was there too. I mean, it's not that hard to actually
> send a quick e-mail to someone and say "hey, Igs said that you said this,
> but that sounds wrong. What did you actually say?".
>
> And did you or did you not express the belief that a Tenney Height of 70
> is the cut-off for JI? There was much ado made over that number a while
> ago, I can't find the quote now but maybe someone else remembers.
>
>
> > > > The all show both features I mentioned: that for simple
> > > > ratios, fields of attraction are wider and dissonance
> > > > increases more rapidly per cent of detuning -- features
> > > > also described by Werckmeister and Partch.
> > >
> > > And I acknowledged this.
> >
> > You didn't.
>
> In message #102845, I wrote:
>
> "There are points they all share in common, such as 3/2 being the most
> concordant interval between 1/1 and 2/1 or 81/64 failing to be a local
> minimum."
>
> Yes, they all have *some* commonalities. Although the Farey series curve
> has an overall downward slope, such that intervals like 15/1 or 17/1 might
> actually be equally-concordant with or even more concordant than intervals
> like 3/2. In fact, the Farey series curve might directly contradict your
> statement. But feel free to ignore that or dismiss the potential validity
> of that curve without any evidence, since you'll probably do that anyway.
> Also, the Vos-curve looks to me like it might violate the "for simple
> ratios, dissonance increases more rapidly per cent of detuning"--the slopes
> around the various minima look pretty similar. Of course, a look at the
> first or second derivative of that curve would settle it.
>
> Also, really--you need to e-mail Paul and ask him if Harmonic Entropy has
> anything to do with "fields of attraction". I've gotten the impression from
> him that he doesn't believe that it does, that it's got nothing to do with
> "interval identities" and is nothing more than discordance. I can recall
> occasions where he's said that interval identity is tied to categorical
> perception, which is a result of conditioning and is not related to
> concordance. But I don't want to open myself up to charges of
> misrepresentation any more, so e-mail him yourself if you don't want to
> take my word for it. And make sure you actually do it, instead of just
> going on assuming you know what he's talking about, or there's no way I'm
> going to believe any arguments you make that are based on harmonic entropy.
>
> > You concern-trolled that the matter was
> > "far from settled" and that "we" lack enough evidence
> > and and and... a bunch of other crap. Then you linked to
> > ten graphs that directly contradicted what you were saying.
>
> If you can tell me how those graphs contradicted what I'm saying (which is
> that the consonance and field of attraction of intervals of the 11-limit
> and up have not been definitively quantified), rather than just wave your
> hands around and call me names, you might actually come out of this looking
> like a civil and intelligent human being, instead of an arrogant jerk who
> has no evidence to back up his claims. You want to settle the matter? Point
> me to some evidence, or start making some compelling arguments. We've been
> over this before. You can't just call me names and tell me what I wrote was
> bullshit and expect the matter to be resolved.
>
> -Igs
>
>
>

--- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
>
> Igs,
>
> it blows my mind that I went through the trouble of digging up a relevant
> example of polyphonic rock music that I can't get a response to on here or
> on FB where I had also posted it before deleting it out of embarrassment of
> being ignored on your wall.

Chris,

I don't know what you wanted from me in terms of a response. I listened to it. No offense but I didn't like it very much and didn't make it through the whole thing because of that, and was hoping to avoid saying so in public, but you wanted a response so here it is. Okay, polyphonic rock music. Different instruments doing different things. I've heard plenty of songs where different instruments play different things and could name probably hundreds. In my own songs there are also plenty of examples of this. I'm not sure what this is supposed to illustrate or why you were so intent on me hearing it, or why you're so testy about my lack of a response.

-Igs

Its immaterial if you liked the piece or not.

The point was I was trying to give you a concrete example of what I said.

> Igs, with all due respect writing 3 part counterpoint doesn't require
> classical training.
> The basic requirement is simply 3 independent melodies combining to form
harmony.

That's all it is? I thought there were all sorts of crazy rules to it,
about certain intervals that shouldn't be used in parallel etc. etc.; if
that's all it is, then I could take a stab at it when I get some time.

-Igs

But please don't let me interfere with continuing the flame war with Carl
over having ... flame wars.

Chris

On Sun, Jan 15, 2012 at 7:04 PM, cityoftheasleep <igliashon@...>wrote:

> **
>
>
> --- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
> >
> > Igs,
> >
> > it blows my mind that I went through the trouble of digging up a relevant
> > example of polyphonic rock music that I can't get a response to on here
> or
> > on FB where I had also posted it before deleting it out of embarrassment
> of
> > being ignored on your wall.
>
> Chris,
>
> I don't know what you wanted from me in terms of a response. I listened to
> it. No offense but I didn't like it very much and didn't make it through
> the whole thing because of that, and was hoping to avoid saying so in
> public, but you wanted a response so here it is. Okay, polyphonic rock
> music. Different instruments doing different things. I've heard plenty of
> songs where different instruments play different things and could name
> probably hundreds. In my own songs there are also plenty of examples of
> this. I'm not sure what this is supposed to illustrate or why you were so
> intent on me hearing it, or why you're so testy about my lack of a response.
>
> -Igs
>
>
>

--- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
>
> Its immaterial if you liked the piece or not.
>
> The point was I was trying to give you a concrete example of what I said.

Right. You mentioned other examples, too, which I was familiar with. The concept was clearly communicated, which I thought I had made clear. You said "three independent voices forming harmony" and I said "that's all it is? Okay, maybe I'll take a stab at it." As you explained it, it couldn't have been clearer. I did not even need an example.

> But please don't let me interfere with continuing the flame war with Carl
> over having ... flame wars.

Now, don't you start too!

-Igs

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Jan 15, 2012, at 2:54 PM, Carl Lumma <carl@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "lobawad" <lobawad@> wrote:
>
> > Quarter-comma meantone, with 3:2 audibly flat and pure 5:4,
> > demonstrates that this observation does not constitute a
> > valid foundational principle for musical tuning.
>
> Incorrect, since you can get quarter-comma meantone tuning
> out of optimizations based on the two features I mentioned.
>
> -Carl
>
> For the third time now, you're failing to communicate your
> point clearly.

Sorry? When were the other two times?

> Now you're arguing with Cameron, and he thinks you're saying
> something very different than you said.

He is? How do you know?

> It sounds like you're saying things that
> invalidate the role of learning in the net perception of consonance,
> instead of invalidating the role of learning in the perception of
> "concordance" specifically.

It does??? I said you 1/4-comma meantone is the result
of optimizations based on the features of consonance I
mentioned. That's true and it invalidates Cameron's point.
Graham said the same thing. Meanwhile, in several
recent posts I directly addressed the question of
concordance and training. But not in this post so I'm
not sure why you brought it up.

-Carl

Igs wrote:

> And did you or did you not express the belief that a Tenney
> Height of 70 is the cut-off for JI?

Correct. I've always taken extreme pains to note that an
exact TH threshold is not known. You can play he-said-she-said
with Paul all you want, but I'd rather not.

> > You concern-trolled that the matter was
> > "far from settled" and that "we" lack enough evidence
> > and and and... a bunch of other crap. Then you linked to
> > ten graphs that directly contradicted what you were saying.
>
> If you can tell me how those graphs contradicted what I'm
> saying (which is that the consonance and field of attraction
> of intervals of the 11-limit and up have not been definitively
> quantified),

Is that what you've been saying? Maybe I misunderstood.
I'm open to that possibility. Here's the initial paragraph:

>> I don't want to assume anything about consonance and
>> dissonance, nor fields of attraction. I want to assume as
>> little as possible. Fields of attraction are debatable.
>> Consonance and dissonance are debatable. There are about a
>> dozen HE curves that I've seen, with none of them being
>> clearly universally-superior and several of them conflicting
>> with each other. See the XA facebook group photos section.
>> However, the absolute distance of a tempered interval from
>> a rational interval is not debatable. I want to measure how
>> close each ET gets to the various subgroup tonality diamonds,
>> and then other people can debate what those measurements
>> mean as far as consonance/dissonance and intervallic
>> identities. This way if someone asks "which subgroup is most
>> accurately represented in 15-TET?", I can say "2.a.b.c.d" and
>> not have to worry about what the weighting did or did not do
>> to the error calculations.

I guess really don't know how to parse this, and maybe I
jumped to a conclusion. If consonance and dissonance are
debatable, any error formula is debatable, so I'm not sure
why you think unweighted error isn't. Pretty much everybody
uses weighted error these days, so it seems like it ought to
be less debatable than unweighted error.

I also don't know what a subgroup tonality diamond is. But
I think what you're calling a subgroup is actually the basis
of a subgroup, and you want the tonality diamond formed by
the basis elements. If so you may be thinking of the bases
as chords, which is what I tried to bring up before: if you're
interested in chords, measure the error of chords and don't
worry about subgroups. Subgroups are for when you aren't
targeting a particular chord.

-Carl

--- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
>
> Its immaterial if you liked the piece or not.
>
> The point was I was trying to give you a concrete example
> of what I said.

As I recall, your point was that the definition of "polyphonic"
doesn't really include the rules of classical voice leading,
as Igs seemed to think. That's true.

-Carl

Nevermind, I see Igs has already responded that he'd already
gotten the point. -Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@> wrote:
> >
> > Its immaterial if you liked the piece or not.
> >
> > The point was I was trying to give you a concrete example
> > of what I said.
>
> As I recall, your point was that the definition of "polyphonic"
> doesn't really include the rules of classical voice leading,
> as Igs seemed to think. That's true.
>
> -Carl
>

On Sun, Jan 15, 2012 at 5:13 AM, lobawad <lobawad@...> wrote:
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> > The all show both features I mentioned: that for simple
> > ratios, fields of attraction are wider and dissonance
> > increases more rapidly per cent of detuning -- features
> > also described by Werckmeister and Partch.
>
> Quarter-comma meantone, with 3:2 audibly flat and pure 5:4, demonstrates that this observation does not constitute a valid foundational principle for musical tuning.

OK Cameron, let me ask you a question: let's say that you take Carl's
claims to only apply to the specific psychoacoustic phenomenon whereby
a set of notes in a simple harmonic ratio generates a virtual
fundamental, or fuses into the sensation of a single complex pitch, or
something like that. So in that context, let's interpret what he's
saying as referring only to the likelihood that a set of notes
generates a strong one of those, and the ways in which this behavior
changes as you go up to more complex harmonics. You are free to care
or not to care about this particular phenomenon in your music as much
as you want.

Do you then take issue to anything that was said?

-Mike

On Mon, Jan 16, 2012 at 2:33 AM, Mike Battaglia <battaglia01@...> wrote:
>
> OK Cameron, let me ask you a question: let's say that you take Carl's
> claims to only apply to the specific psychoacoustic phenomenon whereby
> a set of notes in a simple harmonic ratio generates a virtual
> fundamental, or fuses into the sensation of a single complex pitch, or
> something like that.

Also, let's throw beatlessness in there too. So VFs and beatlessness.
You know, the usual sorts of effects that happen when you play otonal
chords. You can consider the "consonance" Carl's referring to as being
the extent to which intervals exhibit these qualities, not really the
"net consonance" or "pleasure" or whatever exhibited by a listener at
the end of the day.

I'm asking you to consider an interpretation where the statements made
only apply to these very raw, basic, psychoacoustic phenomena, and
completely independent of any larger learned system of JI logic that
might show you to make use of these intervals that don't exhibit these
qualities in isolation and apart from musical context. Just the raw
qualities themselves.

-Mike

On Mon, Jan 16, 2012 at 2:16 AM, Carl Lumma <carl@...> wrote:
> >
> > For the third time now, you're failing to communicate your
> > point clearly.
>
> Sorry? When were the other two times?

This is the third time I've tried to get you to clarify, to no avail.

> > Now you're arguing with Cameron, and he thinks you're saying
> > something very different than you said.
>
> He is? How do you know?

We'll see if I have to take this statement back, but I don't think so.

> > It sounds like you're saying things that
> > invalidate the role of learning in the net perception of consonance,
> > instead of invalidating the role of learning in the perception of
> > "concordance" specifically.
>
> It does??? I said you 1/4-comma meantone is the result
> of optimizations based on the features of consonance I
> mentioned. That's true and it invalidates Cameron's point.
> Graham said the same thing. Meanwhile, in several
> recent posts I directly addressed the question of
> concordance and training. But not in this post so I'm
> not sure why you brought it up.

Cameron's second reply, which says Igs hasn't launched into any
diatribes, suggests he's following what you said to Igs, and that his
overall post should be interpreted partially as a response to the
things you've been saying in general. And what you said to Igs was
this:

> The fields of attraction are narrower for higher-limit
> consonances, but the increase in dissonance per cent
> detuning is far less than for simple ratios. 15/14 doesn't
> even have a field of attraction outside of lab conditions.
> 15/7 sometimes does, and 4:7:15 or 7:14:15 usually will.
> This 15 vs 7 thing gets its identity more from musical
> context than from its size. By the time you get to 81/64,
> there's no field of attraction at all.

And then you followed it up with

> Actually it's not. And it can't be conditioned, at least
> not by any means anyone can do while leading a normal life.

And now we're about to launch into an argument about "fields of
attraction" again for the 21837912837th time since I joined the tuning
list. How do you know that Cameron even understands what you're saying
here? People who tend to compose in JI will probably go on and learn
to identify/categorize a lot of JI intervals, beyond the threshold
where psychoacoustic concordance ends. They'll also probably learn to
use them in musical contexts which could then be remembered when they
play the intervals in isolation, and this might change the net
perceptual "consonance" of the interval. It seems like you're saying
that they can't. If I hadn't just had this huge discussion with you
about categorical perception, I would think that's what you're saying.

-Mike

Why are you putting words in my mouth and then asking
someone if they have a problem with it?

-Carl

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> So in that context, let's interpret what he's
> saying as referring only to the likelihood that a set of notes
> generates a strong one of those, and the ways in which this behavior
> changes as you go up to more complex harmonics.
[snip]
> Do you then take issue to anything that was said?
>
> -Mike
>

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

> > Sorry? When were the other two times?
>
> This is the third time I've tried to get you to clarify,
> to no avail.

Clarify what??????

> Cameron's second reply, which says Igs hasn't launched into
> any diatribes, suggests he's following what you said to Igs,
> and that his overall post should be interpreted partially as

Cameron can clarify, but what he meant seems pretty
straightforward. He's saying 1/4-comma meantone shouldn't
be so popular if the pain increase per cent detuning for 3:2
is higher than for 5:4, given that the former bears more
tempering than the latter in 1/4-comma meantone. The answer
is that the temperament mapping can lead to this relationship
even with weighted error.

-Carl

On Mon, Jan 16, 2012 at 3:12 AM, Carl Lumma <carl@...> wrote:
>
> Why are you putting words in my mouth and then asking
> someone if they have a problem with it?
>
> -Carl

I didn't put any words in your mouth. I asked Cameron how he felt in
response to a certain interpretation of what you said. If you feel
that's not the right interpretation, feel free to clarify what the
proper interpretation is. This is now the fourth time I'm asking you
to clarify, and I'm the second person to do so, and you have still
not.

-Mike

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> Igs wrote:
>
> > And did you or did you not express the belief that a Tenney
> > Height of 70 is the cut-off for JI?
>
> Correct. I've always taken extreme pains to note that an
> exact TH threshold is not known. You can play he-said-she-said
> with Paul all you want, but I'd rather not.

Then I've grossly misunderstood remarks you've made in the past. You've suggested the number 70 to me before, but perhaps you were saying that's a "guaranteed safe" threshold, rather than an absolute cut-off. If you don't believe in an exact TH threshold, then we're on the same page (if not necessarily the same paragraph of it).

> Is that what you've been saying? Maybe I misunderstood.
> I'm open to that possibility. Here's the initial paragraph:
>
> >> I don't want to assume anything about consonance and
> >> dissonance, nor fields of attraction. I want to assume as
> >> little as possible. Fields of attraction are debatable.
> >> Consonance and dissonance are debatable. There are about a
> >> dozen HE curves that I've seen, with none of them being
> >> clearly universally-superior and several of them conflicting
> >> with each other. See the XA facebook group photos section.
> >> However, the absolute distance of a tempered interval from
> >> a rational interval is not debatable. I want to measure how
> >> close each ET gets to the various subgroup tonality diamonds,
> >> and then other people can debate what those measurements
> >> mean as far as consonance/dissonance and intervallic
> >> identities. This way if someone asks "which subgroup is most
> >> accurately represented in 15-TET?", I can say "2.a.b.c.d" and
> >> not have to worry about what the weighting did or did not do
> >> to the error calculations.
>
> I guess really don't know how to parse this, and maybe I
> jumped to a conclusion. If consonance and dissonance are
> debatable, any error formula is debatable, so I'm not sure
> why you think unweighted error isn't.

Okay. Try to read this without jumping to any conclusions, and if I am still not making sense, please ask for further clarification.

What I don't understand is why consonance and dissonance are necessarily inherent in error measures. I know why we, in this group, build consonance into our error metrics--because we are interested in consonance. But I can think of cases where someone seeking to apply Partch's principle (that complex intervals need to be tuned more accurately) would find Tenney weighting ass-backwards for their purposes. *You* might want to argue with them about the merits of Tenney weighting or the spuriousness of Partch's principle; I don't want to argue with them, and would rather just be able to say "okay, you don't like the weighting? Well, here's the unweighted error, make of it what you will." This is something Paul does a lot on XA--"you don't think this HE curve adequately represents your experience of consonance? Here, look at this other one, it's got a lower s (or a different probability distribution, etc.)." I'd prefer a variety of things to look at and offer people. That is all!

Of course unweighted error is debatable (you can debate whether it accurately reflects how consonant the intervals are, or how accurately it reflects the integrity of intervallic identity), but it makes the fewest assumptions about what error *should* reflect. It's also the "raw" information, which can be manipulated further more easily than any weighted forms.

> Pretty much everybody
> uses weighted error these days, so it seems like it ought to
> be less debatable than unweighted error.

It would be less *debated*, among this group which has reached a consensus, but no less *debatable*, as those outside the group may find issue with it. And for the record, I'm not saying we shouldn't look at weighted error as well. I just want the option to look at unweighted error, in the event that I may someday be confronted with someone who wants to debate the weighting methods we use.

> I also don't know what a subgroup tonality diamond is. But
> I think what you're calling a subgroup is actually the basis
> of a subgroup, and you want the tonality diamond formed by
> the basis elements.

Yeah, you've got it.

> If so you may be thinking of the bases
> as chords, which is what I tried to bring up before: if you're
> interested in chords, measure the error of chords and don't
> worry about subgroups. Subgroups are for when you aren't
> targeting a particular chord.

Okay. I think I need an alternative word to "subgroup". Maybe "subset"? I mean, the chords I'm looking at are subsets of the 15-limit, and the dyadic intervals formed between basis elements of the chords form a subset of the 15-limit tonality diamond. Does that make sense?

Now I'm going to write a post about Tenney weighting, because I have some questions that I want clarified.

-Igs

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

> Cameron can clarify, but what he meant seems pretty
> straightforward. He's saying 1/4-comma meantone shouldn't
> be so popular if the pain increase per cent detuning for 3:2
> is higher than for 5:4, given that the former bears more
> tempering than the latter in 1/4-comma meantone. The answer
> is that the temperament mapping can lead to this relationship
> even with weighted error.
>
> -Carl

First of all, it is a mistake, or a deliberate deception, to say that "the former (i.e., the fifth) bears more tempering than the latter (i.e., the major third) in 1/4-comma meantone."

The major third in quarter-comma meantone bears NO tempering: it is Just.

It is an anachronism to think of quarter-comma meantone as a "regular temperament" when "regular temperament" is meant as used on these lists. Quarter-comma meantone is Just in the same way Pythagorean tuning is Just: the intervals considered most vital are tuned Just. Neither tuning is based on approximation of Just intervals.

Neither you, nor Igliashon, nor Graham, gave an appropriate response by bringing up mapping and distribution of "error". There is NO error in the principal, and principle, harmonic interval of quarter-comma meantone. It is simply not a regular temperament in the same sense "regular temperament" is used here.

Let's look at the Erlich quote Igliashon provided:

"...it makes sense to scale them so that mistuning a simple ratio by a given amount (in cents) corresponds to more damage than mistuning a complex ratio by the same amount"

Quarter-comma meantone tuning, by this logic, does not make sense. It won't do to blather about distribution of error, mini-max, etc., for the 5:4 is not tempered at all.

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Sun, Jan 15, 2012 at 5:13 AM, lobawad <lobawad@...> wrote:
> >
> > --- In tuning@yahoogroups.com, "Carl Lumma" <carl@> wrote:
> >
> > > The all show both features I mentioned: that for simple
> > > ratios, fields of attraction are wider and dissonance
> > > increases more rapidly per cent of detuning -- features
> > > also described by Werckmeister and Partch.
> >
> > Quarter-comma meantone, with 3:2 audibly flat and pure 5:4, demonstrates that this observation does not constitute a valid foundational principle for musical tuning.
>
> OK Cameron, let me ask you a question: let's say that you take Carl's
> claims to only apply to the specific psychoacoustic phenomenon whereby
> a set of notes in a simple harmonic ratio generates a virtual
> fundamental, or fuses into the sensation of a single complex pitch, or
> something like that. So in that context, let's interpret what he's
> saying as referring only to the likelihood that a set of notes
> generates a strong one of those, and the ways in which this behavior
> changes as you go up to more complex harmonics. You are free to care
> or not to care about this particular phenomenon in your music as much
> as you want.
>
> Do you then take issue to anything that was said?
>
> -Mike

6:5 is, for example, a simple interval which neither fuses into a single complex pitch, nor does it generate a virtual fundamental which is not subjective. That leaves us "something like that". I'm cool with that- let's call it "doing that blending, thing, you know what I mean".

Yes, I can hear "that thing", so can everyone I've ever pointed it out to. Do that thing change, specifically diminish or become harder to perceive, the higher up the harmonic series the ratios in question are found? Yes. The "more complex", that, is, higher up the harmonic series, the ratio which is doing that thing is, the easier it is to make it fail to do that thing by tuning it away from the harmonic series.

This means that if it is maximizing "that thing" is what we want in a tuning, we must be careful to have our intervals from higher in the harmonic series as close as possible to their harmonic tuning, else they will fail to do that thing.

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

> I didn't put any words in your mouth. I asked Cameron how he felt in
> response to a certain interpretation of what you said. If you feel
> that's not the right interpretation,

It's not the right interpretation. -Carl

> feel free to clarify what the
> proper interpretation is. This is now the fourth time I'm asking you
> to clarify, and I'm the second person to do so, and you have still
> not.

Clarify what?

-Carl

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

> Do that thing change, specifically diminish or become harder to >perceive, the higher up the harmonic series the ratios in question are >found? Yes. The "more complex", that, is, higher up the harmonic >series, the ratio which is doing that thing is, the easier it is to >make it fail to do that thing by tuning it away from the harmonic >series.

Here I forgot to say "generally speaking" in reference to "higher" and "more complex". "More/less prominent partials" would be a better way to approach a harmonic series- scraping idly at my erhu, with its unusually strong 11th partial and x3 partials, it is hard NOT to wind up hitting a sweet 11:6, but I doubt I could find anything like a true 7:5.

--- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:
>> Quarter-comma meantone tuning, by this logic, does not make sense.
It won't do to blather about distribution of error, mini-max, etc., for
the 5:4 is not tempered at all.

Well, it just so happens that the maximum 5-odd limit (unweighted)
error is minimized when the major third is exactly 5:4. Try changing
the fifth from 5^(1/4) to sharper and flatter and you'll see that the
max error among 5:4, 3:2, 6:5 increases in both directions. Try it!

Kalle

On Jan 16, 2012, at 1:59 PM, "Carl Lumma" <carl@...> wrote:

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

> I didn't put any words in your mouth. I asked Cameron how he felt in
> response to a certain interpretation of what you said. If you feel
> that's not the right interpretation,

It's not the right interpretation. -Carl

Then you'll have to clarify what the right interpretation is. This is
request #5.

-Mike

--- In tuning@yahoogroups.com, "Kalle Aho" <kalleaho@...> wrote:

> --- In tuning@yahoogroups.com, "lobawad" <lobawad@> wrote:
> >> Quarter-comma meantone tuning, by this logic, does not make sense.
> It won't do to blather about distribution of error, mini-max, etc., for
> the 5:4 is not tempered at all.
>
> Well, it just so happens that the maximum 5-odd limit (unweighted)
> error is minimized when the major third is exactly 5:4. Try changing
> the fifth from 5^(1/4) to sharper and flatter and you'll see that the
> max error among 5:4, 3:2, 6:5 increases in both directions. Try it!
>
> Kalle
>

Unweighted error cannot be brought in as evidence by those whose position is based on the idea of weighting "inherent" in perception of harmonic series intervals.

At any rate, this does not change the fact that the simpler ratio of 3:2 is quite heavily tempered and the more complex interval of 5:4 is not tempered at all. The fundamental concept of more complex ratios "bearing" more temperament plainly clashes with quater-comma meantone.

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

>>> And did you or did you not express the belief that a Tenney
>>> Height of 70 is the cut-off for JI?
>>
>> Correct. I've always taken extreme pains to note that an
>> exact TH threshold is not known. You can play he-said-she-said
>> with Paul all you want, but I'd rather not.
>
> Then I've grossly misunderstood remarks you've made in the past.

Seems so. Look at my posts where I discuss the TH threshold.
There are probably a dozen of them since 2008. I took pains
to type again and again how it wasn't a hard cutoff, precisely
to avoid one day someone twisting my words in an argument such
as just happened.

> You've suggested the number 70 to me before, but perhaps you
> were saying that's a "guaranteed safe" threshold, rather than
> an absolute cut-off.

Yes. It's a number that doesn't include many questionable
ratios. Probably 100 is the number most frequently named
by myself and others. Usually I say things like "the
relationship starts to break down around..." For example
this entry in my FAQ
http://lumma.org/tuning/faq/#harmonicentropy
(which was originally taken from a post)

There's no way I can correct all the misconceptions you've
fired at me in the past 48 hours, but for one, whether Paul
can tune 17/13 by eliminating beats is entirely beside the
point since in normal musical settings one does not have the
luxury to examine individual intervals and tune them up or
down while listening for beats. That's why I said "outside
of laboratory conditions" in the parent post. And it's
ironic that Paul is the counterparty, since he was the most
vigorous and successful attacker of rational intonation
dogma probably in all of history. One of the first threads
I joined on this list consisted of Paul and I arguing over
whether there was a significant difference in the beating
patterns of 300 cents and 19/16 (Mills Digest 1217).

In any case the entire situation is bizarre, since I was
only agreeing with your statement that 'some people say the
identity of complex ratios is more quickly lost through
detuning'. Another way to say that is that the fields of
attraction are smaller. So I was just agreeing. But I also
pointed out that musical context helps with identification,
and that discordance increase per cent detuning is also
relevant, and that almost everyone since Werckmeister agrees
that 2:1 should bear less error than 6:5 if possible, and
hence almost all RMP work is done using weighted error.

> What I don't understand is why consonance and dissonance are
> necessarily inherent in error measures.

Error is only defined this way, full stop.

> I know why we, in this group, build consonance into our error
> metrics--because we are interested in consonance.

A thousand times no. We do not build consonance into error
metrics. We build error metrics to measure consonance.

> But I can think of cases where someone seeking to apply
> Partch's principle (that complex intervals need to be tuned
> more accurately) would find Tenney weighting ass-backwards
> for their purposes.

21/16 should be tuned as accurately as 2/1? Is that what
you think, or not?

> *You* might want to argue

What *I* want is completely immaterial.

> This is something Paul does a lot on XA--"you don't think this
> HE curve adequately represents your experience of consonance?
> Here, look at this other one, it's got a lower s (or a different
> probability distribution, etc.)."

All HE curves (or nearly all) have the features that we are
talking about in this thread, which pertain to your ET
profiling project. Paul is fitting curves to people's
stated preferences; an activity I consider to be largely a
waste of time at this point. But it's also relatively safe
because the underlying model is incredibly simple. In no
way does it cast doubt on our ability to measure error and
optimize tunings for temperaments.

> Of course unweighted error ... makes the fewest assumptions
> about what error *should* reflect.

No, that's not true! It makes just as many assumptions,
and, in the context of extrapolating error from a basis,
makes worse ones. Unweighted error can make sense if you
are declaring a couple of chords to be target consonances.
Such as 4:5:6 and 10:12:15 in classical music. These
chords don't mix high and low identities, and they're used
to define the concordance spectrum for an entire genre
of music, so unweighted error can work.

> I just want the option to look at unweighted error,

How many times have I told you it will be there?

> > If so you may be thinking of the bases
> > as chords, which is what I tried to bring up before: if you're
> > interested in chords, measure the error of chords and don't
> > worry about subgroups. Subgroups are for when you aren't
> > targeting a particular chord.
>
> Okay. I think I need an alternative word to "subgroup".
> Maybe "subset"?

I think you want "chord".

> I mean, the chords I'm looking at are subsets of the 15-limit,
> and the dyadic intervals formed between basis elements of the
> chords form a subset of the 15-limit tonality diamond. Does
> that make sense?

Not really. But I think I'll have some data that will
interest you when I get back from Orlando (end of next week).

-Carl

Cameron wrote:

> First of all, it is a mistake, or a deliberate deception, to
> say that "the former (i.e., the fifth) bears more tempering
> than the latter (i.e., the major third) in 1/4-comma meantone."
>
> The major third in quarter-comma meantone bears NO tempering:

Right, less tempering. Take your mind games somewhere else.

> It is an anachronism to think of quarter-comma meantone as a
> "regular temperament"

It is an anachronism to make idiotic statements on this
mailing list, but who's going to throw stones?

> Neither you, nor Igliashon, nor Graham, gave an appropriate
> response by bringing up mapping and distribution of "error".

Maybe your attitude as a student is to blame?

-Carl

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

> It's not the right interpretation. -Carl
>
> Then you'll have to clarify what the right interpretation is.
> This is request #5.

I have NO idea what you're talking about.

-Carl

On Jan 16, 2012, at 1:16 PM, lobawad <lobawad@...> wrote:

It is an anachronism to think of quarter-comma meantone as a "regular
temperament" when "regular temperament" is meant as used on these lists.
Quarter-comma meantone is Just in the same way Pythagorean tuning is Just:
the intervals considered most vital are tuned Just. Neither tuning is based
on approximation of Just intervals.

Ok, but surely you admit that (5/1)^(1/4) does a little bit of "That Thing"
in the same sense that 3/2 does? Even if you consider it to be conceptually
different for other reasons.

-Mike

--- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "Kalle Aho" <kalleaho@> wrote:
>
> > --- In tuning@yahoogroups.com, "lobawad" <lobawad@> wrote:
> > >> Quarter-comma meantone tuning, by this logic, does not make sense.
> > It won't do to blather about distribution of error, mini-max, etc., for
> > the 5:4 is not tempered at all.
> >
> > Well, it just so happens that the maximum 5-odd limit (unweighted)
> > error is minimized when the major third is exactly 5:4. Try changing
> > the fifth from 5^(1/4) to sharper and flatter and you'll see that the
> > max error among 5:4, 3:2, 6:5 increases in both directions. Try it!
> >
> > Kalle
> >
>
> Unweighted error cannot be brought in as evidence by those whose
position is based on the idea of weighting "inherent" in perception
of harmonic series intervals.
>
> At any rate, this does not change the fact that the simpler ratio
of 3:2 is quite heavily tempered and the more complex interval of 5:4
is not tempered at all. The fundamental concept of more complex
ratios "bearing" more temperament plainly clashes with quater-comma
meantone.

Saying that more complex ratios bear more tempering doesn't mean that
they always are bearing more tempering than simpler ratios. That they
bear more tempering should be understood as saying that they are able
to bear or withstand more tempering. But in the case of meantone they
don't have to and should not for the reason I mentioned.

Kalle

On Jan 16, 2012, at 2:47 PM, Carl Lumma <carl@...> wrote:

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

> It's not the right interpretation. -Carl
>
> Then you'll have to clarify what the right interpretation is.
> This is request #5.

I have NO idea what you're talking about.

-Carl

I deliberately put out the interpretation of your statements that makes the
least assumptions. It only considers error to measure the extent to which
certain psychoacoustic phenomena occur. "Fields of attraction" refer
exclusively to these psychoacoustic phenomena, not to "interval
identities," which is a vague and subjective term that could conceivably
refer to a number of different phenomena, some categorical in nature.

Please state explicitly what specific elements of this interpretation you
consider to not be in your view, or outside the consensus of the list.

-Mike

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

> Quarter-comma meantone tuning, by this logic, does not make sense. It won't do to blather about distribution of error, mini-max, etc., for the 5:4 is not tempered at all.

Intervals which aren't tempered are what minimax tunings always give us.

--- In tuning@yahoogroups.com, "Kalle Aho" <kalleaho@...> wrote:

> Well, it just so happens that the maximum 5-odd limit (unweighted)
> error is minimized when the major third is exactly 5:4. Try changing
> the fifth from 5^(1/4) to sharper and flatter and you'll see that the
> max error among 5:4, 3:2, 6:5 increases in both directions. Try it!

