Yahoo Tuning Groups Ultimate Backup tuning The Elusive "Meantone Killer" (was RE: Middle Path 11-limit Temperaments)

Now, I'm not sure if any of you guys are actually trying to find "the Meantone killer" with all of these "best-of" temperament lists. I'm pretty sure most of you could give a rat's ass about a "guaranteed meantone successor". But perhaps some of you are generally concerned with this problem; if so, read on.

I think this is an important theoretical problem, perhaps the most important one faced by this community, but one that is still a long way from being properly addressed. Carl wrote:

>The regular mapping paradigm is broadly useful, but one of
>its uses is to generalize Western polyphonic music under
>the assumption that it required a specialized tuning system
>and, through cultural evolution, found one. For composers
>interested in writing polyphonic music with melody, harmony,
>motivic structure, etc. but a different tuning system, the
>theory ought to be able reduce the number of systems they
>need to try before finding one. That would be useful since
>trying novel systems is apparently hard (maybe even requiring
>generations of effort). If we can furnish a top-9 list
>guaranteed to contain at least one viable meantone successor,
>it would be a good thing. In fact we can answer the question
>"Why hasn't this been done yet?" by saying that the evolution
>of music was stuck in a local minimum and only deliberate
>theory (not a random walk) could get it out.

Meantone (and eventually, 12-TET) arose as the solution to compositional problems, after centuries of cultural "natural selection". There are many reasons to believe that it is, in fact, the "best" solution to the problems it was meant to solve. Because of this, the way we are currently applying the regular mapping paradigm to the problem of finding a "guaranteed meantone successor"--by this I mean the process of making these best-of lists for various prime limits--is, I believe, doomed to failure.

We are not going to find a temperament that is better at solving all the same problems as meantone/12-TET. This should be patently obvious by now. Think about what the problems *are* that meantone/12-TET solve: these tunings optimize the competing factors of having many intervals that sound very concordant, few intervals that sound very discordant, and few enough intervals to be comfortably played on an acoustic instrument. 12-TET (but not meantone in general) also solves the problems of being able to freely modulate to any key without a change in concordance, and also some other problems that are more instrument- or pedagogy-specific (which we don't need to worry about addressing just yet). After decades of systematic exploration via the RMP, we know now that there are more accurate temperaments, and there are simpler temperaments, but there is no temperament that is both more accurate on the 5-limit AND simpler (or even equally-accurate but simpler or equally-simple but more accurate...or even equally-accurate and equally-simple!). We also know, thanks to Keenan Pepper's exploration of the average dyadic harmonic entropy of rank-2 scales of comparable size to meantone and 12-TET, that meantone[7] is *significantly* lower in average dyadic HE than any other scale of 7 or more notes.

Therefore, any other 5-limit (or 7-limit, or 11-limit, or 13-limit) temperament is going to be in some respect inferior to meantone at solving the compositional problems that meantone solves. Can we all agree on that?

Now, I don't think this means a "meantone killer" is impossible. But to find such a temperament, we have to instead look to compositional problems that meantone *does not* excel in solving. There are a lot of these, so what we really need to find is a problem not solved by meantone that is actually musically-relevant in the modern musical climate. We have not even been making the slightest effort to examine this so far as I've seen in all my time in this community, despite the fact that the composers among us (and the preferences they have developed) could potentially give some great insights into this question.

We have instead taken pretty much all of our cues from the advocates of higher-limit JI (since one thing meantone doesn't do is give a lot of 7, 11, and 13-limit intervals), and looked for temperaments of the 7-, 11-, and 13-limit. But we've done so without taking a good, hard look at what compositional problems are solved by higher-limit JI (and temperaments thereof). Without having such an anchor in the practical, there's no reason to think that our "best-of" lists here are going to have a better-than-random chance at leading to a "guaranteed meantone successor".

So maybe now would be a good time to open up the floor to some compositional problems that could be optimally solved by something other than meantone?

🔗genewardsmith <genewardsmith@...>

🔗Mike Battaglia <battaglia01@...>

🔗Keenan Pepper <keenanpepper@...>

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@> wrote:
>
> > So maybe now would be a good time to open up the floor to some compositional problems that could be optimally solved by something other than meantone?

Here's my totally personal opinion, that I've only recently developed:

The "problem", or rather the thing missing, is 10:11:12. The thing we desire is "quartertones", where that simply means anything sufficiently far from 12edo intervals and is exemplified by the 11th harmonic. We want harmonic, tonal music where "quartertones" are an integral part of the scale. The solution is porcupine.

Here's basically how I'm going to tune my marimba:

! MEANTONE-KILLER.scl
!
15 circulating notes of porcupine (/ sort of nusecond in the far keys)
15
!
67.
161.
228.
319.
390.
477.
552.
635.
714.
793.
876.
951.
1038.
1109.
1200.

It only takes 3 extra notes per octave to get a circulating temperament that really gives 12edo a run for its money. This is an amazing revelation to me.

If somebody wants to jam with me on a 15edo guitar, that works fine because this tuning is only +/- 7 cents from 15edo (if you shift it correctly). If somebody wants to jam on a 22edo guitar, that *also* works as long as we stick to a few nearby porcupine keys.

12edo and dominant temperament are great because, as Mike B quipped, it's like a wild party where everyone's swimming in 4:5:6:7. I want to be swimming in 8:9:10:11:12, and the pool is called porcupine.

The other obvious solution to the same "problems" is mohaha (or maqamic/mohajira/migration). These scales are also great, but I personally perfer porcupine because it takes slightly fewer notes to get a good circulating temperament (15 rather than 17), and you can blow people's minds with xenharmonic comma pumps.

> Have you been asleep while I've been posting all these lists of essentially tempered chords?

Porcupine[7] is one big essentially tempered chord. The temperament is swimming in them.

Keenan

🔗Mike Battaglia <battaglia01@...>

On Mon, Jan 2, 2012 at 2:14 PM, Keenan Pepper <keenanpepper@...> wrote:
>
> --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
> The "problem", or rather the thing missing, is 10:11:12. The thing we desire is "quartertones", where that simply means anything sufficiently far from 12edo intervals and is exemplified by the 11th harmonic. We want harmonic, tonal music where "quartertones" are an integral part of the scale. The solution is

Mohajira!!!!!

> porcupine.

Yes, like I said, porcupine! However, someday you'll load up a marimba
patch and come to realize that what you really want is Mavila[9],
which solves every single problem in existence except the "make every
chord sound like a circular saw grinding through a bug zapper"
problem.

> If somebody wants to jam with me on a 15edo guitar, that works fine because this tuning is only +/- 7 cents from 15edo (if you shift it correctly). If somebody wants to jam on a 22edo guitar, that *also* works as long as we stick to a few nearby porcupine keys.

This is, in my opinion, the correct way to interpret all of the
unreleased director's cut stuff we did with categorical entropy:
quasi-equal chromatic scales that allow for greater harmonic purity
than the EDO allows for. Then we'll get to be picky about it for
another century or so until people start becoming degraded and evil
and just tune to 15-EDO and don't care anymore.

There is one thing that I want to say though. I associate habitually
played chords with categories; I can "imply" chords with melodic
phrases. And that would seem to require us to be able to distinguish
categories from one another. And I suck at that at with fragments
played at high speed with porcupine in 22-EDO.

-Mike

🔗cityoftheasleep <igliashon@...>

🔗Keenan Pepper <keenanpepper@...>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> > The "problem", or rather the thing missing, is 10:11:12. The thing we desire is "quartertones", where that simply means anything sufficiently far from 12edo intervals and is exemplified by the 11th harmonic. We want harmonic, tonal music where "quartertones" are an integral part of the scale. The solution is
>
> Mohajira!!!!!

Haha, I did mention mohajira later in my post, so give me some credit.

> > porcupine.
>
> Yes, like I said, porcupine! However, someday you'll load up a marimba
> patch and come to realize that what you really want is Mavila[9],
> which solves every single problem in existence except the "make every
> chord sound like a circular saw grinding through a bug zapper"
> problem.

I beg to differ!

> This is, in my opinion, the correct way to interpret all of the
> unreleased director's cut stuff we did with categorical entropy:
> quasi-equal chromatic scales that allow for greater harmonic purity
> than the EDO allows for. Then we'll get to be picky about it for
> another century or so until people start becoming degraded and evil
> and just tune to 15-EDO and don't care anymore.

Yeah, that's sort of how I interpret it. 12edo sounds pretty acceptable in the 5-limit, and can be made really good in some keys if you make it slightly unequal (based on meantone). 15edo sounds somewhat less acceptable (although it's not really *that* much worse objectively), and a more dramatic improvement can be made by making it unequal based on porcupine.

There's nothing wrong with thinking of intervals/chords/scales as musically equivalent even though the specific tuning you're using is an irregular temperament.

> There is one thing that I want to say though. I associate habitually
> played chords with categories; I can "imply" chords with melodic
> phrases. And that would seem to require us to be able to distinguish
> categories from one another. And I suck at that at with fragments
> played at high speed with porcupine in 22-EDO.

I think porcupine is freaking great for this. I feel like I can already tell porcupine intervals/chords/modes apart with the skill of a little kid just starting music lessons (as opposed to that of a completely tone-deaf person, which is where I was months ago). I mean, look at how the 15-tone scale is laid out:

0 Unison
1 Augmented unison
2 Minor second
3 Major second
4 Minor third (6/5)
5 Major third (5/4)
6 Minor fourth (4/3)
7 Major fourth
8 Minor fifth
9 Major fifth (3/2)
10 Minor sixth (8/5)
11 Major sixth (5/3)
12 Minor seventh
13 Major seventh
14 Diminished octave
15 Octave

I mean how much simpler can you get?!

If you think of it in this framework it becomes much easier to hear the differences and "snap it in".

In the same way that the meantone chromatic scale has 12 notes and 19 is a relatively hair-splitting "enharmonic" scale, so the porcupine chromatic scale has 15 notes and 22 is the "enharmonic". The only difference is that where as 12edo is perfectly acceptable for billions (literally billions, right?) of people using meantone, 15edo is somewhat less acceptable as a tuning. But that doesn't mean it should be neglected as a framework.

Sorry, Igs, for hijacking your thread to some extent.

Keenan

🔗Mike Battaglia <battaglia01@...>

🔗cityoftheasleep <igliashon@...>

🔗Mike Battaglia <battaglia01@...>

On Mon, Jan 2, 2012 at 3:17 PM, Keenan Pepper <keenanpepper@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> > > The "problem", or rather the thing missing, is 10:11:12. The thing we desire is "quartertones", where that simply means anything sufficiently far from 12edo intervals and is exemplified by the 11th harmonic. We want harmonic, tonal music where "quartertones" are an integral part of the scale. The solution is
> >
> > Mohajira!!!!!
>
> Haha, I did mention mohajira later in my post, so give me some credit.

OK, you get credit. I've been thinking a lot about mohajira lately:
it's awesome. It's so awesome and intuitive, in fact, that using it is
almost like a cop out. The overall sound of really complex, modal,
MODMOS, mohajira-ish music is already so ingrained in all of our heads
that it just sounds "middle eastern" instead of "xenharmonic", which
basically means that this particular xenharmonic sound has already
been developed a good amount. The fact that an entire culture has
formed its music around this basic melodic structure, given it some
basic harmonic context, and come up with an extremely complicated
system of modes that contain novel musical colors, which rivals the
western system in complexity, is pretty epic. This is another way of
saying it's awesome enough to have seen common use before the tuning
list was formed, which is precisely why it gets so little attention.

Of course, you could argue that it's not really mohajira they're
using, but I'd counter that by saying that you can just apply the
mohajira mapping to that melodic structure, and reharm existing maqam
music to give it extremely crunchy 11-limit harmony.

> > Yes, like I said, porcupine! However, someday you'll load up a marimba
> > patch and come to realize that what you really want is Mavila[9],
> > which solves every single problem in existence except the "make every
> > chord sound like a circular saw grinding through a bug zapper"
> > problem.
>
> I beg to differ!

What problems does mavila have besides not being high in accuracy?

> > This is, in my opinion, the correct way to interpret all of the
> > unreleased director's cut stuff we did with categorical entropy:
> > quasi-equal chromatic scales that allow for greater harmonic purity
> > than the EDO allows for. Then we'll get to be picky about it for
> > another century or so until people start becoming degraded and evil
> > and just tune to 15-EDO and don't care anymore.
>
> Yeah, that's sort of how I interpret it. 12edo sounds pretty acceptable in the 5-limit, and can be made really good in some keys if you make it slightly unequal (based on meantone). 15edo sounds somewhat less acceptable (although it's not really *that* much worse objectively), and a more dramatic improvement can be made by making it unequal based on porcupine.

So maybe we should ignore porcupine[15] entirely, and just cut to the
chase and invent Werckmeister-15.

> > There is one thing that I want to say though. I associate habitually
> > played chords with categories; I can "imply" chords with melodic
> > phrases. And that would seem to require us to be able to distinguish
> > categories from one another. And I suck at that at with fragments
> > played at high speed with porcupine in 22-EDO.
>
> I think porcupine is freaking great for this. I feel like I can already tell porcupine intervals/chords/modes apart with the skill of a little kid just starting music lessons (as opposed to that of a completely tone-deaf person, which is where I was months ago). I mean, look at how the 15-tone scale is laid out:
>
> 0 Unison
> 1 Augmented unison
> 2 Minor second
> 3 Major second
> 4 Minor third (6/5)
> 5 Major third (5/4)
> 6 Minor fourth (4/3)
> 7 Major fourth
> 8 Minor fifth
> 9 Major fifth (3/2)
> 10 Minor sixth (8/5)
> 11 Major sixth (5/3)
> 12 Minor seventh
> 13 Major seventh
> 14 Diminished octave
> 15 Octave
>
> I mean how much simpler can you get?!

I guess I just don't like it in 22-EDO because of the few ambiguous
intervals. For example, 15/8 is both in the "major seventh" class and
in the "diminished octave" class in 22-EDO.

I wish we had 15-tone pianos. I think that part of the reason my
categorical perception is so strong in 12-EDO is that I've basically
had a synesthetic guide my whole life telling me what categories were
supposed to sync up with what pitches in the form of the Halberstadt
keyboard.

> In the same way that the meantone chromatic scale has 12 notes and 19 is a relatively hair-splitting "enharmonic" scale, so the porcupine chromatic scale has 15 notes and 22 is the "enharmonic". The only difference is that where as 12edo is perfectly acceptable for billions (literally billions, right?) of people using meantone, 15edo is somewhat less acceptable as a tuning. But that doesn't mean it should be neglected as a framework.

It's probably only unacceptable for another decade or two at most.
It's basically only unacceptable until someone writes some good pieces
in 15-EDO and people get interested enough to "try something new." And
the unacceptableness of it is definitely going to predominate in the
population least likely to buy music anyway.

-Mike

🔗Mike Battaglia <battaglia01@...>

On Mon, Jan 2, 2012 at 3:29 PM, cityoftheasleep <igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > Meantone doesn't allow us to play music in which every chord sounds
> > like ECT for your auditory system. Moving throughout the MODMOS's of
> > 13-limit tetracot, tuned to 34-EDO, can do the trick with that though.
>
> Are you saying the MODMOS's of 13-limit tetracot are richer in concordance than meantone[7]?

Of course. Once you're willing to use MODMOS's, complexity isn't as
much of an issue, so you can use higher-limit or higher-accuracy
temperaments without worrying so much about complexity. The MODMOS's
of porcupine are similarly colorful. And miracle's been on my list of
things to figure out for a while too.

The real point that I'm not satisfied with is that we don't really
know what we're looking for. The Bach retunings clearly show that
common practice music gets "unintelligible" when the categorical
structure becomes undecipherable, not when the ratios change from what
we're used to. In comparison, the ratios involved tell us to some
extent how "pleasantly intoned" everything is, which is also
important, if not the all-encompassing singular facet of musical
experience. Of course, it could become the all-encompassing singular
facet of musical experience if people start writing music that
prioritizes that over all else, which in itself would be quite a
departure from meantone and lead to a new mode of perception for
music.

The point is that these "best of" temperament lists tell us the best
structures to intone things. They, as well as the theory they derive
from, ignore any other possible dimensions of musical experience which
could exist. This isn't the end of the world, because at least we have
something to start with, and as we come up with new things, we'll just
keep on adding to what we have.

-Mike

🔗Carl Lumma <carl@...>

Igs wrote:

> Meantone (and eventually, 12-TET) arose as the solution to
> compositional problems, after centuries of cultural "natural
> selection". There are many reasons to believe that it is,
> in fact, the "best" solution to the problems it was meant to
> solve. Because of this, the way we are currently applying
> the regular mapping paradigm to the problem of finding a
> "guaranteed meantone successor"--by this I mean the process
> of making these best-of lists for various prime limits--is,
> I believe, doomed to failure.

Natural selection doesn't always find the best solutions.
Neither do markets: a good example is the QWERTY keyboard.

But even if meantone is the best 5-limit system, there's
the idea that music evolves up the harmonic series in a
cumulative or sequential fashion over a long period --
that we had to do 3-limit, then 5-limit etc. And meantone
might not be the best 7-limit system. You could even
argue that the meantone rut might hold up the transition
to the 7-limit.

Ok, I used to think highly of these cultural evolution
arguments and maybe there is something to them, but I'm
more skeptical in my old age that music may not be going
anywhere. It's possible that the complexity of music goes
up and down over time basically at random. I can argue
that the ever-decreasing cost of recorded music has removed
a primary motivator for people to learn to play instruments,
and as a result has made the population tone deaf compared
to what it was in the 1920s or even Elizabethan Britain.

On balance though I still think it's worth pursuing top-9
lists for the reason I gave... especially since I'm trying
to do so myself. ;)

> We are not going to find a temperament that is better at
> solving all the same problems as meantone/12-TET.

I think porcupine is almost as good as meantone in the
5-limit. Good enough to warrant more than 0.0000001%
of 5-limit music being written in it. And I think
pajara is better in the 7-limit.

> After decades of systematic exploration via the RMP,

Decade.

> there is no temperament that is both more accurate on the
> 5-limit AND simpler (or even equally-accurate but simpler or
> equally-simple but more accurate...or even equally-accurate
> and equally-simple!).

Yep, it's a gold medalist.