The same is true of 7-odd limit. And 9-odd limit. And 11-odd-limit in the meanpop extension of meantone. This leads to the 2.5 subgroup in this tuning to be a JI subgroup. This is just how minimax works: in the other main 11-limit extension, we get the 2.11/9 JI subgroup instead.

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

> The same is true of 7-odd limit. And 9-odd limit. And 11-odd-limit in the meanpop extension of meantone. This leads to the 2.5 subgroup in this tuning to be a JI subgroup. This is just how minimax works: in the other main 11-limit extension, we get the 2.11/9 JI subgroup instead.
>

Incidentally, the reason one gets a rank two JI subgroup is that meantone is a rank two temperament. For a rank three temperament, you get a rank three JI subgroup and so forth. For instance, 11-limit marvel gets you 2.9/5.11/9 as a JI subgroup. In JI, the "subgroup" is the entire "temperament"; in rank 1, it's just 2.

Something I meant to ask a little while ago: when we talk about "the
minimax tuning," what is the exact set of target intervals we're
using? I presume the tonality diamond corresponding to the odd-limit
in question?

-Mike

On Mon, Jan 16, 2012 at 3:57 PM, genewardsmith
<genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
> > The same is true of 7-odd limit. And 9-odd limit. And 11-odd-limit in the meanpop extension of meantone. This leads to the 2.5 subgroup in this tuning to be a JI subgroup. This is just how minimax works: in the other main 11-limit extension, we get the 2.11/9 JI subgroup instead.
> >
>
> Incidentally, the reason one gets a rank two JI subgroup is that meantone is a rank two temperament. For a rank three temperament, you get a rank three JI subgroup and so forth. For instance, 11-limit marvel gets you 2.9/5.11/9 as a JI subgroup. In JI, the "subgroup" is the entire "temperament"; in rank 1, it's just 2.

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

> In any case the entire situation is bizarre, since I was
> only agreeing with your statement that 'some people say the
> identity of complex ratios is more quickly lost through
> detuning'. Another way to say that is that the fields of
> attraction are smaller. So I was just agreeing. But I also
> pointed out that musical context helps with identification,
> and that discordance increase per cent detuning is also
> relevant, and that almost everyone since Werckmeister agrees
> that 2:1 should bear less error than 6:5 if possible, and
> hence almost all RMP work is done using weighted error.

The only claim I made involves other peoples' beliefs. I personally am agnostic as regards "fields of attraction", but that's moot in this discussion. In any case, why is it impossible to look at error from the perspective of fields of attraction, rather than consonance? Size of field of attraction is inversely proportional to consonance, suggesting that the exact opposite weighting should be used.

> > What I don't understand is why consonance and dissonance are
> > necessarily inherent in error measures.
>
> Error is only defined this way, full stop.

Explain. I understand error to be difference between a tempered interval and a rational interval; nothing in my understanding requires any definition of consonance or dissonance. It's just a difference between two numbers.

> > I know why we, in this group, build consonance into our error
> > metrics--because we are interested in consonance.
>
> A thousand times no. We do not build consonance into error
> metrics. We build error metrics to measure consonance.

What's the difference? And why can't error metrics be used for other purposes?

> > But I can think of cases where someone seeking to apply
> > Partch's principle (that complex intervals need to be tuned
> > more accurately) would find Tenney weighting ass-backwards
> > for their purposes.
>
> 21/16 should be tuned as accurately as 2/1? Is that what
> you think, or not?

*I* don't think anything. But I want to allow for a multitude of interpretations. Some people might think a fudged 2/1 is more sensible than a fudged 21/16. I don't begrudge them that. I can see, for instance, how 1215 cents still sounds like a 2/1 in a way that 485 cents no longer sounds like a 21/16, even if the former loses more consonance in the mistuning than the latter. I can also see some sense in the idea that simple ratios have *more* to lose, and going by the HE graphs it looks like a 3/2 can be mistuned *a lot* before it becomes as discordant as a pure 13/8 (for instance)...so it's sort of a "rob a rich man, or rob a poor man" kind of question--the rich man has more to lose, but can also bear a small loss more easily than the poor man. But like I said, I don't have a conviction either way.

> > *You* might want to argue
>
> What *I* want is completely immaterial.

Coulda fooled me!

> All HE curves (or nearly all) have the features that we are
> talking about in this thread, which pertain to your ET
> profiling project. Paul is fitting curves to people's
> stated preferences; an activity I consider to be largely a
> waste of time at this point. But it's also relatively safe
> because the underlying model is incredibly simple. In no
> way does it cast doubt on our ability to measure error and
> optimize tunings for temperaments.

What about the Farey series HE curve, with a downward overall slope? You seem to be avoiding responding to that.

> > Of course unweighted error ... makes the fewest assumptions
> > about what error *should* reflect.
>
> No, that's not true! It makes just as many assumptions,
> and, in the context of extrapolating error from a basis,
> makes worse ones.

Clearly I am missing something. How does unweighted error make any assumptions?

> > I just want the option to look at unweighted error,
>
> How many times have I told you it will be there?

Then why are you arguing with me about it?

> > Okay. I think I need an alternative word to "subgroup".
> > Maybe "subset"?
>
> I think you want "chord".

Okay, chord it is.

> > I mean, the chords I'm looking at are subsets of the 15-limit,
> > and the dyadic intervals formed between basis elements of the
> > chords form a subset of the 15-limit tonality diamond. Does
> > that make sense?
>
> Not really. But I think I'll have some data that will
> interest you when I get back from Orlando (end of next week).
>
> -Carl
>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> Something I meant to ask a little while ago: when we talk about "the
> minimax tuning," what is the exact set of target intervals we're
> using? I presume the tonality diamond corresponding to the odd-limit
> in question?

If it's not the q-limit diamond you need to say what it is. But you could come up with minimax no-twos stuff if you are into that, for instance, or other subgroup targets. Minimax machine, for instance, has a generator of (16/11)^(1/3), which is closer to 11edo than the POTE tuning.

On Mon, Jan 16, 2012 at 4:30 PM, genewardsmith
<genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> >
> > Something I meant to ask a little while ago: when we talk about "the
> > minimax tuning," what is the exact set of target intervals we're
> > using? I presume the tonality diamond corresponding to the odd-limit
> > in question?
>
> If it's not the q-limit diamond you need to say what it is. But you could come up with minimax no-twos stuff if you are into that, for instance, or other subgroup targets. Minimax machine, for instance, has a generator of (16/11)^(1/3), which is closer to 11edo than the POTE tuning.

Wait, do diamonds include ratios of 2 by default? I thought they didn't.

Is it that the minimax tuning by default has as a set of target
intervals that thing which is like a diamond, but also has 2's in it?

-Mike

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

> Wait, do diamonds include ratios of 2 by default?

That's the definition here:

http://xenharmonic.wikispaces.com/Diamonds

But obviously anything else could be the interval of equivalence.

Oh, I see; one is called a "diamond," and the other is called a
"tonality diamond." OK.

-Mike

On Mon, Jan 16, 2012 at 4:36 PM, genewardsmith
<genewardsmith@...> wrote:
>
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > Wait, do diamonds include ratios of 2 by default?
>
> That's the definition here:
>
> http://xenharmonic.wikispaces.com/Diamonds
>
> But obviously anything else could be the interval of equivalence.

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> Cameron wrote:
>
> > First of all, it is a mistake, or a deliberate deception, to
> > say that "the former (i.e., the fifth) bears more tempering
> > than the latter (i.e., the major third) in 1/4-comma meantone."
> >
> > The major third in quarter-comma meantone bears NO tempering:
>
> Right, less tempering. Take your mind games somewhere else.
>

Calling no tempering at all "less tempering" is silly at best. At worst, the way of thinking that causes such an error leads to the unproductive- antiproductive- wild goose chases you have been on all these years.

> > It is an anachronism to think of quarter-comma meantone as a
> > "regular temperament"
>
> It is an anachronism to make idiotic statements on this
> mailing list, but who's going to throw stones?
>
> > Neither you, nor Igliashon, nor Graham, gave an appropriate
> > response by bringing up mapping and distribution of "error".
>
> Maybe your attitude as a student is to blame?
>
> -Carl
>

Any calm and thoughtful observer can see that the things I am saying are reasonable. I think most who have put in the real effort have already figured out that you are no more qualified to "teach" musical thinking than Charles Lucy or L. Ron Hubbard, but have fun in your fantasy.

In the meantime I will continue to try now and again to make some simple and pertinent observations, for the benefit of any onlookers.

--- In tuning@yahoogroups.com, "Kalle Aho" <kalleaho@...> wrote:

> Saying that more complex ratios bear more tempering doesn't mean that
> they always are bearing more tempering than simpler ratios. That they
> bear more tempering should be understood as saying that they are able
> to bear or withstand more tempering. But in the case of meantone they
> don't have to and should not for the reason I mentioned.
>
> Kalle
>

However, more complex ratios do not bear more tempering, if the "melding" effect of coincident partials is what you are after. That sensation disappears more rapidly with fainter sonorities. If this sensation is not important, then thinking of musical intervals in terms of ratios is unnecessary.

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Jan 16, 2012, at 1:16 PM, lobawad <lobawad@...> wrote:
>
>
>
>
> It is an anachronism to think of quarter-comma meantone as a "regular
> temperament" when "regular temperament" is meant as used on these lists.
> Quarter-comma meantone is Just in the same way Pythagorean tuning is Just:
> the intervals considered most vital are tuned Just. Neither tuning is based
> on approximation of Just intervals.
>
> Ok, but surely you admit that (5/1)^(1/4) does a little bit of "That Thing"
> in the same sense that 3/2 does? Even if you consider it to be conceptually
> different for other reasons.
>
> -Mike
>

Sure. The partials of reference are clear and out in the open. They are not melding, but in quarter-comma meantone they are wobbling together in a "fat" way reminiscent of typical analog synth pads.

I thnk that what is important to note is that we have had, for the most part, Pythagorean tuning with its pure octaves, pure fifths and dissonant (not physically concordant or melding) intervals of color, then quarter-comma meantone, with its pure octaves, pure thirds and dissonant intervals of color, and then with 12-tET a return to pure octaves, pure (might as well be) fifths, and dissonant intervals of color.

I am not saying that this fundamental approach is the "best", merely that Occam's razor favors this description of what really has been going on over either "temperament" or "Just Intonation".

In short, it might be said that "we" have almost NO tolerance for "error", and history argues that what "we want" is frankly Just intervals, and frankly Unjust intervals.

These are reasonable observations pertinent to the subject "Pure-Octave Temperament Error".

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

> Well, I don't buy the whole "field of attraction" thing, that's all learning and conditioning. But other people do buy it and I hate debating it, so I won't.

Igliashon, let me ask you something: what, other than the sensation that beating near-conicident partials "should" or "want to" stop beating and blend into one, could "field of attraction" possibly mean?

If this is the only reasonable thing "field of attraction" can refer to, then why could we not call this same field the "field of revulsion", and cite the massive evidence for human delight in nearè coincident partials beating and NOT melding?

I think should we not observe that humans love both effects, and realize that we are dealing with "fields of interaction", and that neither attraction nor repulsion have the status of "should be".

On Jan 16, 2012, at 5:30 PM, "lobawad" <lobawad@...> wrote:

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Jan 16, 2012, at 1:16 PM, lobawad <lobawad@...> wrote:
>
Sure. The partials of reference are clear and out in the open. They are not
melding, but in quarter-comma meantone they are wobbling together in a
"fat" way reminiscent of typical analog synth pads.

OK.

I thnk that what is important to note is that we have had, for the most
part, Pythagorean tuning with its pure octaves, pure fifths and dissonant
(not physically concordant or melding) intervals of color, then
quarter-comma meantone, with its pure octaves, pure thirds and dissonant
intervals of color, and then with 12-tET a return to pure octaves, pure
(might as well be) fifths, and dissonant intervals of color.

Right.

I am not saying that this fundamental approach is the "best", merely that
Occam's razor favors this description of what really has been going on over
either "temperament" or "Just Intonation".

What do you mean?? I don't think anyone would disagree with your analysis.

Is your criticism a purely semantic one, over the use of the word
"temperament?"

In short, it might be said that "we" have almost NO tolerance for "error",
and history argues that what "we want" is frankly Just intervals, and
frankly Unjust intervals.

What would be a middle ground type interval ignored by history?

-Mike

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

> I am not saying that this fundamental approach is the "best", merely that
> Occam's razor favors this description of what really has been going on over
> either "temperament" or "Just Intonation".
>
> What do you mean?? I don't think anyone would disagree with your analysis.
>
> Is your criticism a purely semantic one, over the use of the word
> "temperament?"

Not semantic, but conceptual. The concept of "error" as used here is used consistently, but is not consistent with the concept of "error" as actually historically practiced, if we look at the bulk of Western tuning history. With all the discussion of cognition and perception that goes on here, I don't think we should ignore the grand historical "tests".

> What would be a middle ground type interval ignored by history?

First we'd have to say, listening to the dominant systems of 1/4 comma, 12-tET and Pythagorean, can we really find any intervals which are not either Just, damn near Just, or concretely NOT Just? I don't think so.

An example of "middle ground" intervals, that is, pretty-much-Just rather than (damn near) Just-plus- openly-beating would be the meantones that were happening between 1/4 comma and 12-tET. (The well-temperaments were more of the pure-plus-beating-combo mentality).
7/26 comma meantone, things like that. Not "ignored" by history, but "transitional" or something like that.

On Jan 16, 2012, at 5:48 PM, lobawad <lobawad@...> wrote:

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

> Well, I don't buy the whole "field of attraction" thing, that's all
learning and conditioning. But other people do buy it and I hate debating
it, so I won't.

Igliashon, let me ask you something: what, other than the sensation that
beating near-conicident partials "should" or "want to" stop beating and
blend into one, could "field of attraction" possibly mean?

Other than beatlessness, another relevant psychoacoustic phenomenon is
virtual pitch integration. Another is periodicity buzz. Another might be
effects resulting from combination tones, if you believe those have any
weight.

Even if you're using sine waves with no partials, there's still plenty of
stuff that happens when you play simple JI dyads and chords.

If this is the only reasonable thing "field of attraction" can refer to,
then why could we not call this same field the "field of revulsion", and
cite the massive evidence for human delight in nearè coincident partials
beating and NOT melding?

"Attraction" doesn't mean people are attracted to the sound; it's just an
attractor field for these phenomena.

One can just model the extent to which the effects occur and leave value
judgments out of it.

-Mike

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

> Igliashon, let me ask you something: what, other than the sensation that beating near-
> conicident partials "should" or "want to" stop beating and blend into one, could "field of
> attraction" possibly mean?

As someone who's studied middle-eastern music, you should know better than I that intervals can have a field of attraction that doesn't require the coincidence of partials. Once you are exposed to an interval enough, it develops a field of attraction to you. 1000 cents as a minor 7th has a field of attraction to people trained in 12-TET, such that they often report initially hearing a 7/4 as being a "flat minor 7th", i.e. in the field of attraction of 1000 cents but flat of being in the center of it. Some people report similar experiences even with 5/4 and 400 cents. Kind of like how I'm so used to the sound of 400 cents that I can usually tune my B string 400 cents above the open G in 12-TET by finding that just-right texture by ear, since I've done it so damn many times. 462 and 553 cents between the strings of my 13-ED2 guitar are getting there, too. Am I homing in on 17/13 and 11/8? I doubt it, unless I have the gain jacked up enough to hear the combination tones lock in. I think I've just familiarized myself enough with the character of those intervals that I can recognize them by ear. Meaning they now have fields of attraction for me. I'm sure oud players develop similar fields for the various maqamat.

-Igs

On Mon, Jan 16, 2012 at 6:22 PM, lobawad <lobawad@...> wrote:
>
> With all the discussion of cognition and perception that goes on here, I don't think we should ignore the grand historical "tests".

I don't have much to say in response to this, because the entire
"discussion of cognition and perception" that you're referencing, the
one which has continually taken place over the past few years, is
goofy and stupid. The traffic on here has been dead for a few months
because everyone's moved to the Xenharmonic Alliance group on
Facebook, where the vibe is a lot different, and which you should
check out. Paul Erlich is on there, for one thing, and there's a lot
more people playing and writing music, for another. Theorists over
there are trying to come up with tunings that composers like, and
composers think the theory is neat and they're trying to learn it.

Most importantly, the stuff we're fighting over seems to be these
stupid little nits that weren't really foundational to what the
"consensus" paradigm actually was. Go through the archives and you'll
see plenty of posts by Paul which are exceedingly careful to refrain
from making overbroad assertions about music cognition (except for
some of his early Mills posts, which are pretty funny). And Gene
obviously doesn't buy into the whole thing either, because he's
currently documenting all of these 13-limit essentially tempered
chords, with dyads like 13/10 and 14/11 in them, which aren't local
minima of HE.

You'll note that I said nothing to criticize Carl's specific views in
the above, mainly because I don't know what they are. Maybe he has
much harsher, more conservative views on consonance than everyone
else. Or, maybe people don't understand them. But regardless of his
views, the level of discourse on here has taken a total dive. I've talked
to Paul on the phone a million times about the way the tuning list
seems to have changed after he left, and all he can say is that he's
glad he left. And now that we're back to this kind of bullshit, it's taken
a step backwards.

> > What would be a middle ground type interval ignored by history?
>
> First we'd have to say, listening to the dominant systems of 1/4 comma, 12-tET and Pythagorean, can we really find any intervals which are not either Just, damn near Just, or concretely NOT Just? I don't think so.
>
> An example of "middle ground" intervals, that is, pretty-much-Just rather than (damn near) Just-plus- openly-beating would be the meantones that were happening between 1/4 comma and 12-tET. (The well-temperaments were more of the pure-plus-beating-combo mentality).
> 7/26 comma meantone, things like that. Not "ignored" by history, but "transitional" or something like that.

What's the difference between just-plus-beating and middle-ground?

-Mike

On Mon, Jan 16, 2012 at 7:44 PM, cityoftheasleep
<igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:
>
> > Igliashon, let me ask you something: what, other than the sensation that beating near-
> > conicident partials "should" or "want to" stop beating and blend into one, could "field of
> > attraction" possibly mean?
>
> As someone who's studied middle-eastern music, you should know better than I that intervals can have a field of attraction that doesn't require the coincidence of partials. Once you are exposed to an interval enough, it develops a field of attraction to you. 1000 cents as a minor 7th has a field of attraction to people trained in 12-TET, such that they often report initially hearing a 7/4 as being a "flat minor 7th", i.e. in the field of attraction of 1000 cents but flat of being in the center of it.

There's no effing possible way that you can possibly claim that this
is what you think Carl meant by fields of attraction.

So Carl, do you still think that people were clear on your statements
not referring to categorical perception?

-Mike

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

I wrote:

> > As someone who's studied middle-eastern music, you should know better than I that intervals can have a field of attraction that doesn't require the coincidence of partials. Once you are exposed to an interval enough, it develops a field of attraction to you. 1000 cents as a minor 7th has a field of attraction to people trained in 12-TET, such that they often report initially hearing a 7/4 as being a "flat minor 7th", i.e. in the field of attraction of 1000 cents but flat of being in the center of it.
> >

Mike wrote:

> There's no effing possible way that you can possibly claim that this
> is what you think Carl meant by fields of attraction.

I don't know what Carl means by fields of attraction. I can think of several possible meanings of the term, which are easily conflated with each other in practice. Hence the endless debates here about interval identities, HE minima, categorical perception, the role of conditioning, etc. What I know is that people can learn to reproduce or identify just about any interval (as defined in cents, at least) with decent-to-amazing accuracy. What this means to anybody's idea about fields of attraction, I can't say and won't speculate.

-Igs

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

> Other than beatlessness, another relevant psychoacoustic phenomenon >is virtual pitch integration.

Also called subjective pitch. The "wow, it's magic" virtual pitch is the missing fundamental of a harmonic series. The (truly subjective) subjective perceived root tone of, for example, even a simple dyad such as 6:5 should tell you plainly that virtual pitch integration does not exert a universal "force" we could call a field of attraction in the way f.o.a. is used on these lists.

>Another is periodicity buzz.

Periodicity buzz exerts a field of attraction?

>Another might be
> effects resulting from combination tones, if you believe those have >any
> weight.
> Even if you're using sine waves with no partials, there's still >plenty of
> stuff that happens when you play simple JI dyads and chords.

The fact that the ear is a non-linear device should slow any rushes to numerology hear.

>
> If this is the only reasonable thing "field of attraction" can refer to,
> then why could we not call this same field the "field of revulsion", and
> cite the massive evidence for human delight in nearè coincident partials
> beating and NOT melding?
>
> "Attraction" doesn't mean people are attracted to the sound; it's just an
> attractor field for these phenomena.

Why say "attraction" if all you mean is the region in which such effects occur? Why not then say "field of interaction", as I already suggested?

>
> One can just model the extent to which the effects occur and leave >value
> judgments out of it.

Yes: field of interaction. "Field of attraction" specifically and deliberately assumes human perception, and if you've read Partch, assumed "value" judgements.

On Tue, Jan 17, 2012 at 1:40 AM, lobawad <lobawad@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > Other than beatlessness, another relevant psychoacoustic phenomenon >is virtual pitch integration.
>
> Also called subjective pitch. The "wow, it's magic" virtual pitch is the missing fundamental of a harmonic series.

OK? How does that change anything I said?

> The (truly subjective) subjective perceived root tone of, for example, even a simple dyad such as 6:5 should tell you plainly that virtual pitch integration does not exert a universal "force" we could call a field of attraction in the way f.o.a. is used on these lists.

I never said it wasn't subjective, but as a general rule, simple
ratios cause the behavior to happen more than more complex ones, yes?

How is it being used on these lists? That's the only sense in which I
use it, and the only one I know of in which Paul uses it. Carl may be
using it differently, but I don't know.

> >Another is periodicity buzz.
>
> Periodicity buzz exerts a field of attraction?

Sure; if you're really close to 5/4 it'll start to sound more and more
like it's buzzing, and as you get away from it it'll start to warble
more and hit a maximum of warbliness until you get to another JI
ratio, and so on.

> >Another might be
> > effects resulting from combination tones, if you believe those have >any
> > weight.
> > Even if you're using sine waves with no partials, there's still >plenty of
> > stuff that happens when you play simple JI dyads and chords.
>
> The fact that the ear is a non-linear device should slow any rushes to numerology hear.

???? What did I say that's "numerology?"

And how do nonlinearities in the ear invalidate anything I've said?
I'm describing the behavior of various nonlinear effects that happen,
so you can't evoke the presence of nonlinearities to invalidate them.

> > "Attraction" doesn't mean people are attracted to the sound; it's just an
> > attractor field for these phenomena.
>
> Why say "attraction" if all you mean is the region in which such effects occur? Why not then say "field of interaction", as I already suggested?

I'm not the one who originally used the term, but I don't really care
about semantics.

> > One can just model the extent to which the effects occur and leave >value
> > judgments out of it.
>
> Yes: field of interaction. "Field of attraction" specifically and deliberately assumes human perception, and if you've read Partch, assumed "value" judgements.

It doesn't assume that to me. All you have to do is tell me what it
means for me to not assume it means something else. But if you want me
to call it a "field of interaction" with you from now on, I'll do
that, as long as we have something to talk about. There's no point
arguing over what words we use if there's nothing to say.

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Tue, Jan 17, 2012 at 1:40 AM, lobawad <lobawad@...> wrote:
> >
> > --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
> >
> > > Other than beatlessness, another relevant psychoacoustic phenomenon >is virtual pitch integration.
> >
> > Also called subjective pitch. The "wow, it's magic" virtual pitch is the missing fundamental of a harmonic series.
>
> OK? How does that change anything I said?

The perceived fundamental frequency of a single tone is simply not what is meant by "field of attraction" of an interval (dyad).

>
> > The (truly subjective) subjective perceived root tone of, for example, even a simple dyad such as 6:5 should tell you plainly that virtual pitch integration does not exert a universal "force" we could call a field of attraction in the way f.o.a. is used on these lists.
>
> I never said it wasn't subjective, but as a general rule, simple
> ratios cause the behavior to happen more than more complex ones, yes?

Then why don't you just say that simpler ratios have stronger psychoacoustic effects, or something like that?

>
> How is it being used on these lists? That's the only sense in which I
> use it, and the only one I know of in which Paul uses it. Carl may be
> using it differently, but I don't know.
>
> > >Another is periodicity buzz.
> >
> > Periodicity buzz exerts a field of attraction?
>
> Sure; if you're really close to 5/4 it'll start to sound more and more
> like it's buzzing, and as you get away from it it'll start to warble
> more and hit a maximum of warbliness until you get to another JI
> ratio, and so on.

And this has to do with "attraction" how?

>
> > >Another might be
> > > effects resulting from combination tones, if you believe those have >any
> > > weight.
> > > Even if you're using sine waves with no partials, there's still >plenty of
> > > stuff that happens when you play simple JI dyads and chords.
> >
> > The fact that the ear is a non-linear device should slow any rushes to numerology hear.
>
> ???? What did I say that's "numerology?"

"Sine waves with no partials". Sine have dyads and chords "have partials" in the human ear.

>
> And how do nonlinearities in the ear invalidate anything I've said?
> I'm describing the behavior of various nonlinear effects that happen,
> so you can't evoke the presence of nonlinearities to invalidate them.
>
> > > "Attraction" doesn't mean people are attracted to the sound; it's just an
> > > attractor field for these phenomena.
> >
> > Why say "attraction" if all you mean is the region in which such effects occur? Why not then say "field of interaction", as I already suggested?
>
> I'm not the one who originally used the term, but I don't really >care
> about semantics.

Don't be mentally lazy and dismiss any thoughtful look at fundamental concepts as "semantics".
>
> > > One can just model the extent to which the effects occur and leave >value
> > > judgments out of it.
> >
> > Yes: field of interaction. "Field of attraction" specifically and deliberately assumes human perception, and if you've read Partch, assumed "value" judgements.
>
> It doesn't assume that to me. All you have to do is tell me what it
> means for me to not assume it means something else. But if you want me
> to call it a "field of interaction" with you from now on, I'll do
> that, as long as we have something to talk about. There's no point
> arguing over what words we use if there's nothing to say.
>
> -Mike
>

Read Partch and you will see that "field of attraction" is a VERY loaded term.

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

> I don't know what Carl means by fields of attraction.

Until otherwise informed, we can hardly do anything but assume that the idea is being used in the sense Partch meant.

What Partch meant by "fields of attraction" was far more than psychoacoustics of dyads, and is something you might very well not want to swallow. On the other hand you might agree with the concept of "natural" hierarchies,gravitation toward a "1/1" etc. I think it's horseshit.

On Jan 17, 2012, at 5:01 AM, "lobawad" <lobawad@...> wrote:

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Tue, Jan 17, 2012 at 1:40 AM, lobawad <lobawad@...> wrote:
> >
> > --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
> >
> > > Other than beatlessness, another relevant psychoacoustic phenomenon
>is virtual pitch integration.
> >
> > Also called subjective pitch. The "wow, it's magic" virtual pitch is
the missing fundamental of a harmonic series.
>
> OK? How does that change anything I said?

The perceived fundamental frequency of a single tone is simply not what is
meant by "field of attraction" of an interval (dyad).

Meant by who?

> > The (truly subjective) subjective perceived root tone of, for example,
even a simple dyad such as 6:5 should tell you plainly that virtual pitch
integration does not exert a universal "force" we could call a field of
attraction in the way f.o.a. is used on these lists.
>
> I never said it wasn't subjective, but as a general rule, simple
> ratios cause the behavior to happen more than more complex ones, yes?

Then why don't you just say that simpler ratios have stronger
psychoacoustic effects, or something like that?

That's exactly what I said.

> Sure; if you're really close to 5/4 it'll start to sound more and more
> like it's buzzing, and as you get away from it it'll start to warble
> more and hit a maximum of warbliness until you get to another JI
> ratio, and so on.

And this has to do with "attraction" how?

Alright, "interaction" or whatever.

> > The fact that the ear is a non-linear device should slow any rushes to
numerology hear.
>
> ???? What did I say that's "numerology?"

"Sine waves with no partials". Sine have dyads and chords "have partials"
in the human ear.

Sorry, I'm lost. Sines have dyads?

> > Why say "attraction" if all you mean is the region in which such
effects occur? Why not then say "field of interaction", as I already
suggested?
>
> I'm not the one who originally used the term, but I don't really >care
> about semantics.

Don't be mentally lazy and dismiss any thoughtful look at fundamental
concepts as "semantics".

I'm all for discussing fundamental concepts, but it doesn't seem like we
are. It seems like you're saying the term "field of attraction" is
misleading and that you'd prefer a different term. OK, that's not a
terrible idea. Now what?

There is another sense in which I think the term "field of attraction" is
important, and that's for intervallic categorical perception. It's
precisely in this sense that I'd like Carl's statements to not be
interpreted.

-Mike

On Jan 17, 2012, at 5:27 AM, lobawad <lobawad@...> wrote:

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

> I don't know what Carl means by fields of attraction.

Until otherwise informed, we can hardly do anything but assume that the
idea is being used in the sense Partch meant.

What Partch meant by "fields of attraction" was far more than
psychoacoustics of dyads, and is something you might very well not want to
swallow. On the other hand you might agree with the concept of "natural"
hierarchies,gravitation toward a "1/1" etc. I think it's horseshit.

Was he using it in a sense more consistent with what we'd call categorical
perception? As in, does he assume that people have some kind of built-in
categorical perception for JI intervals?

-Mike

--- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "Kalle Aho" <kalleaho@> wrote:
>
> > Saying that more complex ratios bear more tempering doesn't mean that
> > they always are bearing more tempering than simpler ratios. That they
> > bear more tempering should be understood as saying that they are able
> > to bear or withstand more tempering. But in the case of meantone they
> > don't have to and should not for the reason I mentioned.
> >
> > Kalle
> >
>
> However, more complex ratios do not bear more tempering, if
the "melding" effect of coincident partials is what you are after.
That sensation disappears more rapidly with fainter sonorities. If
this sensation is not important, then thinking of musical intervals
in terms of ratios is unnecessary.

I'm not taking sides on the question whether complex ratios (are able
to) bear more tempering. I was just objecting to your claim that
quarter comma meantone is some kind of counterexample to this idea.

Kalle

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

> It is an anachronism to think of quarter-comma meantone as a "regular
temperament" when "regular temperament" is meant as used on these
lists. Quarter-comma meantone is Just in the same way Pythagorean
tuning is Just: the intervals considered most vital are tuned Just.
Neither tuning is based on approximation of Just intervals.

I object to the claim that quarter-comma meantone is not based on
approximation of just intervals. Theorists like Zarlino and Aaron
recognized 3:2 and 6:5 as the ideal intonations for the fifth and the
minor third. There is no evidence that flexible pitch instrumentalists
or vocalists targeted meantone tempered intervals in harmonies.

Kalle

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

> I deliberately put out the interpretation of your statements
> that makes the least assumptions. It only considers error to
> measure the extent to which certain psychoacoustic phenomena occur.
> "Fields of attraction" refer exclusively to these psychoacoustic
> phenomena, not to "interval identities," which is a vague and
> subjective term that could conceivably refer to a number of
> different phenomena, some categorical in nature.

I don't know what you mean. No psychoacoustic interpretation
is needed. Concordance and fields of attraction are
both experimentally-observed quantities.

-Carl

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

> So Carl, do you still think that people were clear on your statements
> not referring to categorical perception?

I think my statements were clear to anyone wanting to
read them. Apparently that did not include you, but it
seems to have included Gene, Graham, Kalle, and Igliashon.
I didn't mention categorical perception so I'm not sure
why you thought I was talking about it. Then again you
seem to think everyone at all times is talking about
categorical perception.

-Carl

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

> I don't know what you mean. No psychoacoustic interpretation
> is needed. Concordance and fields of attraction are
> both experimentally-observed quantities.

Citations/references?

-Igs

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

> I think my statements were clear to anyone wanting to
> read them. Apparently that did not include you, but it
> seems to have included Gene, Graham, Kalle, and Igliashon.

Did you see the part where I said "I don't know what Carl means by fields of attraction"?

-Igs

On Jan 17, 2012, at 4:24 PM, Carl Lumma <carl@...> wrote:

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

> I deliberately put out the interpretation of your statements
> that makes the least assumptions. It only considers error to
> measure the extent to which certain psychoacoustic phenomena occur.
> "Fields of attraction" refer exclusively to these psychoacoustic
> phenomena, not to "interval identities," which is a vague and
> subjective term that could conceivably refer to a number of
> different phenomena, some categorical in nature.

I don't know what you mean. No psychoacoustic interpretation
is needed. Concordance and fields of attraction are
both experimentally-observed quantities.

-Carl

This post still doesn't make clear what is being observed, nor what your
definition of "concordance" is.

-Mike

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

> I don't know what Carl means by fields of attraction.

Sorry, I thought you knew what fields of attraction are.
It's observed that when people are given a tunable tone
generator, set randomly, and are instructed to "tune" it,
they tend to turn the knob until they hit a simple ratio.
It's assumed that, on average, where they started is in
the field of attraction of the thing they stop at.

The preference for simple ratios along with the structure
of the rational numbers is all you need to get fields of
attraction. Partch coined the term. Genesis is generally
considered core reading for participating on this list,
but fields of attraction have been discussed in detail
here by Erlich and others (see the archives). The Stern-
Brocot tree is a good model of fields of attraction, as
are the maximum-maximum ranges of harmonic entropy curves.

> I can think of several possible meanings of the term,

Why do that when you can look it up (or ask)?

> categorical perception,

Categorical perception is a different phenomenon, which may
be related since the scales people learn hit many simple
ratios.

-Carl

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

> Did you see the part where I said "I don't know what Carl
> means by fields of attraction"?

I assumed Mike was still talking about lobowad's statement
about error optimization, though it's hard to tell since
all he seems to want to do is count how many times he's
asked me to "clarify".

So, do you have any questions on the error optimization
point? -Carl

On Jan 17, 2012, at 4:35 PM, "Carl Lumma" <carl@...> wrote:

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

> So Carl, do you still think that people were clear on your statements
> not referring to categorical perception?

I think my statements were clear to anyone wanting to
read them. Apparently that did not include you, but it
seems to have included Gene, Graham, Kalle, and Igliashon.

Nobody understands exactly what you're saying, and I certainly know for a
fact that neither Gene or Kalle have views in line with the ones you seem
to be advocating here.

I didn't mention categorical perception so I'm not sure
why you thought I was talking about it.

I didn't. I said that other people did. Igs, for example, said that
exposure to an interval like 1000 cents in 12-EDO can cause you to develop
a "field of attraction" to that that interval, and that he can tune 400
cents on his guitar by ear. Sounds like he's talking about categorical
perception to me. He then went on to say that he wasn't sure if this is
what you meant by "fields" of attraction.

-Mike

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

> This post still doesn't make clear what is being observed, nor
> what your definition of "concordance" is.

What's your definition of "green"? What is being observed
when we ask people to turn a color wheel until it is "green"?
What can we say about it? We say that it roughly corresponds
to light wavelengths of 525-575nm. This varies from person
to person. It's been shown that painters have a more
refined sense of color - more ways to describe it, and they're
sensitive to finer gradations. But none of this presents
much trouble for the term "green" and its meaning. One can
spend 6 hours/day looking at colors, and 650nm light will
not start to appear green. We can go into explanations about
rods and cones in the eye. We can talk about the composition
of sunlight and how it may have shaped the evolution of human
eyesight. If such explanations are upsetting, forget them.

-Carl

On Jan 17, 2012, at 4:46 PM, Carl Lumma <carl@...> wrote:

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

> I don't know what Carl means by fields of attraction.

Sorry, I thought you knew what fields of attraction are.
It's observed that when people are given a tunable tone
generator, set randomly, and are instructed to "tune" it,
they tend to turn the knob until they hit a simple ratio.
It's assumed that, on average, where they started is in
the field of attraction of the thing they stop at.

Alright, and what about people who hear things like 7/4 as "flat" at first
because they're used to 12-EDO and haven't adjusted yet? This is
specifically what I want you to "clarify" about.

-Mike

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

> I think my statements were clear to anyone wanting to
> read them. Apparently that did not include you, but it
> seems to have included Gene, Graham, Kalle, and Igliashon.
>
> Nobody understands exactly what you're saying,

Gene, Graham and Kalle understood the point perfectly
(not that they needed to wait for me to write it).

>> I didn't mention categorical perception so I'm not sure
>> why you thought I was talking about it.
>
> I didn't. I said that other people did. Igs, for example,

Sounds like you should be replying to them about it.

-Carl

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

> Alright, and what about people who hear things like 7/4
> as "flat" at first because they're used to 12-EDO and
> haven't adjusted yet? This is specifically what I want
> you to "clarify" about.

Categorical perception clearly affects people's behavior.
That's why psychologists came up with the concept.
I'm not a psychologist so I'm not an expert on categorical
perception. I don't know what to clarify about it.
I took one semester 101-level cogpsy in college. You'd
probably like it. Look into a cogpsy mailing list, or
try an online course.

-Carl

On Jan 17, 2012, at 5:02 PM, "Carl Lumma" <carl@...> wrote:

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

> This post still doesn't make clear what is being observed, nor
> what your definition of "concordance" is.

What's your definition of "green"? What is being observed
when we ask people to turn a color wheel until it is "green"?
What can we say about it?

OK, I'll rephrase: you've taken psychoustics out of it, and you're simply
stating that people have preferences for simple ratios, and that this has
been observed by watching people retune intervals and measuring the points
they consider to be maximally in tune. Correct?

So when you talk about fields of attraction, you're talking about fields of
people's preferences, not any specific psychoacoustic phenomenon in
particular. Correct?

-Mike

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> "cityoftheasleep" <igliashon@> wrote:
>
> > I don't know what Carl means by fields of attraction.
>
> Sorry, I thought you knew what fields of attraction are.

I used to think I knew what a lot of things were. But as with most learning curves, deeper knowledge often leads to greater uncertainty.

> It's observed that when people are given a tunable tone
> generator, set randomly, and are instructed to "tune" it,
> they tend to turn the knob until they hit a simple ratio.
> It's assumed that, on average, where they started is in
> the field of attraction of the thing they stop at.

I'd like to see the study this is based on. Can you point me to it?

> The preference for simple ratios along with the structure
> of the rational numbers is all you need to get fields of
> attraction. Partch coined the term. Genesis is generally
> considered core reading for participating on this list,
> but fields of attraction have been discussed in detail
> here by Erlich and others (see the archives). The Stern-
> Brocot tree is a good model of fields of attraction, as
> are the maximum-maximum ranges of harmonic entropy curves.

I read Genesis long ago. I did not much care for it at the time, and apparently missed absorbing some of the more salient points of it.

> > categorical perception,
>
> Categorical perception is a different phenomenon, which may
> be related since the scales people learn hit many simple
> ratios.

Let's not go there just yet.

-Igs

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

> So, do you have any questions on the error optimization
> point? -Carl

Only about whether different HE (or other models of discordance) curves would suggest different weighting procedures or not.

-Igs

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

> > > What I don't understand is why consonance and dissonance
> > > are necessarily inherent in error measures.
> >
> > Error is only defined this way, full stop.
>
> Explain. I understand error to be difference between a
> tempered interval and a rational interval; nothing in my
> understanding requires any definition of consonance or
> dissonance. It's just a difference between two numbers.

A "tempered interval" can mean something you get from a
mapping, or it can be any interval that is within another
interval's field of attraction. Error is the difference
between a consonant interval and a tempered one of the
latter type. Any decent mapping should give you tempered
intervals of the latter type also, at least when the
interval being mapped is consonant.

> > > I know why we, in this group, build consonance into our
> > > error metrics--because we are interested in consonance.
> >
> > A thousand times no. We do not build consonance into error
> > metrics. We build error metrics to measure consonance.
>
> What's the difference? And why can't error metrics be used
> for other purposes?

You can define error for anything, like the average
number of spelling mistakes in my posts. By all means,
proceed!

> > 21/16 should be tuned as accurately as 2/1? Is that what
> > you think, or not?
>
> *I* don't think anything.

Too bad! You should try tuning an instrument to play
2/1 and also 21/16, and then try detuning them by set
amounts.

> But like I said, I don't have a conviction either way.

You should try it if you're interested in this theory
stuff!

> > > *You* might want to argue
> >
> > What *I* want is completely immaterial.
>
> Coulda fooled me!

Sorry I gave you such an impression. Everything I
believed about music theory got proved wrong twice so far.
Finally it's to the point where that can't happen again.
RMP is far from perfect, but there are now clear limits
as to how wrong it can be, and a full research program
with well-funded experiments and tenure-track positions
would likely be required to improve these limits.
Even so, they aren't likely to improve a great deal.

> > All HE curves (or nearly all) have the features that we are
> > talking about in this thread, which pertain to your ET
> > profiling project. Paul is fitting curves to people's
> > stated preferences; an activity I consider to be largely a
> > waste of time at this point. But it's also relatively safe
> > because the underlying model is incredibly simple. In no
> > way does it cast doubt on our ability to measure error and
> > optimize tunings for temperaments.
>
> What about the Farey series HE curve, with a downward
> overall slope? You seem to be avoiding responding to that.

Eh? It's the first you've mentioned it. And why am I
constantly being accused of avoiding responses, when I
spend something like an hour/day reading and responding
to people here? Also, why haven't you apologized for
playing whisper down the lane with Paul, attributing
things to me that are directly contradicted in my FAQ?

> > > Of course unweighted error ... makes the fewest assumptions
> > > about what error *should* reflect.
> >
> > No, that's not true! It makes just as many assumptions,
> > and, in the context of extrapolating error from a basis,
> > makes worse ones.
>
> Clearly I am missing something. How does unweighted error
> make any assumptions?

Unweighted error is actually a weighting of course.
Just don't tell lobowad lest he fly into hysterics.

> > > I just want the option to look at unweighted error,
> >
> > How many times have I told you it will be there?
>
> Then why are you arguing with me about it?

I'm not!!!!!!!!! :)

-Carl

> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@> wrote:
> > It's observed that when people are given a tunable tone
> > generator, set randomly, and are instructed to "tune" it,
> > they tend to turn the knob until they hit a simple ratio.
> > It's assumed that, on average, where they started is in
> > the field of attraction of the thing they stop at.

I should note that this is how I define "being heard as": interval a can be said to be "heard as" interval b by a given listener if, given the opportunity to freely re-tune a so that it sounds maximally "in-tune" or otherwise "right", the listener in question would tune a to b.

Of course, this is all very listener-dependent and it makes no sense to me to talk about fields of attraction as entities that exist apart from a specific listener. Does 1/1 have a field of attraction if a particular listener cannot tune it accurately or consistently?

I wonder if anyone's isolated a neurological or physiological deficit that explains tone-deafness in a similar way to how color-blindness is explained....

-Igs

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

> > So, do you have any questions on the error optimization
> > point? -Carl
>
> Only about whether different HE (or other models of discordance)
> curves would suggest different weighting procedures or not.

The answer is no for any Gaussian HE. For Vos curves, I'd
have to think about it. -Carl

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

> > > It's observed that when people are given a tunable tone
> > > generator, set randomly, and are instructed to "tune" it,
> > > they tend to turn the knob until they hit a simple ratio.
> > > It's assumed that, on average, where they started is in
> > > the field of attraction of the thing they stop at.
>
> I should note that this is how I define "being heard as":
> interval a can be said to be "heard as" interval b by a given
> listener if, given the opportunity to freely re-tune a so that
> it sounds maximally "in-tune" or otherwise "right", the listener
> in question would tune a to b.

Yes, Paul used to use this phase to mean this, and it
caught on somewhat (I'm sure I have too).

> Of course, this is all very listener-dependent and it makes
> no sense to me to talk about fields of attraction as entities
> that exist apart from a specific listener.

The point is that it isn't listener-independent. The
concordance of octaves has even been observed in animal
models. It's just like the situation with green.

> I wonder if anyone's isolated a neurological or physiological
> deficit that explains tone-deafness in a similar way to how
> color-blindness is explained....

There are one or more conditions that lead to something
that might be called "tone deafness", but they are
extremely rare (faaar more rare than color blindness).

-Carl

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

> OK, I'll rephrase: you've taken psychoustics out of it, and
> you're simply stating that people have preferences for simple
> ratios, and that this has been observed by watching people
> retune intervals and measuring the points they consider to be
> maximally in tune. Correct?
> So when you talk about fields of attraction, you're talking
> about fields of people's preferences, not any specific
> psychoacoustic phenomenon in particular. Correct?

Now that I've taken out a life insurance policy... yes.

-Carl

On Tue, Jan 17, 2012 at 5:35 PM, Carl Lumma <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > OK, I'll rephrase: you've taken psychoustics out of it, and
> > you're simply stating that people have preferences for simple
> > ratios, and that this has been observed by watching people
> > retune intervals and measuring the points they consider to be
> > maximally in tune. Correct?
> > So when you talk about fields of attraction, you're talking
> > about fields of people's preferences, not any specific
> > psychoacoustic phenomenon in particular. Correct?
>
> Now that I've taken out a life insurance policy... yes.

Phew! So your "fields of attraction" are experimentally observed
entities that refer to people's preferences of intervals. OK.

Next question: You earlier said this, which started this entire thread

> The fields of attraction are narrower for higher-limit
> consonances, but the increase in dissonance per cent
> detuning is far less than for simple ratios. 15/14 doesn't
> even have a field of attraction outside of lab conditions.
> 15/7 sometimes does, and 4:7:15 or 7:14:15 usually will.
> This 15 vs 7 thing gets its identity more from musical
> context than from its size. By the time you get to 81/64,
> there's no field of attraction at all.

OK, so you've said to interpret the phrase "fields of attraction" as
being completely psychoacoustics-agnostic and referring entirely to
people's preferences. So above, it appears that you're describing
patterns of behavior for people's preferences. You're talking about
how much different intervals can take a beating before people stop
preferring them, in this case saying that simple intervals can take
less of a beating. And you're saying that as intervals get more
complex, people eventually stop preferring them at all. Correct?

-Mike

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

> A "tempered interval" can mean something you get from a
> mapping, or it can be any interval that is within another
> interval's field of attraction. Error is the difference
> between a consonant interval and a tempered one of the
> latter type. Any decent mapping should give you tempered
> intervals of the latter type also, at least when the
> interval being mapped is consonant.

But sometimes mappings give you intervals that are outside the field of attraction of the interval they're supposed to represent. Like Bug, which when optimized gives you a 6/5 that's squarely within the field of attraction of a 7/6. Or Father, which when optimized gives you an 8/3 and a 5/2 which are both in the field of attraction of 13/5 (or maybe even 18/7). It seems like that should be problematic for your description of what "error" is, but not for mine.

And are you also saying it's nonsense to define error for non-consonant intervals? It seems to me we can define the error for, say, 75/64 in 9-ET just fine (it's 7.9158 cents flat, FYI), despite the fact that 75/64 is not itself a consonance and is actually in the field of attraction of 7/6.

> > What's the difference? And why can't error metrics be used
> > for other purposes?
>
> You can define error for anything, like the average
> number of spelling mistakes in my posts. By all means,
> proceed!

First you say error is necessarily defined in relation to concordance. Now you say it can be defined for anything. Which is it?

> > > 21/16 should be tuned as accurately as 2/1? Is that what
> > > you think, or not?
> >
> > *I* don't think anything.
>
> Too bad! You should try tuning an instrument to play
> 2/1 and also 21/16, and then try detuning them by set
> amounts.

What good would that do? I can't move inductively from my experiences and preferences to something universal. Every time I do that, Gene tells me to give up the guitar!

> > But like I said, I don't have a conviction either way.
>
> You should try it if you're interested in this theory
> stuff!

Try having convictions? I used to! But like you, I've been proven wrong often enough that I've given up taking a stance one way or the other. I have too many questions that are unanswered, and maybe unanswerable in the current state of this field.

> Sorry I gave you such an impression. Everything I
> believed about music theory got proved wrong twice so far.

Only twice? You're doing better than I am!

> Finally it's to the point where that can't happen again.

What makes you so certain of this?

> RMP is far from perfect, but there are now clear limits
> as to how wrong it can be, and a full research program
> with well-funded experiments and tenure-track positions
> would likely be required to improve these limits.
> Even so, they aren't likely to improve a great deal.

What are those limits, how were they made clear, and how can you justify statements about the likelihood (or lack thereof) of its future improvement?

> > What about the Farey series HE curve, with a downward
> > overall slope? You seem to be avoiding responding to that.
>
> Eh? It's the first you've mentioned it.

The hell it is! It's at least the 3rd time I've mentioned it. It was among those graphs I linked to that you claimed all contradicted what I was saying, and I tried to call your attention to it again, and I even made a post here about it. Now, care to answer the question (which, to repeat it in case you missed it, is "how would we weight error if we wanted to reflect this model of concordance"? Or, alternatively, "if this (Farey series) curve turns out to be a better model for discordance than one of the non-sloping curves, what would that mean for Tenney weighting"?)

> And why am I
> constantly being accused of avoiding responses, when I
> spend something like an hour/day reading and responding
> to people here?

I dunno, you respond to some parts of my posts but not to others, and I just have to wonder whether you missed it or are deliberately ignoring it. I'm not accusing you of anything.

> Also, why haven't you apologized for
> playing whisper down the lane with Paul, attributing
> things to me that are directly contradicted in my FAQ?

Probably for the same reason you haven't apologized for calling me a troll, or for calling my questions bullshit or nihilism (even after admitting you misunderstood me).

> > Clearly I am missing something. How does unweighted error
> > make any assumptions?
>
> Unweighted error is actually a weighting of course.

Right, just like the null hypothesis is still a hypothesis. The only assumption I see it making is that we don't know how to correctly weight errors. Since I haven't seen the evidence yet that we *do* know how to correctly weight errors, it's an assumption I'm prepared to make.

-Igs

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

> > > So, do you have any questions on the error optimization
> > > point? -Carl
> >
> > Only about whether different HE (or other models of discordance)
> > curves would suggest different weighting procedures or not.
>
> The answer is no for any Gaussian HE. For Vos curves, I'd
> have to think about it. -Carl

Please do think about it, and please also consider the downward-sloping Farey series curve.

-Igs

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
> > Of course, this is all very listener-dependent and it makes
> > no sense to me to talk about fields of attraction as entities
> > that exist apart from a specific listener.
>
> The point is that it isn't listener-independent. The
> concordance of octaves has even been observed in animal
> models. It's just like the situation with green.

Concordance, sure, I'll buy that. But I'm talking about fields of attraction. You know, like when people try to tune a guitar or a piano or sing an interval, and they suck at it. They can't tell that the unison (or octave, or fifth, or whatever) is out-of-tune, and just blithely plow onward. I can think of hundreds of real-world cases where people have demonstrated this, and I'm sure you can too. This is no different than the experiment you're talking about--they have essentially random intervals (whatver the instrument is tuned to when they pick it up/sit down at it, or whatever note their voice hits when they start to sing), and a "knob" with which to freely tune it. And many consistently fail to hit even the simplest of simple ratios (the 1/1). If these fields of attraction are real and listener-independent, why aren't we all born with the ability to tune instruments by ear and sing perfect harmony?

-Igs

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
> > I should note that this is how I define "being heard as":
> > interval a can be said to be "heard as" interval b by a given
> > listener if, given the opportunity to freely re-tune a so that
> > it sounds maximally "in-tune" or otherwise "right", the listener
> > in question would tune a to b.
>
> Yes, Paul used to use this phase to mean this, and it
> caught on somewhat (I'm sure I have too).

This strikes me as a very useful operational definition.

> > Of course, this is all very listener-dependent and it makes
> > no sense to me to talk about fields of attraction as entities
> > that exist apart from a specific listener.
>
> The point is that it isn't listener-independent. The
> concordance of octaves has even been observed in animal
> models. It's just like the situation with green.

Saying that fields of attraction for all intervals are listener-independent is an extraordinary claim! (Unless you're only saying that octaves are listener-independent?) I demand extraordinary evidence.

It's interesting that you bring up color words, because their fields of attraction are definitely not the same across all languages. If you ask an average Vietnamese speaker to find the color "xanh", for example, I'm sure they're going to come up with something different from the average English "green". In fact, "xanh" has a much wider field of attraction than English color words, covering most of the colors referred to by both "green" and "blue" in English. Other languages might have separate, basic color words for what we'd call "light green" and "dark green".

If you're claiming that this situation never occurs in music, i.e. that JI is a truly universal musical language, you need some serious evidence to back that up.

Keenan

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

> First you say error is necessarily defined in relation to
> concordance. Now you say it can be defined for anything.
> Which is it?

Error in the context of RMP is about concordance.

> > Too bad! You should try tuning an instrument to play
> > 2/1 and also 21/16, and then try detuning them by set
> > amounts.
>
> What good would that do?

If trying it is no good, talking about it isn't likely to
be much better. I worked with marimbas and a giant hammer
dulcimer tuned up to the 32nd harmonic. It was an eye-
opener for me, anyway.

> > Finally it's to the point where that can't happen again.
>
> What makes you so certain of this?

RMP has been hammered on relentlessly by a wide variety of
people, including some very smart people, for 15 years on
mailing lists -- and there's a clear historical lineage for
it back as far as you want to go. It's consistent with all
known experiments. It can only be so wrong.

> > RMP is far from perfect, but there are now clear limits
> > as to how wrong it can be, and a full research program
> > with well-funded experiments and tenure-track positions
> > would likely be required to improve these limits.
> > Even so, they aren't likely to improve a great deal.
>
> What are those limits, how were they made clear, and how can
> you justify statements about the likelihood (or lack thereof)
> of its future improvement?

For example: a top 10 list isn't going to differ much
regardless of what error weighting comes back from any new
experiments we'd perform. Partly we know this because Paul,
Gene et al have tried nearly every reasonable weighting.
Partly because we get rank 2 temperaments out of dyadic
entropy minimizers. etc

> > > What about the Farey series HE curve, with a downward
> > > overall slope? You seem to be avoiding responding to that.
> >
> > Eh? It's the first you've mentioned it.
>
> The hell it is! It's at least the 3rd time I've mentioned it.
> It was among those graphs I linked to that you claimed all
> contradicted what I was saying, and I tried to call your
> attention to it again, and I even made a post here about it.

If you mentioned the 'Farey slope', I only saw it mentioned
along with a lot of other stuff (s parameter etc etc) that
I already said didn't matter.

> Now, care to answer the question (which, to repeat it in
> case you missed it, is "how would we weight error if we
> wanted to reflect this model of concordance"?

Same way (see my subsequent post).

> > > Clearly I am missing something. How does unweighted error
> > > make any assumptions?
> >
> > Unweighted error is actually a weighting of course.
>
> Right, just like the null hypothesis is still a hypothesis.

Unweighted error says that the errors of the primes are
equally important. That's more than a null hypothesis.
The null hypothesis would be: results are insensitive to
changes in weighting. That's ruled out (though as I noted
above, the results for *reasonable* weightings are
similar).

-Carl

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> > The answer is no for any Gaussian HE. For Vos curves, I'd
> > have to think about it. -Carl
>
> Please do think about it, and please also consider the
> downward-sloping Farey series curve.

I said any Gaussian HE, and that includes HEs based on a
Farey series.

I just re-skimmed the Vos paper Paul based the Vos-curve
entropy on. I'm not terribly convinced it's a good idea,
since for pure tones Vos reports that purity went down
linearly with detuning. Paul seems to be using the results
Vos' experiment with complex tones, where an exponential
relationship was found. I guess that means the Vos HE
curves reflect tones with partials. But the HE PDFs are
supposed to reflect interval recognition, not interval
purity judgements, though they probably could be interpreted
either way. But the Vos HE curves still have the feature,
also reported in other Vos papers, that the concordance of
simple ratios deteriorates faster per cent detuning, and my
point still holds about complex ratios getting their identity
from musical context (appearing in larger chords) more than
from their exact dyadic tunings. So I think you'll have to
look elsewhere for a clear justification of heavier weighting
for higher primes. Of course there's nothing against trying
and seeing what comes out.

-Carl

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

> And many consistently fail to hit even the simplest of simple
> ratios (the 1/1). If these fields of attraction are real and
> listener-independent, why aren't we all born with the ability
> to tune instruments by ear and sing perfect harmony?
>
> -Igs

Tuning a unison by elimination of beats is something almost
anyone can do. Who are these many people who can't? -C.

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

> > > Of course, this is all very listener-dependent and it makes
> > > no sense to me to talk about fields of attraction as entities
> > > that exist apart from a specific listener.
> >
> > The point is that it isn't listener-independent. The
> > concordance of octaves has even been observed in animal
> > models. It's just like the situation with green.
>
> Saying that fields of attraction for all intervals are
> listener-independent is an extraordinary claim!

I try to write carefully to avoid this kind of thing.
Did I say they were listener-independent? No! The fields
of attraction for different listeners are correlated --
namely, around 5- and 7-limit JI dyads.

> If you ask an average Vietnamese speaker to find the color
> "xanh", for example, I'm sure they're going to come up with
> something different from the average English "green". In fact,
> "xanh" has a much wider field of attraction than English
> color words, covering most of the colors referred to by both
> "green" and "blue" in English. Other languages might have
> separate, basic color words for what we'd call "light green"
> and "dark green".

That sounds like Sapir-Whorf and I demand extraordinary
evidence that there is any difference in perception behind
such differences in language.

> If you're claiming that this situation never occurs in
> music, i.e. that JI is a truly universal musical language,
> you need some serious evidence to back that up.

Howabout the fact that nowhere have people ever failed
to enjoy Western tonality? You can read the accounts of
Fillmore (composer and cousin to the President IIRC) on
how delightful native Americans found Western harmony.

-Carl

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
> > It's observed that when people are given a tunable tone
> > generator, set randomly, and are instructed to "tune" it,
> > they tend to turn the knob until they hit a simple ratio.
> > It's assumed that, on average, where they started is in
> > the field of attraction of the thing they stop at.
>
> I'd like to see the study this is based on. Can you
> point me to it?

Benade's experiments are described in his book
http://www.amazon.com/Fundamentals-Musical-Acoustics-Second-Revised/dp/048626484X

We already mentioned Partch
http://www.amazon.com/Genesis-Music-Creative-Fulfillments-Paperback/dp/030680106X/

Houtsma & Goldstein 1971 (Technical Report 484) found that
ability to identify pure-tone dyads (by identifying their VFs)
went down as the complexity of the frequency ratios involved
went up.

The dissonance curves of Plomp & Levelt, Kameoka & Kuriyagawa,
Sethares, and Erlich are often understood to show fields of
attraction.

-Carl

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

> Phew! So your "fields of attraction"

Not mine!

> > The fields of attraction are narrower for higher-limit
> > consonances, but the increase in dissonance per cent
> > detuning is far less than for simple ratios. 15/14 doesn't
> > even have a field of attraction outside of lab conditions.
> > 15/7 sometimes does, and 4:7:15 or 7:14:15 usually will.
> > This 15 vs 7 thing gets its identity more from musical
> > context than from its size. By the time you get to 81/64,
> > there's no field of attraction at all.
>
> OK, so you've said to interpret the phrase "fields of
> attraction" as being completely psychoacoustics-agnostic and
> referring entirely to people's preferences.

Not necc. preferences.

> So above, it appears that you're describing patterns of
> behavior for people's preferences. You're talking about how
> much different intervals can take a beating before people stop
> preferring them, in this case saying that simple intervals can
> take less of a beating.

Simple intervals can take more of a beating before people
will stop trying to tune back to them. They take less of
a beating before people can recognize that they're beating.

-Carl

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

> Tuning a unison by elimination of beats is something almost
> anyone can do. Who are these many people who can't? -C.

Clearly, you don't go to many open mics, and have not played in many rock bands, and have also not taught many guitar students. I have yet to meet a guitar student who didn't have to be taught what beats were, and how to eliminate them (and who didn't need months to years of practice doing so to get good at the practice).

-Igs

On Tue, Jan 17, 2012 at 7:52 PM, Carl Lumma <carl@...> wrote:
>
> > If you're claiming that this situation never occurs in
> > music, i.e. that JI is a truly universal musical language,
> > you need some serious evidence to back that up.
>
> Howabout the fact that nowhere have people ever failed
> to enjoy Western tonality?

Whoa, whoa, whoa, whoa, whoa, whoa, whoa!! Evidence?

-Mike

And again, why is it that some people cannot sing a harmony in-tune? Ever see a high school choir perform? Why is it that only good singers can sing pure harmony reliably?

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@> wrote:
>
> > And many consistently fail to hit even the simplest of simple
> > ratios (the 1/1). If these fields of attraction are real and
> > listener-independent, why aren't we all born with the ability
> > to tune instruments by ear and sing perfect harmony?
> >
> > -Igs
>
> Tuning a unison by elimination of beats is something almost
> anyone can do. Who are these many people who can't? -C.
>

On Tue, Jan 17, 2012 at 8:04 PM, Mike Battaglia <battaglia01@...> wrote:
> On Tue, Jan 17, 2012 at 7:52 PM, Carl Lumma <carl@...> wrote:
>>
>> > If you're claiming that this situation never occurs in
>> > music, i.e. that JI is a truly universal musical language,
>> > you need some serious evidence to back that up.
>>
>> Howabout the fact that nowhere have people ever failed
>> to enjoy Western tonality?
>
> Whoa, whoa, whoa, whoa, whoa, whoa, whoa!! Evidence?

Also, even besides evidence, where did this notion of "enjoying" stuff
come from? Didn't you just say that fields of attraction don't
necessarily reflect "preferences?" But now you're back to talking
about preferences again???

-Mike

The wikipedia entry
http://en.wikipedia.org/wiki/Sapir_Whorf#Color_terminology_research
concludes,
"Like Berlin and Kay, Maclaury found no significant room for
linguistic relativity in this domain, but rather concluded as
did Berlin and Kay that the domain is governed mostly by physical-
biological universals of human color perception.[44][45]"

The main page on the topic
http://en.wikipedia.org/wiki/Linguistic_relativity_and_the_color_naming_debate#Vision_science_and_theoretical_compatibility
after an excruciating account of the history of the debate in
linguistics, concludes,
"...there appear to be nontrivial biological constraints on
color categorization ... the available evidence seems compatible
with a position of moderate universality that leads to
expectations of probabilistic rather than deterministic cross-
cultural correspondence ... in color, relativism appears to
overlay a universalist foundation.[25]"

-Carl

> That sounds like Sapir-Whorf and I demand extraordinary
> evidence that there is any difference in perception behind
> such differences in language.

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
> > Tuning a unison by elimination of beats is something almost
> > anyone can do. Who are these many people who can't? -C.
>
> Clearly, you don't go to many open mics, and have not played
> in many rock bands,

Actually I have! When I worked at Keyboard I played a new
keyboard out with area bands at least once a month.

>(and who didn't need months to years of practice doing so to
>get good at the practice).

I've never met a guitarist who couldn't tune, in an emergency,
using the 5th-fret method. However they do seem to be unable
to tell you what chords they're using.

-Carl

I was in high school choir, and bicounty choir, and both sang
with beautiful intonation. I'm hoping to digitize some of the
VHS from our concerts soon. -C.

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> And again, why is it that some people cannot sing a harmony
> in-tune? Ever see a high school choir perform? Why is it
> that only good singers can sing pure harmony reliably?

Mike wrote:

>>>> If you're claiming that this situation never occurs in
>>>> music, i.e. that JI is a truly universal musical language,
>>>> you need some serious evidence to back that up.
>>>
>>> Howabout the fact that nowhere have people ever failed
>>> to enjoy Western tonality?
>>
>> Whoa, whoa, whoa, whoa, whoa, whoa, whoa!! Evidence?
>
> Also, even besides evidence, where did this notion of
> "enjoying" stuff come from? Didn't you just say that fields
> of attraction don't necessarily reflect "preferences?"
> But now you're back to talking about preferences again???

I believe I was reacting to (Keenan's? your?) statement
about JI being a universal musical language. If JI-based
music, such as Western music, were enjoyed in all nations
then I think that's evidence it is. Anyway I do submit
that it is, because the universality of concordance/
discordance contrast means it must be used or not, but
can't be completely ignored, in musical forms.

And I do submit that Western music -- both imported and
locally-made -- charts in every nation on Earth, while
local traditional forms chart seldom locally and never
internationally. Traditional forms are enjoyed by
enthusiasts (often Western scholars explicitly trying to
preserve them against extinction).

I submit that the Chinese spend more on pianos than on
traditional Chinese instruments, and I reckon they may
produce more pianos per capita than any Western nation.
That Africa slaves kept other elements of their traditional
music but adopted Western harmony with gusto.

I already mentioned the Fillmore account.

It may be objected that not only music, but language,
banking, and other elements of Western culture have spread
worldwide, often by violent means. My response, sure to
cause controversy that I will conveniently ignore, is that
there was not enough violence to account for the success
with which Western ideas spread, and that this spread is
really due to quasi-independent contests in each domain
being won by Western technologies, which were more complex
and more subtly and deeply connected to physical reality.
Violence was only one such contest -- Western guns killed
better. Banking was another -- Westerners had robust
property rights and contract law, abstract (trust-based)
media of exchange, and quantification of the time value of
money (interest). Western languages had larger vocabularies
and could be exchanged through reading, writing, and
printing (Western scholars developed phonetic systems for
many indigenous languages). Western music was the
xenharmonic music of its day, having 12 rather than 7 or 5
notes, 5-limit harmony, and meantone (and later diminished,
augmented, and dominant) comma pumps.

Now, I really must pack for Orlando. Sorry I'm such
a douche!

-Carl

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

> Actually I have! When I worked at Keyboard I played a new
> keyboard out with area bands at least once a month.

My guess is you were playing with seasoned vets, not the kind of garage punk bands I cut me teeth in (and still play with every now and again). Try spending more time with real amateur musicians.