/tuning-math/message/17107
/tuning-math/message/17991

> We also know, thanks to Keenan Pepper's exploration of the
> average dyadic harmonic entropy of rank-2 scales of comparable
> size to meantone and 12-TET, that meantone[7] is
> *significantly* lower in average dyadic HE than any other
> scale of 7 or more notes.

Yes (Paul got a similar result).

> Therefore, any other 5-limit (or 7-limit, or 11-limit,
> or 13-limit) temperament is going to be in some respect
> inferior to meantone at solving the compositional problems
> that meantone solves. Can we all agree on that?

If you're willing to go up to 10/oct I'm not sure it's
still true. I'd have to review Keenan's results.

> We have instead taken pretty much all of our cues from the
> advocates of higher-limit JI (since one thing meantone doesn't
> do is give a lot of 7, 11, and 13-limit intervals), and looked
> for temperaments of the 7-, 11-, and 13-limit. But we've done
> so without taking a good, hard look at what compositional
> problems are solved by higher-limit JI (and temperaments
> thereof). Without having such an anchor in the practical,
> there's no reason to think that our "best-of" lists here are
> going to have a better-than-random chance at leading to a
> "guaranteed meantone successor".

Writing polyphonic 7-limit music in pajara[10] should be
pretty straightforward. Meantone[7] has really crappy
7-limit accuracy.

-Carl

🔗genewardsmith <genewardsmith@...>

🔗gbreed@...

Only one interval of seven

Graham

------Original message------
From: genewardsmith <genewardsmith@...>
To: <tuning@yahoogroups.com>
Date: Monday, January 2, 2012 9:56:07 PM GMT-0000
Subject: [tuning] Re: The Elusive "Meantone Killer" (was RE: Middle Path 11-limit Temperaments)

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

> Meantone[7] has really crappy
> 7-limit accuracy.

The accuracy is good. The problem is, there's only one 7-limit interval.

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🔗gbreed@...

Evolution doesn't lead to increasing complexity. Most life forms are still single cells. What does tend to happen is that more niches open up over time and some of them are occupied by more complex organisms.
The analogy seems to work fine. The higher limit temperament niche is bigger than ever before. That doesn't mean pentatonics will ever disappear.

Graham

------Original message------
From: Carl Lumma <carl@...>
To: <tuning@yahoogroups.com>
Date: Monday, January 2, 2012 9:22:52 PM GMT-0000
Subject: [tuning] Re: The Elusive "Meantone Killer" (was RE: Middle Path 11-limit Temperaments)

Igs wrote:

Natural selection doesn't always find the best solutions.
Neither do markets: a good example is the QWERTY keyboard.

On balance though I still think it's worth pursuing top-9
lists for the reason I gave... especially since I'm trying
to do so myself. ;)

> We are not going to find a temperament that is better at
> solving all the same problems as meantone/12-TET.

I think porcupine is almost as good as meantone in the
5-limit. Good enough to warrant more than 0.0000001%
of 5-limit music being written in it. And I think
pajara is better in the 7-limit.

> After decades of systematic exploration via the RMP,

Decade.

Yep, it's a gold medalist.

/tuning-math/message/17107
/tuning-math/message/17991

Yes (Paul got a similar result).

If you're willing to go up to 10/oct I'm not sure it's
still true. I'd have to review Keenan's results.

Writing polyphonic 7-limit music in pajara[10] should be
pretty straightforward. Meantone[7] has really crappy
7-limit accuracy.

-Carl

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

🔗cityoftheasleep <igliashon@...>

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

> Natural selection doesn't always find the best solutions.
> Neither do markets: a good example is the QWERTY keyboard.

Sure; but the problem of intonation has also been subjected to centuries of theoretical inquiry, of which we are just the latest batch of enquirers. Still haven't found a better tuning than meantone for the sort of music that meantone is good for.

> But even if meantone is the best 5-limit system, there's
> the idea that music evolves up the harmonic series in a
> cumulative or sequential fashion over a long period --
> that we had to do 3-limit, then 5-limit etc. And meantone
> might not be the best 7-limit system. You could even
> argue that the meantone rut might hold up the transition
> to the 7-limit.

Really? I thought the 7-limit transition happened many decades ago, when jazz and blues musicians started using dom7 chords all over the place, taking advantage of the fact that 12-TET is both a Pajara and Meantone temperament (and thus also a Dominant temperament).

> Ok, I used to think highly of these cultural evolution
> arguments and maybe there is something to them, but I'm
> more skeptical in my old age that music may not be going
> anywhere. It's possible that the complexity of music goes
> up and down over time basically at random. I can argue
> that the ever-decreasing cost of recorded music has removed
> a primary motivator for people to learn to play instruments,
> and as a result has made the population tone deaf compared
> to what it was in the 1920s or even Elizabethan Britain.

This is sort of what I was driving at. While there were obvious sets of compositional desideratum that meantone and then 12-TET can be said to clearly fulfill, as expressed in the compositional approaches taken around the time of their development and adoption, I don't see any cultural forces driving music to evolve further up the harmonic series. Well, perhaps what Keenan's getting at, the fusion of Western tonal harmony with Eastern melodic forms (which obviously suggests incorporating one or both of the 11th and 13th harmonics and harmonies thereof). Or maybe there is something to be said for "novelty" as a driving force, particularly in the form of harmonies in the "xen" zone between the 7 and 17-limit.

> On balance though I still think it's worth pursuing top-9
> lists for the reason I gave... especially since I'm trying
> to do so myself. ;)

The reason you gave was that a top-9 list would be worthwhile if it saved people time and gave at least one guaranteed meantone successor. This assumes that we know what a meantone successor looks like, or that we know what constitutes the sort of thing that people are looking for. I'm not convinced we do, nor that we've spent enough time considering these more basic questions. Instead, it's like we just said "meantone does lots of good 5-limit harmonies, and some pretty good 7-limit harmonies when extended a bit; let's generalize the idea of temperament so we can find other things that do what meantone does, and people will be sure to like the results!".

> I think porcupine is almost as good as meantone in the
> 5-limit.

Who's gonna pay twice the price for something of less quality? "Almost as good" isn't good enough. And I wouldn't even call porcupine "almost as good" as meantone in the 5-limit--the one advantage porcupine has over the 5-limit JI diatonic only makes sense if we look at it as an 11-limit (or 2.3.5.11 subgroup) temperament. A 7-note MOS with only 4 concordant 5-limit triads, tuned even less accurately than in meantone, is pathetic, and if that's the best we can do for a "guaranteed meantone successor", then we're screwed and we should stop now. Even the JI diatonic gives 5 concordant 5-limit triads. Meantone's chief advantage is that it provides even more 5-limit concords than JI; porcupine lacks that advantage. It only looks worthwhile if we interpret it the way Keenan likes to, as substituting 11-limit concords in place of 5-limit discords. But we still ought to be asking just how concordant the 11-limit really is, what the point of using it over a lower limit system might be, and who (if anyone) would be interested in apply it--what's it good for, anyway?

> Good enough to warrant more than 0.0000001%
> of 5-limit music being written in it. And I think
> pajara is better in the 7-limit.

Sure, pajara's great...12-TET FTW with both meantone and pajara!

> > After decades of systematic exploration via the RMP,
>
> Decade.

It only goes back to 2001? Dang, I practically got in on the ground floor.

> > Therefore, any other 5-limit (or 7-limit, or 11-limit,
> > or 13-limit) temperament is going to be in some respect
> > inferior to meantone at solving the compositional problems
> > that meantone solves. Can we all agree on that?
>
> If you're willing to go up to 10/oct I'm not sure it's
> still true. I'd have to review Keenan's results.

No temperament of greater than 7 notes will have lower average dyadic HE than the best temperament of 7 notes or fewer. The more notes you add, the more small steps you get, and those jack up the average HE.

> Writing polyphonic 7-limit music in pajara[10] should be
> pretty straightforward. Meantone[7] has really crappy
> 7-limit accuracy.

7-limit music in pajara[10]? Bet we could find plenty of it if we analyzed enough jazz. Let's also not forget Augene[9] and August[9] (which intersect at 12-TET IIRC), Dimisept[8], and Injera[10]--all among the shortlist of 7-limt temperaments according to Paul's paper, all represented in 12-TET and probably utilized in extant music to a significant extent. The only compositional problems solved by more optimal meantone[7] and pajara[10] tunings is the problem of discordance, which patently seems to be a non-issue in modern musical culture. There is a subculture interested in greater concordance than 12-TET, and it is unquestionably the dominant force in microtonal music and theory, but it's pretty solidly divorced from mainstream musical taste...and also probably more interested in JI and micro temperaments than anything meantone-like anyway.

-Igs

🔗Keenan Pepper <keenanpepper@...>

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@>
> > The "problem", or rather the thing missing, is 10:11:12. The thing
> > we desire is "quartertones", where that simply means anything
> > sufficiently far from 12edo intervals and is exemplified by the 11th
> > harmonic. We want harmonic, tonal music where "quartertones" are an
> > integral part of the scale. The solution is porcupine.
>
> Great idea. May I ask you to expand a little bit on why you think this is what is missing, and/or why the 11th harmonic rather than the 7th or 13th?

I can't find the specific Harry Partch quote that says this better, but 11 is the first harmonic that's not even remotely implied by 12edo. The 7th harmonic is pretty badly implied, but ask anyone whether 7/4 is a "supermajor sixth" or "subminor seventh" and they'll know which it is (if they understand what you're talking about at all). The simplest possible interpretation of the tritone is 7/5.

In other words, dominant temperament really "works" and sounds like a 7-limit temperament, albeit not a very accurate one. On the other hand, neither "arnold" temperament nor 11-limit dominant actually sound like 11-limit temperaments at all.

Keenan

🔗cityoftheasleep <igliashon@...>

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

> Of course. Once you're willing to use MODMOS's, complexity isn't as
> much of an issue, so you can use higher-limit or higher-accuracy
> temperaments without worrying so much about complexity. The MODMOS's
> of porcupine are similarly colorful. And miracle's been on my list of
> things to figure out for a while too.

I guess Keenan only really looked at MOS's...maybe there is indeed a MODMOS out there that is as simple as meantone but more concordant? Perhaps even several? I did try sensi[8] in 27-ED2 and it was all "BZZZ BRZZZ FLRRNN" all over the place with pretty much any combination of notes.

> The real point that I'm not satisfied with is that we don't really
> know what we're looking for.

Couldn't agree more! Do we even know *why* we're looking, and if so, can we articulate and/or formalize it?

> The point is that these "best of" temperament lists tell us the best
> structures to intone things. They, as well as the theory they derive
> from, ignore any other possible dimensions of musical experience which
> could exist. This isn't the end of the world, because at least we have
> something to start with, and as we come up with new things, we'll just
> keep on adding to what we have.

As I see it, the RMP has two main components: the "structural" part and the "optimization" part. I tend to ignore the latter, because I've already placed such strict complexity bounds on what I'll consider that I take what accuracy I can get. I think the RMP is and will be very important in helping us out once we know what we're really looking for--i.e. what a "guaranteed meantone successor" might look like. The fulminant interest in subgroups and essentially-tempered chords is encouraging, because it means we're finally past the "music will evolve by increasing in scalar and harmonic complexity" stage and conceding that music will evolve by branching in probably a few different dimensions simultaneously, probably most of which will not increase substantially in complexity but will instead probably swap out some old elements for some new elements. Maybe we'll go from the awesomely-simple 2.3.5.7.17.19 harmonies of 12-TET (Hendrix chord! Minor 6th chord! Don't get all "there's no such thing as the 19-limit in 12-TET" to me) to some equally-awesomely simple other subgroup. But who knows what subgroup it is (and which temperament thereof) that will be the solution, if we don't even know what the problem is?

-Igs

🔗cityoftheasleep <igliashon@...>

🔗Keenan Pepper <keenanpepper@...>

🔗Mike Battaglia <battaglia01@...>

On Mon, Jan 2, 2012 at 6:24 PM, cityoftheasleep <igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > Of course. Once you're willing to use MODMOS's, complexity isn't as
> > much of an issue, so you can use higher-limit or higher-accuracy
> > temperaments without worrying so much about complexity. The MODMOS's
> > of porcupine are similarly colorful. And miracle's been on my list of
> > things to figure out for a while too.
>
> I guess Keenan only really looked at MOS's...maybe there is indeed a MODMOS out there that is as simple as meantone but more concordant? Perhaps even several? I did try sensi[8] in 27-ED2 and it was all "BZZZ BRZZZ FLRRNN" all over the place with pretty much any combination of notes.

You'll just change modes every single chord, like they do in jazz.

If I want to play C9#11, I'll play C lydian dominant (C D E F# G A Bb
C). If I want to play the same chord but with a b9, I'll play C
diminished (C Db D# E F# G A Bb C). If I want to play C augmented
maj7, I'll play C lydian augmented (C D E F# G# A B C) or C lydian
augmented #2 (C D# E F# G# A B C) or whatever. Each chord implies a
range of modes, and each mode has its own "feeling" because the other
notes can be used as "extensions" on top of your chosen chord. The
modes commonly used are from the diatonic, melodic minor, harmonic
minor, and harmonic major scales, as well as the diminished scale
sometimes.

Well, except at first, that's not how it works. At first, a lot of
modes just sound dumb, and like versions of things you know that have
one note changed to not make sense. But once you hear a capable
musician "activate" each mode with some trippy chord progression or
voicing or what have you that only exists in that mode, you'll
remember the sound forever. And in that way you can learn some sort of
"characteristic sound" of each scale. That's how the MODMOS's are for
other temperaments. They're going to all sound like stupid variations
on the MOS until you realize that they each contain some chord/chord
progression/sound/whatever that's only in that MODMOS, and then you'll
realize what its "sound" is and what makes it unique, and start
building a vocabulary, and so on. So the train of thought is

1) Think of chord you want to play
2) Go to the database in your head of modes which contain that chord
3) Play chord and as many other notes from that mode as you want - "extensions"
4) Use the mode you chose for melody

So there isn't going to be a single MODMOS we all use, but that's
fine. People have been using this approach to play chords in meantone
that are too complex for the 7-note MOS going back almost a century
now.

> Couldn't agree more! Do we even know *why* we're looking, and if so, can we articulate and/or formalize it?

I dunno, I'm burned out on philosophy now. What I know is that what
you said to Carl here

"Really? I thought the 7-limit transition happened many decades ago,
when jazz and blues musicians started using dom7 chords all over the
place, taking advantage of the fact that 12-TET is both a Pajara and
Meantone temperament (and thus also a Dominant temperament)."

probably needs revising. For example, the German aug6 chord in
quarter-comma meantone is 4:5:6:7, and far more accurate than it is in
12-EDO, but it's about as unstable as a chord can get. So what does it
mean to "play 7-limit music?" What's more 7-limit, the 12-EDO 4:5:6:7
chord used as a tonic, or the 31-EDO 4:5:6:7 chord used as a German
aug6 chord? I think the whole concept makes no sense.

> > The point is that these "best of" temperament lists tell us the best
> > structures to intone things. They, as well as the theory they derive
> > from, ignore any other possible dimensions of musical experience which
> > could exist. This isn't the end of the world, because at least we have
> > something to start with, and as we come up with new things, we'll just
> > keep on adding to what we have.
//snip
> But who knows what subgroup it is (and which temperament thereof) that will be the solution, if we don't even know what the problem is?

The problem is that most of music doesn't seem to have anything at all
to do with ratios. You know something's horribly wrong when 225 cents
in 16-EDO can either sound sad or not sad depending on how you want to
flip your perception around (is it 2\12 or 3\12?).

-Mike

🔗Chris Vaisvil <chrisvaisvil@...>

Its been a while since I''ve been here.

This (quoted paragraph) really caught my imagination. Care to elaborate
Mike?? It sounds like something I may want to try to do.

Chris

"In comparison, the ratios involved tell us to some
extent how "pleasantly intoned" everything is, which is also
important, if not the all-encompassing singular facet of musical
experience. Of course, it could become the all-encompassing singular
facet of musical experience if people start writing music that
prioritizes that over all else, which in itself would be quite a
departure from meantone and lead to a new mode of perception for
music."

On Mon, Jan 2, 2012 at 4:03 PM, Mike Battaglia <battaglia01@...>wrote:

> **
>
>
>
>
> The Bach retunings clearly show that
> common practice music gets "unintelligible" when the categorical
> structure becomes undecipherable, not when the ratios change from what
> we're used to. In comparison, the ratios involved tell us to some
> extent how "pleasantly intoned" everything is, which is also
> important, if not the all-encompassing singular facet of musical
> experience. Of course, it could become the all-encompassing singular
> facet of musical experience if people start writing music that
> prioritizes that over all else, which in itself would be quite a
> departure from meantone and lead to a new mode of perception for
> music.
>
>
> -Mike
>
>
>
>

🔗Mike Battaglia <battaglia01@...>

BTW, I take back everything I said about mohajira beating out
porcupine. Check out the pieces that Chris wrote

http://micro.soonlabel.com/15-ET/daily20111231-porcupine15-indian.mp3

http://micro.soonlabel.com/15-ET/daily20111231-porcupine15-piano.mp3

http://micro.soonlabel.com/15-ET/daily20111231-porcupine15-prickly-side-of-love.mp3

Something about what Chris did in the indian one transformed porcupine
in my perception from being a random scale that sort of sounds like 12
into this shining new entity in which the generator contains harmonic
information about how it generates chords.

So Igs, maybe that's what we're looking for: temperaments in which it
is easiest to understand how melody implies harmony.

-Mike

On Mon, Jan 2, 2012 at 6:58 PM, Chris Vaisvil <chrisvaisvil@...> wrote:
>
>
>
> Its been a while since I''ve been here.
>
> This (quoted paragraph) really caught my imagination. Care to elaborate Mike?? It sounds like something I may want to try to do.
>
> Chris
>
>
>
> "In comparison, the ratios involved tell us to some
> extent how "pleasantly intoned" everything is, which is also
> important, if not the all-encompassing singular facet of musical
> experience. Of course, it could become the all-encompassing singular
> facet of musical experience if people start writing music that
> prioritizes that over all else, which in itself would be quite a
> departure from meantone and lead to a new mode of perception for
> music."
>
> On Mon, Jan 2, 2012 at 4:03 PM, Mike Battaglia <battaglia01@...> wrote:
>>
>>
>>
>>
>>
>> The Bach retunings clearly show that
>> common practice music gets "unintelligible" when the categorical
>> structure becomes undecipherable, not when the ratios change from what
>> we're used to. In comparison, the ratios involved tell us to some
>> extent how "pleasantly intoned" everything is, which is also
>> important, if not the all-encompassing singular facet of musical
>> experience. Of course, it could become the all-encompassing singular
>> facet of musical experience if people start writing music that
>> prioritizes that over all else, which in itself would be quite a
>> departure from meantone and lead to a new mode of perception for
>> music.
>>
>>
>> -Mike
>>
>>
>
>

🔗Chris Vaisvil <chrisvaisvil@...>

With all due respect your explanation doesn't seem to cover, at least in my
mind.