> >(and who didn't need months to years of practice doing so to
> >get good at the practice).
>
> I've never met a guitarist who couldn't tune, in an emergency,
> using the 5th-fret method.

Ever taught someone the guitar as their first musical instrument? Learning to tune by ear and tune *well* is a skill that takes a long time to develop. It can be learned, and some people pick it up faster than others (those with AP pick it up right quick, it seems), but it does have to be learned. Mostly because there's little to distinguish a perfect 1/1 from an interval a few cents sharp or flat of it (unless you tune with overdrive on), and it's hard to tell if you're sharp or flat--and those little errors add up in a big way over two octaves. Most guitarists I know still struggle with it; the guys in my current band will sit there screwing around with the tuning pegs for 5-10 minutes and then give up and grab the tuner.

> However they do seem to be unable
> to tell you what chords they're using.

Yeah, that's a common problem.

-Igs

Lucky you! Maybe people from my neck of the woods just can't sing? In my high school, there were two choirs--"regular" (anyone could enroll) and "chorale" (audition required). The chorale audition involved singing a rehearsed melody in unison with a piano. Most of the boys that tried out failed the audition; I was one of 8 boys who passed. The tenors and basses were outnumbered roughly 5:1 by the altos and sopranos (girls, IOW). And only two of the boys passed with flying colors; I was not one of them, as I flubbed a few notes. In the "regular" choir were all the people who could not sing unison to a rehearsed melody--this choir was roughly twice the size of the chorale, and this is *after* people self-selected based on self-perceived musical ability and/or desire to participate in music. And even in the chorale, I'd hardly call our intonation "beautiful". I can probably track down some of our recordings if you don't believe me.

-Igs

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> I was in high school choir, and bicounty choir, and both sang
> with beautiful intonation. I'm hoping to digitize some of the
> VHS from our concerts soon. -C.
>
> --- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@> wrote:
> >
> > And again, why is it that some people cannot sing a harmony
> > in-tune? Ever see a high school choir perform? Why is it
> > that only good singers can sing pure harmony reliably?
>

On Tue, Jan 17, 2012 at 9:59 PM, Carl Lumma <carl@...> wrote:
>
> Mike wrote:
>
> Anyway I do submit that it is, because the universality of concordance/
> discordance contrast means it must be used or not, but
> can't be completely ignored, in musical forms.
//snip

I'm not going to say that Western music has any more intrinsic value
than the music of any other culture. But, for the sake of argument,
let's say there are things that Western tonality has that other styles
of music don't have, and these things are rather agreeable to most
people.

I still doubt that concordance is the most important part of Western
tonality. There's a million other things that we haven't even fully
explored. There's this huge, overarching logical structure of how
intervals are laid out, connect with one another, "resolve" to one
another, combine with one another, form scales, are arranged in order
with respect to one another, are habitually used in an unspoken
logical/musical context with one another, etc.

The Bach retunings preserve almost all of those things except for the
concordance, and although concordant tunings add a sweetness to the
whole thing which only adds to the enjoyment of it all (at least in
this case), the other things do more to establish the effect of
"tonality" more than the concordance does. You can claim that
eliminating the concordance makes it suck, but there's a lot of us who
don't share that value judgment. And these are things I don't think we
know much about.

What I do know is that this "background logical structure" I talked
about, which is fundamental to western tonality, means a lot. It means
that when you play two part inventions, you get the sensation of
triadic harmony, complete with corresponding western emotions, whether
or not you ever end up playing three notes at the same time. It means
that you constantly have some kind of background "key" or "scale" or
"mode" or whatever in your mind, typically something like the major or
minor scale, which you change in small doses as new notes are added.
It means that certain chords which are extremely concordant, like
4:5:6:7, can be suddenly very dissonant, like in German sixth chords.
It means that if you warp the hell out of the diatonic structure so
that the augmented fourths are closer to 3/2 than the perfect fifths,
the augmented fourths will sound like tritones that'd be nice if they
resolved. None of this necessarily has anything to do with concordance
at all, although concordance can be used as a tool to augment
different aspects of this structure.

And the more you start playing in different tunings, the more at least
some people start building similar background logical structures for
that tuning, and actual concordance matters less and less; sooner or
later 11/8 now sounds like it's implying 8:9:10:11:12 and at this
point I have to take 4 tabs of LSD and go on a guided Zen meditation
to become aware of all of the stuff I'm filtering out and projecting
onto the sound.

That's my experience, anyway. Background logical structural stuff
>>>>>>>>>>>> concordance.

> Now, I really must pack for Orlando. Sorry I'm such
> a douche!

Have fun! Is it vacation?

-Mike

On Wed, Jan 18, 2012 at 1:08 AM, Mike Battaglia <battaglia01@...> wrote:
> It means that if you warp the hell out of the diatonic structure so
> that the augmented fourths are closer to 3/2 than the perfect fifths,
> the augmented fourths will sound like tritones that'd be nice if they
> resolved.

Typo, I meant that the 3/2's will sound like tritones that'd be nice
if they resolved.

-Mike

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
> I believe I was reacting to (Keenan's? your?) statement
> about JI being a universal musical language. If JI-based
> music, such as Western music, were enjoyed in all nations
> then I think that's evidence it is. Anyway I do submit
> that it is, because the universality of concordance/
> discordance contrast means it must be used or not, but
> can't be completely ignored, in musical forms.

But Western music isn't in JI. It's in meantone and 12edo.

So this would be an argument that everyone really has fields of attraction to diatonic intervals, not to JI intervals. For example it'd be perfectly reasonable for someone to hear 7/4, think "that's flat, better sharpen it", and sharpen it until it gets near 9/5, then eliminate the beats from the 9/5. This makes no sense if the fields of attraction are based on JI, because 7/4 is a simpler fraction than 9/5, but it makes perfect sense if they're based on the ubiquitous scale all over the world.

Keenan

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

> Lucky you! Maybe people from my neck of the woods just can't
> sing? In my high school, there were two choirs--"regular"
> (anyone could enroll) and "chorale" (audition required).
> The chorale audition involved singing a rehearsed melody in
> unison with a piano. Most of the boys that tried out failed
> the audition; I was one of 8 boys who passed. The tenors and
> basses were outnumbered roughly 5:1 by the altos and sopranos
> (girls, IOW). And only two of the boys passed with flying
> colors; I was not one of them, as I flubbed a few notes. In
> the "regular" choir were all the people who could not sing
> unison to a rehearsed melody--this choir was roughly twice the
> size of the chorale, and this is *after* people self-selected
> based on self-perceived musical ability and/or desire to
> participate in music. And even in the chorale, I'd hardly
> call our intonation "beautiful". I can probably track down
> some of our recordings if you don't believe me.

My sense moving around the country is that the area in
Pennsylvania I'm from (near Allentown) has/had an unusually
rich music culture. It wasn't uncool to be in choir and band
(perhaps because all the pretty girls were in choir and many
were also in band).

Lots of parents were in the local concert band (founded 1900),
which shared its director with the HS band:
http://www.redhillband.org

Likewise there was an excellent adult choir directed by the
our HS choir director: http://www.valchor.com

The HS choir required an audition every year. Bicounty choir
and tricounty band were assembled out of the first 2-3 chairs
of each section of each participating school. These do exist
all over the country. There were also states but I didn't
make it (my friend Jeff did, and he later went to Julliard):
http://www.jeffreywohlbach.com

I had been singing in church choirs since I was 4 or 5. My
Dad also sang in the church choir some years. His dad had
a polka band (near Detroit):
/makemicromusic/topicId_22864.html#22864

My Mom's mom taught piano her whole life. I just realized
we don't have any recordings of her playing! She was the
best musician in my family, by far. She gave me lessons
when I was little. Her favorite composer was Chopin, which
she played competently.

Our HS choir sang not only every day during school for a
full period, but also at a different local church every
Sunday during the winter.

Towards Allentown (20-30min away) there were very strong
groups like the Bethlehem Bach Choir: http://www.bach.org

Allentown band: http://www.allentownband.com

and Willard Martin's harpsichord shop - the guy who made
the chromatic harpsichord
http://www.christopherstembridge.org/cromatico.htm
used on this album
http://www.amazon.com/Consonanze-Stravaganti-Giovanni-Macque/dp/B000002K1U

Toward Philadelphia (45-60min away), the Curtis school,
Philadelphia brass (quintet), Philadelphia orchestra, etc.

There were several rock bands in my graduating class that
bought studio time to make albums (tapes): Tom's Unit, Slug,
the Ka, Jungle Green... There was a "battle of the bands"
every year with an applause-o-meter.

Spending time in North Florida and California, I got the
sense the local populations were musically illiterate by
comparison. But a good 15 years has passed and things may
have declined in PA for all I know. In Indiana there were
lots of talented musicians, but I almost never left campus,
where there was a conservatory, so it's not a good sample.

With this background it's amazing I didn't become a more
accomplished musician... a tribute to my slacking off as
much as possible.

In any case, to replicate this kind of thing for my kids in
the East bay would cost upwards of $40,000/yr... to send
them both to Crowden.

-Carl

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

> The Bach retunings preserve almost all of those things except for the
> concordance, and although concordant tunings add a sweetness to the
> whole thing which only adds to the enjoyment of it all (at least in
> this case), the other things do more to establish the effect of
> "tonality" more than the concordance does.

I don't disagree.

> > Now, I really must pack for Orlando. Sorry I'm such
> > a douche!
>
> Have fun! Is it vacation?

My friend's getting hitched. Big party / reunion!

-Carl

--- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@...> wrote:
> But Western music isn't in JI.

For my purposes in that discussion, it is. Circa 1700, it
was the only indigenous music to use 5-limit harmony, or
really harmony at all. And most of it at that time was
performed in adaptive JI.

> So this would be an argument that everyone really has fields
> of attraction to diatonic intervals, not to JI intervals.

No.

> For example it'd be perfectly reasonable for someone to hear
> 7/4, think "that's flat, better sharpen it", and sharpen it
> until it gets near 9/5, then eliminate the beats from the 9/5.
> This makes no sense if the fields of attraction are based
> on JI, because 7/4 is a simpler fraction than 9/5, but it makes
> perfect sense if they're based on the ubiquitous scale all over
> the world.

Benade observed people tuning 7/4, not 9/5. And if you
try to tune them, you'll find it's a lot harder to get 9/5
than 7/4.

-Carl

I have great difficulty with fifth fret tuning. But it helps to play a tune between the two strings because then I can spot where it's wrong.
I think I have some kind of AP but that's a different story

Graham

------Original message------
From: cityoftheasleep <igliashon@...>
To: <tuning@yahoogroups.com>
Date: Wednesday, January 18, 2012 5:46:01 AM GMT-0000
Subject: [tuning] Re: Pure-Octave Temperament Error

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

> Actually I have! When I worked at Keyboard I played a new
> keyboard out with area bands at least once a month.

My guess is you were playing with seasoned vets, not the kind of garage punk bands I cut me teeth in (and still play with every now and again). Try spending more time with real amateur musicians.

> >(and who didn't need months to years of practice doing so to
> >get good at the practice).
>
> I've never met a guitarist who couldn't tune, in an emergency,
> using the 5th-fret method.

Ever taught someone the guitar as their first musical instrument? Learning to tune by ear and tune *well* is a skill that takes a long time to develop. It can be learned, and some people pick it up faster than others (those with AP pick it up right quick, it seems), but it does have to be learned. Mostly because there's little to distinguish a perfect 1/1 from an interval a few cents sharp or flat of it (unless you tune with overdrive on), and it's hard to tell if you're sharp or flat--and those little errors add up in a big way over two octaves. Most guitarists I know still struggle with it; the guys in my current band will sit there screwing around with the tuning pegs for 5-10 minutes and then give up and grab the tuner.

> However they do seem to be unable
> to tell you what chords they're using.

Yeah, that's a common problem.

-Igs

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

> And I do submit that Western music -- both imported and
> locally-made -- charts in every nation on Earth, while
> local traditional forms chart seldom locally and never
> internationally. Traditional forms are enjoyed by
> enthusiasts (often Western scholars explicitly trying to
> preserve them against extinction).

What counts as "Western"? Do you just mean "in Western tuning"?

> That Africa slaves kept other elements of their traditional
> music but adopted Western harmony with gusto.

...in ways that were rarely if ever used in Western music, and with copious microtonal melodic inflections, that went on to dominate the strict Western approaches that they borrowed from.

> It may be objected that not only music, but language,
> banking, and other elements of Western culture have spread
> worldwide, often by violent means. My response, sure to
> cause controversy that I will conveniently ignore, is that
> there was not enough violence to account for the success
> with which Western ideas spread, and that this spread is
> really due to quasi-independent contests in each domain
> being won by Western technologies, which were more complex
> and more subtly and deeply connected to physical reality.

More effective at manifesting human desires, I'd say. And look what else that's got us: global warming (automobiles, coal power), nuclear weaponry and global warfare, epidemic obesity (McDonald's, Coca-Cola, Bud Lite, etc) and mental illness (look at prescription drug sales statistics), topsoil erosion and declining nutrient density in the food supply (factory farms, monocultured and GM foods), depleted fisheries and toxic levels of mercury in seafood, declining biodiversity (mass extinctions on a global scale), multi-drug-resistant diseases...NASCAR, Two and a Half Men, and Justin Bieber.

> Violence was only one such contest -- Western guns killed
> better. Banking was another -- Westerners had robust
> property rights and contract law, abstract (trust-based)
> media of exchange, and quantification of the time value of
> money (interest). Western languages had larger vocabularies
> and could be exchanged through reading, writing, and
> printing (Western scholars developed phonetic systems for
> many indigenous languages). Western music was the
> xenharmonic music of its day, having 12 rather than 7 or 5
> notes, 5-limit harmony, and meantone (and later diminished,
> augmented, and dominant) comma pumps.

No question, our Western forebears really figured out how to milk the reward-centers in our brains via technological and social innovation. But the problem is, Western music didn't succeed by being xenharmonic (as you say), but by being the opposite. Western music takes the "strange" out of "strange and familiar", and taps directly into whatever neurological reward pathways music is capable of triggering. And has *evolved* to do so with greater and greater efficiency, leading to modern top-40 radio, and especially techno music. Simpler and simpler forms, slicker and slicker presentation. A single person can now wield all the grandiosity of an orchestra. Sorry, but following your way of thinking, the future of Western music is I-V-vi-IV over and over again, forever:

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

Because nothing gives us the shivers quite like this chord progression, and no xenharmonic progression will ever top it.

-Igs

On Wed, Jan 18, 2012 at 3:09 AM, cityoftheasleep
<igliashon@...> wrote:
>
> No question, our Western forebears really figured out how to milk the reward-centers in our brains via technological and social innovation. But the problem is, Western music didn't succeed by being xenharmonic (as you say), but by being the opposite. Western music takes the "strange" out of "strange and familiar", and taps directly into whatever neurological reward pathways music is capable of triggering.

I don't know about that. In a lot of ways this is the most xenharmonic
piece I've yet heard

http://www.youtube.com/watch?v=DCnUpl6B46M

The really crazy part is in the second section, specifically at about
4:57, but you need to get chilled out and listen to the whole thing
for the whole effect.

This is also Western music, although not quite as popular as good ol I-IV-vi-IV.

-Mike

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

> But Western music isn't in JI. It's in meantone and 12edo.

And the physical reality of 12-tET harmony, the measurable coincidence (or lack thereof) of partials, is clearly and unequivocably Pythagorean. The actual sonorities are created by a chain of pure (or damn near pure) fifths.

We could conceivably travel through the last several thousand years (at the least) all over Eurasia (at the least) and be certain that untold numbers of musicians who tuned by chains of fifths (and fourths of course) would find the raw reality of 12-tET intervals completely familiar.

That Western music which "dominates" boils down, as far as tuning and scalar matters go, to "diatonic, tuned Pythagorean". On a most "raw" intonational level (which is the level we address when we make any claims about things like preferences for certain intervals in abstracted environments) we don't have something any newer than, say, ancient Sumeria.

Justifying Just by presenting the popularity of Western music is nonsense.

13-limit results can diverge a fair bit. Mystery (29&58) is top of my odd limit lists (13/15) but won't always make the top ten for cangwu badness. I forget the details.

Graham

------Original message------
From: Carl Lumma <carl@...>
To: <tuning@yahoogroups.com>
Date: Wednesday, January 18, 2012 12:31:34 AM GMT-0000
Subject: [tuning] Re: Pure-Octave Temperament Error

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

> First you say error is necessarily defined in relation to
> concordance. Now you say it can be defined for anything.
> Which is it?

Error in the context of RMP is about concordance.

> > Too bad! You should try tuning an instrument to play
> > 2/1 and also 21/16, and then try detuning them by set
> > amounts.
>
> What good would that do?

If trying it is no good, talking about it isn't likely to
be much better. I worked with marimbas and a giant hammer
dulcimer tuned up to the 32nd harmonic. It was an eye-
opener for me, anyway.

> > Finally it's to the point where that can't happen again.
>
> What makes you so certain of this?

RMP has been hammered on relentlessly by a wide variety of
people, including some very smart people, for 15 years on
mailing lists -- and there's a clear historical lineage for
it back as far as you want to go. It's consistent with all
known experiments. It can only be so wrong.

> > RMP is far from perfect, but there are now clear limits
> > as to how wrong it can be, and a full research program
> > with well-funded experiments and tenure-track positions
> > would likely be required to improve these limits.
> > Even so, they aren't likely to improve a great deal.
>
> What are those limits, how were they made clear, and how can
> you justify statements about the likelihood (or lack thereof)
> of its future improvement?

For example: a top 10 list isn't going to differ much
regardless of what error weighting comes back from any new
experiments we'd perform. Partly we know this because Paul,
Gene et al have tried nearly every reasonable weighting.
Partly because we get rank 2 temperaments out of dyadic
entropy minimizers. etc

> > > What about the Farey series HE curve, with a downward
> > > overall slope? You seem to be avoiding responding to that.
> >
> > Eh? It's the first you've mentioned it.
>
> The hell it is! It's at least the 3rd time I've mentioned it.
> It was among those graphs I linked to that you claimed all
> contradicted what I was saying, and I tried to call your
> attention to it again, and I even made a post here about it.

If you mentioned the 'Farey slope', I only saw it mentioned
along with a lot of other stuff (s parameter etc etc) that
I already said didn't matter.

> Now, care to answer the question (which, to repeat it in
> case you missed it, is "how would we weight error if we
> wanted to reflect this model of concordance"?

Same way (see my subsequent post).

> > > Clearly I am missing something. How does unweighted error
> > > make any assumptions?
> >
> > Unweighted error is actually a weighting of course.
>
> Right, just like the null hypothesis is still a hypothesis.

Unweighted error says that the errors of the primes are
equally important. That's more than a null hypothesis.
The null hypothesis would be: results are insensitive to
changes in weighting. That's ruled out (though as I noted
above, the results for *reasonable* weightings are
similar).

-Carl

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Benade's experiments relevant to this discussion constitute following the instruction to find beatlessness within a given narrow region, over a fixed mid-range drone. From this we obviously cannot leap to a universal tedency or preference for Justly intoned intervals.

Partch takes pain to stress that his experiments are upon himself, and are not properly "scientific" at all. In addition, his use of "field of attraction" is mixed freely with "magnetism", "gravity" and so on, and cannot be separated from his concepts of tonality, rootedness, voice-leading, resolution, etc. In other words it is a compositional concept for Partch.

Virtual fundamentals for sonorities beyond the very most simple intervals are renowned for their subjective nature (Partch has a great comment on this). Ease of perception of VFs constitutes zero evidence for the grand claims made about Western music. In fact, it can be argued that the opposite is true, and that it is ambiguous because harmonically complex sonorities which enable the great accomplishments of Western harmony. This argument can be extrapolated from, guess whom? Benade. Read the chapter that addresses Werkmeister.

Claiming that interpreting dissonance curves in terms of fields of attraction constitutes any kind of evidence for the validity of the concept (which has yet to be clearly defined, for crying out loud) of field of attraction is, of course, begging the question. At least some of those dissonance curves were most likely formulated with the concept of field of attraction taken as gospel in the first place. I'll buy that kind of "science" the same day I buy a copy of "Dianetics".

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@> wrote:
> > > It's observed that when people are given a tunable tone
> > > generator, set randomly, and are instructed to "tune" it,
> > > they tend to turn the knob until they hit a simple ratio.
> > > It's assumed that, on average, where they started is in
> > > the field of attraction of the thing they stop at.
> >
> > I'd like to see the study this is based on. Can you
> > point me to it?
>
> Benade's experiments are described in his book
> http://www.amazon.com/Fundamentals-Musical-Acoustics-Second-Revised/dp/048626484X
>
> We already mentioned Partch
> http://www.amazon.com/Genesis-Music-Creative-Fulfillments-Paperback/dp/030680106X/
>
> Houtsma & Goldstein 1971 (Technical Report 484) found that
> ability to identify pure-tone dyads (by identifying their VFs)
> went down as the complexity of the frequency ratios involved
> went up.
>
> The dissonance curves of Plomp & Levelt, Kameoka & Kuriyagawa,
> Sethares, and Erlich are often understood to show fields of
> attraction.
>
> -Carl
>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Jan 17, 2012, at 5:01 AM, "lobawad" <lobawad@...> wrote:
>
>
>
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
> >
> > On Tue, Jan 17, 2012 at 1:40 AM, lobawad <lobawad@> wrote:
> > >
> > > --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
> > >
> > > > Other than beatlessness, another relevant psychoacoustic phenomenon
> >is virtual pitch integration.
> > >
> > > Also called subjective pitch. The "wow, it's magic" virtual pitch is
> the missing fundamental of a harmonic series.
> >
> > OK? How does that change anything I said?
>
> The perceived fundamental frequency of a single tone is simply not what is
> meant by "field of attraction" of an interval (dyad).
>
> Meant by who?

Meant by anyone using the term, for however it is understood, it refers to intervals. A single tone is not an interval, and it is the VF of a single tone which is firmly established as a psychoacoustic reality ("bass maximizers" and mixing engineers make use of this, for example). As soon as a more complex sound entity is presented, the multitude of other factors, conditioning, context, etc., which you rightly insist on bringing up all the time, kick in.

>
> > > The fact that the ear is a non-linear device should slow any rushes to
> numerology hear.
> >
> > ???? What did I say that's "numerology?"
>
> "Sine waves with no partials". Sine have dyads and chords "have partials"
> in the human ear.
>
> Sorry, I'm lost. Sines have dyads?

Sorry, typographical error there. "Sine dyads and chords "have partials" in the human ear. That is, we can't truly test dyads and chords of "simple sines" with the human ear.

>
> I'm all for discussing fundamental concepts, but it doesn't seem >like we
> are. It seems like you're saying the term "field of attraction" is
> misleading and that you'd prefer a different term. OK, that's not a
> terrible idea. Now what?

Dump the whole circular argument about "JI" being the foundation of Western music, which is the most bestest no duh cuz everybody luvs it,
and everybody luvs it because it is natural, man, and that's why it's the foundation, etc. etc.

Invoking the magic of "fields of attraction" is key to that bogus argument.

>
> There is another sense in which I think the term "field of >attraction" is
> important, and that's for intervallic categorical perception. It's
> precisely in this sense that I'd like Carl's statements to not be
> interpreted.

That's an area we could go into without talking nonsense, but fields of interaction (or something like that), tuning tolerances, references to partials, etc. would be a better concepts to use. Clearly "M3" is NOT attached to 5:4, but how far from 2:1 can we go and retain the qualities and structural nature that we attach to "octave"? I don't know.

--- In tuning@yahoogroups.com, "Kalle Aho" <kalleaho@...> wrote:
>
>
>
>
>
> --- In tuning@yahoogroups.com, "lobawad" <lobawad@> wrote:
> >
> >
> >
> > --- In tuning@yahoogroups.com, "Kalle Aho" <kalleaho@> wrote:
> >
> > > Saying that more complex ratios bear more tempering doesn't mean that
> > > they always are bearing more tempering than simpler ratios. That they
> > > bear more tempering should be understood as saying that they are able
> > > to bear or withstand more tempering. But in the case of meantone they
> > > don't have to and should not for the reason I mentioned.
> > >
> > > Kalle
> > >
> >
> > However, more complex ratios do not bear more tempering, if
> the "melding" effect of coincident partials is what you are after.
> That sensation disappears more rapidly with fainter sonorities. If
> this sensation is not important, then thinking of musical intervals
> in terms of ratios is unnecessary.
>
> I'm not taking sides on the question whether complex ratios (are able
> to) bear more tempering. I was just objecting to your claim that
> quarter comma meantone is some kind of counterexample to this idea.

But what I said was that quarter-comma meantone is a counterexample to this idea being a foundational principle of tuning. Quarter-comma meantone patently is not based on the idea of more complex ratios bearing more tempering.

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

> But what I said was that quarter-comma meantone is a counterexample to this idea being a foundational principle of tuning. Quarter-comma meantone patently is not based on the idea of more complex ratios bearing more tempering.

It would be more reasonable to claim that it's based on the idea that all consonant intervals bear exactly the same amount of tempering.

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

> It would be more reasonable to claim that it's based on the idea that all consonant intervals bear exactly the same amount of tempering.

Except for octaves, which bear no tempering whatever.

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "lobawad" <lobawad@> wrote:
>
> > But what I said was that quarter-comma meantone is a counterexample to this idea being a foundational principle of tuning. Quarter-comma meantone patently is not based on the idea of more complex ratios bearing more tempering.
>
> It would be more reasonable to claim that it's based on the idea that all consonant intervals bear exactly the same amount of tempering.
>

But the 5:4 isn't tempered at all. However, the actual target of consonance was not an interval, but a triad. Which makes what you say reasonable, for we have the best UNWEIGHTED solution. The best unweighted solution contradicts the weighted solutions you necessarily have if you proceed from the concept of more complex intervals bearing more tempering.

What I said was that idea of more complex intervals bearing more tempering is not a foundational principle of tuning (we're assuming some target rational intervals in "tuning" here). If one values the actual effects of rational intervals, rather than appealing to their alleged magical properties, the idea is in fact backwards.

--- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "Kalle Aho" <kalleaho@> wrote:
> >
> >
> >
> >
> >
> > --- In tuning@yahoogroups.com, "lobawad" <lobawad@> wrote:
> > >
> > >
> > >
> > > --- In tuning@yahoogroups.com, "Kalle Aho" <kalleaho@> wrote:
> > >
> > > > Saying that more complex ratios bear more tempering doesn't mean that
> > > > they always are bearing more tempering than simpler ratios. That they
> > > > bear more tempering should be understood as saying that they are able
> > > > to bear or withstand more tempering. But in the case of meantone they
> > > > don't have to and should not for the reason I mentioned.
> > > >
> > > > Kalle
> > > >
> > >
> > > However, more complex ratios do not bear more tempering, if
> > the "melding" effect of coincident partials is what you are after.
> > That sensation disappears more rapidly with fainter sonorities. If
> > this sensation is not important, then thinking of musical intervals
> > in terms of ratios is unnecessary.
> >
> > I'm not taking sides on the question whether complex ratios (are able
> > to) bear more tempering. I was just objecting to your claim that
> > quarter comma meantone is some kind of counterexample to this idea.
>
> But what I said was that quarter-comma meantone is a counterexample
to this idea being a foundational principle of tuning. Quarter-comma
meantone patently is not based on the idea of more complex ratios
bearing more tempering.

OK, but TOP Meantone also has more tempering in 3:2 than in 5:4
despite being Tenney-weighted.

Kalle

Then TOP cannot be based on the idea of more complex intervals bearing more tempering.

--- In tuning@yahoogroups.com, "Kalle Aho" <kalleaho@...> wrote:
>
>
>
>
>
> --- In tuning@yahoogroups.com, "lobawad" <lobawad@> wrote:
> >
> >
> >
> > --- In tuning@yahoogroups.com, "Kalle Aho" <kalleaho@> wrote:
> > >
> > >
> > >
> > >
> > >
> > > --- In tuning@yahoogroups.com, "lobawad" <lobawad@> wrote:
> > > >
> > > >
> > > >
> > > > --- In tuning@yahoogroups.com, "Kalle Aho" <kalleaho@> wrote:
> > > >
> > > > > Saying that more complex ratios bear more tempering doesn't mean that
> > > > > they always are bearing more tempering than simpler ratios. That they
> > > > > bear more tempering should be understood as saying that they are able
> > > > > to bear or withstand more tempering. But in the case of meantone they
> > > > > don't have to and should not for the reason I mentioned.
> > > > >
> > > > > Kalle
> > > > >
> > > >
> > > > However, more complex ratios do not bear more tempering, if
> > > the "melding" effect of coincident partials is what you are after.
> > > That sensation disappears more rapidly with fainter sonorities. If
> > > this sensation is not important, then thinking of musical intervals
> > > in terms of ratios is unnecessary.
> > >
> > > I'm not taking sides on the question whether complex ratios (are able
> > > to) bear more tempering. I was just objecting to your claim that
> > > quarter comma meantone is some kind of counterexample to this idea.
> >
> > But what I said was that quarter-comma meantone is a counterexample
> to this idea being a foundational principle of tuning. Quarter-comma
> meantone patently is not based on the idea of more complex ratios
> bearing more tempering.
>
> OK, but TOP Meantone also has more tempering in 3:2 than in 5:4
> despite being Tenney-weighted.
>
> Kalle
>

--- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:
>
> Then TOP cannot be based on the idea of more complex intervals bearing more tempering.

Read again what I wrote:

"Saying that more complex ratios bear more tempering doesn't mean
that they always are bearing more tempering than simpler ratios. That
they bear more tempering should be understood as saying that they are
able to bear or withstand more tempering."

In TOP, error is weighted by 1/log(n*d). But you still get a meantone
tuning where 3:2 is tempered more than 5:4.

Kalle

>
> --- In tuning@yahoogroups.com, "Kalle Aho" <kalleaho@> wrote:
> >
> >
> >
> >
> >
> > --- In tuning@yahoogroups.com, "lobawad" <lobawad@> wrote:
> > >
> > >
> > >
> > > --- In tuning@yahoogroups.com, "Kalle Aho" <kalleaho@> wrote:
> > > >
> > > >
> > > >
> > > >
> > > >
> > > > --- In tuning@yahoogroups.com, "lobawad" <lobawad@> wrote:
> > > > >
> > > > >
> > > > >
> > > > > --- In tuning@yahoogroups.com, "Kalle Aho" <kalleaho@> wrote:
> > > > >
> > > > > > Saying that more complex ratios bear more tempering doesn't mean that
> > > > > > they always are bearing more tempering than simpler ratios. That they
> > > > > > bear more tempering should be understood as saying that they are able
> > > > > > to bear or withstand more tempering. But in the case of meantone they
> > > > > > don't have to and should not for the reason I mentioned.
> > > > > >
> > > > > > Kalle
> > > > > >
> > > > >
> > > > > However, more complex ratios do not bear more tempering, if
> > > > the "melding" effect of coincident partials is what you are after.
> > > > That sensation disappears more rapidly with fainter sonorities. If
> > > > this sensation is not important, then thinking of musical intervals
> > > > in terms of ratios is unnecessary.
> > > >
> > > > I'm not taking sides on the question whether complex ratios (are able
> > > > to) bear more tempering. I was just objecting to your claim that
> > > > quarter comma meantone is some kind of counterexample to this idea.
> > >
> > > But what I said was that quarter-comma meantone is a counterexample
> > to this idea being a foundational principle of tuning. Quarter-comma
> > meantone patently is not based on the idea of more complex ratios
> > bearing more tempering.
> >
> > OK, but TOP Meantone also has more tempering in 3:2 than in 5:4
> > despite being Tenney-weighted.
> >
> > Kalle
> >
>

--- In tuning@yahoogroups.com, "Kalle Aho" <kalleaho@...> wrote:
>
> --- In tuning@yahoogroups.com, "lobawad" <lobawad@> wrote:
> >
> > Then TOP cannot be based on the idea of more complex intervals bearing more tempering.
>
> Read again what I wrote:
>
> "Saying that more complex ratios bear more tempering doesn't mean
> that they always are bearing more tempering than simpler ratios. That
> they bear more tempering should be understood as saying that they are
> able to bear or withstand more tempering."
>
> In TOP, error is weighted by 1/log(n*d). But you still get a meantone
> tuning where 3:2 is tempered more than 5:4.
>
> Kalle

Yes, I see that. But obviously there are other factors than simply that of more complex ratios bearing more tempering, else TOP meantone would not have more complex ratios bearing less tempering.

--- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "Kalle Aho" <kalleaho@> wrote:
> >
> > --- In tuning@yahoogroups.com, "lobawad" <lobawad@> wrote:
> > >
> > > Then TOP cannot be based on the idea of more complex intervals bearing more tempering.
> >
> > Read again what I wrote:
> >
> > "Saying that more complex ratios bear more tempering doesn't mean
> > that they always are bearing more tempering than simpler ratios. That
> > they bear more tempering should be understood as saying that they are
> > able to bear or withstand more tempering."
> >
> > In TOP, error is weighted by 1/log(n*d). But you still get a meantone
> > tuning where 3:2 is tempered more than 5:4.
> >
> > Kalle
>
> Yes, I see that. But obviously there are other factors than simply
that of more complex ratios bearing more tempering, else TOP meantone
would not have more complex ratios bearing less tempering.

Error for ratio n:d is weighted by 1/log(n*d). That embodies the idea
that more complex ratios are able to bear more tempering. Then you
find the tuning where the max Tenney-weighted error among all n-prime
limit intervals is minimized. It turns out that you can do that
simply by minimizing the max Tenney-weighted error among the primes
of that prime limit. Now, what other factors are needed?

Kalle

I'm not saying Western music didn't develop some significant xenharmonic attributes. Jazz was the xenharmonic music of its day, for sure, and is still probably the most xenharmonic thing going. But Carl's point about Western music's "universal appeal", when supported with relevant international record sales chart data, leads to the obvious conclusion that what's responsible for Western music's appeal is that which is becoming increasingly refined and distilled in modern pop music--sweet, smooth harmony with simple beats, simple melodies, and trite lyrics that are the aural equivalent of a Big Mac with fries and a 24-oz Coke. Western culture's success comes from its ability to separate out the pleasurable or desirable attributes of anything, refine them, concentrate them, and then sell them cheaply, allowing us all to constantly sustain a massive dopamine high (as long as we keep consuming, that is).

-Igs

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Wed, Jan 18, 2012 at 3:09 AM, cityoftheasleep
> <igliashon@...> wrote:
> >
> > No question, our Western forebears really figured out how to milk the reward-centers in our brains via technological and social innovation. But the problem is, Western music didn't succeed by being xenharmonic (as you say), but by being the opposite. Western music takes the "strange" out of "strange and familiar", and taps directly into whatever neurological reward pathways music is capable of triggering.
>
> I don't know about that. In a lot of ways this is the most xenharmonic
> piece I've yet heard
>
> http://www.youtube.com/watch?v=DCnUpl6B46M
>
> The really crazy part is in the second section, specifically at about
> 4:57, but you need to get chilled out and listen to the whole thing
> for the whole effect.
>
> This is also Western music, although not quite as popular as good ol I-IV-vi-IV.
>
> -Mike
>

Oh, darn. You said "which I will conveniently ignore". Great, I'll have to save this post and re-post when you get back.

-Igs

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@> wrote:
>
> > And I do submit that Western music -- both imported and
> > locally-made -- charts in every nation on Earth, while
> > local traditional forms chart seldom locally and never
> > internationally. Traditional forms are enjoyed by
> > enthusiasts (often Western scholars explicitly trying to
> > preserve them against extinction).
>
> What counts as "Western"? Do you just mean "in Western tuning"?
>
> > That Africa slaves kept other elements of their traditional
> > music but adopted Western harmony with gusto.
>
> ...in ways that were rarely if ever used in Western music, and with copious microtonal melodic inflections, that went on to dominate the strict Western approaches that they borrowed from.
>
> > It may be objected that not only music, but language,
> > banking, and other elements of Western culture have spread
> > worldwide, often by violent means. My response, sure to
> > cause controversy that I will conveniently ignore, is that
> > there was not enough violence to account for the success
> > with which Western ideas spread, and that this spread is
> > really due to quasi-independent contests in each domain
> > being won by Western technologies, which were more complex
> > and more subtly and deeply connected to physical reality.
>
> More effective at manifesting human desires, I'd say. And look what else that's got us: global warming (automobiles, coal power), nuclear weaponry and global warfare, epidemic obesity (McDonald's, Coca-Cola, Bud Lite, etc) and mental illness (look at prescription drug sales statistics), topsoil erosion and declining nutrient density in the food supply (factory farms, monocultured and GM foods), depleted fisheries and toxic levels of mercury in seafood, declining biodiversity (mass extinctions on a global scale), multi-drug-resistant diseases...NASCAR, Two and a Half Men, and Justin Bieber.
>
> > Violence was only one such contest -- Western guns killed
> > better. Banking was another -- Westerners had robust
> > property rights and contract law, abstract (trust-based)
> > media of exchange, and quantification of the time value of
> > money (interest). Western languages had larger vocabularies
> > and could be exchanged through reading, writing, and
> > printing (Western scholars developed phonetic systems for
> > many indigenous languages). Western music was the
> > xenharmonic music of its day, having 12 rather than 7 or 5
> > notes, 5-limit harmony, and meantone (and later diminished,
> > augmented, and dominant) comma pumps.
>
> No question, our Western forebears really figured out how to milk the reward-centers in our brains via technological and social innovation. But the problem is, Western music didn't succeed by being xenharmonic (as you say), but by being the opposite. Western music takes the "strange" out of "strange and familiar", and taps directly into whatever neurological reward pathways music is capable of triggering. And has *evolved* to do so with greater and greater efficiency, leading to modern top-40 radio, and especially techno music. Simpler and simpler forms, slicker and slicker presentation. A single person can now wield all the grandiosity of an orchestra. Sorry, but following your way of thinking, the future of Western music is I-V-vi-IV over and over again, forever:
>
> http://www.youtube.com/watch?v=oOlDewpCfZQ
>
> Because nothing gives us the shivers quite like this chord progression, and no xenharmonic progression will ever top it.
>
> -Igs
>

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
But Carl's point about Western music's "universal appeal", when supported with relevant international record sales chart data, leads to the obvious conclusion that what's responsible for Western music's appeal is that which is becoming increasingly refined and distilled in modern pop music--sweet, smooth harmony with simple beats, simple melodies, and trite lyrics that are the aural equivalent of a Big Mac with fries and a 24-oz Coke.

Yeah, that explains the enduring popularity of Bach and Beethoven pretty well.

If people who learned to play music in 12-TET could be shown to tune major 3rds to 5/4 when given the opportunity to freely tune them, I think that's fair evidence that people are hearing the major 3rds "as" 5/4. The fact that adaptive 5-limit JI exists among musical ensembles in a 12-TET-oriented society is, I think, some evidence that 12-TET is being heard as and treated as a 5-limit tuning. Your argument that 12-TET is not a 5-limit tuning makes as much sense as saying meantone doesn't represent the 3-limit, since clearly 696 cents lacks the coincidence of partials held by a 3/2 (and even more obviously than 400 cents vs. 5/4, owing to the greater loudness of the 3rd and 2nd partials). Essentially you're arguing that nothing can represent a rational interval except the rational interval itself, which is wrong.

-Igs

--- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:
>
> --- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@> wrote:
>
> > But Western music isn't in JI. It's in meantone and 12edo.
>
> And the physical reality of 12-tET harmony, the measurable coincidence (or lack thereof) of partials, is clearly and unequivocably Pythagorean. The actual sonorities are created by a chain of pure (or damn near pure) fifths.
>
> We could conceivably travel through the last several thousand years (at the least) all over Eurasia (at the least) and be certain that untold numbers of musicians who tuned by chains of fifths (and fourths of course) would find the raw reality of 12-tET intervals completely familiar.
>
> That Western music which "dominates" boils down, as far as tuning and scalar matters go, to "diatonic, tuned Pythagorean". On a most "raw" intonational level (which is the level we address when we make any claims about things like preferences for certain intervals in abstracted environments) we don't have something any newer than, say, ancient Sumeria.
>
> Justifying Just by presenting the popularity of Western music is nonsense.
>

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

> Yeah, that explains the enduring popularity of Bach and Beethoven pretty well.

I think you mean "the declining popularity".

-Igs

On Wed, Jan 18, 2012 at 6:18 AM, lobawad <lobawad@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> >
> > The perceived fundamental frequency of a single tone is simply not what is
> > meant by "field of attraction" of an interval (dyad).
> >
> > Meant by who?
>
> Meant by anyone using the term, for however it is understood, it refers to intervals. A single tone is not an interval, and it is the VF of a single tone which is firmly established as a psychoacoustic reality ("bass maximizers" and mixing engineers make use of this, for example). As soon as a more complex sound entity is presented, the multitude of other factors, conditioning, context, etc., which you rightly insist on bringing up all the time, kick in.

Oh, I didn't see that you'd thrown the word "single tone" in a while ago.

> > "Sine waves with no partials". Sine have dyads and chords "have partials"
> > in the human ear.
> >
> > Sorry, I'm lost. Sines have dyads?
>
> Sorry, typographical error there. "Sine dyads and chords "have partials" in the human ear. That is, we can't truly test dyads and chords of "simple sines" with the human ear.

OK, but I don't think that these partials are going to be too loud. If
you actually look up the characteristics of the distortion products
generated by the ear - like the kind they use to measure your hearing,
called DPOAE's - they're just not all that loud. But this is one
subject I'm not a total expert on, so you should take that with a
grain of salt. But either way, even if you believe this sort of thing
is important, then this is still a totally psychoacoustic thing, and
that there's a certain limited sense in which psychoacoustic things
like this can be interpreted as having "fields of attraction" or
"fields of interaction" or "fields of wakalix" or whatever word you
want to use.

> > I'm all for discussing fundamental concepts, but it doesn't seem >like we
> > are. It seems like you're saying the term "field of attraction" is
> > misleading and that you'd prefer a different term. OK, that's not a
> > terrible idea. Now what?
>
> Dump the whole circular argument about "JI" being the foundation of Western music, which is the most bestest no duh cuz everybody luvs it,
> and everybody luvs it because it is natural, man, and that's why it's the foundation, etc. etc.
>
> Invoking the magic of "fields of attraction" is key to that bogus argument.

No arguments here, but apparently Carl "doesn't disagree" too.

> > There is another sense in which I think the term "field of >attraction" is
> > important, and that's for intervallic categorical perception. It's
> > precisely in this sense that I'd like Carl's statements to not be
> > interpreted.
>
> That's an area we could go into without talking nonsense, but fields of interaction (or something like that), tuning tolerances, references to partials, etc. would be a better concepts to use. Clearly "M3" is NOT attached to 5:4, but how far from 2:1 can we go and retain the qualities and structural nature that we attach to "octave"? I don't know.

Wow. Well, that's a hell of a question. Maybe we should see if Graham
can implement octave stretching in Lilypond and do some more examples.

-Mike

On Wed, Jan 18, 2012 at 2:49 PM, cityoftheasleep
<igliashon@...> wrote:
>
> I'm not saying Western music didn't develop some significant xenharmonic attributes. Jazz was the xenharmonic music of its day, for sure, and is still probably the most xenharmonic thing going. But Carl's point about Western music's "universal appeal", when supported with relevant international record sales chart data, leads to the obvious conclusion that what's responsible for Western music's appeal is that which is becoming increasingly refined and distilled in modern pop music--sweet, smooth harmony with simple beats, simple melodies, and trite lyrics that are the aural equivalent of a Big Mac with fries and a 24-oz Coke. Western culture's success comes from its ability to separate out the pleasurable or desirable attributes of anything, refine them, concentrate them, and then sell them cheaply, allowing us all to constantly sustain a massive dopamine high (as long as we keep consuming, that is).

I don't even think it's that. I don't get anywhere near a dopamine
high from Justin Bieber as I do from Miles. I think it's more like
Western pop music has become something more like a movie soundtrack,
where the musical elements don't even really matter too much, but just
provide a nice background effect to support the context of the movie.
The "movie" in this case is more abstract and consists of a set of
American cultural norms which are transmitted by the lyrics, by the
music video, by the artwork, by conforming to the background musical
elements which are present in other songs, etc. It's pretty clear to
me that when people are buying Western pop music, they're buying into
American social norms, not into some psychoacoustically ideal chord
progression we keep evolving towards.

-Mike

On Wed, Jan 18, 2012 at 3:36 PM, cityoftheasleep
<igliashon@...> wrote:
>
> If people who learned to play music in 12-TET could be shown to tune major 3rds to 5/4 when given the opportunity to freely tune them, I think that's fair evidence that people are hearing the major 3rds "as" 5/4.

I don't know how to parse this. We just had a big discussion about
what "heard as," "fields of attraction", etc all mean, and you gave an
operational definition of "heard as" that defines that term as the
result of a particular experiment. I was trying to get a definition
out of someone that made clear whether we're talking about comparing
intervals with internalized reference points (categorical perception),
or about purely psychoacoustic fields of interaction (apparently not),
etc.

The definition that was decided on was that we're not going to assume
anything about what's going on behind the scenes, just define that A
is "heard as" B if someone would tune A to B in the experiment Carl
mentioned. But now you're using this definition circularly to show
that the definition is evidence that A is "heard as" B in situations
where the definition holds.

I could have defined "heard as" differently, and easily arrived at a
definition where Western listeners hear 5/4 as a major third, not the
other way around.

-Mike

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@> wrote:
>
> > Yeah, that explains the enduring popularity of Bach and Beethoven pretty well.
>
> I think you mean "the declining popularity".

They'll be around 100 years from now. How much of your universally appealing simple beats, simple melodies, and trite lyrics will?

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

> I don't even think it's that. I don't get anywhere near a dopamine
> high from Justin Bieber as I do from Miles.

Right, just like I don't get a dopamine high from drinking a Coke because I'm hung up on how gross it actually is, in terms of ingredients. There are plenty of people who hate J-Beebs, hate McDonald's, hate cars, etc....but there are a LOT more who love that shit. I mean, not everyone who does cocaine gets hooked. I didn't, I tried it twice and said "no thank you." But the exceptions prove the rule.

> I think it's more like
> Western pop music has become something more like a movie soundtrack,
> where the musical elements don't even really matter too much, but just
> provide a nice background effect to support the context of the movie.
> The "movie" in this case is more abstract and consists of a set of
> American cultural norms which are transmitted by the lyrics, by the
> music video, by the artwork, by conforming to the background musical
> elements which are present in other songs, etc. It's pretty clear to
> me that when people are buying Western pop music, they're buying into
> American social norms, not into some psychoacoustically ideal chord
> progression we keep evolving towards.

I agree completely--but the music is a very necessary component of the package, and it wouldn't really work without the particular features it maximizes. American culture would not be quite as memetically viral without the features that Carl has pointed out.

But on the other hand, as I pointed out before, there are serious drawbacks to the relative hedonism of American culture. And fortunately for us, there are counter-memes from a counterculture that rejects the absolute pleasure-maximizing aspects of American culture--people who bike when they could drive, mend their possessions instead of disposing and replacing, eat for nutrition instead of taste, read instead of watching TV, and listen to music for intellectual stimulation instead of whatever motivates people to listen to Justin Bieber. We xenharmonists might strike it lucky some day and figure out how to make the concept go viral, the way the term "sustainable" has become viral in the counterculture.

I agree with Carl that Western music spread globally because it maximizes certain desirable features of music that run deeper than culture and can bring pleasure to anyone, regardless of culture. But the high is going to wear off, and for many of us it already has--because there's more to life than being "high" all the time and having your desires and expectations fulfilled as easily as possible.

-Igs

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

> They'll be around 100 years from now. How much of your universally appealing simple
> beats, simple melodies, and trite lyrics will?

I see no reason to predict a future where the popularity of Beethoven and Bach surpasses that of the Beatles, the Rolling Stones, Led Zeppelin, or the Who. I don't have to remind you that the Bay Area has two classic rock stations, one "oldies" station that also plays a lot of classic rock, a modern rock station that also plays what is only another decade away from being "classic rock"...and (last I checked) no commercial classical stations, since 102.1 turned into a classic rock station. Or that public funding and public institutions are possibly the only thing keeping classical music from dying out entirely.

But of course the point is entirely that no "enduring" works are being produced in the current super-pop climate, just like fine craftsmanship is increasingly rare and niche. The ultimate conclusion of the Western mindset is ubiquity and disposability, after all. So 100 years from now, if current trends continue, yes, a small community of devotees will still be worshipping at the altar of Bach, and no one will remember the pop stars of the 20th and 21st century, because they'll be too infatuated with the pop stars of the 22nd century, who in turn will be disposed of and replaced by those of the 23rd century, and so forth.

-Igs

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

> The definition that was decided on was that we're not going to assume
> anything about what's going on behind the scenes, just define that A
> is "heard as" B if someone would tune A to B in the experiment Carl
> mentioned. But now you're using this definition circularly to show
> that the definition is evidence that A is "heard as" B in situations
> where the definition holds.

How is applying the definition circular? We established the definition of what it would mean for 400 cents to be "heard as" 5/4. Then we established that, in fact, people sometimes demonstrate behavior that indicates they *are* hearing 400 cents "as" 5/4, according to our definition. What's the problem?

> I could have defined "heard as" differently, and easily arrived at a
> definition where Western listeners hear 5/4 as a major third, not the
> other way around.

I'm not making any universal claims, or ruling out that some people might tune 5/4 sharp to 400 cents. But if it's true that people are hearing 400 cents as a 5/4 (according to our operational definition), then that is evidence that 12-TET can be understood as a 5-limit tuning.

-Igs

On Wed, Jan 18, 2012 at 6:36 PM, cityoftheasleep
<igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > I don't even think it's that. I don't get anywhere near a dopamine
> > high from Justin Bieber as I do from Miles.
>
> Right, just like I don't get a dopamine high from drinking a Coke because I'm hung up on how gross it actually is, in terms of ingredients. There are plenty of people who hate J-Beebs, hate McDonald's, hate cars, etc....but there are a LOT more who love that shit. I mean, not everyone who does cocaine gets hooked. I didn't, I tried it twice and said "no thank you." But the exceptions prove the rule.

Yeah, there's stuff like that, where other cultural norms make you
feel crappy for liking what you'd "naturally" like, so then you don't
like it. My statements were the reverse of that; that things which
display more of the psychoacoustic features that Westerners might
"like" can be viewed as "uncool" in -mainstream- Western society
precisely because Justin Bieber and Taylor Swift and whoever aren't
doing it that way. And people are ultimately buying into what the cool
kids like. And what the cool kids like seems to change dramatically
every 10 years.

You can make the argument that although it changes dramatically every
10 years, stuff like tonality is always a part of it. Well, I dunno if
even that's always true, and it's definitely not true in the stupidly
over-strict classical definition some people apply to tonality, in
which things like Dorian mode aren't tonal (so Santana's Oye Como Va
wouldn't be tonal then). But there are always shifts in how much
dissonance mainstream music has per decade - in the 90s, there was a
lot more dissonance going on with grunge than in the 50s, or so on.
But, even besides that, there have been styles of music that were
periodically extremely popular that didn't have much tonality at all.
Like the Wu-Tang clan. And who are we to say there won't be something
even less tonal that emerges over the course of our lives in the next
60-70 years?

Finally, you can make the assumption that if you just average things
out, ignoring all variation, and you find the style of music that ALL
people are most conditioned to like, it's going to be low in
dissonance and tonal. Well, you're probably right. They did an
experiment about this, actually, and found that this is the most
wanted song:

http://blog.wired.com/music/2008/05/survey-produced.html

In contrast, this is the least wanted song:

http://www.wired.com/listening_post/2008/04/a-scientific-at/

My feeble mind is in danger of snapping when I listen to that second
song, so I'll leave it to you to decide.

-Mike

On Wed, Jan 18, 2012 at 7:18 PM, cityoftheasleep
<igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > The definition that was decided on was that we're not going to assume
> > anything about what's going on behind the scenes, just define that A
> > is "heard as" B if someone would tune A to B in the experiment Carl
> > mentioned. But now you're using this definition circularly to show
> > that the definition is evidence that A is "heard as" B in situations
> > where the definition holds.
>
> How is applying the definition circular? We established the definition of what it would mean for 400 cents to be "heard as" 5/4. Then we established that, in fact, people sometimes demonstrate behavior that indicates they *are* hearing 400 cents "as" 5/4, according to our definition. What's the problem?

Because you said this:

> If people who learned to play music in 12-TET could be shown to tune major 3rds to 5/4 when given the opportunity to freely tune them, I think that's fair evidence that people are hearing the major 3rds "as" 5/4.

What do you mean it would be fair evidence? What is being evidenced by
this? It sounds like you're applying your defined term to the outcome
of a certain experiment, and then saying that outcome is evidence for
that term...?

> > I could have defined "heard as" differently, and easily arrived at a
> > definition where Western listeners hear 5/4 as a major third, not the
> > other way around.
>
> I'm not making any universal claims, or ruling out that some people might tune 5/4 sharp to 400 cents. But if it's true that people are hearing 400 cents as a 5/4 (according to our operational definition), then that is evidence that 12-TET can be understood as a 5-limit tuning.

What do you mean by "understood as a 5-limit tuning?" Is this
different from "heard as?"

-MIke

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

> Finally, you can make the assumption that if you just average things
> out, ignoring all variation, and you find the style of music that ALL
> people are most conditioned to like, it's going to be low in
> dissonance and tonal. Well, you're probably right.

Carl's argument is that there was something about Western music (and Western culture in general) that transcends conditioning and thereby accounts for its memetic fitness and viral spread throughout the globe. And I think he's probably right, considering that while many ideas from colonized cultures did cross-pollenate significantly into Western thought (see, for instance, Marco Polo), music is one area where adoption of Western norms is almost universal, despite that it's also one of the least value-laden aspects of the culture (unlike, say, religion). There's got to be some reason for that, and I just put forward one hypothesis I have. It could be wrong.

Contrary to Carl's observation, it is worth noting that there was harmonic Western music prior to the advent of meantone, which used thirds harmonically even though they were dissonant. It's also worth noting that the Chinese developed 12-tone equal temperament long before we adopted it in the West, and never produced the kind of sophisticated harmony that we did. It's also also worth noting that the copious use of extended chords was rare in Western music until the advent of jazz, which came directly from the interaction of African musicians in America trying to adapt to the Western musical norms (and trying to adapt those norms to their own ends as well). You might even say that jazz is the most harmonically-advanced music yet seen on the planet, and that it's not entirely western in origin, and that it gave birth to modern pop music (the most viral form of music yet seen), thereby proving that NOT western music but a hybrid east/west music is that which is now found endemically all over the globe. You might also conjecture about the possibility of an even-more-advanced harmonic future emanating from the Middle East, arising from the integration of quarter-tone melody with Western harmony by invoking the 11- and 13-limit, as a sort of "reverse colonization".

Still, all we know for sure right now is that nobody finds 5-limit tonal harmony unpleasant, all else being equal. The same cannot be said of any other form of harmony (except perhaps 3-limit Pythagorean), and I don't believe there is any reason to consider the source of that to be conditioning. It hints at a certain universality, I think, at least about what people *will* like if given the chance.

-Igs

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> What do you mean it would be fair evidence? What is being evidenced by
> this? It sounds like you're applying your defined term to the outcome
> of a certain experiment, and then saying that outcome is evidence for
> that term...?

I really don't see what's problematic here. We define "heard as" in terms of a behavior pattern. Using this definition, we can say a subject hears x as y if the subject demonstrates the defined behavior. Then, if we want to test whether subjects hear x as y, we give them an opportunity to demonstrate or fail to demonstrate this behavior. If the behavior is demonstrated, then by definition they are hearing x as y.

Let me demonstrate this with something less contentious. We'll define the term "averse to" as follows: "a subject is averse to x if the subject recoils when exposed to x, or otherwise attempts to get away from x when exposed to x." Then we want to see if people are averse to spiders. We expose several subjects to spiders, and they all recoil. Then we can say "people are averse to spiders". Same thing! This sort of behavioral definition gets rid of the problems of subjectivity and inaccessibility to internal states.

> What do you mean by "understood as a 5-limit tuning?" Is this
> different from "heard as?"

12-TET can be understood as a 5-limit tuning iff it can be heard as a 5-limit tuning.

-Igs

On Wed, Jan 18, 2012 at 9:16 PM, cityoftheasleep
<igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> > What do you mean it would be fair evidence? What is being evidenced by
> > this? It sounds like you're applying your defined term to the outcome
> > of a certain experiment, and then saying that outcome is evidence for
> > that term...?
>
> I really don't see what's problematic here.

It's problematic because I tried to deliberately get everyone to state
what they thought was happening on a lower level, or what they thought
was being implied or evidenced by these experiments. In the end, we
agreed on a definition that is almost completely agnostic to any
explanation of what's happening "under the hood," and just said that
we're defining x as being "heard as" y if the subject would tune x to
y when instructed to tune the interval until it's the most in tune.

So I'm happy with that purely agnostic definition and going with that.
But you've introduced this word "evidence" into it, and I don't see
what is being evidenced.

> We define "heard as" in terms of a behavior pattern. Using this definition, we can say a subject hears x as y if the subject demonstrates the defined behavior. Then, if we want to test whether subjects hear x as y, we give them an opportunity to demonstrate or fail to demonstrate this behavior. If the behavior is demonstrated, then by definition they are hearing x as y.

Right, this is great. I happen to think that the "heard as"
terminology here is loaded, however, and possibly misleading to
newcomers, but as usual I don't care what terms we use for anything,
as long as we're communicating.

> Let me demonstrate this with something less contentious. We'll define the term "averse to" as follows: "a subject is averse to x if the subject recoils when exposed to x, or otherwise attempts to get away from x when exposed to x." Then we want to see if people are averse to spiders. We expose several subjects to spiders, and they all recoil. Then we can say "people are averse to spiders". Same thing! This sort of behavioral definition gets rid of the problems of subjectivity and inaccessibility to internal states.

Sure, but what you said was the equivalent of "if they recoil to
spiders, that's evidence that they're averse to spiders," which makes
it sound like you're talking about their recoil implying something
else.

> > What do you mean by "understood as a 5-limit tuning?" Is this
> > different from "heard as?"
>
> 12-TET can be understood as a 5-limit tuning iff it can be heard as a 5-limit tuning.

OK, so "understood as" is exactly identical to "heard as." Then what
does this mean?

> I'm not making any universal claims, or ruling out that some people might tune 5/4 sharp to 400 cents. But if it's true that people are hearing 400 cents as a 5/4 (according to our operational definition), then that is evidence that 12-TET can be understood as a 5-limit tuning.

It sounds like you're literally saying "if people under laboratory
conditions behave by retuning 400 cents to 5/4 in this experiment,
then that is evidence that people will behave in general under further
laboratory conditions by retuning 12-TET intervals to only those with
at most a prime factor of 5?"

-Mike

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>Essentially you're arguing that nothing can represent a rational >interval except the rational interval itself, which is wrong.

How could I call 12-tET Pythagorean if "nothing can represent a rational interval except the interval itself"?

Clearly the PERFECT coincidence of third and second partials is not needed to create a "3:2". A chorusing effect can actually highlight the relationship.

>
> If people who learned to play music in 12-TET could be shown to >tune major 3rds to 5/4 when given the opportunity to freely tune >them, I think that's fair evidence that people are hearing the major >3rds "as" 5/4. The fact that adaptive 5-limit JI exists among >musical ensembles in a 12-TET-oriented society is, I think, some >evidence that 12-TET is being heard as and treated as a 5-limit >tuning.

My experience is that people who sing in choirs recognize 5:4 right off as Major 3rd and piano players recognize it as "flat" (whether or not they think it sounds good). I think my wife's perception is very telling: she recognizes "5-limit" music instantly because she hates it. Eeewww, church music!

Depends on which music, depends on which people. I was trained in an old-fashioned (pre-War) way, sharping forward/upward motion, flatting in repose. You can hear this approach in old records, it's considered schmalzig these days.

>Your argument that 12-TET is not a 5-limit tuning makes as much >sense as saying meantone doesn't represent the 3-limit, since >clearly 696 cents lacks the coincidence of partials held by a 3/2 >(and even more obviously than 400 cents vs. 5/4, owing to the >greater loudness of the 3rd and 2nd partials).

Not so terribly long before 1/4 comma became common, we had parallel organum. If we look at the history of Western harmony, by the time we're in "common practice", parallel movement by fifths, with which parallel organum was rife, was "forbidden". Any of the rare instances by a famous CP composer will surely be singled out by a composition teacher, but not so many centuries earlier, an entire tune could be harmonized by a running parallel fifth.

Rock guitar is full of parallel organum. Power chords, barre chords. It sounds good. Now look at the tunings of the times involved. When fifths were pure, it was cool to have loads of parallel fifths. When fifths were not pure 3:2s, parallel fifths went out. Fifths are damn near pure now, parallel fifths are in.

We don't need to get into a chicken-or-egg debate, it doesn't matter if parallel fifths were already out, enabling detuning of 3:2, or if the heavily tempered 3:2 pushed out the practice and no one cared because they were enjoying the pure thirds so much.

The principle sonority of the 1/4 comma era was the smooth triad, and definitely not open or parallel fifths. It is an anachronism to look at 1/4 comma meantone the way it is looked at on these lists. There is nothing wrong with this, as long as you wear a condom on your time travels, so to speak.

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

>
> I could have defined "heard as" differently, and easily arrived at a
> definition where Western listeners hear 5/4 as a major third, not the
> other way around.

Exactly.

It is easy as pie to compress a tetrachord such that what is allegedly a major third, because supposedly under the magic spell of 5:4, is heard as Fa, and utterly un-M3.

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

> Contrary to Carl's observation, it is worth noting that there was harmonic Western music prior to the advent of meantone, which used thirds harmonically even though they were dissonant. It's also worth noting that the Chinese developed 12-tone equal temperament long before we adopted it in the West, and never produced the kind of sophisticated harmony that we did.

We more than just about anyone should know there's a difference between defining a tuning theoretically, or even constructing a prototype, and actually seeing that tuning adopted.

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

> My experience is that people who sing in choirs recognize 5:4 right >off as Major 3rd and piano players recognize it as "flat" (whether or >not they think it sounds good). I think my wife's perception is very >telling: she recognizes "5-limit" music instantly because she hates >it. Eeewww, church music!
>

I should add that in my experience my wife is not the only one repulsed by the smoothness of "5-limit", and that those choir-folk who recognize 5:4 as "M3" distinguish it from piano M3. In real life, people generally go by "feel". A 5/4 simply does not feel the same as 400 cents.

On Thu, Jan 19, 2012 at 12:34 AM, lobawad <lobawad@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> >
> > I could have defined "heard as" differently, and easily arrived at a
> > definition where Western listeners hear 5/4 as a major third, not the
> > other way around.
>
> Exactly.

It's basically just that people are using this "heard as" terminology
in one particular way, which I happen to it unintuitive. But, I think
this list falls so often into pathological terminology squabbles that
I've resolved to use whatever words people want as long as we're
saying something that's well-defined. I can't stand any more debates
over vague, emotional sounding terminology where nobody knows what
anyone else is saying.

To be totally honest, the actual definition that I would like to
assign to "heard as" has to do entirely with categorical perception
and not with psychoacoustics at all. There are certain circumstances
in which I'll hear 21/16 "as" a perfect fourth, other circumstances
where it might be a really sharp major third, etc. There are also
experiments that measure categorical boundaries, typically showing
that categories are delineated at like 150, 250, 350, 450 cents
(although the unison is different), and we could have easily used the
word to refer to the outcomes of those experiments instead. I'm going
to basically avoid this "heard as" term and just talk with as specific
terminology as possible, but for the purposes of this conversation if
we're set on that than OK. (I just hope when people read the archives,
they find the Rosetta stone first...)

I want to know if people are going to make the claim if low-numbered
ratios are more intrinsically enjoyable than other things, independent
of conditioning or all of the other far more magical levels to music
besides the intonation that only come with training. It sometimes
seems like people are making the claim that there is no such
conditioning, or that the effects of it are negligible. Or, sometimes
it seems like people are saying that gravitation to JI is the
"natural" pattern of behavior, and training can change that. Or
sometimes it's like, screw training, this is the "average" response to
listeners in laboratory conditions in 2012, and so on. I basically
disagree with the first two, and I don't care at all about the last
response, because I'd rather learn about how to write a huge corpus of
work that enjoyably trains any listener who wants to listen. But every
time I think people are making such claims, they back off, reducing it
to this simple pattern of behavior that was experimentally observed,
with no crazy generalizations beyond that. So, ok, I guess it's worth
talking about.

> It is easy as pie to compress a tetrachord such that what is allegedly a major third, because supposedly under the magic spell of 5:4, is heard as Fa, and utterly un-M3.

I did that sort of thing here:

http://soundcloud.com/mikebattagliamusic/sets/the-categorical-experiments/

Note the 72-EDO version. Do tritones still sound like they want to
resolve to you? Are fifths still more or less consonant, and tritones
still more or less dissonant? Well, the aug4's are closer to 3/2 than
the fifths are, so that's interesting.

-Mike

--- In tuning@yahoogroups.com, "Kalle Aho" <kalleaho@...> wrote:

>
> Error for ratio n:d is weighted by 1/log(n*d). That embodies the idea
> that more complex ratios are able to bear more tempering. Then you
> find the tuning where the max Tenney-weighted error among all n-prime
> limit intervals is minimized. It turns out that you can do that
> simply by minimizing the max Tenney-weighted error among the primes
> of that prime limit. Now, what other factors are needed?
>
> Kalle
>

You just described the factor other than the interval error measurement.

"It turns out that you can do that
simply by minimizing the max Tenney-weighted error among the primes
of that prime limit."