"how "pleasantly intoned" everything is, which is also
important, if not the all-encompassing singular facet of musical
experience. Of course, it could become the all-encompassing singular
facet of musical experience if people start writing music that
prioritizes that over all else, "

I thought you were hinting towards a Edgar Varese use of intervallic
xenharmonic material.
Of course that doesn't make your explanation incorrect, of course your know
what you meant.

Chris

On Mon, Jan 2, 2012 at 7:08 PM, Mike Battaglia <battaglia01@...>wrote:

> **
>
>
> On Mon, Jan 2, 2012 at 6:58 PM, Chris Vaisvil <chrisvaisvil@...>
> wrote:
> >
> > Its been a while since I''ve been here.
> >
> > This (quoted paragraph) really caught my imagination. Care to elaborate
> Mike?? It sounds like something I may want to try to do.
> >
> > Chris
>
> I mean that sometimes, people complain that there's more to music than
> ratios. Meanwhile, Gene sometimes rebuts that there's more to music
> than having independent categories.
>
> The assumption for both of these is that there's some predefined way
> that "music" works, which we're supposed to find, presumably
> consisting of some hodgepodge mixture of random things with no
> unifying theme. It's more likely that in retrospect, a hundred or two
> years from now, Gene will have kicked off the style of music that
> prioritizes extremely accurate, high-limit, crunchy harmony, whereas
> Igs will have kicked off the style that prioritizes categorical
> economy over harmonic accuracy. It's like watching Debussy argue with
> Bach over whether polyphony beats modal harmony or something.
>
> -Mike
>
>
>

🔗Mike Battaglia <battaglia01@...>

🔗Chris Vaisvil <chrisvaisvil@...>

Hi Mike,

I think your statement may point towards some music that involves using
contrasting static xenharmonic structures.

Of course very likely that other xenharmonic composers have done this. I
know I have heard this in Varese (I'm pretty sure) and also in the late
90's I actually
had an internet conversation with David Cope about algorithmic music. There
was a piece he showed me that he described
as a newly born fawn trying to stand up and falling back down. There is a
Varese piece, perhaps Hyperprism, that visually
is the equivalent of a Pollack painting with essentially static harmonies
being thrown up into the air only to fall back down again
for reorganization and another attempt at standing.

Chris

On Mon, Jan 2, 2012 at 7:19 PM, Mike Battaglia <battaglia01@...>wrote:

> **
>
>
> On Mon, Jan 2, 2012 at 7:17 PM, Chris Vaisvil <chrisvaisvil@...>
> wrote:
> >
> > With all due respect your explanation doesn't seem to cover, at least in
> my mind.
> >
> > "how "pleasantly intoned" everything is, which is also
> > important, if not the all-encompassing singular facet of musical
> > experience. Of course, it could become the all-encompassing singular
> > facet of musical experience if people start writing music that
> > prioritizes that over all else, "
>
> I mean that having huge, crunchy, high-limit, accurate otonal chords
> isn't the only thing that matters. Unless, of course, you write music
> in a style in which it is the only thing that matters. Then, it's the
> only thing that matters.
>
> -Mike
>
>
>

🔗dkeenanuqnetau <d.keenan@...>

Great thread. Meta-stable intervals anyone? JI and MI? Justice _and_ Mercy?

I'm agreeing mostly with Igs and Keenan so far, and anyone who's saying there's more to good scales than approximations of simple rationals.

I think the regular mapping paradigm has run its course in terms of generating new resources for composers to experiment with. The experimentation by composers should go on, of course. And I would still like to see those error/complexity scatter plots.

But I wish some of us who like using computers to try to find good scales according to various criteria, would begin to look at the intervals on the _peaks_ of the harmonic entropy curve as well as the troughs, many of which appear to be at simple noble numbers rather than simple rationals.

I suspect that's what we _really_ like about some supposed 11-limit or 13-limit temperaments, because in most timbres 11th and 13th harmonics are at low levels and the typical mistunings of the supposed ratios of 11 and 13 in these temperaments violate Partch's principle (visible on a harmonic entropy plot) that the higher the identity the more precisely it must be tuned or it loses its identity.
/tuning/files/dyadic/margo3.gif

This is also consistent with Keenan's desire that the new intervals be as far from 12-ET as possible.

Margo Schulter and Cameron Bobro come to mind as pioneering composers in this field that includes both JI and its shadow, MI.

A short piece by Cameron can be heard here.
http://sagittal.org/gift/FinalEpisode.htm
Incidentally, I believe I've fixed the problem with the sagittal.org domain, but if anyone still can't access it, please let me know, and instead try
http://dkeenan.com/sagittal/gift/FinalEpisode.htm

And I think this sampler of MI/JI cadences by Margo makes the case well.
/tuning/topicId_73833.html#74319

Another resource is this chart of noble intervals.
/tuning/topicId_77502.html#77502?source=1&var=0&l=1

And I understand the term "crunchy chord", as coined by Keenan Pepper's music theory teacher many years ago, means a chord in which all the intervals except one are consonant.
/tuning/topicId_11922.html#11922

-- Dave Keenan

🔗Carl Lumma <carl@...>

🔗Mike Battaglia <battaglia01@...>

On Mon, Jan 2, 2012 at 9:36 PM, dkeenanuqnetau <d.keenan@...> wrote:
>
> Great thread. Meta-stable intervals anyone? JI and MI? Justice _and_ Mercy?
>
> I'm agreeing mostly with Igs and Keenan so far, and anyone who's saying there's more to good scales than approximations of simple rationals.

*ahem*

> I think the regular mapping paradigm has run its course in terms of generating new resources for composers to experiment with. The experimentation by composers should go on, of course. And I would still like to see those error/complexity scatter plots.

I'd just like for someone to provide an adequate explanation of this

http://soundcloud.com/mikebattagliamusic/sets/the-categorical-experiments/

You know, I used to get in these really spirited arguments back in the
day over this stuff, and I'm not sure I have the energy anymore. I
just want to know if there's a whole dimension to music that I'm
completely missing out on because of stuff like the above.

Also props to Keenan Pepper for plowing ahead undeterred anyway. I
feel like we're coming up to the first wave of integrating this stuff
back with ratios again. Maybe a few more cycles of this departure and
reintegration and we'll have it all figured out...

> I suspect that's what we _really_ like about some supposed 11-limit or 13-limit temperaments, because in most timbres 11th and 13th harmonics are at low levels and the typical mistunings of the supposed ratios of 11 and 13 in these temperaments violate Partch's principle (visible on a harmonic entropy plot) that the higher the identity the more precisely it must be tuned or it loses its identity.
> /tuning/files/dyadic/margo3.gif
>
> This is also consistent with Keenan's desire that the new intervals be as far from 12-ET as possible.

Yeah, but is it consistent with the Bach retunings? Or Herman's warped
canon page? For me, not really.

-Mike

🔗Carl Lumma <carl@...>

Igs wrote:
> Really? I thought the 7-limit transition happened many decades
> ago, when jazz and blues musicians started using dom7 chords all
> over the place, taking advantage of the fact that 12-TET is both
> a Pajara and Meantone temperament (and thus also a Dominant
> temperament).

There's an argument to be made there, yes. OTOH we could
say it was a 'large chords' transition. The emphasis seems
to be on Maj7s & min7s, not dom7s.

> This is sort of what I was driving at. While there were
> obvious sets of compositional desideratum that meantone and
> then 12-TET can be said to clearly fulfill, as expressed in
> the compositional approaches taken around the time of their
> development and adoption, I don't see any cultural forces
> driving music to evolve further up the harmonic series.

There are people here who want to. Maybe that's enough.

> Instead, it's like we just said "meantone does lots of good
> 5-limit harmonies, and some pretty good 7-limit harmonies
> when extended a bit; let's generalize the idea of temperament
> so we can find other things that do what meantone does, and
> people will be sure to like the results!".

Works for me!

> > I think porcupine is almost as good as meantone in the
> > 5-limit.
>
> Who's gonna pay twice the price for something of
> less quality?

Some folks have used it, ya know...

> "Almost as good" isn't good enough. And I wouldn't even
> call porcupine "almost as good" as meantone in the 5-limit

It's better than diminished, which had its followers in
the French organ school and led to a sizable body of music
considered by many to be truly great.

> Meantone's chief advantage is that it provides even more
> 5-limit concords than JI; porcupine lacks that advantage.

It provides more concords than its corresponding Fokker
block. All temperaments do. And it'll provide more
concords per note than any JI block once you get above
a certain threshold of scale size.

> It only looks worthwhile if we interpret it the way Keenan
> likes to, as substituting 11-limit concords in place of
> 5-limit discords. But we still ought to be asking just how
> concordant the 11-limit really is, what the point of using
> it over a lower limit system might be, and who (if anyone)
> would be interested in apply it--what's it good for, anyway?

The 11-limit is PLENTY concordant. I'll go so far as to
say there's no room for argument about that.

> Sure, pajara's great...12-TET FTW with both meantone
> and pajara!

Nah, it's a lousy pajara system.

> It only goes back to 2001? Dang, I practically got in on
> the ground floor.

You did indeed.

> No temperament of greater than 7 notes will have lower
> average dyadic HE than the best temperament of 7 notes
> or fewer. The more notes you add, the more small steps
> you get, and those jack up the average HE.

The same is true of scales of 5 notes vs 7. I don't
know many musicians who would be happy with pentatonic
instruments for the rest of their lives (though there
are some).

> > Writing polyphonic 7-limit music in pajara[10] should be
> > pretty straightforward. Meantone[7] has really crappy
> > 7-limit accuracy.
>
> 7-limit music in pajara[10]? Bet we could find plenty of
> it if we analyzed enough jazz.

> There is a subculture interested in greater concordance
> than 12-TET, and it is unquestionably the dominant force
> in microtonal music and theory, but it's pretty solidly
> divorced from mainstream musical taste...

I don't believe that. I think people respond to pleasant
sounds straight away. The difference in 7-limit accuracy
between 12 and 22 is bigger than the difference between
cassette quality and CD quality.

-Carl

🔗Keenan Pepper <keenanpepper@...>

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@> wrote:
> >
> > I can't find the specific Harry Partch quote that says this better, but 11 is the first harmonic > that's not even remotely implied by 12edo. The 7th harmonic is pretty badly implied, but
> > ask anyone whether 7/4 is a "supermajor sixth" or "subminor seventh" and they'll know
> > which it is (if they understand what you're talking about at all). The simplest possible
> > interpretation of the tritone is 7/5.
>
> What about the 13th? If you're gung ho on 10:11:12, why not 8:9:11:12:13:14? Mohaha/Maqamic and Bleu are both a lot closer to optimal in 17-TET than Porcupine is in 15-TET...and as you demonstrated yourself, the "neutral 3rds" heptatonic is the closest we get in the heptatonic range to meantone[7] for average dyadic HE (or do I misremember that?).

It's nothing more than personal preference that I prefer 10:11:12 to 12:13:14. If you like 12:13:14, then neutral third scales and bleu are great, as you say, as well as negri (specifically this version: http://x31eq.com/cgi-bin/rt.cgi?ets=19_10&limit=2_3_5_7_13 ).

And call me conservative, but I'm still really attached to 5-limit harmony. The idea of being able to play real major and minor chords, plus all this 11-limit stuff, in a circulating "chromatic" scale of only 15 notes is really exciting to me. That's part of why 8:10:11:12 is great to me, because it's something you can add on to a normal major chord which sounds really "weird" but still major and "happy" or whatever. The utonal "minor" version is also great. In contrast 8:12:13:14 still sounds otonal, but not "major", if that makes sense.

As for average HE, porcupine[7] actually beats out neutral thirds [7] slightly for "medium" HE ( https://docs.google.com/open?id=0B9CMyeCjAMQGMDJlOTA3NmQtNDhkMy00NTYxLThjMTMtOTM2YTI2M2Q2YTE5 ). The way I'd charaterize it, though, is that meantone is the clear winner, and there are several runners up that are about equally good.

🔗dkeenanuqnetau <d.keenan@...>

🔗Mike Battaglia <battaglia01@...>

On Mon, Jan 2, 2012 at 11:06 PM, dkeenanuqnetau <d.keenan@...> wrote:
>
> > Yeah, but is it consistent with the Bach retunings? Or Herman's warped
> > canon page? For me, not really.
>
> If I attend to the melody lines of individual voices it seems like basically the same piece for fifth generators from about 26-EDO to 22-EDO, maybe a little further. But if I attend to the harmonies, the cadences, sequences of consonance and dissonance, I can only accept the range from 19-EDO to 17-EDO before it starts to sound like a different piece, and if it wasn't such a lively piece, i.e. if the chords were sustained longer, then I suspect I wouldn't tolerate 17-EDO.
>
> Is there something about this that you feel needs explanation? Or do you perceive it very differently from me?

Yes, I don't perceive it like that at all. I mean, I can claim to be
really sensitive and picky to the intonation and say that the 32-EDO
version sounds basically like a different piece, but it doesn't to me
because it essentially sounds like the same piece being intoned
differently. I hear major which is happy, and minor which is sad, and
so on and so forth, basically as long as I can figure out what the
intervals are - so at the extremes of the spectrum when major and
minor get too close to tell apart, things get ambiguous, and likewise
when major thirds and perfect fourths get too close to tell apart,
etc. But, even more strangely, I can still pick out the basic features
of "major" and "minor" even in 5-EDO.

I can very clearly tell that the intonation is changing, which changes
some aspect of the mood of it, but it's not like the whole thing
becomes a totally unintelligible, different piece of music once it
gets outside the realm of the 5-limit. Most people on XA seemed to
indicate something similar; that the piece didn't become
unintelligible when the ratios changed. Even the people who claimed to
hear a profound difference between "supermajor" and "major" still
admitted that supermajor and major were more similar than major and
minor, for instance. And some people, particularly those with more
melodic approaches, didn't even get what I was trying to do and didn't
understand why it was even supposed to be notable a stretched diatonic
scale sounded exactly like a stretched diatonic scale.

"Preferences" were also pretty much all over the place; I liked the
17-EDO version best, Gene liked 31-EDO, Keenan liked the really flat
ones, a lot of people thought the 75-EDO one was interesting, etc.

Anyway, for me, personally, this signifies that there's something else going on.

-Mike

🔗genewardsmith <genewardsmith@...>

🔗cityoftheasleep <igliashon@...>

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

> There's an argument to be made there, yes. OTOH we could
> say it was a 'large chords' transition. The emphasis seems
> to be on Maj7s & min7s, not dom7s.

I'll let Mike weigh in on that claim.

> There are people here who want to. Maybe that's enough.

Maybe; I won't rule it out.

> Works for me!

Then where's all the music you've written in Magic, Miracle, Hanson, Helmholtz (etc.)?

> > Who's gonna pay twice the price for something of
> > less quality?
>
> Some folks have used it, ya know...

Sure, and about as many have used 13-EDO, by my count. If you want to talk "guaranteed meantone successor", you've got a ways to go to make the case that Porcupine is it....

> > "Almost as good" isn't good enough. And I wouldn't even
> > call porcupine "almost as good" as meantone in the 5-limit
>
> It's better than diminished, which had its followers in
> the French organ school and led to a sizable body of music
> considered by many to be truly great.

Well, is it better? I'm not sure we know enough about what makes a temperament "good" to make that statement.

> It provides more concords than its corresponding Fokker
> block. All temperaments do. And it'll provide more
> concords per note than any JI block once you get above
> a certain threshold of scale size.

That claim could be made for a lot of temperaments. Why pick a fokker block with fewer concords than the garden-variety 5-limit diatonic? I don't see any pure 5-limit perspective from which Porcupine looks competitive with Meantone. If it's truly second-place, it's a distant second, as far as the 5-limit is concerned.

> The 11-limit is PLENTY concordant. I'll go so far as to
> say there's no room for argument about that.

Weren't you the same guy telling me a Tenney Height of 70 is the cutoff for JI? Most of the 11-limit intervals that share the same octave as the root are above this cutoff--11/7, 11/8, 11/9, 11/10, and their inversions, for instance. Now the 11-limit is PLENTY concordant?

> > Sure, pajara's great...12-TET FTW with both meantone
> > and pajara!
>
> Nah, it's a lousy pajara system.

But it's still a Pajara system...and an Injera system! Where else can you get so many great 7-limit temperaments together in the same place as so many great 5-limit temperaments?

> The same is true of scales of 5 notes vs 7. I don't
> know many musicians who would be happy with pentatonic
> instruments for the rest of their lives (though there
> are some).

I also don't know many who are keen on using scales of 9+ notes.

> I don't believe that. I think people respond to pleasant
> sounds straight away. The difference in 7-limit accuracy
> between 12 and 22 is bigger than the difference between
> cassette quality and CD quality.

And yet, there does not seem to be a significant preference in the microtonal music-consuming public for music made in concordant tunings over discordant ones. Even asking people about their favorite Blackwood etudes, I don't know anybody who'll claim "19 notes" as their top choice. Society at one time had its choice between 31, 19, and 12...and went with 12. I'd say people do indeed respond to pleasant sounds, but "pleasant" is more a property of timbres than harmonic intonation.

-Igs

🔗Mike Battaglia <battaglia01@...>

On Tue, Jan 3, 2012 at 12:55 AM, cityoftheasleep
<igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> > There's an argument to be made there, yes. OTOH we could
> > say it was a 'large chords' transition. The emphasis seems
> > to be on Maj7s & min7s, not dom7s.
>
> I'll let Mike weigh in on that claim.

To the extent that he's talking about early-mid 20th century
"extended" harmony, he's right. Maj7 and maj6 and maj6/9 chords
replaced the major triad as the basic "major unit," and m6/m7/mMaj7
and so on for minor. Chords in general started having lots of
extensions on everything.