It's Tenney Optimized Primes, not Tenney Optimized Intervals.

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

> >
> > Sorry, typographical error there. "Sine dyads and chords "have partials" in the human ear. That is, we can't truly test dyads and chords of "simple sines" with the human ear.
>
> OK, but I don't think that these partials are going to be too loud. If
> you actually look up the characteristics of the distortion products
> generated by the ear - like the kind they use to measure your hearing,
> called DPOAE's - they're just not all that loud. But this is one
> subject I'm not a total expert on, so you should take that with a
> grain of salt. But either way, even if you believe this sort of thing
> is important, then this is still a totally psychoacoustic thing, and
> that there's a certain limited sense in which psychoacoustic things
> like this can be interpreted as having "fields of attraction" or
> "fields of interaction" or "fields of wakalix" or whatever word you
> want to use.

My point was merely that abstracting simple ratios, is, well, abstract: the effect of "the ratio itself" is not something we can measure. The closest we could get to doing this would be with pure sines, but small as the impurities are, they are there.

This does not prove that simple ratios do NOT have a power in the mind, of course.

If you accept the "pleasing proportions" of the ancients (which is what this simple ratio stuff actually is), and follow it through, as the ancients did, you do not wind up with "JI" as it seems to be held in these online tuning communities. The harmonic mean is a very simple proportion. The square root of two is a simple proportion. The proportion described by the golden cut is a very simple proportion. Pi describes a very simple proportion. It is pure numerology to think of these as complex just because the numbers desribing them are so big.

> >
> > That's an area we could go into without talking nonsense, but fields of interaction (or something like that), tuning tolerances, references to partials, etc. would be a better concepts to use. Clearly "M3" is NOT attached to 5:4, but how far from 2:1 can we go and retain the qualities and structural nature that we attach to "octave"? I don't know.
>
> Wow. Well, that's a hell of a question. Maybe we should see if Graham
> can implement octave stretching in Lilypond and do some more examples.

That would be cool.

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

>
> > It is easy as pie to compress a tetrachord such that what is allegedly a major third, because supposedly under the magic spell of 5:4, is heard as Fa, and utterly un-M3.
>
> I did that sort of thing here:
>
> http://soundcloud.com/mikebattagliamusic/sets/the-categorical-experiments/
>
> Note the 72-EDO version. Do tritones still sound like they want to
> resolve to you? Are fifths still more or less consonant, and tritones
> still more or less dissonant? Well, the aug4's are closer to 3/2 than
> the fifths are, so that's interesting.
>
> -Mike
>

That's what I'm talking about. The whole thing acquires a south-east Asian character, that's the timbre of the whole of the relationships between partials, but the "identity" and contextual action of the intervals does not disappear. The old-fashioned names of functional harmony are better than number-names or ratio based-names: dominant, mediant, etc.

On Thu, Jan 19, 2012 at 12:57 AM, lobawad <lobawad@...> wrote:
>
>
> You just described the factor other than the interval error measurement.
>
> "It turns out that you can do that
> simply by minimizing the max Tenney-weighted error among the primes
> of that prime limit."
>
> It's Tenney Optimized Primes, not Tenney Optimized Intervals.

You may not understand the nature of TOP. The point of TOP is to
optimize for "all intervals," in a sense, not just the primes. It was
worked out mathematically that the error over a larger set of target
intervals correlates to the MAX weighted error for the primes, not the
average. It still uses Tenney weighting.

The point is that we're doing this clever trick with the primes which
at first seems counterintuitive - minimizing the max weighted error,
not all weighted error - because it indirectly ends up minimizing the
average weighted error over a larger set of target intervals which are
"composite." The goal is still to minimize the average weighted error,
and to use Tenney weighting, and TOP does both of those things. It's
just clever in the specific, counter-intuitive way it optimizes the
primes which ends up indirectly yielding the desired results.

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Thu, Jan 19, 2012 at 12:57 AM, lobawad <lobawad@...> wrote:
> >
> >
> > You just described the factor other than the interval error measurement.
> >
> > "It turns out that you can do that
> > simply by minimizing the max Tenney-weighted error among the primes
> > of that prime limit."
> >
> > It's Tenney Optimized Primes, not Tenney Optimized Intervals.
>
> You may not understand the nature of TOP. The point of TOP is to
> optimize for "all intervals," in a sense, not just the primes. It was
> worked out mathematically that the error over a larger set of target
> intervals correlates to the MAX weighted error for the primes, not the
> average. It still uses Tenney weighting.
>
> The point is that we're doing this clever trick with the primes which
> at first seems counterintuitive - minimizing the max weighted error,
> not all weighted error - because it indirectly ends up minimizing the
> average weighted error over a larger set of target intervals which are
> "composite." The goal is still to minimize the average weighted error,
> and to use Tenney weighting, and TOP does both of those things. It's
> just clever in the specific, counter-intuitive way it optimizes the
> primes which ends up indirectly yielding the desired results.
>
> -Mike
>

The intervals in the tuning- the actual intervals we use and hear- do NOT conform to greater tempering of higher ratios. Yes or no?

On Thu, Jan 19, 2012 at 4:30 AM, lobawad <lobawad@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> The intervals in the tuning- the actual intervals we use and hear- do NOT conform to greater tempering of higher ratios. Yes or no?

The intervals in TOP tuning do, in general, attempt to conform to
greater tempering of higher ratios. This does not necessarily mean
that 2/1 will end be tempered less than 3/1 which will be tempered
less than 5/1 which will be tempered less than 3/2, in perfect,
strict, ascending order like that. I doubt that it's even possible for
it to be "perfect" like that in a tempered system. But TOP should end
up getting it as close to that as you possibly can.

The goal is to minimize weighted average error over all intervals,
which is accomplished by minimizing the max weighted error over the
primes. If breaking the ordering I mentioned above means that the
average weighted error gets lowered, the order will break, but all in
the name of minimizing avg weighted error.

-Mike

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

> > The point is that we're doing this clever trick with the primes which
> > at first seems counterintuitive - minimizing the max weighted error,
> > not all weighted error - because it indirectly ends up minimizing the
> > average weighted error over a larger set of target intervals which are
> > "composite."

Yes: composite. As I said earlier in this thread and I've been saying for several years now, the target sonority of 1/4 comma meantone was the major triad.

So you could say ha! 4:5:6 man, and 5:6 is more tempered than 4:5! And I would have to agree. But in doing so you'd have to agree that 1/4 meantone has a relationship to 3:2 that is fundamentally different from that of 12-tET.

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Thu, Jan 19, 2012 at 4:30 AM, lobawad <lobawad@...> wrote:
> >
> > --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
> >
> > The intervals in the tuning- the actual intervals we use and hear- do NOT conform to greater tempering of higher ratios. Yes or no?
>
> The intervals in TOP tuning do, in general, attempt to conform to
> greater tempering of higher ratios. This does not necessarily mean
> that 2/1 will end be tempered less than 3/1 which will be tempered
> less than 5/1 which will be tempered less than 3/2, in perfect,
> strict, ascending order like that. I doubt that it's even possible for
> it to be "perfect" like that in a tempered system. But TOP should end
> up getting it as close to that as you possibly can.
>
> The goal is to minimize weighted average error over all intervals,
> which is accomplished by minimizing the max weighted error over the
> primes. If breaking the ordering I mentioned above means that the
> average weighted error gets lowered, the order will break, but all in
> the name of minimizing avg weighted error.
>
> -Mike
>

Okay, that's TOP tunings. That's fine. I was pointing out the success of meantone as a counterexample to that principle being a fundamental principle of tuning (obviously assuming "good" Just approximation in this case).

On Thu, Jan 19, 2012 at 4:56 AM, lobawad <lobawad@...> wrote:
>
> --- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:
> >
>
> Yes: composite. As I said earlier in this thread and I've been saying for several years now, the target sonority of 1/4 comma meantone was the major triad.

Yes, who disagrees with that? That's always the point of TOP, to
optimize for major triads and even larger sets of intervals. I tried
working out some kind of pure-octave POTE optimization using only
primes and Paul had to correct me on it because the results wouldn't
extend out to the tonality diamond and chords and other larger sets of
intervals in general the way that I did it. TOP was pretty clever in
that regard (TE as well).

> So you could say ha! 4:5:6 man, and 5:6 is more tempered than 4:5! And I would have to agree. But in doing so you'd have to agree that 1/4 meantone has a relationship to 3:2 that is fundamentally different from that of 12-tET.

What do you mean fundamentally different? It's more tempered, yes...

-Mike

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

>
> > So you could say ha! 4:5:6 man, and 5:6 is more tempered than 4:5! And I would have to agree. But in doing so you'd have to agree that 1/4 meantone has a relationship to 3:2 that is fundamentally different from that of 12-tET.
>
> What do you mean fundamentally different? It's more tempered, yes...
>
> -Mike
>

3:2 in 1/4-comma meantone is incidental, as it were, to the major triad. That's how it can be heavily tempered. See what I wrote earlier about parallel fifths.

The 3:2 in 12-tET is not incidental. It is primary. 12-tET is the ultimate Pythagorean tuning.

This is a deep difference. It is obvious to "naive" listeners who distinguish without effort between "church music" and "regular music".

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

> The point is that we're doing this clever trick with the primes which
> at first seems counterintuitive - minimizing the max weighted error,
> not all weighted error - because it indirectly ends up minimizing the
> average weighted error over a larger set of target intervals which are
> "composite."

You can define TOP in a way which does not mention prime numbers at all, as here:

http://xenharmonic.wikispaces.com/TOP+tuning

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> It sounds like you're literally saying "if people under laboratory
> conditions behave by retuning 400 cents to 5/4 in this experiment,
> then that is evidence that people will behave in general under further
> laboratory conditions by retuning 12-TET intervals to only those with
> at most a prime factor of 5?"

No, that's not what I'm saying. Cameron's claim is that 12-TET is NOT a 5-limit tuning. That's a universal negative. That's saying "under no circumstances can 12-TET be heard as or understood as a 5-limit tuning". My response is to give evidence that there do exist cases where 12-TET *is* heard as a 5-limit tuning, for our definition of "heard as". A local positive is sufficient to disprove a universal negative, a universal positive is not necessary. And we have our local positive, ergo the universal negative is false.

-Igs

--- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:
> 3:2 in 1/4-comma meantone is incidental, as it were, to the major triad. That's how it can
> be heavily tempered. See what I wrote earlier about parallel fifths.

That's absurd. The 3:2 is a *part* of the major triad. It can't be any more "incidental" to it than any other interval in the triad.

And seeing as how 12-TET was adopted after meantone, and considered compatible with the meantone repertoire, your implication that the major triad is somehow less primary or more incidental in 12-TET is equally-absurd. People did not go back to treating 3rds as dissonances when we adopted 12-TET. In fact, people even *stopped* treating things like 7ths and 9ths as dissonances when we developed jazz (which I'll note developed out of ragtime, which being played on piano is probably as close to strict 12-TET as was available in those days).

-Igs

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, "lobawad" <lobawad@> wrote:
> > 3:2 in 1/4-comma meantone is incidental, as it were, to the major triad. That's how it can
> > be heavily tempered. See what I wrote earlier about parallel fifths.
>
> That's absurd. The 3:2 is a *part* of the major triad. It can't be any more "incidental" to it than any other interval in the triad.

You conflate the "sol" of "do-mi-sol" with "3:2". 1/4-comma meantone very obviously does not. Your own ears do not, else you would not hear "major triads" in wildly non 4:5:6 tunings. I hear them too. That's because "major triad" is not the same thing as "4:5:6".

>
> And seeing as how 12-TET was adopted after meantone, and considered >compatible with the meantone repertoire, your implication that the >major triad is somehow less primary or more incidental in 12-TET is >equally-absurd.

4:5:6 was less primary.

--- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:
> You conflate the "sol" of "do-mi-sol" with "3:2". 1/4-comma meantone very obviously does > not. Your own ears do not, else you would not hear "major triads" in wildly non 4:5:6
> tunings. I hear them too. That's because "major triad" is not the same thing as "4:5:6".

The hell meantone doesn't! 4:5:6 *contains* 3/2. You can't target 4:5:6 and have 3/2 be "incidental", despite what you may want to believe, any more than you can have 5/4 or 6/5 be incidental. What *is* incidental is the fact that 1/4-comma meantone (which is far from the only meantone that was in use at the time, and never dominated the Western world to the extent that 12-TET now does) tunes 5/4 justly.

> 4:5:6 was less primary.

That's an extraordinary claim. There is no evidence that 4:5:6 took a back seat in primacy to the Pythagorean trine with the adoption of 12-TET, unless you want to cite punk rock, which is still less popular than the combined varieties of 12-TET music that do feature triadic harmonies.

-Igs

I want to point out just one issue I disagree with. Not a big one, but
important.

Copious use of extended chords started with the mid to late romantic period
in the west. Some of Debussian harmony sounds like a premonition of Jazz
and Wagner pretty much breaks attempts at common practice rationalization
of his harmonic language - and his music is not lone representative of that
period. And lets not forget the harmonies Stravinsky and pre-serialism
Schoenberg and others introduced. And then there is Charles Ives.

And I'll add this observation that so far in this thread no one mentioned -
what I see as one of the real innovations of 20th century in western music
is the assimilation of percussion and the development of the drum kit.

In Urbana Rob Scott gave an excellent lecture on the history of the drumset
which I was fortunate enough to video.

http://www.youtube.com/watch?v=XPYEP9G8Lqc

Chris

On Wed, Jan 18, 2012 at 9:00 PM, cityoftheasleep <igliashon@...>wrote:

> **
>
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> It's also also worth noting that the copious use of extended chords was
> rare in Western music until the advent of jazz,
>

On Thu, Jan 19, 2012 at 2:29 PM, cityoftheasleep
<igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:
> > You conflate the "sol" of "do-mi-sol" with "3:2". 1/4-comma meantone very obviously does > not. Your own ears do not, else you would not hear "major triads" in wildly non 4:5:6
> > tunings. I hear them too. That's because "major triad" is not the same thing as "4:5:6".
>
> The hell meantone doesn't! 4:5:6 *contains* 3/2. You can't target 4:5:6 and have 3/2 be "incidental", despite what you may want to believe, any more than you can have 5/4 or 6/5 be incidental. What *is* incidental is the fact that 1/4-comma meantone (which is far from the only meantone that was in use at the time, and never dominated the Western world to the extent that 12-TET now does) tunes 5/4 justly.

At the risk of sounding like a broken record, the fact that "major
triad" is not the same thing as "4:5:6" is the same as saying that
"major third" is not the same thing as "5/4."

-Mike

On Thu, Jan 19, 2012 at 3:29 PM, Chris Vaisvil <chrisvaisvil@...> wrote:
>
> I want to point out just one issue I disagree with. Not a big one, but important.
>
> Copious use of extended chords started with the mid to late romantic period in the west. Some of Debussian harmony sounds like a premonition of Jazz and Wagner pretty much breaks attempts at common practice rationalization of his harmonic language - and his music is not lone representative of that period. And lets not forget the harmonies Stravinsky and pre-serialism Schoenberg and others introduced.  And then there is Charles Ives.

Yeah, Debussy is like the rock from which all modern harmony doth
spring, as far as I'm concerned. Well, there's also apparently some of
Lizst's later stuff, and the other impressionists, and some late
Romantic stuff was sort of a premonition of Debussy, but I still view
his work as being a monumental leap forward in terms of harmony.

-Mike

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

> Yeah, Debussy is like the rock from which all modern harmony doth
> spring, as far as I'm concerned. Well, there's also apparently some of
> Lizst's later stuff, and the other impressionists, and some late
> Romantic stuff was sort of a premonition of Debussy, but I still view
> his work as being a monumental leap forward in terms of harmony.

Debussy was influenced both by Liszt, a personal friend, and his fasination with Wagner.

On Thu, Jan 19, 2012 at 6:22 PM, genewardsmith
<genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > Yeah, Debussy is like the rock from which all modern harmony doth
> > spring, as far as I'm concerned. Well, there's also apparently some of
> > Lizst's later stuff, and the other impressionists, and some late
> > Romantic stuff was sort of a premonition of Debussy, but I still view
> > his work as being a monumental leap forward in terms of harmony.
>
> Debussy was influenced both by Liszt, a personal friend, and his fasination with Wagner.

Alright, but you can't deny that Debussy was the first to do a lot of
things that are still in use. He explored a ton of meantone MODMOS
modes, for one thing, which isn't something I know of anyone else
doing.

-Mike

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

> At the risk of sounding like a broken record, the fact that "major
> triad" is not the same thing as "4:5:6" is the same as saying that
> "major third" is not the same thing as "5/4."

That's tangential. Cameron is saying that 1/4-comma meantone treats 3/2 as incidental to 4:5:6. Whether a 4:5:6 is a major triad or not has nothing whatsoever to do with the fact that targeting a 4:5:6 by necessity means targeting 3/2 as well. You can't have 4:5:6 without a 3/2. End of story.

-Igs

On Thu, Jan 19, 2012 at 8:45 PM, cityoftheasleep
<igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > At the risk of sounding like a broken record, the fact that "major
> > triad" is not the same thing as "4:5:6" is the same as saying that
> > "major third" is not the same thing as "5/4."
>
> That's tangential. Cameron is saying that 1/4-comma meantone treats 3/2 as incidental to 4:5:6. Whether a 4:5:6 is a major triad or not has nothing whatsoever to do with the fact that targeting a 4:5:6 by necessity means targeting 3/2 as well. You can't have 4:5:6 without a 3/2. End of story.

It seemed like Cameron was saying what I was saying above, because he said this

> You conflate the "sol" of "do-mi-sol" with "3:2". 1/4-comma meantone very obviously does not. Your own ears do not, else you would not hear "major triads" in wildly non 4:5:6 tunings. I hear them too. That's because "major triad" is not the same thing as "4:5:6".

I'll leave him to clarify though.

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> It seemed like Cameron was saying what I was saying above, because he said this
>
> > You conflate the "sol" of "do-mi-sol" with "3:2". 1/4-comma meantone very obviously does not. Your own ears do not, else you would not hear "major triads" in wildly non 4:5:6 tunings. I hear them too. That's because "major triad" is not the same thing as "4:5:6".
>

Again, "major triad" has nothing to do with what we're talking about. We can leave that term entirely out of this conversation and my objection will still stand.

I'll say it again: you can't target 4:5:6 *and* ignore 3/2, anymore than you can ignor 5/4 or 6/5. 3/2 is not, and cannot be, "incidental" to 1/4-comma meantone.

-Igs

On Thu, Jan 19, 2012 at 9:06 PM, cityoftheasleep
<igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> > It seemed like Cameron was saying what I was saying above, because he said this
> >
> > > You conflate the "sol" of "do-mi-sol" with "3:2". 1/4-comma meantone very obviously does not. Your own ears do not, else you would not hear "major triads" in wildly non 4:5:6 tunings. I hear them too. That's because "major triad" is not the same thing as "4:5:6".
> >
>
> Again, "major triad" has nothing to do with what we're talking about. We can leave that term entirely out of this conversation and my objection will still stand.
>
> I'll say it again: you can't target 4:5:6 *and* ignore 3/2, anymore than you can ignor 5/4 or 6/5. 3/2 is not, and cannot be, "incidental" to 1/4-comma meantone.

Ok, how about this: the people who invented quarter-comma meantone
cared about 3/2 less and 4:5:6 more. Yes? No?

-Mike

On Thu, Jan 19, 2012 at 9:12 PM, Mike Battaglia <battaglia01@...> wrote:
>
> Ok, how about this: the people who invented quarter-comma meantone
> cared about 3/2 less and 4:5:6 more. Yes? No?

In fact, I don't even like that. The people who invented quarter-comma
meantone cared about making "major triads" sound concordant more than
they cared about making "perfect fifths" sound concordant. How about
that? And I'm using my own definition of concordant, the one which is
entirely psychoacoustic and has nothing to do with happiness or how
much people like things or whatever.

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> Ok, how about this: the people who invented quarter-comma meantone
> cared about 3/2 less and 4:5:6 more. Yes? No?

How about this--the people who invented quarter-comma meantone cared about the full 5-limit, rather than only the 3-limit. The 5-limit contains the 3-limit, and the 3-limit never stopped being an important part of Western music. If people weren't playing major triads, but instead something like parallel 5/4's everywhere, and replaced the diatonic scale with Wuerschmidt[7] (a temperament which only gets to an approximate 3/2 at 8 generators), then I'd buy what Cameron was saying. The fact that music remind thoroughly diatonic, and utilized 4:5:6 and 10:12:15 triads extensively, contradicts his claim that 3/2 suddenly became some "incidental" interval with the advent of quarter-comma meantone. 3/2 was not deposed by 5/4, it was just joined by it.

-Igs

I want to say this though:

On Thu, Jan 19, 2012 at 2:09 PM, lobawad <lobawad@...> wrote:
>
> --- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> > And seeing as how 12-TET was adopted after meantone, and considered >compatible with the meantone repertoire, your implication that the >major triad is somehow less primary or more incidental in 12-TET is >equally-absurd.
>
> 4:5:6 was less primary.

I don't think that the shift to 12-EDO had anything to do with a
conscious desire to make 3/2 better, if that's what you're saying. I
note that people had to be specifically taught to distinguish between
chromatic and diatonic semitones, and that many perceived the wolf
fifth as being just that - a "fifth" which is "out of tune," as
opposed to a completely categorically different interval. So it seems
that a lot of people understood meantone[12] as being sort of a
quasi-12-EDO anyway, given that the next historical step was to try
and intone "all of the keys" more nicely.

I think the intonation was something incidental to the rest of it;
something to optimize to keep the auditory system happy* while
transmitting information on a different level. You know, the same
level that contains all of these scalar, "logical," etc features that
we've all "not disagreed" are more important to the establishment of
tonality than the intonation. The ones which seem to be intact no
matter what you tune the generator to, so long as 5L2s is involved in
some fashion.

-Mike

*I don't really think auditory systems can be happy.

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

> In fact, I don't even like that. The people who invented quarter-comma
> meantone cared about making "major triads" sound concordant more than
> they cared about making "perfect fifths" sound concordant. How about
> that? And I'm using my own definition of concordant, the one which is
> entirely psychoacoustic and has nothing to do with happiness or how
> much people like things or whatever.

Okay, sure. I can agree to that wording. But the point is that the concordance of perfect 5ths is a part of the concordance of major triads; you can't have a concordant major triad if the perfect fifth is discordant. Try applying the Wuerschmidt mapping to 28-ED2 or 25-ED2.

-Igs

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

> Again, "major triad" has nothing to do with what we're talking about. We can leave that term entirely out of this conversation and my objection will still stand.
>
> I'll say it again: you can't target 4:5:6 *and* ignore 3/2, anymore than you can ignor 5/4 or 6/5. 3/2 is not, and cannot be, "incidental" to 1/4-comma meantone.
>
> -Igs
>

"Major triad" has everything to do with what meantone was talking about.

And I did not say "incidental". What I said was ""incidental", so to speak".

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Thu, Jan 19, 2012 at 9:12 PM, Mike Battaglia <battaglia01@...> wrote:
> >
> > Ok, how about this: the people who invented quarter-comma meantone
> > cared about 3/2 less and 4:5:6 more. Yes? No?
>
> In fact, I don't even like that. The people who invented quarter-comma
> meantone cared about making "major triads" sound concordant more than
> they cared about making "perfect fifths" sound concordant. How about
> that? And I'm using my own definition of concordant, the one which is
> entirely psychoacoustic and has nothing to do with happiness or how
> much people like things or whatever.
>
> -Mike
>

"the people who invented quarter-comma meantone
cared about 3/2 less and 4:5:6 more"

cannot be sanely denied- it would be a trivial observation had we no other tunings with which to compare. For example:

"the people who invented 12-tET cared about 3:2 more and 4:5:6 less".

And yes, it's really about "major triad" and "perfect fifth", not the ratios.

Historically, Just Intonation was intonation OF intervals, and those intervals were already "given". The ancients argued about how to tune, that is, fine tune, intervals such as "middle finger". That there would be a string or fret there so many scale steps from such-and-such was given.

Even if you cannot find books on the subject, theorists such as Tartini and so on are quoted extensively in academic papers available on JSTOR, which your university library will have. There you will find that this same principle continued in the West: intonation is intonation OF. There is a pre-existing object of this intonation, and that object retains its identity whether tuned Just or not.

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

> "the people who invented quarter-comma meantone
> cared about 3/2 less and 4:5:6 more"
>
> cannot be sanely denied- it would be a trivial observation had we no other tunings with > which to compare.

What does that even mean, to care about 3/2 less and 4:5:6 more? Did they care about 6/5 less, as well? Did the people who invented 1/3-comma meantone care about 6/5 more, and 5/4 less (and 3/2 even less)? Did the people who invented 1/6-comma meantone care about 3/2 more, and 4:5:6 less? I mean, WTF are you even talking about?

> For example:
>
> "the people who invented 12-tET cared about 3:2 more and 4:5:6 less".

That's patently false. The people who invented 12-TET cared about modulation more and intonation less. That 12-TET has purer 3/2's and less-pure 4:5:6's is incidental. And somehow or another, this shift to an intonation with less-pure 4:5:6's did not put an end to consonant triadic harmony in the West. The opposite happened--regardless of who exactly you want to credit for the birth of extended harmony, it's after the adoption of 12-TET. The fact that 12-TET supplanted or dominated not just all varieties of meantone, but also all well-temperaments, and the native tunings of more than a few cultures, *is* evidence that the more complex ratios *can* bear more mistuning than the simpler ones. 0-400-700-1000 cents as a 4:5:6:7 readily demonstrates this. It's a sonority few people find objectionable--see the entire blues and jazz piano and guitar corpora--and which is also notably intoned adaptively as a 4:5:6:7 when given the chance (either as a C-E-G-Bb dom7, or as a C-E-G-A# augmented 6th)--see the entire barbershop corpus.

The fact that some (perhaps many or most) people tend to say, of 5-limit and 7-limit JI, that they sound "more in-tune" than 12-TET, indicates they don't give the Just tunings a different mental category than the 12-TET ones. You tell me what the obvious conclusion is when people hear two distinctly-tuned chords and say that one is a better-tuned version of the other.

> And yes, it's really about "major triad" and "perfect fifth", not the ratios.

What is this "it" you speak of?

This all started because of your claim that quarter-comma meantone somehow disproves the commonly-accepted principle that more complex ratios lose concordance more slowly with mistuning than do simpler ratios. How does this have anything to do with "major triad" and "perfect fifth"?

-Igs

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

> This all started because of your claim that quarter-comma meantone >somehow disproves the commonly-accepted principle that more complex >ratios lose concordance more slowly with mistuning than do simpler >ratios. How does this have anything to do with "major triad" and >"perfect fifth"?

I never said this. I said that 1/4 comma meantone shows that this phenomena is not a foundational principle of musical tuning ("tuning" incorporating approximation of rationals understood, I should have made that clear).

The irony here is that it is not impossible that you, Igliashon Jones, are more familiar, in actual experience, with the validity of what I am saying, than anyone... ever.

Let me put it this way: what are the major and minor triads of 20 equal division of the octave?

>
> --- In tuning@yahoogroups.com, "lobawad" <lobawad@> wrote:
>
> > "the people who invented quarter-comma meantone
> > cared about 3/2 less and 4:5:6 more"
> >
> > cannot be sanely denied- it would be a trivial observation had we no other tunings with > which to compare.
>
> What does that even mean, to care about 3/2 less and 4:5:6 more? Did they care about 6/5 less, as well? Did the people who invented 1/3-comma meantone care about 6/5 more, and 5/4 less (and 3/2 even less)? Did the people who invented 1/6-comma meantone care about 3/2 more, and 4:5:6 less? I mean, WTF are you even talking about?
>
> > For example:
> >
> > "the people who invented 12-tET cared about 3:2 more and 4:5:6 less".
>
> That's patently false. The people who invented 12-TET cared about modulation more and intonation less. That 12-TET has purer 3/2's and less-pure 4:5:6's is incidental. And somehow or another, this shift to an intonation with less-pure 4:5:6's did not put an end to consonant triadic harmony in the West. The opposite happened--regardless of who exactly you want to credit for the birth of extended harmony, it's after the adoption of 12-TET. The fact that 12-TET supplanted or dominated not just all varieties of meantone, but also all well-temperaments, and the native tunings of more than a few cultures, *is* evidence that the more complex ratios *can* bear more mistuning than the simpler ones. 0-400-700-1000 cents as a 4:5:6:7 readily demonstrates this. It's a sonority few people find objectionable--see the entire blues and jazz piano and guitar corpora--and which is also notably intoned adaptively as a 4:5:6:7 when given the chance (either as a C-E-G-Bb dom7, or as a C-E-G-A# augmented 6th)--see the entire barbershop corpus.
>
> The fact that some (perhaps many or most) people tend to say, of 5-limit and 7-limit JI, that they sound "more in-tune" than 12-TET, indicates they don't give the Just tunings a different mental category than the 12-TET ones. You tell me what the obvious conclusion is when people hear two distinctly-tuned chords and say that one is a better-tuned version of the other.
>
> > And yes, it's really about "major triad" and "perfect fifth", not the ratios.
>
> What is this "it" you speak of?
>

>
> -Igs
>

--- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:
> I never said this. I said that 1/4 comma meantone shows that this phenomena is not a
> foundational principle of musical tuning ("tuning" incorporating approximation of
> rationals understood, I should have made that clear).

If by "foundational" you mean "necessary", then I can agree with you. But as far as tunings go, meantone's really kind of a blip and its existence doesn't prove much. It was both preceded and succeeded by tunings that more strongly emphasized the purity of 3/2 over 4/3...and the absolute purity of 2/1 is absolutely demanded throughout most of the world-history of harmonic music. Compromising the 3/2 for the sake of 4:5:6 was an experiment that culture at large ultimately rejected.

> The irony here is that it is not impossible that you, Igliashon Jones, are more familiar, in > actual experience, with the validity of what I am saying, than anyone... ever.

My experience is that what *I* like has little correlation with what is considered by most to be concordant. And lots of people seem to like my music. Lots of other people lament that I'm wasting my talents on nasty-sounding tunings. While I do believe damn near any tuning can be used successfully in certain applications, I am not sure if I believe that a tuning notably less concordant than 12-TET will succeed in attracting the kind of widespread and sustained interest I would like to see. Simultaneously with these creeping doubts, I am growing tired of ceaseless novelty and experimentalism, and am starting to want to settle down with a couple tunings...maybe buy a house, raise a few kids, that kind of thing.

I've already seen the failure of other tunings to thrive--31-TET was too big to make it, and too complicated at almost thrice the size of 12-TET (with between 5 and 7 sizes of 3rd, depending on if you want to count the 8/7 and 21/16 as "3rds" or not, that's between 25 and 49 triads, 125 to 343 tetrads, and 625 to 2401 pentads to sift through); 22-TET has problems that are harder to define, but for some reason it just doesn't seem to attract the kind of interest people think it should--maybe it's too large, maybe it's lacking accessible tonal structures, maybe 11-limit harmony isn't actually interesting to many people, or maybe it's too close to 24-TET that people would rather go that direction; 19-TET is a great meantone but just doesn't sound that good outside that context, and theorists have pushed it as hard as any tuning has ever been pushed to scant avail. So far, no one's seriously proposed 11, 13, 14, 18, 20, 21, or 23, and proposals for 15, 16, and 17 have generated some interest but have been made too recently to evaluate.

JI has appeal as a general approach, but no single JI pitch-set seems poised for dominance, or demonstrates any clear superiority over alternatives. Partch's 43-tone construction probably gets the most press. Without a single scale, it's hard to construct a practical music theory, or to develop a compositional language comparable to what we have with 12-TET.

Oddly, next to JI the one tuning that seems to be thriving more than anything else is BP, which is macrotonal, equally-tempered, non-octave, and so thoroughly unlike all prior Western tunings that it's about as divorced from common-practice theory as one can possibly get. Yet it offers concordant harmony 1:3:5:7:9 harmonies (if you avoid all the dissonances) and it's super-simple. Next to BP and JI, quarter-tones are the only real visible alternative tuning system in the West.

So I'm looking for a tuning that won't fail to thrive the way just about everything we discuss here has. And I'm pretty sure that means giving up my "nihilism" (as Carl calls it) and just accepting that concordance in some form is important and necessary to get any more than a handful of rugged individualists to pay attention. The only question still open, as far as I'm concerned, is what form concordance needs to take.

> Let me put it this way: what are the major and minor triads of 20 equal division of the
> octave?

Good question! You might want me to say, "0-420-720 and 0-300-720 cents, obviously", but 0-360-720 could just as easily stand in for both of them, or 0-360-660 and 0-300-660 could, too. If you gave me any of those and told me "tune this so it sounds in tune" (and I didn't feel like being pedantic), I'd tune it to some 5-limit chord.

-Igs

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, "lobawad" <lobawad@> wrote:
> > I never said this. I said that 1/4 comma meantone shows that this >phenomena is not a
> > foundational principle of musical tuning ("tuning" incorporating >approximation of
> > rationals understood, I should have made that clear).
>
> If by "foundational" you mean "necessary", then I can agree with >you.

"Essential", "key", "guiding principle", that's the kind of thing I meant.

I could also have said "24-edo FTW!" as a sarcastic response. Because if you take "fields of attraction", "identities", the idea of tall tertian chords evolving as incorporating successive odd harmonics, and the phenomenon of lower ratios beating more obviously more quickly, and put it all together, there's no reason why 24-edo shouldn't be the messiah Just temperament for Western music.

These ideas fail to explain why 24-edo sounds like a bone saw harmonically.

> But as far as tunings go, meantone's really kind of a blip and its >existence doesn't prove much. It was both preceded and succeeded by >tunings that more strongly emphasized the purity of 3/2 over >4/3...and the absolute purity of 2/1 is absolutely demanded >throughout most of the world-history of harmonic music. >Compromising the 3/2 for the sake of 4:5:6 was an experiment that >culture at large ultimately rejected.

I'm sure a lot of people would strongly disagree with the idea that 1/4 comma meantone was a blip. Either way, my original point was about principles of approximating Just. 1/4-comma kicks ass at feeling like 4:5:6. Try a major triad with the fifth a quarter-comma sharp from 3:2, rather than flat. I'd say it is certainly less 4:5:6 sounding, wouldn't you?

> My experience is that what *I* like has little correlation with >what is considered by most to be concordant.

All the music we know on any large scale, or any scale beyond a handful of people for that matter, has strong visual, social, cultural, sartorial, racial, gastronomical, etc. associations, whether we're aware of them or not.

You cannot know what "people" think about your music until, like every other music that "people" listen to, your music has a cultural context, what believers in absolute music would view as extramusical associations (apparently oblivious to the fact that the various "absolute musics" of the past had extramusical associations coming out the ears).

>And lots of people >seem to like my music. Lots of other people >lament that I'm wasting >my talents on nasty-sounding tunings. >While I do believe damn near >any tuning can be used successfully in >certain applications, I am >not sure if I believe that a tuning >notably less concordant than >12-TET will succeed in attracting the >kind of widespread and >sustained interest I would like to see.

Maybe you'll have the same experience I did some year ago: one day you'll hear 12-tET and say hey, that's not actually very "concordant" at all, it's more dry and "neutral", and the effects of concordance and discordance are actually achieved by the spectacular array of timbres used in Western music.

>
> 22-TET has problems that are harder to define,

Oh I don't know if it's so hard to define: 22 sounds cheesey, like playing EVERYTHING on a DX-7.

> 19-TET is a great meantone but just doesn't sound that good outside >>that context, and theorists have pushed it as hard as any tuning >has ever been pushed to scant avail.

I'd like to hear work in 19-edo rather than 19-tET. I think 19-tET sounds like soggy meantone, people have commented on this over the last half-century or more.

>So far, no one's seriously proposed 11, 13, 14, 18, 20, 21, or 23, >and proposals for 15, 16, and 17 have generated some interest but >have been made too recently to evaluate.

17 works for me. 16 is very pleasant, I am looking forward to using it in some soundtrack-type context someday.

>
> JI has appeal as a general approach, but no single JI pitch-set >seems poised for dominance, or demonstrates any clear superiority >over alternatives. Partch's 43-tone construction probably gets the >most press.

Partch, Carrillo and Wyshnegradsky get almost all the press. As is to be expected- in both theory and music they are completely non-threatening to entrenched hegemonies.

> Without a single scale, it's hard to construct a practical music >theory, or to develop a compositional language comparable to what we >have with 12-TET.

There are other ways, but that would be long discussion. But I see what you mean.

>
> Oddly, next to JI the one tuning that seems to be thriving more >than anything else is BP, which is macrotonal, equally-tempered, >non-octave, and so thoroughly unlike all prior Western tunings that >it's about as divorced from common-practice theory as one can >possibly get. Yet it offers concordant harmony 1:3:5:7:9 harmonies >(if you avoid all the dissonances) and it's super-simple.

BP is also non-threatening to entrenched hegemonies, because it has such a specific character. I think BP sounds very nice indeed, though.

>Next to BP and JI, quarter-tones are the only real visible >alternative tuning system in the West.

A century of evidence tells us that quarter-tones just don't work for non-satanic harmony. Given appropriately written music, an ensemble could be trained to read quartertones but play sensitively to adaptive Just interpretations. This in my opinion is what should have happened with quartertones, but audibly did not.

>
> So I'm looking for a tuning that won't fail to thrive the way just >about everything we discuss here has. And I'm pretty sure that >means giving up my "nihilism" (as Carl calls it) and just accepting >that concordance in some form is important and necessary to get any >more than a handful of rugged individualists to pay attention. The >only question still open, as far as I'm concerned, is what form >concordance needs to take.

Or you could put together a hard and heavy band and be the king of discord.

>
> > Let me put it this way: what are the major and minor triads of 20 equal division of the
> > octave?
>
> Good question! You might want me to say, "0-420-720 and 0-300-720 cents, obviously", but 0-360-720 could just as easily stand in for both of them, or 0-360-660 and 0-300-660 could, too. If you gave me any of those and told me "tune this so it sounds in tune" (and I didn't feel like being pedantic), I'd tune it to some 5-limit chord.

Yes there's more than one, isn't there? But how is this so? If "major triad" were 4:5:6, and you buy the whole thing about approximation by proximity, you'd have to choose 0-360-720. And sure enough if I'm listening in a JI way, for smoothness, that's the best 4:5:6. But as soon as you start playing it, it is clear that the other choices you mention offer actual major and minor chords, whereas 0-360-720, despite being the best 4:5:6, is not a major triad at all. A major triad has a major third and a minor third.

0-420-720 and 0-360-660 both work, and even sound, like major triads. The ability to alternate with minor, without needing additional interval sizes (you could have said "0-360-720 and 0-300-720") is part of the definition of "major triad". In the case of 20-edo you can see this essential characteristic brutally override approximation of 4:5:6.

On the other hand you could conceive your 20-edo music in terms of JI smoothness and throw out the stuff that makes major/minor as we hold it.

Either way, I think this is a clear example of how 4:5:6 and "major triad" do not equate. But I'm not trying to create a false dichotomy- clearly in practice there is a continuum between the two concepts.

On Fri, Jan 20, 2012 at 4:06 PM, lobawad <lobawad@...> wrote:
>
> I could also have said "24-edo FTW!" as a sarcastic response. Because if you take "fields of attraction", "identities", the idea of tall tertian chords evolving as incorporating successive odd harmonics, and the phenomenon of lower ratios beating more obviously more quickly, and put it all together, there's no reason why 24-edo shouldn't be the messiah Just temperament for Western music.
>
> These ideas fail to explain why 24-edo sounds like a bone saw harmonically.

Why do you think it sounds like a bone saw?

> I'm sure a lot of people would strongly disagree with the idea that 1/4 comma meantone was a blip. Either way, my original point was about principles of approximating Just. 1/4-comma kicks ass at feeling like 4:5:6. Try a major triad with the fifth a quarter-comma sharp from 3:2, rather than flat. I'd say it is certainly less 4:5:6 sounding, wouldn't you?

I dunno, I happen to like the major triads in 34-EDO and 22-EDO...

> You cannot know what "people" think about your music until, like every other music that "people" listen to, your music has a cultural context, what believers in absolute music would view as extramusical associations (apparently oblivious to the fact that the various "absolute musics" of the past had extramusical associations coming out the ears).

Yeah, why doesn't he just write in 12-EDO?! He must be a Democrat.

> >
> > 22-TET has problems that are harder to define,
>
> Oh I don't know if it's so hard to define: 22 sounds cheesey, like playing EVERYTHING on a DX-7.

I love 22-EDO. I think you're all just hatin'. I did an improv on it here

http://www.youtube.com/watch?v=WMtp9Wk0tO0

Sounds nice to me, anyway, although I should probably record another
one now that I can play the instrument better.

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Fri, Jan 20, 2012 at 4:06 PM, lobawad <lobawad@...> wrote:
> >
> > I could also have said "24-edo FTW!" as a sarcastic response. Because if you take "fields of attraction", "identities", the idea of tall tertian chords evolving as incorporating successive odd harmonics, and the phenomenon of lower ratios beating more obviously more quickly, and put it all together, there's no reason why 24-edo shouldn't be the messiah Just temperament for Western music.
> >
> > These ideas fail to explain why 24-edo sounds like a bone saw harmonically.
>
> Why do you think it sounds like a bone saw?

Beats me- I suspect that close-but-no-cigar approximation is responsible. Same goes for a lot of regular temperaments around here, but the effect is generally what I perceive as queasy, spongy. Gene's microtemperaments don't sound either sawing or queasy, they sound like "explorations of higher partials" as advertised.

>
> > I'm sure a lot of people would strongly disagree with the idea that 1/4 comma meantone was a blip. Either way, my original point was about principles of approximating Just. 1/4-comma kicks ass at feeling like 4:5:6. Try a major triad with the fifth a quarter-comma sharp from 3:2, rather than flat. I'd say it is certainly less 4:5:6 sounding, wouldn't you?
>
> I dunno, I happen to like the major triads in 34-EDO and 22-EDO...

Neither has 3:2 a quarter-comma sharp. And "like" doesn't necessarily have much or anything to do with accurate approximation- I like the "major triad" of 16-edo.

>
> > You cannot know what "people" think about your music until, like every other music that "people" listen to, your music has a cultural context, what believers in absolute music would view as extramusical associations (apparently oblivious to the fact that the various "absolute musics" of the past had extramusical associations coming out the ears).
>
> Yeah, why doesn't he just write in 12-EDO?! He must be a Democrat.
>
> > >
> > > 22-TET has problems that are harder to define,
> >
> > Oh I don't know if it's so hard to define: 22 sounds cheesey, like playing EVERYTHING on a DX-7.
>
> I love 22-EDO. I think you're all just hatin'. I did an improv on it here
>
> http://www.youtube.com/watch?v=WMtp9Wk0tO0
>
> Sounds nice to me, anyway, although I should probably record another
> one now that I can play the instrument better.

Rhythmic chopping and modal shredding like Paul Erlich's don't count in this discussion about consonant tertian chords. Play some slow clean sustained tall chords and then look down to see if your pants haven't mysteriously turned into polyester bell-bottoms.

--- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:
> I could also have said "24-edo FTW!" as a sarcastic response. Because if you take "fields of attraction", "identities", the idea of tall tertian chords evolving as incorporating successive odd harmonics, and the phenomenon of lower ratios beating more obviously more quickly, and put it all together, there's no reason why 24-edo shouldn't be the messiah Just temperament for Western music.
>
> These ideas fail to explain why 24-edo sounds like a bone saw harmonically.

No one I've seen yet has used 24-edo in the way you describe above. Most of the quarter-toners were an offshoot of the atonalists. 24-edo is perfectly capable of sounding as good as most 13-limit temperaments (for whatever that's worth), better than many if you drop the attempt at implying the 7th harmonic. I'm not entirely sure where such 13-limit harmony might lead, stylistically, but I've definitely considered the possibility that 24-edo may in fact be the "messiah Just temperament" for Western music.

> I'm sure a lot of people would strongly disagree with the idea that 1/4 comma meantone > was a blip.

In the history of world music, it is undeniably a blip. It enjoyed a few centuries of non-exclusive use in select European countries.

>Either way, my original point was about principles of approximating Just. 1/4-comma kicks ass at feeling like 4:5:6. Try a major triad with the fifth a quarter-comma sharp from 3:2, rather than flat. I'd say it is certainly less 4:5:6 sounding, wouldn't you?
>

Nope. Sounds about as good to me.

> Maybe you'll have the same experience I did some year ago: one day you'll hear 12-tET
> and say hey, that's not actually very "concordant" at all, it's more dry and "neutral", and
> the effects of concordance and discordance are actually achieved by the spectacular
> array of timbres used in Western music.

I have deluded myself in the past into thinking 12-TET sounds awful and discordant compared to nice, pure, 5-limit harmony. The revelation I eventually had was that it actually doesn't. It's quite a nice tuning. 300 cents and 400 cents are both lovely 5-limit intervals in a variety of other temperaments, plenty smooth and nice to my ears.

> Oh I don't know if it's so hard to define: 22 sounds cheesey, like playing EVERYTHING on > a DX-7.

I dunno, Paul's "Tibia" was pretty legit. But otherwise I tend to agree. At least about my own music in 22.

> I'd like to hear work in 19-edo rather than 19-tET. I think 19-tET sounds like soggy
> meantone, people have commented on this over the last half-century or more.

It sounds like a fine meantone to me. Can't tell it apart from 31, TBH.

> A century of evidence tells us that quarter-tones just don't work for non-satanic
> harmony. Given appropriately written music, an ensemble could be trained to read
> quartertones but play sensitively to adaptive Just interpretations. This in my opinion is
> what should have happened with quartertones, but audibly did not.

Well, they don't go away, and the only major-label band I've seen use microtones used 24-edo. Some schools actually teach quarter-tone techniques in composition. And there's a huge field of theory based on bastardizing Middle Eastern music into the quarter-tone system. I'm sure someone will eventually figure out that if you use some of the alternate MOS's in 24, you can get non-Satanic harmony. Barbados[9] sounds pretty nice, so does Mohajira[10].

> Or you could put together a hard and heavy band and be the king of discord.

No one will hear the difference. Did you hear that Swedish quarter-tone metal band? Fat lot of charm the quarter-tones added.

> Yes there's more than one, isn't there? But how is this so?

Because none of them quite gets 4:5:6 right, but they're all in the rough vicinity of it. They all approximate it to some extent, to the extent that it's reasonable to say any chord approximates any other chord.

-Igs

On Fri, Jan 20, 2012 at 4:34 PM, lobawad <lobawad@...> wrote:
>
>
> Beats me- I suspect that close-but-no-cigar approximation is responsible. Same goes for a lot of regular temperaments around here, but the effect is generally what I perceive as queasy, spongy. Gene's microtemperaments don't sound either sawing or queasy, they sound like "explorations of higher partials" as advertised.

Have you tried messing with 8:10:11:12:13 chords in 24-EDO?

> > > I'm sure a lot of people would strongly disagree with the idea that 1/4 comma meantone was a blip. Either way, my original point was about principles of approximating Just. 1/4-comma kicks ass at feeling like 4:5:6. Try a major triad with the fifth a quarter-comma sharp from 3:2, rather than flat. I'd say it is certainly less 4:5:6 sounding, wouldn't you?
> >
> > I dunno, I happen to like the major triads in 34-EDO and 22-EDO...
>
> Neither has 3:2 a quarter-comma sharp. And "like" doesn't necessarily have much or anything to do with accurate approximation- I like the "major triad" of 16-edo.

A quarter of 81/80 is about 5.377 cents, so a 3/2 that's a quarter
comma sharp is about 707.332 cents. The 3/2 of 17-EDO is 1.45 cents
below this at 705.882 cents, whereas the 3/2 of 22-EDO is 1.76 cents
sharp at 709.091 cents. So it's in the range.

If you mean purely psychoacoustically, I think that the 4:5:6's in
22-EDO, which have mostly just 5/4's and 3/2's a bit sharp of a
quarter comma, plenty resemble JI 4:5:6's. I hear the sound open up
and imply a virtual fundamental, I hear a bit of periodicity buzz,
etc. The main difference is that there's a little bit of warbling
which isn't there in an actual 4:5:6, and the strength of this
warbling is almost completely dependent on the brightness of the
timbre you use. On my guitar, I barely even notice it. In GM with a
reed organ patch, it's obvious. But if I know 22-EDO enough to know
the warbling is going to be there, I'll probably filter it out and not
really notice it at all, and it'll require a guided meditation with a
spirit shaman for me to become aware of it again.

> > I love 22-EDO. I think you're all just hatin'. I did an improv on it here
> >
> > http://www.youtube.com/watch?v=WMtp9Wk0tO0
> >
> > Sounds nice to me, anyway, although I should probably record another
> > one now that I can play the instrument better.
>
> Rhythmic chopping and modal shredding like Paul Erlich's don't count in this discussion about consonant tertian chords. Play some slow clean sustained tall chords and then look down to see if your pants haven't mysteriously turned into polyester bell-bottoms.

I've done that, and they'll sound fine. Emaj Amaj Dmaj Amaj Emaj
sounds pretty much like you'd expect. Sometimes it irritates me
because I -want- it to sound better than 12-EDO, but the improvement
isn't too noticeable.

-Mike

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, "lobawad" <lobawad@> wrote:
> > I could also have said "24-edo FTW!" as a sarcastic response. Because if you take "fields of attraction", "identities", the idea of tall tertian chords evolving as incorporating successive odd harmonics, and the phenomenon of lower ratios beating more obviously more quickly, and put it all together, there's no reason why 24-edo shouldn't be the messiah Just temperament for Western music.
> >
> > These ideas fail to explain why 24-edo sounds like a bone saw harmonically.
>
> No one I've seen yet has used 24-edo in the way you describe above. Most of the quarter-toners were an offshoot of the atonalists. 24-edo is perfectly capable of sounding as good as most 13-limit temperaments (for whatever that's worth), better than many if you drop the attempt at implying the 7th harmonic. I'm not entirely sure where such 13-limit harmony might lead, stylistically, but I've definitely considered the possibility that 24-edo may in fact be the "messiah Just temperament" for Western music.

12-tone "atonal" music played by instruments of flexible pitch can sound lovely, when it is not played to strict 12-tET. I'd be tickled pink to find 24 worth a darn, and I periodically check it to see if my perception has changed enough to dig it.

>
> > I'm sure a lot of people would strongly disagree with the idea that 1/4 comma meantone > was a blip.
>
> In the history of world music, it is undeniably a blip. It enjoyed a few centuries of non-exclusive use in select European countries.

So you also do not think of 12-tET as a meantone?

>
> >Either way, my original point was about principles of approximating Just. 1/4-comma kicks ass at feeling like 4:5:6. Try a major triad with the fifth a quarter-comma sharp from 3:2, rather than flat. I'd say it is certainly less 4:5:6 sounding, wouldn't you?
> >
>
> Nope. Sounds about as good to me.

I didn't say "good", I said "like 4:5:6".

>
> > Maybe you'll have the same experience I did some year ago: one day you'll hear 12-tET
> > and say hey, that's not actually very "concordant" at all, it's more dry and "neutral", and
> > the effects of concordance and discordance are actually achieved by the spectacular
> > array of timbres used in Western music.
>
> I have deluded myself in the past into thinking 12-TET sounds awful and discordant compared to nice, pure, 5-limit harmony. The revelation I eventually had was that it actually doesn't. It's quite a nice tuning. 300 cents and 400 cents are both lovely 5-limit intervals in a variety of other temperaments, plenty smooth and nice to my ears.

I'm not really much of a fan of nice, pure 5-limit harmony. And I don't think 12-tET sounds discordant. It sounds dry and neutral. Pretty blank. Which turns out to be a wonderful thing, in hindsight- the amount of timbral variety developed to compensate is astronomically greater than all the instrumental timbres of all the other cultures with far more colorful tunings, put together.

>
> > Oh I don't know if it's so hard to define: 22 sounds cheesey, like playing EVERYTHING on > a DX-7.
>
> I dunno, Paul's "Tibia" was pretty legit. But otherwise I tend to agree. At least about my own music in 22.
>
> > I'd like to hear work in 19-edo rather than 19-tET. I think 19-tET sounds like soggy
> > meantone, people have commented on this over the last half-century or more.
>
> It sounds like a fine meantone to me. Can't tell it apart from 31, TBH.

I think all meantones have a certain sogginess about them, including 1/4-comma. Then again 4:5:6 has a languid quality that isn't far from soggy.

Sometimes there is a fine line between moist and fetid.
>
>
> > A century of evidence tells us that quarter-tones just don't work for non-satanic
> > harmony. Given appropriately written music, an ensemble could be trained to read
> > quartertones but play sensitively to adaptive Just interpretations. This in my opinion is
> > what should have happened with quartertones, but audibly did not.
>
> Well, they don't go away, and the only major-label band I've seen use microtones used 24-edo. Some schools actually teach quarter-tone techniques in composition. And there's a huge field of theory based on bastardizing Middle Eastern music into the quarter-tone system. I'm sure someone will eventually figure out that if you use some of the alternate MOS's in 24, you can get non-Satanic harmony. Barbados[9] sounds pretty nice, so does Mohajira[10].
>
> > Or you could put together a hard and heavy band and be the king of discord.
>
> No one will hear the difference. Did you hear that Swedish quarter-tone metal band? Fat lot of charm the quarter-tones added.

I meant actually hard and heavy, not heavy metal.

>
> > Yes there's more than one, isn't there? But how is this so?
>
> Because none of them quite gets 4:5:6 right, but they're all in the >rough vicinity of it. They all approximate it to some extent, to >the extent that it's reasonable to say any chord approximates any >other chord.

You're missing the point that the most accurate approximation to 4:5:6 offered in the tuning is simply not a major triad.

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Fri, Jan 20, 2012 at 4:34 PM, lobawad <lobawad@...> wrote:
> >
> >
> > Beats me- I suspect that close-but-no-cigar approximation is responsible. Same goes for a lot of regular temperaments around here, but the effect is generally what I perceive as queasy, spongy. Gene's microtemperaments don't sound either sawing or queasy, they sound like "explorations of higher partials" as advertised.
>
> Have you tried messing with 8:10:11:12:13 chords in 24-EDO?

Of course. For years, periodically- I would be thrilled to find 24 useful, are you kidding?

I don't know what it is. The lack of 5/4? That certainly doesn't bother be in other tunings. 350 and 850 cents are like main axe stuff for me. I think I downright prefer 950 cents to a pure 7/4. But the whole thing together... it just doesn't work.

Maybe it's the step sizes. 100 cents too big, 50 cents too small.

>
> If you mean purely psychoacoustically, I think that the 4:5:6's in
> 22-EDO, which have mostly just 5/4's and 3/2's a bit sharp of a
> quarter comma, plenty resemble JI 4:5:6's. I hear the sound open up
> and imply a virtual fundamental, I hear a bit of periodicity buzz,
> etc. The main difference is that there's a little bit of warbling
> which isn't there in an actual 4:5:6, and the strength of this
> warbling is almost completely dependent on the brightness of the
> timbre you use. On my guitar, I barely even notice it. In GM with a
> reed organ patch, it's obvious. But if I know 22-EDO enough to know
> the warbling is going to be there, I'll probably filter it out and not
> really notice it at all, and it'll require a guided meditation with a
> spirit shaman for me to become aware of it again.

I don't really equate "4:5:6" and "good". It's just a thing.

On Fri, Jan 20, 2012 at 5:29 PM, lobawad <lobawad@...> wrote:
>
> > If you mean purely psychoacoustically, I think that the 4:5:6's in
> > 22-EDO, which have mostly just 5/4's and 3/2's a bit sharp of a
> > quarter comma, plenty resemble JI 4:5:6's. I hear the sound open up
> > and imply a virtual fundamental, I hear a bit of periodicity buzz,
> > etc. The main difference is that there's a little bit of warbling
> > which isn't there in an actual 4:5:6, and the strength of this
> > warbling is almost completely dependent on the brightness of the
> > timbre you use. On my guitar, I barely even notice it. In GM with a
> > reed organ patch, it's obvious. But if I know 22-EDO enough to know
> > the warbling is going to be there, I'll probably filter it out and not
> > really notice it at all, and it'll require a guided meditation with a
> > spirit shaman for me to become aware of it again.
>
> I don't really equate "4:5:6" and "good". It's just a thing.

I didn't say anything about "good" above. I only talked about the things I hear.

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Fri, Jan 20, 2012 at 5:29 PM, lobawad <lobawad@...> wrote:
> >
> > > If you mean purely psychoacoustically, I think that the 4:5:6's in
> > > 22-EDO, which have mostly just 5/4's and 3/2's a bit sharp of a
> > > quarter comma, plenty resemble JI 4:5:6's. I hear the sound open up
> > > and imply a virtual fundamental, I hear a bit of periodicity buzz,
> > > etc. The main difference is that there's a little bit of warbling
> > > which isn't there in an actual 4:5:6, and the strength of this
> > > warbling is almost completely dependent on the brightness of the
> > > timbre you use. On my guitar, I barely even notice it. In GM with a
> > > reed organ patch, it's obvious. But if I know 22-EDO enough to know
> > > the warbling is going to be there, I'll probably filter it out and not
> > > really notice it at all, and it'll require a guided meditation with a
> > > spirit shaman for me to become aware of it again.
> >
> > I don't really equate "4:5:6" and "good". It's just a thing.
>
> I didn't say anything about "good" above. I only talked about the things I hear.
>
> -Mike
>

I was just making an observation. I am curious as to why we don't have a huge body of 22 works coming from this list and related community, considering the fact that by the standards elaborated, 22 is undeniably the bee's knees.

--- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:
> 12-tone "atonal" music played by instruments of flexible pitch can sound lovely, when it > is not played to strict 12-tET. I'd be tickled pink to find 24 worth a darn, and I
> periodically check it to see if my perception has changed enough to dig it.

It's hard to like 24 unless you can allow yourself to like 12, also. I still struggle with this.

> In the history of world music, it is undeniably a blip. It enjoyed a few centuries of
> non-exclusive use in select European countries.
>
> So you also do not think of 12-tET as a meantone?

Quarter-comma meantone was what we were specifically talking about. 12-TET is a lot of things, including a meantone.

> > Nope. Sounds about as good to me.
>
> I didn't say "good", I said "like 4:5:6".

And that's what I meant by "good"--it's sounds like as good of a 4:5:6 as the other version. I echo Mike's sentiments on the matter.

> I think all meantones have a certain sogginess about them, including 1/4-comma. Then > again 4:5:6 has a languid quality that isn't far from soggy.
>
> Sometimes there is a fine line between moist and fetid.

I can dig that.

> I meant actually hard and heavy, not heavy metal.

As in...?

> You're missing the point that the most accurate approximation to 4:5:6 offered in the
> tuning is simply not a major triad.

What, 0-360-720? That's not the most accurate one. 0-420-720 has lower average dyadic error (of 5/4, 6/5, and 3/2), whether weighted or unweighted, than either of the other two triads:

Triad: Unwtd: Wtd:
0 360 720 29.78 7.41
0 420 720 22.25 5.95
0 360 660 27.75 8.46

So...you were saying?

-Igs

--- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:
> I was just making an observation. I am curious as to why we don't have a huge body of 22 > works coming from this list and related community, considering the fact that by the
> standards elaborated, 22 is undeniably the bee's knees.

It does make you wonder, doesn't it? Too bad Carl's not here to stick up for the 22-tone corpus. I've recorded more songs in 22-TET than anybody else whose music is available on the web, so it might be significant if I say it failed to thrill me. Who knows, though? I am getting more and more serious about my threat to visit Mike and Paul over the summer, shanghai a drummer, drag them into a studio and knock out a quick 22-TET album. If that fails to get some compelling 22-tone music into the world, I'm out of ideas.

-Igs

On Fri, Jan 20, 2012 at 6:35 PM, cityoftheasleep
<igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:
> > I was just making an observation. I am curious as to why we don't have a huge body of 22 > works coming from this list and related community, considering the fact that by the
> > standards elaborated, 22 is undeniably the bee's knees.
>
> It does make you wonder, doesn't it? Too bad Carl's not here to stick up for the 22-tone corpus. I've recorded more songs in 22-TET than anybody else whose music is available on the web, so it might be significant if I say it failed to thrill me. Who knows, though? I am getting more and more serious about my threat to visit Mike and Paul over the summer, shanghai a drummer, drag them into a studio and knock out a quick 22-TET album. If that fails to get some compelling 22-tone music into the world, I'm out of ideas.

Hell yeah dude! Paul's headed down to NYC sometime soon, or else I'm
headed up there. Got me an axis and an acoustic 22-tone to contend
with, for what it's worth. But even if three people who have never
played before can't spit out a top 40 album in a microtonal tuning,
I'm still pretty convinced 22 is awesome.

-Mike

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, "lobawad" <lobawad@> wrote:
> > 12-tone "atonal" music played by instruments of flexible pitch can sound lovely, when it > is not played to strict 12-tET. I'd be tickled pink to find 24 worth a darn, and I
> > periodically check it to see if my perception has changed enough to dig it.
>
> It's hard to like 24 unless you can allow yourself to like 12, also. I still struggle with this.

"Allow"? That's like when someone tells me I don't like watching sports because I'm "trying to be different". Sorry I have no interest in being "different" for the sake of being different, I even try to like sports, but in the end I'd simply be lying to myself if I became a sports fan.

>
> > In the history of world music, it is undeniably a blip. It enjoyed a few centuries of
> > non-exclusive use in select European countries.
> >
> > So you also do not think of 12-tET as a meantone?
>
> Quarter-comma meantone was what we were specifically talking about. 12-TET is a lot of things, including a meantone.

Surely what is "meantone" in 12-tET is inherited from the actual meantone era.

> > I meant actually hard and heavy, not heavy metal.
>
> As in...?

You'd have to invent it. It would be really cool to hear something intrinsically "dark" rather than campfire music through noisy effects.

>
> > You're missing the point that the most accurate approximation to 4:5:6 offered in the
> > tuning is simply not a major triad.
>
> What, 0-360-720? That's not the most accurate one. 0-420-720 has lower average dyadic error (of 5/4, 6/5, and 3/2), whether weighted or unweighted, than either of the other two triads:
>
> Triad: Unwtd: Wtd:
> 0 360 720 29.78 7.41
> 0 420 720 22.25 5.95
> 0 360 660 27.75 8.46
>
> So...you were saying?

So, you think 0-420-720 sounds more smooth and stable than 0-360-720?

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, "lobawad" <lobawad@> wrote:
> > I was just making an observation. I am curious as to why we don't have a huge body of 22 > works coming from this list and related community, considering the fact that by the
> > standards elaborated, 22 is undeniably the bee's knees.
>
> It does make you wonder, doesn't it? Too bad Carl's not here to stick up for the 22-tone corpus. I've recorded more songs in 22-TET than anybody else whose music is available on the web, so it might be significant if I say it failed to thrill me. Who knows, though? I am getting more and more serious about my threat to visit Mike and Paul over the summer, shanghai a drummer, drag them into a studio and knock out a quick 22-TET album. If that fails to get some compelling 22-tone music into the world, I'm out of ideas.
>
> -Igs
>

That's a great idea!

Of course we don't know what people are doing out in real life. I don't put up my (real life) stuff, there may be all kinds of people out there doing 22-equal, for all we know.

--- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:
> "Allow"? That's like when someone tells me I don't like watching sports because I'm "trying to be different". Sorry I have no interest in being "different" for the sake of being different, I even try to like sports, but in the end I'd simply be lying to myself if I became a sports fan.
>

I dunno, man...YMMV, but for me it's become next-to-impossible to tell what I really don't like, and what I've trained myself to avoid. For instance, I love tons of 12-TET music, and don't think it would sound better in a different tuning, but every time I pick up a 12-TET guitar, I feel like my subconscious is tasering me any time I start to think it sounds neat or cool. *zzzap* "No you don't! It's 12-TET and it's boring and stupid and trite!" *zzzap*

> Surely what is "meantone" in 12-tET is inherited from the actual meantone era.

It's impossible to prove or disprove that claim. Would we have had triadic harmony if we went straight from pythagorean to 12-TET? No one will ever be able to say.

> > > I meant actually hard and heavy, not heavy metal.
> >
> > As in...?
>
> You'd have to invent it. It would be really cool to hear something intrinsically "dark"
> rather than campfire music through noisy effects.

"Intrinsically dark", eh? 17-TET seems great for that. 16-TET, too, for that matter.

> So, you think 0-420-720 sounds more smooth and stable than 0-360-720?

Absolutely. It fits my categorical perception best, and also happens to be the closest to 4:5:6, and also happens to be the variant I find most pleasant.

-Igs

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, "lobawad" <lobawad@> wrote:
> > "Allow"? That's like when someone tells me I don't like watching sports because I'm "trying to be different". Sorry I have no interest in being "different" for the sake of being different, I even try to like sports, but in the end I'd simply be lying to myself if I became a sports fan.
> >
>
> I dunno, man...YMMV, but for me it's become next-to-impossible to >tell what I really don't like, and what I've trained myself to >avoid. For instance, I love tons of 12-TET music, and don't think >it would sound better in a different tuning, but every time I pick >up a 12-TET guitar, I feel like my subconscious is tasering me any >time I start to think it sounds neat or cool. *zzzap* "No you >don't! It's 12-TET and it's boring and stupid and trite!" *zzzap*

Yeah, I can imagine that. I was worried that I was getting a syndrome similar to that about 4/4, so I made a piece mostly in 4/4 and realized no, it really is just the relentless sameness on the radio in every pub in town that bugs me, I'm totally cool with 4/4 itself.

At the moment I can't think of any strictly 12-tET music that I could honestly say I've ever "loved". Old orchestral recordings are not 12-tET, live orchestras are not 12-tET, and every rock thing I like draws criticisms of being "out of tune". Oh- I've always loved electronic "atonal" serial music. Yeah, I'm cool with 12-tET, it's just not well suited for making emotional connection with me. It's definitely nothing about "consonance". 17 isn't any more or less consonant than 12-tET.