What you're saying is also true, that it also became common for
dominant 7 chords to be used as a "bluesy" tonic sonority, which led
to interesting crossover styles like this

http://www.youtube.com/watch?v=Plm-791wglY&feature=related

But as I said in response to your post, I'm still not sure that
comprises an "evolution into the 7-limit," because much more accurate
7-limit chords were in use way back when everyone was using quarter
comma meantone and playing German 6th chords. And for whatever reason,
some other, -non-ratio- aspect of the music causes them to be unstable
and want to resolve, even if they're obviously crunchy and intoned as
4:5:6:7.

So how do we know that the use of the 12-EDO dom7 chord comprises an
evolution into the 7-limit? Out of all of the things that evolved when
the blues came into being, why should this be the most important one?
How do we know that this apparent 7-limit evolution wasn't accompanied
by an evolution of something far more important which doesn't have to
do with ratios?

-Mike

🔗Carl Lumma <carl@...>

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

> Then where's all the music you've written in Magic, Miracle,
> Hanson, Helmholtz (etc.)?

I only entertained the idea of becoming a musician for about
a year, and most of it was before I knew about microtuning.
Since then I've been busy trying to earn a living. I'll get
back to it eventually though.

> Sure, and about as many have used 13-EDO, by my count.
> If you want to talk "guaranteed meantone successor", you've
> got a ways to go to make the case that Porcupine is it....

Yeah, but the results with porcupine have been way better
than with 13-EDO. Besides, if popularity were any guide
in 1350 we wouldn't have gotten meantone either.

> > It's better than diminished, which had its followers in
> > the French organ school and led to a sizable body of music
> > considered by many to be truly great.
>
> Well, is it better?

Yup.

> > It provides more concords than its corresponding Fokker
> > block. All temperaments do. And it'll provide more
> > concords per note than any JI block once you get above
> > a certain threshold of scale size.
>
> That claim could be made for a lot of temperaments.

All of them, actually.

> Why pick a fokker block with fewer concords than the garden-
> variety 5-limit diatonic?

Because there are 72092375203984234204 pieces of music
written in the diatonic already and we're a bit bored
of it?

> I don't see any pure 5-limit perspective from which Porcupine
> looks competitive with Meantone.

As I said, it isn't.

> > The 11-limit is PLENTY concordant. I'll go so far as to
> > say there's no room for argument about that.
>
> Weren't you the same guy telling me a Tenney Height of 70 is
> the cutoff for JI?

For dyads.

> > Nah, it's a lousy pajara system.
>
> But it's still a Pajara system...and an Injera system! Where
> else can you get so many great 7-limit temperaments together
> in the same place as so many great 5-limit temperaments?

1-EDO! It contains all those systems plus a few others.

> > I don't believe that. I think people respond to pleasant
> > sounds straight away. The difference in 7-limit accuracy
> > between 12 and 22 is bigger than the difference between
> > cassette quality and CD quality.
>
> And yet, there does not seem to be a significant preference
> in the microtonal music-consuming public for music made in
> concordant tunings over discordant ones. Even asking people
> about their favorite Blackwood etudes, I don't know anybody
> who'll claim "19 notes" as their top choice.

The two 19-ET pieces are like my 2nd and 3rd favorites
on there.

If you made one of your snazzy pop tunes in a tuning that
actually sounded good I wager almost everyone would
prefer it. Just sayin'.

-Carl

🔗Mike Battaglia <battaglia01@...>

🔗genewardsmith <genewardsmith@...>

🔗Carl Lumma <carl@...>

Mike Battaglia <battaglia01@...> wrote:

> What you're saying is also true, that it also became common for
> dominant 7 chords to be used as a "bluesy" tonic sonority, which
> led to interesting crossover styles like this
> http://www.youtube.com/watch?v=Plm-791wglY&feature=related

And where the conditions were right to escape the 12-ET
straightjacket, it actually led to a full 7-limit style where
dominant 7ths are the norm: barbershop. Everywhere else they
turned to ever more extravagant means for squeezing blood
from a penny, such as quartal harmony etc. (Not to say such
chords are bad! They are essentially tempered chords in
12-ET, after all...)

> So how do we know that the use of the 12-EDO dom7 chord
> comprises an evolution into the 7-limit? Out of all of the
> things that evolved when the blues came into being, why
> should this be the most important one? How do we know that
> this apparent 7-limit evolution wasn't accompanied by an
> evolution of something far more important which doesn't
> have to do with ratios?

I've been putting off tackling this because it's led to
arguments in the past... but from time to time you seem to
say that someone, maybe me, thinks ratios have to do with
categorical perception. I don't know anyone who thinks this.
Your experiments with it, like the Bach thing, always baffle
me. I think I remember you linking to one once and saying
something like What Now!, but all I could hear was an
airplane going over my head. If I thought ratios were all-
important, I wouldn't spend time with scale theory and things
like Rothenberg equivalence. And I've always said that
rhythm is more primary than pitch. Feel free to respond
offlist... maybe I'm all wet here. Above, I certainly didn't
mean to say that a 7-limit transition (or failure of one) is
the most important thing about African-American music.

-Carl

🔗dkeenanuqnetau <d.keenan@...>

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "dkeenanuqnetau" <d.keenan@> wrote:
>
> > I think the regular mapping paradigm has run its course in terms of generating new resources for composers to experiment with.
>
> Have you been around in the last year? Because a hell of a lot has been happening.
>

I have not read the tuning lists much in the past year and it _does_ seem like a hell of a lot has been happening. But to refute my point you would need to say what else still _needs_ to happen?

What I see is a very substantial temperament catalog on the wiki and a good set of metrics and a thoroughly perfected temperament finder and I understand over 800 temperaments have been named. Related discussions seem to now revolve around increasingly fine details.

I suppose there's an argument that planar temperaments and their periodicity blocks have not been much explored.

But it seems to be all predicated on _minimising_ harmonic entropy or something very like it. What if we wanted to generate scales that minimise say the absolute value of the first derivative of HE wrt interval size, so as to treat HE maxima as equally valuable as minima?

I have myself argued that the concentration on HE minima is justified because dissonance is easy to find and will turn up accidentally in pretty much any scale with more than 6 pitches per octave. But perhaps it's time for a more systematic approach.

Perhaps this could still fall under the RMP. We'd certainly still be interested in the "regular" part. But I can't see how an algebra of prime mappings and prime exponent vectors can get us there. Has it already been started and I missed it?

-- Dave Keenan

🔗Mike Battaglia <battaglia01@...>

On Tue, Jan 3, 2012 at 2:10 AM, Carl Lumma <carl@...> wrote:
>
> > What you're saying is also true, that it also became common for
> > dominant 7 chords to be used as a "bluesy" tonic sonority, which
> > led to interesting crossover styles like this
> > http://www.youtube.com/watch?v=Plm-791wglY&feature=related
>
> And where the conditions were right to escape the 12-ET
> straightjacket, it actually led to a full 7-limit style where
> dominant 7ths are the norm: barbershop. Everywhere else they
> turned to ever more extravagant means for squeezing blood
> from a penny, such as quartal harmony etc. (Not to say such
> chords are bad! They are essentially tempered chords in
> 12-ET, after all...)

Alright, but what does "evolution into the 7-limit" mean? That a
7-limit chord was used as the tonic triad?

> > So how do we know that the use of the 12-EDO dom7 chord
> > comprises an evolution into the 7-limit? Out of all of the
> > things that evolved when the blues came into being, why
> > should this be the most important one? How do we know that
> > this apparent 7-limit evolution wasn't accompanied by an
> > evolution of something far more important which doesn't
> > have to do with ratios?
>
> I've been putting off tackling this because it's led to
> arguments in the past... but from time to time you seem to
> say that someone, maybe me, thinks ratios have to do with
> categorical perception.

This is a response to Igs.

> I don't know anyone who thinks this.

I'm sure you know some people who think this. Either that, or they
don't think that categorical perception is real, or that every ratio
has its own identity, or what not.

> Your experiments with it, like the Bach thing, always baffle
> me. I think I remember you linking to one once and saying
> something like What Now!, but all I could hear was an
> airplane going over my head.

I don't know what's so baffling about them: you retune the piece and
major, minor, and diminished all retain some essential aspect of their
"quality" and "function," despite the ratio changing, until the
categorical structure gets out of whack and you can't figure out
what's going on. Some aspect of the sound changes as the intonation
changes, and another aspect doesn't, and it's this other aspect that
is more important to my ears, and the ears of most people who listened
to the examples. The two exceptions I've come across so far are Dave
Keenan and Michael S, and I'm not entirely sure Mike knew what I'm
asking. You're the only person who's described them as baffling, and I
don't know what you mean by an airplane.

> If I thought ratios were all-
> important, I wouldn't spend time with scale theory and things
> like Rothenberg equivalence. And I've always said that
> rhythm is more primary than pitch. Feel free to respond
> offlist... maybe I'm all wet here. Above, I certainly didn't
> mean to say that a 7-limit transition (or failure of one) is
> the most important thing about African-American music.

Again, that was a response to Igs.

-Mike

🔗cityoftheasleep <igliashon@...>

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
> I only entertained the idea of becoming a musician for about
> a year, and most of it was before I knew about microtuning.
> Since then I've been busy trying to earn a living. I'll get
> back to it eventually though.

I hope so!

> Yeah, but the results with porcupine have been way better
> than with 13-EDO.

Better by what standards?

> > Well, is it better?
>
> Yup.

Again, by what standards?

> > Why pick a fokker block with fewer concords than the garden-
> > variety 5-limit diatonic?
>
> Because there are 72092375203984234204 pieces of music
> written in the diatonic already and we're a bit bored
> of it?

Well, now we're getting somewhere...but, the logic still looks like "we're bored of using these nice tools that are ideally suited to our task, so we're going to use some crappier tools that don't do the job as well." Or, in other words, like the guaranteed successor to our hammer is a smaller and somewhat damaged hammer. (Or if you're naming Pajara instead of Porcupine as the guaranteed successor, then a larger and somewhat shinier hammer. Big whoop.)

> > I don't see any pure 5-limit perspective from which Porcupine
> > looks competitive with Meantone.
>
> As I said, it isn't.

So, what is?

> > Weren't you the same guy telling me a Tenney Height of 70 is
> > the cutoff for JI?
>
> For dyads.

So is it triads that bring the 11-limit back into concordance land? Or do we need tetrads, pentads, hexads, etc.? Not entirely clear what your views on this are.

> > > Nah, it's a lousy pajara system.
> >
> > But it's still a Pajara system...and an Injera system! Where
> > else can you get so many great 7-limit temperaments together
> > in the same place as so many great 5-limit temperaments?
>
> 1-EDO! It contains all those systems plus a few others.

LOL.

> The two 19-ET pieces are like my 2nd and 3rd favorites
> on there.

After, IIRC, the 15-ET piece. Which even I find discordant. You can't explain that! (/billoreilly)

> If you made one of your snazzy pop tunes in a tuning that
> actually sounded good I wager almost everyone would
> prefer it. Just sayin'.

Guess all those songs I wrote in 31, 22, and 19 didn't count? C'mon, man...my "Early Microtonal Works" uses accurate tunings exclusively, unless you want to discount the two 17-TET songs, and it's waaaaay down there at the bottom of my listener charts on last.fm. No one ever talks about it. 10 tracks of 22-ET, no one bats an eyelash (though the two metal songs did get a pretty good response from a couple people when I pimped them here and at MMM...not that they use much in the way of harmony). I've gotten waaaay more positive interest over the years for playing in goofy tunings than I have in nice ones.

But hey, if you want to make it interesting, we can always pop over to XA and do a poll!

🔗Carl Lumma <carl@...>

Igs wrote:

> And yet, there does not seem to be a significant preference
> in the microtonal music-consuming public for music made in
> concordant tunings over discordant ones.

There's a microtonal music-consuming public?

Let's see... which of these movements & artists is
more popular?

classical Indian music Vs classical Thai/Indonesian music

musica reservata Vs ______

barbershop Vs ______

Partch/Groven/Harrison/Johnston Vs Carrillo/Haba/Wyschnegradsky

Riley/Young/R.Rich/M.Harrison/Catlers Vs Ivor Darreg

S.J.Taylor/A.Dreyblatt/H.A.Stamm/Haverstick&Co Vs ______

rest of JI Network Vs Facebook XA

Neutral:
maqam music, Fokker school, E.Blackwood, W.Carlos,
M.Hobbs, K.Grady
(and I think this is generous, as was giving Facebook XA
entirely to the non-JI side)

Maybe it's just me but it looks like JI wins by a mile.
You said "microtonal" but for fun we might add

rest of Western music Vs atonal serialism

-Carl

🔗Carl Lumma <carl@...>

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

> > And where the conditions were right to escape the 12-ET
> > straightjacket, it actually led to a full 7-limit style where
> > dominant 7ths are the norm: barbershop. Everywhere else they
> > turned to ever more extravagant means for squeezing blood
> > from a penny, such as quartal harmony etc. (Not to say such
> > chords are bad! They are essentially tempered chords in
> > 12-ET, after all...)
>
> Alright, but what does "evolution into the 7-limit" mean?
> That a 7-limit chord was used as the tonic triad?

Did I use that phrase? I consider barbershop 7-limit
because nearly every major triad is extended to a 7-limit
otonality, performed in accurate just intonation. Minor
triads often remain 5-limit, or are extended to minor 7ths
(intoned as 9-limit ASSs). 4:6:7:9 and other 9-limit
chords are occasionally heard. If not sure if dim7 chords
are consistently intoned, but I can think of a few cases
where I thought the intonation approached 10:12:15:17.

> > Your experiments with it, like the Bach thing, always baffle
> > me. I think I remember you linking to one once and saying
> > something like What Now!, but all I could hear was an
> > airplane going over my head.
>
> I don't know what's so baffling about them: you retune the
> piece and major, minor, and diminished all retain some
> essential aspect of their "quality" and "function," despite
> the ratio changing, until the categorical structure gets
> out of whack and you can't figure out what's going on.

With the Bach experiment it all sounds like Bach, even
the 5-ET version. That's probably because you primed us
with the piece and the rhythm and melodic contours aren't
changed. I'm not sure what it has to do with categorical
perception.

> The two exceptions I've come across so far are Dave
> Keenan and Michael S, and I'm not entirely sure Mike knew
> what I'm asking.

I definitely don't know what you're asking (and I wonder
how you'd know if anyone did).

> You're the only person who's described them as baffling,
> and I don't know what you mean by an airplane.

It was meant to be a lighthearted reference to the gesture
of wooshing one's hand over one's head.

> Again, that was a response to Igs.

Sorry. -C.

🔗Carl Lumma <carl@...>

Igs wrote:

> > Yeah, but the results with porcupine have been way better
> > than with 13-EDO.
>
> Better by what standards?

My subjective opinion. :)

> > > Well, is it better?
> >
> > Yup.
>
> Again, by what standards?

The whole badness thing we've been talking about (error
and complexity). See http://lumma.org/music/theory/tctmo/

> Or if you're naming Pajara instead of Porcupine as the
> guaranteed successor, then a larger and somewhat shinier
> hammer. Big whoop.)

> > > I don't see any pure 5-limit perspective from which
> > > Porcupine looks competitive with Meantone.
> >
> > As I said, it isn't.
>
> So, what is?

I don't claim to know. Probably pajara, if there has
to be one.

> So is it triads that bring the 11-limit back into
> concordance land? Or do we need tetrads, pentads, hexads,
> etc.? Not entirely clear what your views on this are.

My sense is that most of the 11-limit otonal tetrads have
one or more consonant voicings over a three-octave span.
Of course music isn't made of disconnected chords, so the
stronger ones can help the weaker ones.

> > The two 19-ET pieces are like my 2nd and 3rd favorites
> > on there.
>
> After, IIRC, the 15-ET piece. Which even I find discordant.
> You can't explain that! (/billoreilly)

Yes! 15 is about my limit. I tolerate it for the puns,
which are magnificent. Blackwood is more accurate than
mavila, which is past my limit. Things like 11 and 13,
I have no plans to ever work with. 22 really seems to
hit the sweet spot with pajara and porcupine. Things like
441, which Gene likes... I'd just use JI at that point.
IMO the benefits of temperament max out around schismic
and miracle (like 41 and 72).

> > If you made one of your snazzy pop tunes in a tuning that
> > actually sounded good I wager almost everyone would
> > prefer it. Just sayin'.
>
> Guess all those songs I wrote in 31, 22, and 19 didn't count?
> C'mon, man...my "Early Microtonal Works" uses accurate
> tunings exclusively,

I need to get up on your latest stuff -- I think you've
released two albums that I haven't gotten to yet!
You should charge for those by the way. Anyhow, I fell
for your stuff in the EMW days and that might explain why.

-Carl

🔗Mike Battaglia <battaglia01@...>

On Tue, Jan 3, 2012 at 3:06 AM, Carl Lumma <carl@...> wrote:
>
> --- Mike Battaglia <battaglia01@...> wrote:
>
> > > And where the conditions were right to escape the 12-ET
> > > straightjacket, it actually led to a full 7-limit style where
> > > dominant 7ths are the norm: barbershop. Everywhere else they
> > > turned to ever more extravagant means for squeezing blood
> > > from a penny, such as quartal harmony etc. (Not to say such
> > > chords are bad! They are essentially tempered chords in
> > > 12-ET, after all...)
> >
> > Alright, but what does "evolution into the 7-limit" mean?
> > That a 7-limit chord was used as the tonic triad?
>
> Did I use that phrase? I consider barbershop 7-limit
> because nearly every major triad is extended to a 7-limit
> otonality, performed in accurate just intonation. Minor
> triads often remain 5-limit, or are extended to minor 7ths
> (intoned as 9-limit ASSs). 4:6:7:9 and other 9-limit
> chords are occasionally heard. If not sure if dim7 chords
> are consistently intoned, but I can think of a few cases
> where I thought the intonation approached 10:12:15:17.

Sorry, I'm getting confused. You're jumping into my replies to Igs. I
thought you were agreeing with his "evolution into the 7-limit" thing.

What you're saying is fine. I think there are also an infinite amount
of ways to define the notion of music being "7-limit" which are also
fine. I prefer to not think in those terms anymore.