>
> > Surely what is "meantone" in 12-tET is inherited from the actual meantone era.
>
> It's impossible to prove or disprove that claim. Would we have had triadic harmony if we went straight from pythagorean to 12-TET? No one will ever be able to say.

I think we would have had triadic harmony without meantone- I think we already did, and meantone evolved as a smoother flavor. Western notation is developed with meantone, though, I am quite sure.

>
> > > > I meant actually hard and heavy, not heavy metal.
> > >
> > > As in...?
> >
> > You'd have to invent it. It would be really cool to hear something intrinsically "dark"
> > rather than campfire music through noisy effects.
>
> "Intrinsically dark", eh? 17-TET seems great for that. 16-TET, >too, for that matter.

It would be so nice to hear something of enduring heaviness- the stuff that seemed heavy to me when I was a teenager sounds so trite and gimmicky. Actually I realized this more than years ago, when I met a kid who knew every Bauhaus song on record and played them on acoustic guitar. Without being loud and distorted with an "out of tune" singer, the complete lack of any inherent darkness and heaviness was very apparent. 12-tET is simply not suited to evil.

>
> > So, you think 0-420-720 sounds more smooth and stable than 0-360-720?
>
> Absolutely. It fits my categorical perception best, and also >happens to be the closest to 4:5:6, and also happens to be the >variant I find most pleasant.

I guess you're cool with my judging "accuracy" by ear rather than number, even if you don't agree with my judgement. "Accurate" to me means "sounds like". I hear no 4:5:6 "Justness", smoothness, stability, etc., in 0-420-720, and but 0-360-720 does have some of
those qualities. A surprising amount, actually.

On Sat, Jan 21, 2012 at 1:32 AM, lobawad <lobawad@...> wrote:
>
> Yeah, I can imagine that. I was worried that I was getting a syndrome similar to that about 4/4, so I made a piece mostly in 4/4 and realized no, it really is just the relentless sameness on the radio in every pub in town that bugs me, I'm totally cool with 4/4 itself.
>
> At the moment I can't think of any strictly 12-tET music that I could honestly say I've ever "loved". Old orchestral recordings are not 12-tET, live orchestras are not 12-tET, and every rock thing I like draws criticisms of being "out of tune". Oh- I've always loved electronic "atonal" serial music. Yeah, I'm cool with 12-tET, it's just not well suited for making emotional connection with me. It's definitely nothing about "consonance". 17 isn't any more or less consonant than 12-tET.

Piano music? http://www.youtube.com/watch?v=unbYI5z4zFU

> > It's impossible to prove or disprove that claim. Would we have had triadic harmony if we went straight from pythagorean to 12-TET? No one will ever be able to say.
>
> I think we would have had triadic harmony without meantone- I think we already did, and meantone evolved as a smoother flavor. Western notation is developed with meantone, though, I am quite sure.

Yeah, we did have triadic harmony before we had meantone. It's just
that thirds "were dissonant," which as far as I can tell means that
they had no idea how to make them sound pleasant. I posted this a week
or two ago

http://www.youtube.com/watch?v=LhC0dWcOA3M

This is apparently a rather historically accurate performance of the
Nicene Creed set to music - the thirds are often rather flat (I guess
these are Margo's "Zalzalian" thirds?), and sung in such a low
register that the whole thing sounds muddy. And then it all clears and
they sometimes sing perfect fifths.

> > "Intrinsically dark", eh? 17-TET seems great for that. 16-TET, >too, for that matter.
>
> It would be so nice to hear something of enduring heaviness- the stuff that seemed heavy to me when I was a teenager sounds so trite and gimmicky. Actually I realized this more than years ago, when I met a kid who knew every Bauhaus song on record and played them on acoustic guitar. Without being loud and distorted with an "out of tune" singer, the complete lack of any inherent darkness and heaviness was very apparent. 12-tET is simply not suited to evil.

The Rite of Spring?

> > Absolutely. It fits my categorical perception best, and also >happens to be the closest to 4:5:6, and also happens to be the >variant I find most pleasant.
>
> I guess you're cool with my judging "accuracy" by ear rather than number, even if you don't agree with my judgement. "Accurate" to me means "sounds like". I hear no 4:5:6 "Justness", smoothness, stability, etc., in 0-420-720, and but 0-360-720 does have some of
> those qualities. A surprising amount, actually.

Neither of them really sound like 4:5:6, if you want to ask me. The
one with the 420 cent third sounds more like a "major chord" though.

-Mike

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, "lobawad" <lobawad@> wrote:
> > I was just making an observation. I am curious as to why we don't have a huge body of 22 > works coming from this list and related community, considering the fact that by the
> > standards elaborated, 22 is undeniably the bee's knees.
>
> It does make you wonder, doesn't it? Too bad Carl's not here to stick up for the 22-tone corpus. I've recorded more songs in 22-TET than anybody else whose music is available on the web, so it might be significant if I say it failed to thrill me. Who knows, though? I am getting more and more serious about my threat to visit Mike and Paul over the summer, shanghai a drummer, drag them into a studio and knock out a quick 22-TET album. If that fails to get some compelling 22-tone music into the world, I'm out of ideas.
>
> -Igs
>

Hey- your "dragged by a storm" is a piece in 22 that sounds really good to me, nice job! The Erlich pieces on the xenwiki are dreadful, like a square making deliberate fun of alternative tunings (like Blackwell's tripe).

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Sat, Jan 21, 2012 at 1:32 AM, lobawad <lobawad@...> wrote:
> >
> > Yeah, I can imagine that. I was worried that I was getting a syndrome similar to that about 4/4, so I made a piece mostly in 4/4 and realized no, it really is just the relentless sameness on the radio in every pub in town that bugs me, I'm totally cool with 4/4 itself.
> >
> > At the moment I can't think of any strictly 12-tET music that I could honestly say I've ever "loved". Old orchestral recordings are not 12-tET, live orchestras are not 12-tET, and every rock thing I like draws criticisms of being "out of tune". Oh- I've always loved electronic "atonal" serial music. Yeah, I'm cool with 12-tET, it's just not well suited for making emotional connection with me. It's definitely nothing about "consonance". 17 isn't any more or less consonant than 12-tET.
>
> Piano music? http://www.youtube.com/watch?v=unbYI5z4zFU

I've never really liked piano music- even as a child it always sounded "snapped to a grid" to me, mechanical. I seriously love demented old uprights, though.

>
> > > It's impossible to prove or disprove that claim. Would we have had triadic harmony if we went straight from pythagorean to 12-TET? No one will ever be able to say.
> >
> > I think we would have had triadic harmony without meantone- I think we already did, and meantone evolved as a smoother flavor. Western notation is developed with meantone, though, I am quite sure.
>
> Yeah, we did have triadic harmony before we had meantone. It's just
> that thirds "were dissonant," which as far as I can tell means that
> they had no idea how to make them sound pleasant. I posted this a week
> or two ago

The thirds were not exactly consonances, but imperfect consonances in the meantone era (as well as now).
>
> http://www.youtube.com/watch?v=LhC0dWcOA3M
>
> This is apparently a rather historically accurate performance of the
> Nicene Creed set to music - the thirds are often rather flat (I guess
> these are Margo's "Zalzalian" thirds?), and sung in such a low
> register that the whole thing sounds muddy. And then it all clears and
> they sometimes sing perfect fifths.

Muddy? I think this sounds fantastic, wow. Thanks for the link.

>
> > > "Intrinsically dark", eh? 17-TET seems great for that. 16-TET, >too, for that matter.
> >
> > It would be so nice to hear something of enduring heaviness- the stuff that seemed heavy to me when I was a teenager sounds so trite and gimmicky. Actually I realized this more than years ago, when I met a kid who knew every Bauhaus song on record and played them on acoustic guitar. Without being loud and distorted with an "out of tune" singer, the complete lack of any inherent darkness and heaviness was very apparent. 12-tET is simply not suited to evil.
>
> The Rite of Spring?

I've never heard the Rite of Spring in 12-tET, though I imagine there are newer recordings which are close enough to qualify. You think the RoS is "dark"? I've always found it quite spritely and fun.

>
> > > Absolutely. It fits my categorical perception best, and also >happens to be the closest to 4:5:6, and also happens to be the >variant I find most pleasant.
> >
> > I guess you're cool with my judging "accuracy" by ear rather than number, even if you don't agree with my judgement. "Accurate" to me means "sounds like". I hear no 4:5:6 "Justness", smoothness, stability, etc., in 0-420-720, and but 0-360-720 does have some of
> > those qualities. A surprising amount, actually.
>
> Neither of them really sound like 4:5:6, if you want to ask me. The
> one with the 420 cent third sounds more like a "major chord" though.
>
> -Mike
>

I don't think any of the possible major triads in 20-edo sound like 4:5:6, either, just that 0-360-720 has some vague Just-like qualities and the other options do not at all, i.e., it's the best approximation by actual sound. 0-420-720 sounds the most like a major chord to me, too.

On Sat, Jan 21, 2012 at 1:53 AM, lobawad <lobawad@...> wrote:
>
> Hey- your "dragged by a storm" is a piece in 22 that sounds really good to me, nice job! The Erlich pieces on the xenwiki are dreadful, like a square making deliberate fun of alternative tunings (like Blackwell's tripe).

That stuff was written I believe in 1999 or so. You have to make a
religious pilgrimage to his house in Boston to hear him play his best
stuff. I do have a recording of him doing some drone stuff in
porcupine posted up

http://www.youtube.com/watch?v=lO5xSjIHyMg

He has some other stuff he played for me IRL too; this was more spontaneous.

There's also this piece by Sevish in 22-EDO which is awesome

http://www.youtube.com/watch?v=XX1ILd9D1aw&feature=related

-Mike

--- In tuning@yahoogroups.com, "Kalle Aho" <kalleaho@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "lobawad" <lobawad@> wrote:
>
> > It is an anachronism to think of quarter-comma meantone as a "regular
> temperament" when "regular temperament" is meant as used on these
> lists. Quarter-comma meantone is Just in the same way Pythagorean
> tuning is Just: the intervals considered most vital are tuned Just.
> Neither tuning is based on approximation of Just intervals.
>
> I object to the claim that quarter-comma meantone is not based on
> approximation of just intervals. Theorists like Zarlino and Aaron
> recognized 3:2 and 6:5 as the ideal intonations for the fifth and the
> minor third. There is no evidence that flexible pitch instrumentalists
> or vocalists targeted meantone tempered intervals in harmonies.
>
> Kalle
>

Okay. The way I see it is that you don't recognize the signifigance of the fact that 5:4 is not tempered at all.

--- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:
> Yeah, I can imagine that. I was worried that I was getting a syndrome similar to that
> about 4/4, so I made a piece mostly in 4/4 and realized no, it really is just the relentless > sameness on the radio in every pub in town that bugs me, I'm totally cool with 4/4 itself.

LOL, I have that same problem, which is why I wrote my last two albums with a lot of 4/4. Just to remind myself that it's fine, I can be just as quirky in common time as in odd time.

> I think we would have had triadic harmony without meantone- I think we already did,
> and meantone evolved as a smoother flavor. Western notation is developed with
> meantone, though, I am quite sure.

Well, you sure can't get 5-limit harmony out of Western notation without meantone, that's for sure.

> It would be so nice to hear something of enduring heaviness- the stuff that seemed
> heavy to me when I was a teenager sounds so trite and gimmicky. Actually I realized this > more than years ago, when I met a kid who knew every Bauhaus song on record and
> played them on acoustic guitar. Without being loud and distorted with an "out of tune"
> singer, the complete lack of any inherent darkness and heaviness was very apparent. 12-> tET is simply not suited to evil.

I concur whole-heartedly. 16-TET, though, on an acoustic guitar, sounds evil as all get-out to me. No production required.

> I guess you're cool with my judging "accuracy" by ear rather than number, even if you
> don't agree with my judgement. "Accurate" to me means "sounds like". I hear no 4:5:6
> "Justness", smoothness, stability, etc., in 0-420-720, and but 0-360-720 does have
> some of those qualities. A surprising amount, actually.

Well, different strokes, as they say. I don't think either sounds like 4:5:6, but if I were to adaptively tune those chords to JI, 0-420-720 would be less of a stretch. 0-360-720 can sort of pass for 10:12:15 if you kind of squint at it, I think it's more like it's own thing. Maybe 18:22:27 or something.

-Igs

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Sat, Jan 21, 2012 at 1:53 AM, lobawad <lobawad@...> wrote:
> >
> > Hey- your "dragged by a storm" is a piece in 22 that sounds really good to me, nice job! The Erlich pieces on the xenwiki are dreadful, like a square making deliberate fun of alternative tunings (like Blackwell's tripe).
>
> That stuff was written I believe in 1999 or so. You have to make a
> religious pilgrimage to his house in Boston to hear him play his best
> stuff. I do have a recording of him doing some drone stuff in
> porcupine posted up
>
> http://www.youtube.com/watch?v=lO5xSjIHyMg

I'm totally cool with little or no "real life" stuff being up on the internet. I've posted plenty of certain-features-of-tunings stuff that I wouldn't even consider music, much less good music. I really like the 22-tone guitar jamming of his on YouTube.

>
> He has some other stuff he played for me IRL too; this was more spontaneous.
>
> There's also this piece by Sevish in 22-EDO which is awesome
>
> http://www.youtube.com/watch?v=XX1ILd9D1aw&feature=related

Yes Sevish has lots of nice stuff. It has that same avoiding-the-tuning quality of 12-tET electronica that I like, though.

On Sat, Jan 21, 2012 at 2:11 AM, lobawad <lobawad@...> wrote:
>
> I've never really liked piano music- even as a child it always sounded "snapped to a grid" to me, mechanical. I seriously love demented old uprights, though.

Say it ain't so.

> > Yeah, we did have triadic harmony before we had meantone. It's just
> > that thirds "were dissonant," which as far as I can tell means that
> > they had no idea how to make them sound pleasant. I posted this a week
> > or two ago
>
> The thirds were not exactly consonances, but imperfect consonances in the meantone era (as well as now).

That's true, that's a better way of putting it. I don't think I'd say
that they're imperfect consonances now. What does imperfect consonance
mean? it seems like you're trying to condition me into being afraid of
thirds or something.

> > http://www.youtube.com/watch?v=LhC0dWcOA3M
> >
> > This is apparently a rather historically accurate performance of the
> > Nicene Creed set to music - the thirds are often rather flat (I guess
> > these are Margo's "Zalzalian" thirds?), and sung in such a low
> > register that the whole thing sounds muddy. And then it all clears and
> > they sometimes sing perfect fifths.
>
> Muddy? I think this sounds fantastic, wow. Thanks for the link.

It does sound fantastic, but I'm noting they're singing thirds in a
really low register, lower than we'd do today. I think it's because
these days, thirds are supposed to be "consonant," so we're trying to
minimizes uses for those intervals that would be "discordant." Back
then, thirds were "dissonant," or "imperfectly consonant," or
whatever, so they didn't mind making them muddier because the whole
point was that they weren't supposed to be really nice and pure and
consonant. Another way to put this is, once they figured out that
major chords sounded good, they also realized they needed to not sing
them in a low, muddy register for that to happen, and now we don't do
stuff like that anymore.That's my half-assed analysis, anyway.

> > The Rite of Spring?
>
> I've never heard the Rite of Spring in 12-tET, though I imagine there are newer recordings which are close enough to qualify. You think the RoS is "dark"? I've always found it quite spritely and fun.

RoS is frickin terrifying. And yet I love it so...

-Mike

"Zalzalian" refers to "neutral" thirds, by the way. IMO the Occam's razor geneology of the middle third (Zalzal gets the credit for it, we have no idea if he really "invented" it) is tying a fret right smack in the (physical) middle pythagorean "m3" and ditone.

As far as Ars Nova tuning, personally I'd tune a piece in C Pythagorean- starting a chain of pure fifths from A, hehe. I don't doubt that some of the time did stuff like that, and other theorists seem to agree (you get "syntonic temperament" on the root). It pays to keep in mind that returning to the tonic as rule is a drab later invention. Ars Nova like plainchant can end up elsewhere, on Re for example.

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Sat, Jan 21, 2012 at 2:11 AM, lobawad <lobawad@...> wrote:
> >
> > I've never really liked piano music- even as a child it always sounded "snapped to a grid" to me, mechanical. I seriously love demented old uprights, though.
>
> Say it ain't so.

Sadly 'tis so.

>
> > > Yeah, we did have triadic harmony before we had meantone. It's just
> > > that thirds "were dissonant," which as far as I can tell means that
> > > they had no idea how to make them sound pleasant. I posted this a week
> > > or two ago
> >
> > The thirds were not exactly consonances, but imperfect consonances in the meantone era (as well as now).
>
> That's true, that's a better way of putting it. I don't think I'd say
> that they're imperfect consonances now. What does imperfect consonance
> mean? it seems like you're trying to condition me into being afraid of
> thirds or something.

Oh no, love your thirds man, love them up.

>
> > > http://www.youtube.com/watch?v=LhC0dWcOA3M
> > >
> > > This is apparently a rather historically accurate performance of the
> > > Nicene Creed set to music - the thirds are often rather flat (I guess
> > > these are Margo's "Zalzalian" thirds?), and sung in such a low
> > > register that the whole thing sounds muddy. And then it all clears and
> > > they sometimes sing perfect fifths.
> >
> > Muddy? I think this sounds fantastic, wow. Thanks for the link.
>
> It does sound fantastic, but I'm noting they're singing thirds in a
> really low register, lower than we'd do today. I think it's because
> these days, thirds are supposed to be "consonant," so we're trying to
> minimizes uses for those intervals that would be "discordant." Back
> then, thirds were "dissonant," or "imperfectly consonant," or
> whatever, so they didn't mind making them muddier because the whole
> point was that they weren't supposed to be really nice and pure and
> consonant. Another way to put this is, once they figured out that
> major chords sounded good, they also realized they needed to not sing
> them in a low, muddy register for that to happen, and now we don't do
> stuff like that anymore.That's my half-assed analysis, anyway.

Half-assed or not, and accurate or not, it's still better musicology than a lot I've read, and I've read a lot. There's a good little book about historical music being invented today, i.e., musicology being loaded with our projections, and I'm with Boulez on not being bothered by that. Kipnis makes modern harpsichordists puke, but hey, he strongly helped the thing become popular, and he's valuable as a sign of HIS times.

As far as RoS, see if you can dig up an ethnomusicological recording of traditional Russian wedding songs, the kind that consist of the grandmothers wailing in sadness. I have misplaced my CD of this. After listening to this, listen to RoS and see if it hasn't gotten a bit more spritely and lite, LOL.

> As far as RoS, see if you can dig up an ethnomusicological recording of traditional Russian wedding songs, the kind that consist of the grandmothers wailing in sadness. I have misplaced my CD of this. After listening to this, listen to RoS and see if it hasn't gotten a bit more spritely and lite, LOL.
>

http://www.youtube.com/watch?v=VHsJqmNEk3s

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

>
> I concur whole-heartedly. 16-TET, though, on an acoustic guitar, sounds evil as all get-out to me. No production required.

Unlike the major triad of 20-edo, in the case of 16 equal divisions of the octave I think that the tetrad 0-5-11-13 really does emphasize or refer to a rational structure: 5:4, 25:16, 7:4. (Justly intoned augmented triad with minor 7th). The major and minor triads are distinctly and strongly major and minor without regard to 3:2, which I think is very cool.

--- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:
> Unlike the major triad of 20-edo, in the case of 16 equal divisions of the octave I think that > the tetrad 0-5-11-13 really does emphasize or refer to a rational structure: 5:4, 25:16, 7:4. > (Justly intoned augmented triad with minor 7th).

Did you mean 0-5-10-13? I think that version sounds more Just...that 7/4 on top really makes the augmented triad sing! What a neat chord. 0-5-11-13 would be more 5/4, 8/5, 7/4, or maybe more 5/4, 13/8, 7/4 (I think that's closer to how I hear it...if I bend the 11 sharp, it sounds more in-tune). That's a nice one, too!

-Igs

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, "lobawad" <lobawad@> wrote:
> > Unlike the major triad of 20-edo, in the case of 16 equal divisions of the octave I think that > the tetrad 0-5-11-13 really does emphasize or refer to a rational structure: 5:4, 25:16, 7:4. > (Justly intoned augmented triad with minor 7th).
>
> Did you mean 0-5-10-13? I think that version sounds more Just...that 7/4 on top really makes the augmented triad sing! What a neat chord. 0-5-11-13 would be more 5/4, 8/5, 7/4, or maybe more 5/4, 13/8, 7/4 (I think that's closer to how I hear it...if I bend the 11 sharp, it sounds more in-tune). That's a nice one, too!
>
> -Igs
>

Yes, 0-5-10-13. 0-5-11-13 is even nicer in different "inversions" (I put that in quotes because the concept of inversions creating the "same" chord is bogus).

--- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "Kalle Aho" <kalleaho@> wrote:
> >
> >
> >
> > --- In tuning@yahoogroups.com, "lobawad" <lobawad@> wrote:
> >
> > > It is an anachronism to think of quarter-comma meantone as a "regular
> > temperament" when "regular temperament" is meant as used on these
> > lists. Quarter-comma meantone is Just in the same way Pythagorean
> > tuning is Just: the intervals considered most vital are tuned Just.
> > Neither tuning is based on approximation of Just intervals.
> >
> > I object to the claim that quarter-comma meantone is not based on
> > approximation of just intervals. Theorists like Zarlino and Aaron
> > recognized 3:2 and 6:5 as the ideal intonations for the fifth and the
> > minor third. There is no evidence that flexible pitch instrumentalists
> > or vocalists targeted meantone tempered intervals in harmonies.
> >
> > Kalle
> >
>
> Okay. The way I see it is that you don't recognize the signifigance
of the fact that 5:4 is not tempered at all.

Yes, I don't. How is 5:4 more important than 6:5, 5:3, 3:2 or 4:3?
Zarlino also described 2/7- and 1/3-comma meantones. All of them were
considered fine when listened to purely empirically. AFAIK, it was
only later understood that 1/4-comma is the minimax tuning for
meantone.

Kalle

--- In tuning@yahoogroups.com, "Kalle Aho" <kalleaho@...> wrote:
> AFAIK, it was
> only later understood that 1/4-comma is the minimax tuning for
> meantone.

I believe the first person to apply a mathematical optimization method to the question of tuning meantone was Wesley Woolhouse, who derived 7/26-comma meantone from 5-limit unweighted least squares.

--- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:
> Yes, 0-5-10-13. 0-5-11-13 is even nicer in different "inversions" (I put that in quotes
> because the concept of inversions creating the "same" chord is bogus).

I couldn't agree more. Inversional equivalence only works with 5-limit harmony, because all inversions are still plenty concordant. But that 0-5-11-13 sounds waaaay cleaner as 0-5-13-27, because there's a huge difference in concordance between 8:10:13:14 and 4:5:7:13.

-Igs

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, "lobawad" <lobawad@> wrote:
> > Yes, 0-5-10-13. 0-5-11-13 is even nicer in different "inversions" (I put that in quotes
> > because the concept of inversions creating the "same" chord is bogus).
>
> I couldn't agree more. Inversional equivalence only works with 5-limit harmony, because all inversions are still plenty concordant. But that 0-5-11-13 sounds waaaay cleaner as 0-5-13-27, because there's a huge difference in concordance between 8:10:13:14 and 4:5:7:13.
>
> -Igs
>

Even in "5-limit" harmony, not all inversions work, as far as retaining perceived root, cf. traditional restrictions on 6-4 voicing.
I have found that in the case of complex harmonies with ambiguous roots, context (of course) suggests roots, as well as the very simple phenomenon of a lowest and emphasized pitch seeming like the root of an ambiguous sonority above.

On Mon, Jan 23, 2012 at 5:47 PM, lobawad <lobawad@...> wrote:
>
> Even in "5-limit" harmony, not all inversions work, as far as retaining perceived root, cf. traditional restrictions on 6-4 voicing.
> I have found that in the case of complex harmonies with ambiguous roots, context (of course) suggests roots, as well as the very simple phenomenon of a lowest and emphasized pitch seeming like the root of an ambiguous sonority above.

You don't hear a root of C for something like G-G'-C'-E'?

-Mike

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
> I believe the first person to apply a mathematical optimization
> method to the question of tuning meantone was Wesley Woolhouse,
> who derived 7/26-comma meantone from 5-limit unweighted least
> squares.

I believe you're right. -C.

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Mon, Jan 23, 2012 at 5:47 PM, lobawad <lobawad@...> wrote:
> >
> > Even in "5-limit" harmony, not all inversions work, as far as retaining perceived root, cf. traditional restrictions on 6-4 voicing.
> > I have found that in the case of complex harmonies with ambiguous roots, context (of course) suggests roots, as well as the very simple phenomenon of a lowest and emphasized pitch seeming like the root of an ambiguous sonority above.
>
> You don't hear a root of C for something like G-G'-C'-E'?
>
> -Mike
>

Over the years I've noticed that it seems to be only those who have been trained to hear strictly in terms of what "should be" rather than what "is" find the root of 6-4 voicings always unambiguous.

As far as I've seen, "everyone else" hears just as "common practice" has insisted for centuries, that the root becomes ambiguous in this inversion, especially with lower-pitched voicings (specifically, sounding like it is suppossed to be a 4-3 sus).

I can- or could- hear it both ways, (clearly rooted or not) but if you actually listen to the thing on a physical level, you'll hear that the root is only definite in triadic theory.

--- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:
> Over the years I've noticed that it seems to be only those who have been trained to hear strictly in terms of what "should be" rather than what "is" find the root of 6-4 voicings always unambiguous.
>
> As far as I've seen, "everyone else" hears just as "common practice" has insisted for centuries, that the root becomes ambiguous in this inversion, especially with lower-pitched voicings (specifically, sounding like it is suppossed to be a 4-3 sus).
>
> I can- or could- hear it both ways, (clearly rooted or not) but if you actually listen to the thing on a physical level, you'll hear that the root is only definite in triadic theory.

"On a physical level", what does "root" mean? This is a serious question.

Keenan

--- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@...> wrote:
>
> --- In tuning@yahoogroups.com, "lobawad" <lobawad@> wrote:
> > Over the years I've noticed that it seems to be only those who have been trained to hear strictly in terms of what "should be" rather than what "is" find the root of 6-4 voicings always unambiguous.
> >
> > As far as I've seen, "everyone else" hears just as "common practice" has insisted for centuries, that the root becomes ambiguous in this inversion, especially with lower-pitched voicings (specifically, sounding like it is suppossed to be a 4-3 sus).
> >
> > I can- or could- hear it both ways, (clearly rooted or not) but if you actually listen to the thing on a physical level, you'll hear that the root is only definite in triadic theory.
>
> "On a physical level", what does "root" mean? This is a serious question.
>
> Keenan
>

Why would you not ask a serious question?

Root, on a physical level, corresponds to a virtual fundamental we could reasonably call more or less objective.

This means it is quite limited phenomena. Given 200, 300, 400, 500...Hz, we'll fill in a virtual fundamental at 100 Hz. Bass maximizer effects rely on this phenomenon. Out in real life, "virtual fundamental" refers almost exclusively to this. It is completely reasonable to extend a bit the range of a "physical root" beyond this most obvious case: an octave dyad, a first position 5-limit triad, have roots which correspond to simple harmonic series.

Beyond this percieved roots become subjective, and rapidly highly subjective.

The second inversion of a major triad does not clearly spell out a single possible harmonic series, its root is too subjective, so to speak, and therefore its use is highly governed in common practice music.

On Fri, Jan 27, 2012 at 5:24 AM, lobawad <lobawad@...> wrote:
>
> Why would you not ask a serious question?
>
> Root, on a physical level, corresponds to a virtual fundamental we could reasonably call more or less objective.

I don't know if I agree with this. For example, I can perceive a
"root" for an arpeggiated chord in which none of the notes are ever
played in simultaneity and hence never produce a virtual fundamental.
If this weren't the case, something like a 2 part invention in minor
would be rather baffling, as the root would be changing and bouncing
all over the place. This means to me that a root is something I
imagine, and not something as simple as a VF that pops out.

You might say "OK, Mike, thanks for nitpicking. But, obviously you've
heard 4:5:6 played in unison before, so you can just re-imagine that
VF when someone arpeggiates it, and that's the root." But, I still
think it's a bit more subtle than that, and that it's possible to
imagine a "root" for a chord which is incongruent with the VF
produced. For example, it's easy for me to imagine the root of a 4:5:6
as being a note that's 6/5 below the 4, so that it just becomes an
upper structure triad for a minor 7 chord.

It might have to do with VFs on some level. It might also have to do
with imagining what note is played habitually in the bass, and it
could just be that we're more likely to play bass notes that reinforce
VFs because it gives the whole sound a really nice thick effect. On
the other hand, sometimes you can hear a note in the bass that you
don't perceive as the root, because you sort of view the bass note as
noise and imagine the real note is right around the corner. Maybe VFs
are still involved to some extend. But, at the very least it suggests
to me that "root" is a much more beautiful and complex phenomenon than
anything psychoacoustic.

> Beyond this percieved roots become subjective, and rapidly highly subjective.

I agree with this only if you're not saying that VFs become
subjective. Well, they do, but I don't think "root" must correlate
with VF.

> The second inversion of a major triad does not clearly spell out a single possible harmonic series, its root is too subjective, so to speak, and therefore its use is highly governed in common practice music.

I somewhat agree, and think of it like this; by itself, 3:4:5
generates a VF that I can hear, more so if it's 3:4:5:7:etc. But, when
you double the lowest note in the bass, what you really get is
3:6:8:10. Or 3:12:16:20. And that's a bit too complex to be heard as a
single, "fused" sonority.

I sort of ran into the same thing when I wrote this throwaway tune to
explore 7:9:11 in 11-EDO here:

http://soundcloud.com/mikebattagliamusic/sets/tonal-study-in-orgone-temperament/

The base sonority, at least in 11-EDO, is 7:9:11. So the net effect to
me is that it's "always in inversion."

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Fri, Jan 27, 2012 at 5:24 AM, lobawad <lobawad@...> wrote:
> >
> > Why would you not ask a serious question?
> >
> > Root, on a physical level, corresponds to a virtual fundamental we could reasonably call more or less objective.
>
> I don't know if I agree with this.

But the rest of your post agrees completely with this. You differentiate between "root", a complex, subtle perception, and the limited cases where "root" and "virtual fundamental" are clearly the same, don't you?

I never said that the root wasn't something that we imagine. It is almost always imagined. There are few cases where we can reasonably say that it's right there, "physically".

>For example, I can perceive a
> "root" for an arpeggiated chord in which none of the notes are ever
> played in simultaneity and hence never produce a virtual fundamental.
> If this weren't the case, something like a 2 part invention in minor
> would be rather baffling, as the root would be changing and bouncing
> all over the place. This means to me that a root is something I
> imagine, and not something as simple as a VF that pops out.
>
> You might say "OK, Mike, thanks for nitpicking. But, obviously you've
> heard 4:5:6 played in unison before, so you can just re-imagine that
> VF when someone arpeggiates it, and that's the root." But, I still
> think it's a bit more subtle than that, and that it's possible to
> imagine a "root" for a chord which is incongruent with the VF
> produced. For example, it's easy for me to imagine the root of a 4:5:6
> as being a note that's 6/5 below the 4, so that it just becomes an
> upper structure triad for a minor 7 chord.
>
> It might have to do with VFs on some level. It might also have to do
> with imagining what note is played habitually in the bass, and it
> could just be that we're more likely to play bass notes that reinforce
> VFs because it gives the whole sound a really nice thick effect. On
> the other hand, sometimes you can hear a note in the bass that you
> don't perceive as the root, because you sort of view the bass note as
> noise and imagine the real note is right around the corner. Maybe VFs
> are still involved to some extend. But, at the very least it suggests
> to me that "root" is a much more beautiful and complex phenomenon than
> anything psychoacoustic.
>
> > Beyond this percieved roots become subjective, and rapidly highly subjective.
>
> I agree with this only if you're not saying that VFs become
> subjective. Well, they do, but I don't think "root" must correlate
> with VF.
>
> > The second inversion of a major triad does not clearly spell out a single possible harmonic series, its root is too subjective, so to speak, and therefore its use is highly governed in common practice music.
>
> I somewhat agree, and think of it like this; by itself, 3:4:5
> generates a VF that I can hear, more so if it's 3:4:5:7:etc. But, when
> you double the lowest note in the bass, what you really get is
> 3:6:8:10. Or 3:12:16:20. And that's a bit too complex to be heard as a
> single, "fused" sonority.
>
> I sort of ran into the same thing when I wrote this throwaway tune to
> explore 7:9:11 in 11-EDO here:
>
> http://soundcloud.com/mikebattagliamusic/sets/tonal-study-in-orgone-temperament/
>
> The base sonority, at least in 11-EDO, is 7:9:11. So the net effect to
> me is that it's "always in inversion."
>
> -Mike
>