> > I don't know what's so baffling about them: you retune the
> > piece and major, minor, and diminished all retain some
> > essential aspect of their "quality" and "function," despite
> > the ratio changing, until the categorical structure gets
> > out of whack and you can't figure out what's going on.
>
> With the Bach experiment it all sounds like Bach, even
> the 5-ET version. That's probably because you primed us
> with the piece and the rhythm and melodic contours aren't
> changed. I'm not sure what it has to do with categorical
> perception.

I don't know what you mean specifically by "sounds like Bach." To me,
I heard the signal get very "noisy" at around 5-EDO, because I can't
always figure out if something was a major third or a perfect fourth,
or a major second or a minor third, or what not. However, despite
that, I did often hear 0-480-720 cents sound like a major chord with a
really sharp third, and 0-240-720 cents sound like a minor third with
a really flat third. Not everyone reported hearing it the same way.

I don't know what you mean by mentioning priming and then saying it
may not have to do with categorical perception. What exactly do you
claim is being primed if not interval categories?

-Mike

🔗genewardsmith <genewardsmith@...>

🔗Carl Lumma <carl@...>

🔗genewardsmith <genewardsmith@...>

🔗Keenan Pepper <keenanpepper@...>

🔗Carl Lumma <carl@...>

"genewardsmith" <genewardsmith@...> wrote:

> > With the Bach experiment it all sounds like Bach, even
> > the 5-ET version.
>
> It did?

Yes. Of course I hear the out-of-tune harmony. But that's
not hard to ignore. In fast counterpoint like this I don't
identify particular intervals, in the sense of consciously
knowing was this or that interval a perfect fourth. I just
listen to melodic patterns. The repeated notes (getting
mapped to the same pitch in 5-ET) were the only interference
there, and it's easy enough to imagine the note it would
have been.

Mike: It might help if you stated what the categories are
that you're testing. Melodic intervals by diatonic
interval class? Harmonic intervals by...? etc.

When the mavila experiments came up I focused on which
tuning was best. I had no trouble deciding that 16 had a
slight melodic edge on 23 (including identifying spots where
I thought it showed) and that 23 and a significant harmonic
edge on the others (error figures subsequently corroborated
that judgement).

So I went back and listened to just the 23-ET versions
for more category-type things. I hear the inversion of
major and minor in familiar pieces. It's neat, but since
the chords are really close to being swapped I don't
quite know what it has to do with perceptual categories.
I could get a similar effect in 12 by rewriting the
chords by hand. The horrid intonation is a lot harder to
ignore in the Mozart and Beethoven.

-Carl

🔗Keenan Pepper <keenanpepper@...>

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
> > So is it triads that bring the 11-limit back into
> > concordance land? Or do we need tetrads, pentads, hexads,
> > etc.? Not entirely clear what your views on this are.
>
> My sense is that most of the 11-limit otonal tetrads have
> one or more consonant voicings over a three-octave span.
> Of course music isn't made of disconnected chords, so the
> stronger ones can help the weaker ones.

Right, I agree with Carl. Also, perhaps more importantly, there's a categorical effect. If 8:9:10:11:12 is consonant (to me it is), and you're familiar with the way a certain scale divides up 11/8 so it can be a part of that consonant chord, then whenever you hear 11/8 in the context of that scale you just *know* intuitively that it's part of an implied consonant harmony, so it sounds consonant to you. Remember that in meantone music, arpeggiated chords sound very similar to simultaneous chords, even thought this obviously eliminates all harmonic interaction between the notes, except in your mind.

> Yes! 15 is about my limit. I tolerate it for the puns,
> which are magnificent. Blackwood is more accurate than
> mavila, which is past my limit. Things like 11 and 13,
> I have no plans to ever work with. 22 really seems to
> hit the sweet spot with pajara and porcupine. Things like
> 441, which Gene likes... I'd just use JI at that point.
> IMO the benefits of temperament max out around schismic
> and miracle (like 41 and 72).

Again our opinions are similar (except that I'm giving mavila a shot since it might interest my gamelan friends). What do you think of the idea of 15-note circulating porcupine, such as I posted?

Keenan

🔗Carl Lumma <carl@...>

🔗dkeenanuqnetau <d.keenan@...>

🔗Mike Battaglia <battaglia01@...>

On Tue, Jan 3, 2012 at 3:38 AM, Carl Lumma <carl@...> wrote:
>
> Well it's hard to talk about, isn't it? I don't know what to
> suggest. Cognitive psychologists have spent decades trying
> to get around the problem with clever experiments, with
> limited success. Maybe I'll just repeat my admonishment that,
> as a possessor of AP, it's possible you relate to music in a
> deeply different manner than most folks.

These are some examples I posted in an informal listening test. I
happened to find them illuminating, as did many others.

The general reaction was that for many observers, there is something
that an interval category like "major third" or "perfect fourth" is
which is independent of the ratio you use to intone it. If for some
reason you don't find the Bach retunings to establish this fact for
you, you might try some of Keenan's warped diatonic scales. If that
still doesn't do the trick, then try playing around with 225 cents in
16-EDO: 0-225-375-675 vs 0-150-750 -> 0-225-675 and see if you can
flip the 225 cent interval into sounding "sad" vs "not sad." If that
still doesn't work, then maybe there's some variance on how it all
works.

Nonetheless, for a great many of us, there is something else that a
thing like a "major third" is which is independent of what ratio you
use to intone it. I haven't yet seen a satisfactory explanation of
what that is. The notion that this sort of ratio-independence only
exists for people with AP isn't supported by the numerous people who
claim to have the same sort of experience.

If there's an underlying difference in perception that isn't being
communicated on which explains everything, that's an interesting
notion that should be taken seriously, but I'm not sure what you're
proposing.

-Mike

🔗Mike Battaglia <battaglia01@...>

🔗Carl Lumma <carl@...>

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

> The general reaction was that for many observers, there is
> something that an interval category like "major third" or
> "perfect fourth" is which is independent of the ratio you
> use to intone it.

Do you mean melodic intervals, harmonic intervals, or both?

What's the complete list of categories? Are they diatonic
interval classes?

Do you have an idea what anchors the categories? Absolute
size ranges? Relative sizes? Something to do with
rationals (which you mentioned)? Relative function to other
things (like larger chords) in music?

> you might try some of Keenan's warped diatonic scales

URL?

> If that still doesn't do the trick, then try playing around
> with 225 cents in 16-EDO: 0-225-375-675 vs 0-150-750 -> 0-225-675
> and see if you can flip the 225 cent interval into sounding "sad"
> vs "not sad."

I don't understand this experiment recipe. Are dash-connected
things simultaneities? What's the difference between
a "vs" and a "->"?

> Nonetheless, for a great many of us, there is something else
> that a thing like a "major third" is which is independent of
> what ratio you use to intone it. I haven't yet seen a
> satisfactory explanation of what that is. The notion that this
> sort of ratio-independence only exists for people with AP isn't
> supported by the numerous people who claim to have the same
> sort of experience.

You seem to be implying I said something about ratios.

I said your perception of music could be deeply different
than the people you're corresponding with. I didn't give
particulars.

I don't know what to think about people's claims. Usually
they're meaningless unless you're terribly careful.

-Carl

🔗Carl Lumma <carl@...>

🔗Mike Battaglia <battaglia01@...>

On Tue, Jan 3, 2012 at 5:42 AM, Carl Lumma <carl@...> wrote:
>
> --- Mike Battaglia <battaglia01@...> wrote:
>
> > The general reaction was that for many observers, there is
> > something that an interval category like "major third" or
> > "perfect fourth" is which is independent of the ratio you
> > use to intone it.
>
> Do you mean melodic intervals, harmonic intervals, or both?

Both.

> What's the complete list of categories? Are they diatonic
> interval classes?

Chromatic interval classes, maybe 12-EDO interval classes.

> Do you have an idea what anchors the categories? Absolute
> size ranges? Relative sizes? Something to do with
> rationals (which you mentioned)? Relative function to other
> things (like larger chords) in music?

Apparently not rationals. What anchors them is something like, at the
end of the day, where the listener perceives the interval as fitting
into a particular rank-order matrix. If the listener is more musically
trained, the rank-order matrix will tend to be more centered around
12-EDO, otherwise it might be more like the diatonic scale.

> > you might try some of Keenan's warped diatonic scales
>
> URL?

They're on the wiki, can't check now.

> > If that still doesn't do the trick, then try playing around
> > with 225 cents in 16-EDO: 0-225-375-675 vs 0-150-750 -> 0-225-675
> > and see if you can flip the 225 cent interval into sounding "sad"
> > vs "not sad."
>
> I don't understand this experiment recipe. Are dash-connected
> things simultaneities? What's the difference between
> a "vs" and a "->"?

The first example is a simultaneous chord which is an approximation of
8:9:10:12 in 16-EDO. The second is a two-chord resolution that starts
with one triad and resolves to another.

> I don't know what to think about people's claims. Usually
> they're meaningless unless you're terribly careful.

This also applies to the listening tests you guys did when working on HE.

-Mike

🔗Mike Battaglia <battaglia01@...>

🔗genewardsmith <genewardsmith@...>

🔗cityoftheasleep <igliashon@...>

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

> > Better by what standards?
>
> My subjective opinion. :)

LOL, well then, I respectfully disagree. I've had my mind blown by at least as many 13-EDO pieces as Porcupine ones. Some of what I've heard in Porcupine (and most of what I tried to write in it, when I was interested in it) just sounded like meantone progressions with someone randomly pitch-bending them. I wonder if there's a reason that, despite an initial zealous interest in the temperament (I built a friggin' tubulong for it, and spent several months trying to internalize the A-H notation, and spent a long time trying to master the guitar fingerings for it in 22), I decided I didn't like it? I also wonder if there's a reason that, after several months of sustained interest, I still think 13 and 16 are tons of fun, and after more than 4 years, my 17 tone guitar is getting more play than ever (yet I couldn't get rid of 19, 22, and 31 fast enough?). I'm not being sarcastic here, by the way--I'm genuinely curious about why my own preferences run the way they do.

> The whole badness thing we've been talking about (error
> and complexity). See http://lumma.org/music/theory/tctmo/

Sure, but what makes you so sure that "badness" is the right way to evaluate a temperament's musical viability?

> > Or if you're naming Pajara instead of Porcupine as the
> > guaranteed successor, then a larger and somewhat shinier
> > hammer. Big whoop.)
>
> :(

What I mean by that is, a bigger and shinier hammer doesn't solve many problems that a smaller more beat-up hammer can't. Now, a screwdriver, on the other hand, or a pair of pliers....

> > > > I don't see any pure 5-limit perspective from which
> > > > Porcupine looks competitive with Meantone.
> > >
> > > As I said, it isn't.
> >
> > So, what is?
>
> I don't claim to know. Probably pajara, if there has
> to be one.

Well, there doesn't. Perhaps our "guaranteed meantone successor" will not be another simple 5-limit temperament, or another simple 7-limit temperament.

> My sense is that most of the 11-limit otonal tetrads have
> one or more consonant voicings over a three-octave span.
> Of course music isn't made of disconnected chords, so the
> stronger ones can help the weaker ones.

Thanks for clarifying. I'm personally a little more charitable about the concordance of 11-limit harmonies, but I guess 6 months of playing in 13-EDO will do that to a person.

> Yes! 15 is about my limit. I tolerate it for the puns,
> which are magnificent.

Seems like you do more than tolerate it, if you like it better than Blackwood's 19-ET pieces.

> Blackwood is more accurate than
> mavila, which is past my limit.

Mavila necessitates a very different approach. But lots of people seem to like it, warts and all.

> Things like 11 and 13,
> I have no plans to ever work with.

That's too bad. They're both amazing subgroup temperaments, of 2.7.9.11.15.17 and 2.5.9.11.13.21, respectively.

> 22 really seems to hit the sweet spot with pajara and porcupine.

I wonder why it's not as popular as 16 and 17? Or hey, why not 19, which is more accurate on the 7-limit than 22?

http://x31eq.com/cgi-bin/rt.cgi?ets=19&limit=7
http://x31eq.com/cgi-bin/rt.cgi?ets=22&limit=7

> I need to get up on your latest stuff -- I think you've
> released two albums that I haven't gotten to yet!

To say nothing of my soundcloud account, which is nearing capacity with less-polished microtonal music in a huge variety of tunings.

> You should charge for those by the way.

Why? They're not costing me anything to make and distribute, above and beyond what I spend for my own recreation and entertainment. But through bandcamp, you are welcome to pay me for them if you wish, whatever amount you like ;->.

> Anyhow, I fell for your stuff in the EMW days and that might explain why.

Well, you're in the minority. "Map of an Internal Landscape" seems to be considered by most to be my landmark album. I may write a sequel to it, some day, to reflect my better understanding of temperaments (especially subgroup temperaments) represented in ETs 9 to 28.

🔗cityoftheasleep <igliashon@...>

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
> Let's see... which of these movements & artists is
> more popular?
>
> classical Indian music Vs classical Thai/Indonesian music

Explainable by the relative sizes of the two countries, and their cultural relationship to the West. Gamelan music is definitely on the up-and-up these days, though, despite this.

> musica reservata Vs ______

Hard to say, never heard of it until now.

> barbershop Vs ______

I dunno, choral music? Most choral music I've heard (and I've heard a lot more of that than barbershop) did not sound remotely like it was approaching JI. The whole "chorus" effect of slight discordance due to intonational inaccuracies across a large group of performers is apparently so desirable that we have invented effects processors to replicate it, which are immensely popular.

> Partch/Groven/Harrison/Johnston Vs Carrillo/Haba/Wyschnegradsky

I'd say it's a close call. The latter trio probably had more of an audience in their heyday than the former group, and perhaps more of an impact on some academic circles. Partch, perhaps by virtue of his theatricality and cult following (and, I dunno, the fact that he was American) seems to have had more of a lingering influence on contemporary music.

> Riley/Young/R.Rich/M.Harrison/Catlers Vs Ivor Darreg

What are we comparing, the whole group on the left vs. the one guy on the right? Why even compare, considering that Ivor also played in JI and advocated 19, 22, and 31 more strongly than any other tuning.

> S.J.Taylor/A.Dreyblatt/H.A.Stamm/Haverstick&Co Vs ______

The Split-Notes crew, the Spectropol records crew (especially including Dan Stearns), Zia?

> rest of JI Network Vs Facebook XA

...and the Boston Microtonal Society, AFMM, Nonoctave.com, the Bohlen-Pierce and Armodue folks.

> Maybe it's just me but it looks like JI wins by a mile.

I wouldn't say a mile, but like I said--it's the dominant force within the subculture itself. My initial point was that the general public could give two shits whether something is in JI or 11-ED2, and I stand by that (assuming other factors, like production quality and musical genre, are equal). The JI crowd has a longer history, a central focus around which to rally, and a better marketing strategy (it's hard to beat "nature's perfect tuning, the purest of all, the standard by which all other tunings are judged", after all), and thus ends up with better performers, better resources to make recordings, and wider avenues to get their music to the public.

In any case, I could also say "all of the above artists and styles vs. people actively and knowingly writing music based on alternative regular temperaments", too. The "Middle Path" is apparently the one with the least traffic. Maybe the "guaranteed meantone successor" is...JI?

-Igs

🔗Mike Battaglia <battaglia01@...>

🔗cityoftheasleep <igliashon@...>

--- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@...> wrote:
>
> It's nothing more than personal preference that I prefer 10:11:12 to 12:13:14. If you like
> 12:13:14, then neutral third scales and bleu are great, as you say, as well as negri
> (specifically this version: http://x31eq.com/cgi-bin/rt.cgi?ets=19_10&limit=2_3_5_7_13 ).

Negri was maybe my favorite scale in 19-TET, though I suspect the MODMOS's of it would have proved even more magical. I'm starting to look at MODMOS's of Bleu[8]...they're pretty sweet, too.

For me, it's really a matter of finding a low ET (under 24-TET) that does as many novel things as possible as well as possible, but without entirely divorcing itself from everything familiar. Since harmonics 7, 11, and 13 are the worst represented in 12-TET, but are significantly concordant in their own right, this makes them appealing as novel musical elements (duh, we've all pretty much agreed on this ages ago). Just looking at 2.7.11.13, 20-TET looks like the stand-out, but maybe pure novelty is a step too far, so adding back in the 3rd or 5th harmonic is probably wise. On 2.3.7.11.13, 17-TET is a very clear winner, basically beating out everything until we get to 36. On 2.5.7.11.13, we have 21-TET as the clear winner, but it's not as accurate on that subgroup as 17-TET is on 2.3.7.11.13 (and, let's face it, most people are probably more comforted by keeping around a solid 3/2 than a solid 5/4). We could demand the full 13-limit, in which case 22-TET wins the day (oddly, given its poor approximations to all ratios of 13...but that's what Graham's app says), but we lose a lot of accuracy compared to the 5-less subgroup. We could also demand less novelty, and say that the full 11-limit is enough, or even 2.3.5.11...this again points to 22, but even on the latter subgroup, the accuracy is not quite as good as 17-TET on the 2.3.7.11.13 subgroup (8.94 cents of adjusted error for 22, vs. 8.56 cents of adjusted error for 17-TET). So 22-TET compared to 17-TET gives less novelty, less accuracy, and greater complexity.

OTOH, there's 19-TET on the 2.3.5.13 subgroup, which is more accurate than 17 is on the 2.3.7.11.13 subgroup (~7.5 cents of adjusted error for 19-TET). 8:9:10:12:13 chords are pretty cool but you won't find them in any DE scale of reasonable size. You gotta MODMOS Meantone or Sensi or Negri, really. Less novelty, greater complexity, greater accuracy.

I think of the ETs under 24, 17 wins...but I also haven't looked at non-integer subgroups yet.

> And call me conservative, but I'm still really attached to 5-limit harmony. The idea of being > able to play real major and minor chords, plus all this 11-limit stuff, in a circulating
> "chromatic" scale of only 15 notes is really exciting to me.

It's pretty cool, no doubt. Have you compared it with George Secor's 17-WT?

> That's part of why 8:10:11:12 is great to me, because it's something you can add on to a
> normal major chord which sounds really "weird" but still major and "happy" or whatever.
> The utonal "minor" version is also great. In contrast 8:12:13:14 still sounds otonal, but not > "major", if that makes sense.

Yeah, it does make sense. I'm probably just a bit less conservative, and willing to accept the approximately-septimal major and minor triads of 17-TET's diatonic scale (and/or those of Bleu, which are the same, basically) as "close enough" to 5-limit harmony to get across the same emotional effect if I want it to. Compared to the 5-limit harmonies of 15-TET, I'm not sure they're any less concordant...they might even be more concordant, actually. Or at least the minor triads are. Minor triads in 17-TET are gorgeous, easily my favorite of all the subminor-type triads found in ETs up to 24-TET.

One of the things I like about the 2.3.7.11.13 subgroup is you have these otonal concordant voicings for augmented and diminished chords--7:9:11 and 9:11:13. That's pretty sweet to me. Then throw the true fundamental on them to make 4:7:9:11 and 4:9:11:13 and see how they suddenly change.

>The way I'd charaterize it, though, is that meantone is the clear winner, and there are
> several runners up that are about equally good.

Yep, probably. As an aside, have you ever considered re-doing the calculations according to the Vos-curve model of HE?

-Igs

🔗Carl Lumma <carl@...>

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

> Thanks for clarifying. I'm personally a little more charitable
> about the concordance of 11-limit harmonies, but I guess
> 6 months of playing in 13-EDO will do that to a person.

That's not all it could do to a person!

> > Yes! 15 is about my limit. I tolerate it for the puns,
> > which are magnificent.
>
> Seems like you do more than tolerate it, if you like it better
> than Blackwood's 19-ET pieces.

There's more to music than intonation, jeez.

> > Things like 11 and 13,
> > I have no plans to ever work with.
>
> That's too bad. They're both amazing subgroup temperaments,
> of 2.7.9.11.15.17 and 2.5.9.11.13.21, respectively.

Machine is nice but I see no reason not to just use 22.
I did some scale-finding in 13 for the 2.5 subgroup back
in the '90s (it's the optimal intonation for a certain
scale if you want it to be proper). I don't buy the rest
of that subgroup and 2.5 ain't much to write home
about either.

> Or hey, why not 19, which is more accurate on the
> 7-limit than 22?

I thought we cleared up this misconception offlist.

> http://x31eq.com/cgi-bin/rt.cgi?ets=19&limit=7
> http://x31eq.com/cgi-bin/rt.cgi?ets=22&limit=7

Those aren't the errors of "19" and "22", but of
ideally stretched versions.

> > You should charge for those by the way.
>
> Why? They're not costing me anything to make and distribute,
> above and beyond what I spend for my own recreation and
> entertainment. But through bandcamp, you are welcome to pay
> me for them if you wish, whatever amount you like ;->.

Links to your soundcloud and bandcamp?

> Well, you're in the minority. "Map of an Internal Landscape"
> seems to be considered by most to be my landmark album.

It's my favorite of yours too, but in spite of the intonation,
not because of it.

-Carl

🔗Carl Lumma <carl@...>

--- "cityoftheasleep" <igliashon@...> wrote:
>
> > musica reservata Vs ______
>
> Hard to say, never heard of it until now.

Think Willaert, Vicentino, Gesualdo.

> > barbershop Vs ______
>
> I dunno, choral music? Most choral music I've heard (and I've
> heard a lot more of that than barbershop) did not sound remotely
> like it was approaching JI.

Really? I have the opposite impression (also having sung in
amateur choirs for 2/3 of my life).

> > Partch/Groven/Harrison/Johnston Vs Carrillo/Haba/Wyschnegradsky
>
> I'd say it's a close call. The latter trio probably had more
> of an audience in their heyday than the former group,

Partch in his heyday outsold everyone else on both sides,
so that can't be right.

> > Riley/Young/R.Rich/M.Harrison/Catlers Vs Ivor Darreg
>
> What are we comparing, the whole group on the left vs. the
> one guy on the right? Why even compare, considering that Ivor
> also played in JI and advocated 19, 22, and 31 more strongly
> than any other tuning.

I was being generous giving Ivor to the other side.
I couldn't think of anyone else to put there.

> > S.J.Taylor/A.Dreyblatt/H.A.Stamm/Haverstick&Co Vs ______
>
> The Split-Notes crew, the Spectropol records crew (especially
> including Dan Stearns), Zia?

Ok, Split-Notes. Dan's stuff I think of more as sound painting
than music in a particular intonation (ditto music concrete).
I'd give Zia 50/50 for her emphasis on 19.

> > rest of JI Network Vs Facebook XA
>
> ...and the Boston Microtonal Society, AFMM, Nonoctave.com,
> the Bohlen-Pierce and Armodue folks.

I'd give AFMM 50/50. Thanks for filling in the others.

> The "Middle Path" is apparently the one with the least traffic.
> Maybe the "guaranteed meantone successor" is...JI?

I'm counting accurate regular temperaments as "JI" here.

-Carl

🔗Carl Lumma <carl@...>

Mike wrote:
> I wanted to test the notion that every ratio inherently has
> its own identity, and that the characteristic sound of major
> is actually the sound of 4:5:6,

Those sound like two very different tests. Clearly every
JI ratio has an identity; at least as much as any other
interval and, according to experiments like those of
Benade, more. The identity "major" could be almost any
kind of thing. I associate it more with the major scale
and major chord progressions than with 4:5:6.

> by doing a series of retunings in which the scalar
> structure remained consistent but the ratios changed.
> I found that for myself, this wasn't the case. I made
> some basic and informal listening tests to see how
> other people reacted, and most people felt the same
> way I did.

Is there a record of these experiments? How can I
participate?

> As a result, I now believe that although major chords can
> be intoned more or less pleasantly by picking a tuning in which
> they're close to something like 4:5:6, the major chord itself is
> something independent of any particular intonation. The regular
> mapping paradigm does not state what that is.

Didn't I say as much when you first showed up here?
Well, for the record, I've always believed this.

-Carl

🔗cityoftheasleep <igliashon@...>

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

> That's not all it could do to a person!

You should try it some time.

> > Seems like you do more than tolerate it, if you like it better
> > than Blackwood's 19-ET pieces.
>
> There's more to music than intonation, jeez.

Clearly. So how will a top-9 list of temperaments find us a guaranteed meantone successor, again?

> > That's too bad. They're both amazing subgroup temperaments,
> > of 2.7.9.11.15.17 and 2.5.9.11.13.21, respectively.
>
> Machine is nice but I see no reason not to just use 22.

Let's not forget Orgone[7], which (on 2.7.9.11.15.17) is also just about optimal in 11-ED2...and has outstanding melodic properties. There was a big discussion about this on XA, courtesy of Andrew Heathwaite, that you may have missed. There's also a subgroup version of Sensi in 11, that Aaron Krister Johnson did a really great-sounding improvisation in. The melodic aspects of 11 are, IMO, more compelling than those of 22, and the harmonies are plenty concordant if handled right.

> I did some scale-finding in 13 for the 2.5 subgroup back
> in the '90s (it's the optimal intonation for a certain
> scale if you want it to be proper). I don't buy the rest
> of that subgroup and 2.5 ain't much to write home
> about either.

You don't even buy 2.5.9.21? Seems like 9/5, 9/4, and 7/6 are some pretty worthwhile consonances to add to the mix. 4:5:9 is even a triad! Well, maybe you'll change your tune on 13 after I write an album in it. The 4:5:9:13 and 4:5:11:13 tetrads in 13-TET sound pretty decent to me. Better than 7-limit tetrads in 15-TET, for sure.

> > http://x31eq.com/cgi-bin/rt.cgi?ets=19&limit=7
> > http://x31eq.com/cgi-bin/rt.cgi?ets=22&limit=7
>
> Those aren't the errors of "19" and "22", but of
> ideally stretched versions.

According to Paul, they're proportional to the non-stretched versions and a valid way to compare. I'm going by "adjusted error". We had a big discussion about this on XA that you must have missed. Graham was even involved, though what he said didn't clarify much for me.

> Links to your soundcloud and bandcamp?

http://cityoftheasleep.bandcamp.com
http://soundcloud.com/cityoftheasleep

> It's my favorite of yours too, but in spite of the intonation,
> not because of it.

That doesn't make a whole lot of sense. For most of those tracks, there's very little that could be done to improve the intonation without totally changing the melody and harmony. Are you suggesting that what you like about it is the timbres and rhythms, as opposed to the pitch organizations?

-Igs

🔗cityoftheasleep <igliashon@...>

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

> Think Willaert, Vicentino, Gesualdo.

Hardly relevant in modern musical culture. Tastes have changed a lot since their day.

> > > barbershop Vs ______
> >
> > I dunno, choral music? Most choral music I've heard (and I've
> > heard a lot more of that than barbershop) did not sound remotely
> > like it was approaching JI.
>
> Really? I have the opposite impression (also having sung in
> amateur choirs for 2/3 of my life).

Maybe you can explain why the "chorus" effect is so named, then, if choirs tend toward exact intonation and beatless harmony? It's pretty rare in my experience to get 30 to 100 singers to all be perfectly on pitch. None of the choirs I saw at UCSC or SFSU could manage it, anyway, let alone the various church choirs I've seen or the "advanced" (i.e. "not completely tone-deaf") high school chorale I sang in.

> > > Partch/Groven/Harrison/Johnston Vs Carrillo/Haba/Wyschnegradsky
> >
> > I'd say it's a close call. The latter trio probably had more
> > of an audience in their heyday than the former group,
>
> Partch in his heyday outsold everyone else on both sides,
> so that can't be right.

Well, alright. But if we leave Partch out of it...I mean, the man skews all statistics, but I'd say it's mostly because of his charisma, uniqueness, nerve, and...theatricality, rather than the pleasantness of his music. I'd say a lot of his music is anything but "pleasant to listen to".

> > > Riley/Young/R.Rich/M.Harrison/Catlers Vs Ivor Darreg
> >
> > What are we comparing, the whole group on the left vs. the
> > one guy on the right? Why even compare, considering that Ivor
> > also played in JI and advocated 19, 22, and 31 more strongly
> > than any other tuning.
>
> I was being generous giving Ivor to the other side.
> I couldn't think of anyone else to put there.

What are these groups supposed to represent? What about Glenn Branca, anyway?

> > > S.J.Taylor/A.Dreyblatt/H.A.Stamm/Haverstick&Co Vs ______
> >
> > The Split-Notes crew, the Spectropol records crew (especially
> > including Dan Stearns), Zia?
>
> Ok, Split-Notes. Dan's stuff I think of more as sound painting
> than music in a particular intonation (ditto music concrete).
> I'd give Zia 50/50 for her emphasis on 19.

Have you heard the new album? 19 is well out-numbered by a combination of 10, 16, 17, and BP. I'd give her 30/70 at most.

> > > rest of JI Network Vs Facebook XA
> >
> > ...and the Boston Microtonal Society, AFMM, Nonoctave.com,
> > the Bohlen-Pierce and Armodue folks.
>
> I'd give AFMM 50/50. Thanks for filling in the others.

No prob.

> I'm counting accurate regular temperaments as "JI" here.

Not exactly fair. I don't think the JIists would allow that.

-Igs

🔗Mike Battaglia <battaglia01@...>

On Tue, Jan 3, 2012 at 3:23 PM, Carl Lumma <carl@...> wrote:
>
> > As a result, I now believe that although major chords can
> > be intoned more or less pleasantly by picking a tuning in which
> > they're close to something like 4:5:6, the major chord itself is
> > something independent of any particular intonation. The regular
> > mapping paradigm does not state what that is.
>
> Didn't I say as much when you first showed up here?
> Well, for the record, I've always believed this.

OK, then I'm going to skip the first two paragraphs where you seem to
disagree. If the vast amount of musical information is being
transmitted by things that aren't ratios, then that limits the scope
of the claims I'm comfortable making about the usefulness of regular
temperament theory in its current form, because there's clearly an
entire dimension of musical experience that it completely misses,
which has nothing to do with intonation and in to my ears is far more
important. I think that any top 10 list of temperaments is going to be
pretty hit or miss until we sort some of that out.

One can make the assumption that points in a tempered lattice will
correspond to interval categories with enough training. That's like
saying: here are some temperaments, we'll assume that intervals in it
will reach the magic information-bearing categorical level with enough
training, and until we know more about what's going on, we're going to
keep on moving. But I'm not entirely sure that's all there is to it.

-Mike

🔗Carl Lumma <carl@...>

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

> > There's more to music than intonation, jeez.
>
> Clearly. So how will a top-9 list of temperaments find us a
> guaranteed meantone successor, again?

I really don't understand your argument here. To date, JI or
near-JI seems to be necessary but not sufficient for making
music with mass appeal and enough subtlety to be fleshed out
by more than one generation of musicians. Atonal serialism,
music concrete, etc. were fads, and since then are niches
with devoted followers, yes. It is fine, yes.

> > Machine is nice but I see no reason not to just use 22.
>
> Let's not forget Orgone[7], which (on 2.7.9.11.15.17) is also
> just about optimal in 11-ED2...and has outstanding melodic
> properties. There was a big discussion about this on XA,
> courtesy of Andrew Heathwaite, that you may have missed.

I generally don't comment on XA because I generally don't
like what I hear, not because I'm not listening.

> The melodic aspects of 11 are, IMO, more compelling than
> those of 22, and the harmonies are plenty concordant if
> handled right.

You can have the 11-tone melodies in 22, too, and even
harmonize them with ratios of 3 and 5 if you dare!

> > I did some scale-finding in 13 for the 2.5 subgroup back
> > in the '90s (it's the optimal intonation for a certain
> > scale if you want it to be proper). I don't buy the rest
> > of that subgroup and 2.5 ain't much to write home
> > about either.
>
> You don't even buy 2.5.9.21?

I don't buy it in 13.

> > > http://x31eq.com/cgi-bin/rt.cgi?ets=19&limit=7
> > > http://x31eq.com/cgi-bin/rt.cgi?ets=22&limit=7
> >
> > Those aren't the errors of "19" and "22", but of
> > ideally stretched versions.
>
> According to Paul, they're proportional to the non-stretched
> versions and a valid way to compare.

Paul's wrong. See our offlist convo.

> > Links to your soundcloud and bandcamp?
>
> http://cityoftheasleep.bandcamp.com
> http://soundcloud.com/cityoftheasleep

Thanks!

> > It's my favorite of yours too, but in spite of the intonation,
> > not because of it.
>
> That doesn't make a whole lot of sense. For most of those
> tracks, there's very little that could be done to improve the
> intonation without totally changing the melody and harmony.
> Are you suggesting that what you like about it is the timbres
> and rhythms, as opposed to the pitch organizations?

Yes. The big problem is most microtonal music sounds
like crap regardless of intonation. Your stuff, on the
other hand, is pro (at least by the time MOAIL came out).
If the intonational systems you use inspire you and
you like them, please continue.

-Carl

🔗genewardsmith <genewardsmith@...>

🔗Carl Lumma <carl@...>

Igs wrote:

> > Think Willaert, Vicentino, Gesualdo.
>
> Hardly relevant in modern musical culture. Tastes have
> changed a lot since their day.

This was an all-time popularity contest. Indian music
is even older.

> Maybe you can explain why the "chorus" effect is so named,
> then, if choirs tend toward exact intonation and beatless
> harmony?

Chorus effect hardly alters just intonation, just as
meantone temperament hardly alters it. Most choirs I've
sang in (including one barbershop choir) achieved
superior average vertical 5-limit intonation to 12-ET.

> What are these groups supposed to represent?

All microtonal musicians.

> What about Glenn Branca, anyway?

> > I'd give Zia 50/50 for her emphasis on 19.
>
> Have you heard the new album? 19 is well out-numbered by
> a combination of 10, 16, 17, and BP. I'd give her 30/70
> at most.

No, but she's been making albums since the '80s.

> > I'm counting accurate regular temperaments as "JI" here.
>
> Not exactly fair. I don't think the JIists would allow that.

I don't care what they think - I'm interested in reality.

-Carl

🔗Mike Battaglia <battaglia01@...>

On Tue, Jan 3, 2012 at 5:59 PM, genewardsmith
<genewardsmith@...> wrote:
>
> >
> > At one point on XA chat you were telling me that not only does it make
> > sense, but that it made so much sense that it was obvious and not
> > novel, because Herman did it a few decades ago with his warped canon
> > page.
>
> So he did, which makes my point--what in hell are you doing, and why do you think there's some big secret out there you are uncovering?

When did I ever claim that I was the first to talk about categorical
perception, or that I'm uncovering some kind of secret? I don't think
I ever said that. Please be careful only to respond to things that
I've said, not assumptions about things that I didn't say.

This is what I just wrote to Carl:
> As a result, I now believe that although major chords can
> be intoned more or less pleasantly by picking a tuning in which
> they're close to something like 4:5:6, the major chord itself is
> something independent of any particular intonation. The regular
> mapping paradigm does not state what that is.

This is what I think. If you have some kind of problem with this
statement, you'd better say what it is. If you don't have a problem
with it, then please stop saying that it doesn't make sense.

-Mike

🔗Carl Lumma <carl@...>

Mike wrote:

>>> As a result, I now believe that although major chords can
>>> be intoned more or less pleasantly by picking a tuning in which
>>> they're close to something like 4:5:6, the major chord itself is
>>> something independent of any particular intonation. The regular
>>> mapping paradigm does not state what that is.
>>
>> Didn't I say as much when you first showed up here?
>> Well, for the record, I've always believed this.
>
> OK, then I'm going to skip the first two paragraphs where
> you seem to disagree.

If you thought I disagreed in those paragraphs you must
be reading what I write in a radically different manner
than intended.

> because there's clearly an entire dimension of musical
> experience that it completely misses, which has nothing to
> do with intonation and in to my ears is far more important.

You mean cultural conditioning and the resulting categorical
perception? The thing I always said was more important and
completely outside the realm of RMP? Sure sounds like it,
sine you're talking about diatonic interval classes.

> I think that any top 10 list of temperaments is going to be
> pretty hit or miss until we sort some of that out.

I think RMP is completely separate and not affected at all.

> One can make the assumption that points in a tempered lattice
> will correspond to interval categories with enough training.

One could, but I'm not sure why one would.

-Carl

🔗genewardsmith <genewardsmith@...>

🔗Carl Lumma <carl@...>

🔗genewardsmith <genewardsmith@...>

🔗Mike Battaglia <battaglia01@...>

On Tue, Jan 3, 2012 at 6:10 PM, Carl Lumma <carl@...> wrote:
>
> Mike wrote:
> > > So he did, which makes my point--what in hell are you doing,
> > > and why do you think there's some big secret out there you
> > > are uncovering?
> >
> > When did I ever claim that I was the first to talk about
> > categorical perception, or that I'm uncovering some kind of
> > secret?
>
> I dunno, but FWIW I have the same impression of what you've
> been saying as Gene. -Carl

No, I don't claim to be the first to figure this out. Maybe I should
say straight up at this point that you and Paul were right, and I was
wrong, and I've come around. I've since read every single post on
tuning and tuning-math with the word "categorical" on it, including
every post I could find on the Mills list (some in which you referred
to Paul as "Mr. Erlich"), and it's clear that you guys have had a
wildly different view of things than I thought you all did a year ago.

I've talked to Paul on the phone at length about this, and his
position is that he has no idea how this aspect of it works or what's
going on, but he knows that whatever categories are, it is definitely
true that ratios are important to intone them, and the theory on here
at least covers that piece of it and does so very well. You sometimes
seem to have a different view of things than Paul does, but I'm not
sure if you claim to have a deeper understanding than that.

So from this perspective, top ten temperament lists are basically top
ten intonation lists. I don't know if they're "top ten alternative
musical system lists," because the only thing they take into account
is the intonation.

-Mike

🔗Mike Battaglia <battaglia01@...>

On Tue, Jan 3, 2012 at 6:13 PM, genewardsmith
<genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > This is what I think. If you have some kind of problem with this
> > statement, you'd better say what it is. If you don't have a problem
> > with it, then please stop saying that it doesn't make sense.
>
> I said it made no sense TO ME. If you can't handle that kind of feedback, why do you keep posting listening tests?

I can handle any sort of feedback, but I don't understand what,
exactly, doesn't make sense to you. Just now, a few minutes ago, you
said that it made sense and was obvious and that you knew it a decade
ago from Herman's page. But now you're saying it doesn't make sense
again.

Can you please tell me which of the following statements you disagree
with or feel is nonsensical?

1) Major chords can be intoned more pleasantly if the tuning sets them
closer to something like 4:5:6, or perhaps as a second-best choice
14:18:21, but in general less pleasantly if they're in a tuning where
the dyads are further from a nice JI ratio.
2) Since a major chord can be intoned multiple ways, this implies that
there is something which a "major chord" is which is independent of
its intonation, at least for some listeners.
3) The regular mapping paradigm does not say what it is, or deal at
all with that aspect of music.

-Mike

🔗cityoftheasleep <igliashon@...>

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

> I really don't understand your argument here. To date, JI or
> near-JI seems to be necessary but not sufficient for making
> music with mass appeal and enough subtlety to be fleshed out
> by more than one generation of musicians. Atonal serialism,
> music concrete, etc. were fads, and since then are niches
> with devoted followers, yes. It is fine, yes.

Nearness to JI is important, sure, but have we any reason to believe it is important beyond a certain threshold? Have we any reason to believe that certain intervals within the broad catalog of (say) 13-limit JI are specifically necessary? How do we know whether we should be looking for a meantone successor in the 5-limit, or the 7-limit, or the 11-limit, or the 13-limit, or within any of the myriad subgroups thereof?

> I generally don't comment on XA because I generally don't
> like what I hear, not because I'm not listening.

LOL.

> > The melodic aspects of 11 are, IMO, more compelling than
> > those of 22, and the harmonies are plenty concordant if
> > handled right.
>
> You can have the 11-tone melodies in 22, too, and even
> harmonize them with ratios of 3 and 5 if you dare!

Sure, but an 11-tone guitar is waaaaay easier to play than a 22-tone one. And you can even make a halberstadt-style keyboard for 11-ET, too.

> > You don't even buy 2.5.9.21?
>
> I don't buy it in 13.

Why not? Oh, and listen to this when you have a moment to mellow out:
http://soundcloud.com/cityoftheasleep/mandrake-tea

> > According to Paul, they're proportional to the non-stretched
> > versions and a valid way to compare.
>
> Paul's wrong. See our offlist convo.

Maybe you had better tell him that. I can't seem to locate that conversation at the moment. So,you can tell me why he's wrong, or I can go on believing him. Mike tried to come up with an error metric for POTE error, but everyone told him he was doing it wrong and IIRC he conceded that he was, and we went back to using the adjusted error from Graham's app.

> > Are you suggesting that what you like about it is the timbres
> > and rhythms, as opposed to the pitch organizations?
>
> Yes.

That's a shame. I might as well have kept writing in 12, then.

> The big problem is most microtonal music sounds
> like crap regardless of intonation. Your stuff, on the
> other hand, is pro (at least by the time MOAIL came out).
> If the intonational systems you use inspire you and
> you like them, please continue.

Life inspires me. The intonational systems I use should ideally just be tools to express that inspiration, not the source of it. Seems what you're saying is that the intonational choices I make are a detriment to the music, rather than a boon, which I really don't understand. So I could take all those songs, eliminate or reduce all vertical structures and movements, and you'd still like them? That makes me feel like crap about choosing to work microtonally, about putting as much care as I do into choosing notes and harmonies.

-Igs

🔗Carl Lumma <carl@...>

Mike Battaglia <battaglia01@...> wrote:

> > > > So he did, which makes my point--what in hell are you doing,
> > > > and why do you think there's some big secret out there you
> > > > are uncovering?
> > >
> > > When did I ever claim that I was the first to talk about
> > > categorical perception, or that I'm uncovering some kind of
> > > secret?
> >
> > I dunno, but FWIW I have the same impression of what you've
> > been saying as Gene. -Carl
>
> No, I don't claim to be the first to figure this out. Maybe
> I should say straight up at this point that you and Paul were
> right, and I was wrong, and I've come around. I've since read
> every single post on tuning and tuning-math with the word
> "categorical" on it, including every post I could find on
> the Mills list (some in which you referred to Paul as
> "Mr. Erlich"), and it's clear that you guys have had a
> wildly different view of things than I thought you all did
> a year ago.

If you go back to just when you joined in 2008 or thereabouts,
you were interested and asking about this stuff from the
start. And my reply was that it's simply cultural conditioning,
that no deeper theory of it is possible, that ratios have
nothing to do with it, that RMP can't say anything about it,
and that the only relevant intonation things I know of are
things like the Miller limit and Rothenberg equivalence.
The latter MAY restrict the number different interval systems
that could be culturally conditioned (say, in all alternative
universes).

> So from this perspective, top ten temperament lists are
> basically top ten intonation lists. I don't know if they're
> "top ten alternative musical system lists," because the
> only thing they take into account is the intonation.

Yes. They don't say anything about rhythm, timbre, lyrics,
cover art, clothing styles, or any other part of music.
They also don't cover things like "set and setting", if
like Frank Herbert, we liken music to a psychoactive drug.

"Set" would be cultural conditioning, which is just a
historical accident, and there's nothing any musician
(even drummers) can do about it. "Setting" would be like
how some Varese piece turns off most listeners if they
listen to a recording, but they might not mind it in the
soundtrack to a movie, and they might really like it if
they sit in the concert hall across from the brass section
with their friends.

-Carl

🔗Mike Battaglia <battaglia01@...>

On Tue, Jan 3, 2012 at 6:05 PM, Carl Lumma <carl@...> wrote:
>
> Mike wrote:
>
> >> Didn't I say as much when you first showed up here?
> >> Well, for the record, I've always believed this.
> >
> > OK, then I'm going to skip the first two paragraphs where
> > you seem to disagree.
>
> If you thought I disagreed in those paragraphs you must
> be reading what I write in a radically different manner
> than intended.

It seemed like you knew all along what I was saying but were giving me
a hard time because I couldn't find the perfect, scientifically
precise way to phrase it.

> > because there's clearly an entire dimension of musical
> > experience that it completely misses, which has nothing to
> > do with intonation and in to my ears is far more important.
>
> You mean cultural conditioning and the resulting categorical
> perception? The thing I always said was more important and
> completely outside the realm of RMP? Sure sounds like it,
> sine you're talking about diatonic interval classes.

Yes, but for trained musicians it can sometimes be more like chromatic
interval classes, which I see Paul has also noted several times in the
archives.

I wasn't aware that you always said it was -more- important. Your
present discussion with Igs doesn't give me that impression. It would
seem that Igs is saying that tuning systems which are higher in error
can be magical for reasons other than their intonation, and you're
saying that intonation is the most important factor. But, yes, you've
said it's important for a while now.

> > I think that any top 10 list of temperaments is going to be
> > pretty hit or miss until we sort some of that out.
>
> I think RMP is completely separate and not affected at all.

RMP is, by your own admission above, handling the aspect of music
which is not the most important. It's apparently not even the most
important thing about music that is played in meantone temperament. So
how will RMP lead us to find a meantone-killer? It might just lead us
to find temperaments that approximate JI ratios, but which lack the
same components that make the magic happen for this other, more
important aspect.

-Mike

🔗genewardsmith <genewardsmith@...>

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

> > I said it made no sense TO ME. If you can't handle that kind of feedback, why do you keep posting listening tests?
>
> I can handle any sort of feedback, but I don't understand what,
> exactly, doesn't make sense to you.

If you morphed a face of Newt Gingrich into a face of Lady Gaga, at some point I would no longer be able to recognize the Newtster, and at some later point I would no longer even be able to place gender. Is this what you mean by "categorical perception"? What, pray tell, is the big deal?

> 1) Major chords can be intoned more pleasantly if the tuning sets them
> closer to something like 4:5:6, or perhaps as a second-best choice
> 14:18:21, but in general less pleasantly if they're in a tuning where
> the dyads are further from a nice JI ratio.

Of course.

> 2) Since a major chord can be intoned multiple ways, this implies that
> there is something which a "major chord" is which is independent of
> its intonation, at least for some listeners.

It does? Since Newt Gingrich can be depicted in various ways, is there a "Newt" which is independent of how distorted the face actually is?

> 3) The regular mapping paradigm does not say what it is, or deal at
> all with that aspect of music.

Convice me it IS an aspect and maybe we can get somewhere.

🔗Carl Lumma <carl@...>

Igs wrote:
> How do we know whether we should be looking for a meantone
> successor in the 5-limit, or the 7-limit, or the 11-limit,
> or the 13-limit, or within any of the myriad subgroups thereof?

We don't, that's why we make lists at each limit. :)

> > > You don't even buy 2.5.9.21?
> >
> > I don't buy it in 13.
>
> Why not? Oh, and listen to this when you have a moment to
> mellow out:
> http://soundcloud.com/cityoftheasleep/mandrake-tea

The harmonies here make me want to run out of the room
screaming. If I relax into it enough I stop noticing it,
kind of like how you stop noticing the dust all over you
after a couple days on the playa.

When I was in Portland in June I played one of your
singles for a guitarist friend of mine. He said he
thought it sounded out of tune, not nice like the 22-tone
choob he'd played some months earlier. I wish I could
remember which piece it was.

> > > According to Paul, they're proportional to the non-stretched
> > > versions and a valid way to compare.
> >
> > Paul's wrong. See our offlist convo.
>
> Maybe you had better tell him that. I can't seem to locate
> that conversation at the moment. So,you can tell me why he's
> wrong, or I can go on believing him. Mike tried to come up
> with an error metric for POTE error, but everyone told him he
> was doing it wrong and IIRC he conceded that he was, and we
> went back to using the adjusted error from Graham's app.

If you're using max error, the optimum error is determined
by the distance between the sharpest and flattest basis
element (prime or subgroup element). Stretching the octave
centers this gap on the zero line. This can change it
arbitrarily for different EDOs depending on how it happened
to be centered before stretching. For RMS (TE) error the
reason why it's wrong is slightly more complicated. The
TOP-max and TOP-RMS 7-limit errors are both higher for
19-ET than for 22-ET.

> That's a shame. I might as well have kept writing in 12, then.

I like the weirdness of the melodies. It's refreshing,
and it more than pays for the blackboard-scratching
harmonies. But systems with more accurate harmony have
weird melodic potentials too...

> Life inspires me.

Hooray! The only thing I can suggest is to experiment
with new intonational systems about 15% of the time.
I think you've done that. From our past discussions, it
doesn't seem like you're really attracted to the sound
of JI, so the systems you choose are probably right
for you. That said, if you've never tried writing 3-part
counterpoint in meantone or porcupine or pajara, you
might enjoy the exercise.

-Carl

🔗Herman Miller <hmiller@...>

🔗Mike Battaglia <battaglia01@...>

On Tue, Jan 3, 2012 at 6:56 PM, Carl Lumma <carl@...> wrote:
>
> Mike wrote:
> > What, exactly is being culturally conditioned?
>
> I was going on what you said: melodic and harmonic intervals
> based on diatonic interval classes (which correspond to
> 12-ET chromatic interval classes, more or less).

Right, but there's a million things going on here.

First, there's the establishment of this perceptual dimension of the
scale as a repeating thing along the pitch continuum. Then, there's
the notion that intervals mark off distances along this continuum like
a ruler. And then there's some deep sort of pattern recognition that
takes place in which one figures out properties like Rothenberg
propriety and other things that we probably aren't aware of. That
establishes the existence of categories at a bare minimum.

Then there's the habitual way in which those categories are used: the
way one combination typically "resolves" into another, the way certain
combinations are played more than others, etc. Then there's the
connections we make, like that a major third is two whole steps, and
each whole step is two perfect fifths. Then there's intonational
things too, like you being aware that playing a certain dyad in a low
register will sound good or crappy, etc. Then there might be scalar
things as well, like where the "rare intervals" are in relation to the
category you're thinking of in the most common modes, etc. Then there
are the ways that categories subdivide into other categories. There
are definitely other things we're not thinking of. There's a million
things, in general.

The whole lump sum of what I wrote above can be thought of as cultural
conditioning. What's the most important part? It doesn't, after the
last year of owning an AXiS and playing with as many tunings as
possible, seem to be the intonation. At any rate, everything I wrote
above is something that can be modeled, so I don't think that theory
will ultimately fail for this particular aspect of musical perception.
And I've learned, as I tackle new tunings, to tease apart some of
these things and associate them differently, and that has made all the
difference.

> > You say it like it
> > isn't a truly magical thing that the happiness of major and the
> > sadness of minor don't seem to have anything at all to do with
> > the intonation of those chords.
>
> I still think the happiness thing traces back to the
> psychoacoustic properties of the chords. The fact that it
> was reflected in an immense body of music you were born
> into and now carries over as you change the intonation
> shouldn't be surprising! If it can leak from a chord into
> a scale into chord progressions and whole songs, why can't
> it leak back? Have a friend try the Ramachandran mirror
> trick on you sometime and see what you think!

I think that's one possibility that's worth considering. But things
like the 16-EDO example I gave, which you should try, really make me
wonder if that's all there is to it. For example, to me, a stack of
450 cent intervals is much less dissonant than a stack of 900 cent
intervals. And to my ears, a stack of POTE sensi intervals is much
less dissonant than a stack of POTE orwell intervals, because the
latter is really dark and sounds like some kind of ultra-diminished
chord, and the former sounds like wind and space and stuff. I don't
see any psychoacoustic reason for that.

I do think that categorical perception is very similar to that sort of
thing, except in my experience the thing you wrote above - that the
sound of minor chords is sad and major is happy because of
psychoacoustics - is as fragile as the hand you see in the mirror.

> > RMP is, by your own admission above, handling the aspect of music
> > which is not the most important. It's apparently not even the most
> > important thing about music that is played in meantone temperament.
> > So how will RMP lead us to find a meantone-killer?
>
> Because "meantone" has to do (is completely defined by)
> precisely all those other less-important things!

Yeah, but that's a much more limited definition of meantone-killer
than people really care about. At that point, actually, why don't we
just use POTE meantone? We're not really used to meantone, but rather
12-EDO, and POTE meantone definitely improves on that.

-Mike

🔗Mike Battaglia <battaglia01@...>

On Tue, Jan 3, 2012 at 6:54 PM, genewardsmith
<genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > > I said it made no sense TO ME. If you can't handle that kind of feedback, why do you keep posting listening tests?
> >
> > I can handle any sort of feedback, but I don't understand what,
> > exactly, doesn't make sense to you.
>
> If you morphed a face of Newt Gingrich into a face of Lady Gaga, at some point I would no longer be able to recognize the Newtster, and at some later point I would no longer even be able to place gender. Is this what you mean by "categorical perception"? What, pray tell, is the big deal?

The big deal is that your "Newt Gingrich" and "Lady Gaga" don't, for
me, correspond to ratios, but rather to steps out of a chromatic scale
backdrop in my head. The fact that I would have to learn to create a
new backdrop which is centered around ratios means that there isn't
one that's just there by default. This seems to be somewhat common
among musicians with a lot of 12-EDO training.

> > 2) Since a major chord can be intoned multiple ways, this implies that
> > there is something which a "major chord" is which is independent of
> > its intonation, at least for some listeners.
>
> It does? Since Newt Gingrich can be depicted in various ways, is there a "Newt" which is independent of how distorted the face actually is?

In nature, there are certain fundamental shapes: squares, circles,
triangles, etc. Every shape, of course, has its own identity: circles
are definitely different from squares, which are different from
triangles, etc. If you now come up with a few depictions of Newt
Gingrich in which his head is square shaped, or circular, or
triangular, or 5/4 shaped, or 9/7 shaped, will there still be some
Newt Gingrichness to it that communicates useful information
nonetheless, even if it's more pleasant to look at perfectly
non-distorted pictures of him?

-Mike

🔗Mike Battaglia <battaglia01@...>

On Tue, Jan 3, 2012 at 7:26 PM, Herman Miller <hmiller@...> wrote:
>
> On 1/2/2012 3:17 PM, Mike Battaglia wrote:
>
> > Meantone doesn't allow us to play music in which every chord sounds
> > like ECT for your auditory system. Moving throughout the MODMOS's of
> > 13-limit tetracot, tuned to 34-EDO, can do the trick with that though.
> >
> > Speaking of which, I hope tetracot made some of these Best
> > Temperaments Ever lists...
>
> It's in Paul's original Middle Path list. In my ranking scheme it's a
> grade B temperament, which is still pretty good (better than mavila,
> diminished, negri, injera etc. which are grade C). A 13-limit version,
> 7&27e [<1 1 1 4 2 4|, <0 4 9 -8 10 -2|] actually makes it to the grade A
> list, between 7&19 flattone and 7&24 mohajira, as does monkey 7&34 [<1 1
> 1 5 2 4|, <0 4 9 -15 10 -2|] (which is a more accurate but more complex
> tetracot).

The 7&27e one is the one I like, which is also 7&34d. I think that one
should be 13-limit tetracot. in comparison, monkey is 7&34p, or just
7&34 if you prefer. The main difference between the two turns up in
the MODMOS's of tetracot[7]. For example, in 7&34d, the "diminished
seventh" is 7/4, whereas 7/4 is the "double diminished seventh" in
monkey. I'm using "diminished" here to mean the smaller size of 7th
that has been flattened by a chroma.

-Mike

🔗cityoftheasleep <igliashon@...>

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

> We don't, that's why we make lists at each limit. :)

I'm hoping that subgroups will continue to gain attention. But in any case, how will you know which list contains the "guaranteed meantone successor", assuming one is ever actually generated? There are a lot of subgroups of the 13-odd limit....

> The harmonies here make me want to run out of the room
> screaming. If I relax into it enough I stop noticing it,
> kind of like how you stop noticing the dust all over you
> after a couple days on the playa.

That's very interesting. At first blush you want to run out of the room screaming, but then you can relax into it. How do you suppose that works? I'll admit there are some wonky chords--the 738-cent intervals in particular--but I find it approximately as jarring as any of, say, Dante Rosati's guitar pieces, or anything written in Orwell[9]. Aside from those 738-cent intervals, I do not experience much if any discordance in this piece, unlike (say) Mike's Mavila retunings. So I'm kind of surprised by your reaction.

> When I was in Portland in June I played one of your
> singles for a guitarist friend of mine. He said he
> thought it sounded out of tune, not nice like the 22-tone
> choob he'd played some months earlier. I wish I could
> remember which piece it was.

Well, I can top that. I demonstrated 19-EDO to a guitarist friend of fine, and he thought it sounded out of tune...and then I demonstrated 16-EDO, and he thought it sounded normal as all get-out. He couldn't see what the big deal was, really. After I let him mess around on both guitars, he said he like 16-EDO the best.

> For RMS (TE) error the reason why it's wrong is slightly more complicated. The
> TOP-max and TOP-RMS 7-limit errors are both higher for
> 19-ET than for 22-ET.

How are you doing the error calculations? And is there a way to make Graham's app spit out the pure-octave error calculations? I'm gonna have to re-do all those damn subgroup calculations if what you say is correct.

> > That's a shame. I might as well have kept writing in 12, then.
>
> I like the weirdness of the melodies. It's refreshing,
> and it more than pays for the blackboard-scratching
> harmonies. But systems with more accurate harmony have
> weird melodic potentials too...

It's not accuracy my music is lacking, per se. It's accuracy in the 3- or 5-limit. Typically I use systems where harmonics 7, 11, and/or 13 are tuned quite accurate (see 16-ED2, 13-ED2, 20-ED2/10-ED2, 17-ED2; or 23-ED2, which doesn't tune hardly any harmonics accurately but does tune lots of 7, 11, and 13-limit intervals accurately--9/4, 7/6, 7/5, 6/5, 5/3, 11/7, 11/6, 11/5, 13/6, 13/4, etc.). I suspect you just have a coarser ear than I for discordance--a high "s" as far as dyadic HE is concerned.

> Hooray! The only thing I can suggest is to experiment
> with new intonational systems about 15% of the time.
> I think you've done that. From our past discussions, it
> doesn't seem like you're really attracted to the sound
> of JI, so the systems you choose are probably right
> for you. That said, if you've never tried writing 3-part
> counterpoint in meantone or porcupine or pajara, you
> might enjoy the exercise.

Meantone (19-EDO):
http://soundcloud.com/cityoftheasleep/stagnant-deity

Porcupine[8] (in 22-EDO):
http://soundcloud.com/cityoftheasleep/porcupiano

Superpyth[12] (not stingy with 5-limit harmonies):
http://soundcloud.com/cityoftheasleep/superpythwaltz22

Injera[12] (empasizing as many 7-limit tetrads as I could figure out how to finger on piano):
http://soundcloud.com/cityoftheasleep/two-pairs-of-socks

A 5-limit 8-note diatonic-like subset of Helmholtz[12] in 29-EDO:
http://soundcloud.com/cityoftheasleep/howling-of-the-holy

Augene[12] in 27-EDO:
http://soundcloud.com/cityoftheasleep/sad-like-winter-trees

Happy now?

I still think all of these sound boring and dull compared to my 10-EDO shred-fests:
http://soundcloud.com/cityoftheasleep/dirty-hands
http://soundcloud.com/cityoftheasleep/anglebath

-Igs

🔗genewardsmith <genewardsmith@...>

🔗cityoftheasleep <igliashon@...>

🔗Mike Battaglia <battaglia01@...>

🔗Carl Lumma <carl@...>

Igs wrote:

> > For RMS (TE) error the reason why it's wrong is slightly more
> > complicated. The TOP-max and TOP-RMS 7-limit errors are both
> > higher for 19-ET than for 22-ET.
>
> How are you doing the error calculations?

With a computer, of course.

> And is there a way to make Graham's app spit out the pure-
> octave error calculations?

Not that I know of.

> Meantone (19-EDO):
> http://soundcloud.com/cityoftheasleep/stagnant-deity

Amazing... that you are being allowed to trade this for
a 13-ET axe without having to pay some sort of fine.

> Porcupine[8] (in 22-EDO):
> http://soundcloud.com/cityoftheasleep/porcupiano

Wow, that sounds great!

> Superpyth[12] (not stingy with 5-limit harmonies):
> http://soundcloud.com/cityoftheasleep/superpythwaltz22

I'm not a big fan of superpyth, but it's miles better
than most of the stuff you've been talking about lately.

> Injera[12] (empasizing as many 7-limit tetrads as I could
> figure out how to finger on piano):
> http://soundcloud.com/cityoftheasleep/two-pairs-of-socks

Marvelous!

> A 5-limit 8-note diatonic-like subset of Helmholtz[12]
> in 29-EDO:
> http://soundcloud.com/cityoftheasleep/howling-of-the-holy

Hot damn!

> Augene[12] in 27-EDO:
> http://soundcloud.com/cityoftheasleep/sad-like-winter-trees

I'm in love.

> Happy now?

None of these have any 3-part counterpoint, but clearly
you know what you're doing. You're also the only artist
I know that cane make reverb and delay sound epic (I usually
don't like them).

> I still think all of these sound boring and dull compared
> to my 10-EDO shred-fests:
> http://soundcloud.com/cityoftheasleep/dirty-hands

That's good fun - I've got no beef with it.

> http://soundcloud.com/cityoftheasleep/anglebath

I like this even better than dirty hands. Both are very
different pieces to the previous ones above. Try 10-ET
without the distortion and with some closer harmony and
its warts would start to show. Still, at its worst it's
not up to the kind of nihilism possible in 13.

-Carl

🔗Mike Battaglia <battaglia01@...>

🔗Carl Lumma <carl@...>

🔗genewardsmith <genewardsmith@...>

🔗cityoftheasleep <igliashon@...>

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

> > How are you doing the error calculations?
>
> With a computer, of course.

Do you have some sort of handy spreadsheet I could use, or something?

> > And is there a way to make Graham's app spit out the pure-
> > octave error calculations?
>
> Not that I know of.

Darn.

> > Meantone (19-EDO):
> > http://soundcloud.com/cityoftheasleep/stagnant-deity
>
> Amazing... that you are being allowed to trade this for
> a 13-ET axe without having to pay some sort of fine.

LOL. What's more amazing is that I thought at one point paying an extra $600 to make triads beat a bit less was a worthwhile investment.

> > Porcupine[8] (in 22-EDO):
> > http://soundcloud.com/cityoftheasleep/porcupiano
>
> Wow, that sounds great!

One of the better-sounding porcupine pieces I've written, but still sounds like seasick meantone to my ears.

> > Superpyth[12] (not stingy with 5-limit harmonies):
> > http://soundcloud.com/cityoftheasleep/superpythwaltz22
>
> I'm not a big fan of superpyth, but it's miles better
> than most of the stuff you've been talking about lately.

I started to really like some things about superpyth after writing this (it was written to compare with flattone[12], see "Between the Branes" on my soundcloud for that piece). One thing I don't think I'll ever like about it is the small melodic steps.

> > Injera[12] (empasizing as many 7-limit tetrads as I could
> > figure out how to finger on piano):
> > http://soundcloud.com/cityoftheasleep/two-pairs-of-socks
>
> Marvelous!

See the 12-TET version for comparison. The difference between the two in concordance is significant, but not significant enough that it changes the feel of the piece.

> > A 5-limit 8-note diatonic-like subset of Helmholtz[12]
> > in 29-EDO:
> > http://soundcloud.com/cityoftheasleep/howling-of-the-holy
>
> Hot damn!

So the 13-EDO harmonies have you running screaming from the room, but you really enjoy this one? Now I'm really stumped. I called this one "howling of the holy" because there is some gnarly beating in the 3rds and wolves (among other intervals), and a lot of the piece sounds really discordant to me, made even more exaggerated by the extremely-pure fifths. You can't really "relax into it" because the contrast is so sharp.

> > Augene[12] in 27-EDO:
> > http://soundcloud.com/cityoftheasleep/sad-like-winter-trees
>
> I'm in love.

This one I really like. If I was going to pick one higher-cardinality ET for near-JI temperaments, I'd probably pick 27. I tried farting around in sensi[8] and some of those MODMOS's of tetracot[7] and they're awesome.

> > Happy now?
>
> None of these have any 3-part counterpoint, but clearly
> you know what you're doing. You're also the only artist
> I know that cane make reverb and delay sound epic (I usually
> don't like them).

I don't know how to write counterpoint, on account of not being classically-trained in any way, shape, or form. Also, you don't like reverb and delay? Oh man. Our tastes are even more different than I thought.

> > I still think all of these sound boring and dull compared
> > to my 10-EDO shred-fests:
> > http://soundcloud.com/cityoftheasleep/dirty-hands
>
> That's good fun - I've got no beef with it.
>
> > http://soundcloud.com/cityoftheasleep/anglebath
>
> I like this even better than dirty hands. Both are very
> different pieces to the previous ones above. Try 10-ET
> without the distortion and with some closer harmony and
> its warts would start to show. Still, at its worst it's
> not up to the kind of nihilism possible in 13.

Why does the distortion smooth over the warts of 10-TET? It exaggerates the warts of 12-TET, creating some nasty combination tones and amplifying the beating between the higher harmonics. Could it be that distortion helps 10-TET because it has near-Just representations of the 7th, 13th, and 15th harmonics? And this means the combination tones actually improve the concordance, and the increased power of the higher harmonics makes their locking-in more audible?

-Igs

🔗Mike Battaglia <battaglia01@...>

🔗Chris Vaisvil <chrisvaisvil@...>

Igs, with all due respect writing 3 part counterpoint doesn't require
classical training.

There are a number of ways to look at the issue in the context of popular
music.

1. Bands like Black Sabbath and Led Zeppelin certainly had many memorable
moments where bass, guitar, and voice were all playing different but
interlocking melodies. Heck. What about Jethro Tull.
2. If you elevate drums to the level of Peter Thoegersen (a full fledged
instrument not a time keeper) there is yet another avenue.

If you want to learn how to write fugues, probably college or at least
composition lessons are a good idea. Otherwise the basic requirement is
simply 3 independent melodies combining to form harmony.
I was messing with that with NO clue of theory when I figured out how to
use two cassette decks to overdub.
Countless bands have done it in one fashion or another. Is it florid
Renaissance counterpoint, pretty much no, but it still IS counterpoint.
Contrapuntal writing is extremely ingrained in western music tradition.
Its been diluted in many cases but it still is there.

And lets not forget Jazz - where the counterpoint is being made up on the
spot.

Chris

On Wed, Jan 4, 2012 at 1:21 PM, cityoftheasleep <igliashon@...>wrote:

> **
>
>
>
> >
> > None of these have any 3-part counterpoint, but clearly
> > you know what you're doing. You're also the only artist
> > I know that cane make reverb and delay sound epic (I usually
> > don't like them).
>
> I don't know how to write counterpoint, on account of not being
> classically-trained in any way, shape, or form. Also, you don't like reverb
> and delay? Oh man. Our tastes are even more different than I thought.
>
>
>

🔗cityoftheasleep <igliashon@...>

🔗Mike Battaglia <battaglia01@...>

On Wed, Jan 4, 2012 at 9:46 PM, cityoftheasleep <igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
> >
> > 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.

If what you want are rules from the usual common practice freshman 8
AM theory class, those are

1) no voices moving in parallel fifth
2) no voices moving in parallel octaves
3) no voice crossing, e.g. no making the tenor lower than the bass and
what have you
4) in 4 voices with triadic harmony, doubling the root is preferred,
the fifth second, the third rarely

Those are the basic rules, sometimes with additional nuances and
exceptions and un-exceptions, and so on. It's not immediately clear to
me how to generalize them to other systems (no parallel 3/2's? no
parallel generators? what?). Sometimes you end up in various
conundrums and you can't obey all the rules at once, so you do the
best you can, and sometimes teachers write a lot about how to avoid
those pitfalls down the road.

I think it's best to take the whole thing with a grain of salt, but
FWIW you do get, more or less, the stereotypical classical
counterpoint effect by avoiding parallel fifths and octaves, not
having voices cross, and doubling roots and fifths more than thirds.
So it might be good to at least grab those few things as guidelines
without being too OCD about it. You are, of course, always free to
leave that style and start mashing on parallel fifths if you want.

-Mike

🔗genewardsmith <genewardsmith@...>

🔗Mike Battaglia <battaglia01@...>

On Wed, Jan 4, 2012 at 10:12 PM, genewardsmith
<genewardsmith@...> wrote:
>
> Rule 3 isn't a rule; in fact breaking it is very common with Renaissance music, as it allows for the polyphonic lines to be more independent and avoids sounding like a chorale. Gradus ad Parnassum, the go-to place for these rules, allowed voice crossing. Are you going to argue with Fux?? And voice crossing marched on after the Renaissance, though less pervasively.
>
> My advice is to ignore Rule 3.

I knew someone was going to take exception to whatever list I came up
with. I was actually expecting people to say that I hadn't included
enough rules, though, and that I should have mentioned stuff about
direct fifths, leading tones, second inversion triads, etc as well. I
left those out because I either don't care about them, because they're
obvious and intuitive and don't need any hypervigilance, or because I
don't know how they generalize to other microtonal systems.

The list I gave was from when I took the AP theory test, FWIW. I don't
remember what the "big picture" is anymore. I remember hearing at one
point that Fux was based on Palestrina's style of polyphony, whereas
the stuff we learned for the AP test was based on Bach's style of
specifically chorale writing. That might not be true though.

Anyway, there is a certain musical effect that you can get if you keep
voice-crossing to a minimum, and Igs should be aware of it. But like
all of this stuff, all of these rules can become OCD little prisons if
you're not careful.

One rule I should have listed but forgot, though, is not to have
voices that are separated by more than an octave except for the bass
and tenor. What say Fux to that?

-Mike

🔗genewardsmith <genewardsmith@...>

🔗Chris Vaisvil <chrisvaisvil@...>

I hold up this fact - if you have parallel anything you don't have
independent melody and are on the path to homophony
http://en.wikipedia.org/wiki/Homophony

So, its a given that true independent melodies would not do 1) or 2) for
any length of time.
Its the 21st century so the rest of the rules can be ignored if so desired.

Most neo-classical composers to ignore at will any and all of those rules.

The essence is the idea of independent melodies forming harmony.
Not even functional harmony if so desired.

On Wed, Jan 4, 2012 at 9:58 PM, Mike Battaglia <battaglia01@...>wrote:

> **
>
>
> 1) no voices moving in parallel fifth
> 2) no voices moving in parallel octaves
> 3) no voice crossing, e.g. no making the tenor lower than the bass and
> what have you
> 4) in 4 voices with triadic harmony, doubling the root is preferred,
> the fifth second, the third rarely
>
> Those are the basic rules, sometimes with additional nuances and
> exceptions and un-exceptions, and so on. It's not immediately clear to
> me how to generalize them to other systems (no parallel 3/2's? no
> parallel generators? what?). Sometimes you end up in various
> conundrums and you can't obey all the rules at once, so you do the
> best you can, and sometimes teachers write a lot about how to avoid
> those pitfalls down the road.
>
> I think it's best to take the whole thing with a grain of salt, but
> FWIW you do get, more or less, the stereotypical classical
> counterpoint effect by avoiding parallel fifths and octaves, not
> having voices cross, and doubling roots and fifths more than thirds.
> So it might be good to at least grab those few things as guidelines
> without being too OCD about it. You are, of course, always free to
> leave that style and start mashing on parallel fifths if you want.
>
> -Mike
>
>
>

🔗Chris Vaisvil <chrisvaisvil@...>

Correction - I was moving too fast - I mean this
" Initially, in Ancient Greece <http://en.wikipedia.org/wiki/Ancient_Greece>,
homophony indicated music in which a single melody is performed by two or
more voices in unison <http://en.wikipedia.org/wiki/Unison> or
octaves<http://en.wikipedia.org/wiki/Octaves>,
i.e. monophony with multiple voices."

On Wed, Jan 4, 2012 at 11:07 PM, Chris Vaisvil <chrisvaisvil@...>wrote:

> I hold up this fact - if you have parallel anything you don't have
> independent melody and are on the path to homophony
> http://en.wikipedia.org/wiki/Homophony
>
> So, its a given that true independent melodies would not do 1) or 2) for
> any length of time.
> Its the 21st century so the rest of the rules can be ignored if so
> desired.
>
> Most neo-classical composers to ignore at will any and all of those rules.
>
> The essence is the idea of independent melodies forming harmony.
> Not even functional harmony if so desired.
>
>
> On Wed, Jan 4, 2012 at 9:58 PM, Mike Battaglia <battaglia01@...>wrote:
>
>> **
>>
>>
>> 1) no voices moving in parallel fifth
>> 2) no voices moving in parallel octaves
>> 3) no voice crossing, e.g. no making the tenor lower than the bass and
>> what have you
>> 4) in 4 voices with triadic harmony, doubling the root is preferred,
>> the fifth second, the third rarely
>>
>> Those are the basic rules, sometimes with additional nuances and
>> exceptions and un-exceptions, and so on. It's not immediately clear to
>> me how to generalize them to other systems (no parallel 3/2's? no
>> parallel generators? what?). Sometimes you end up in various
>> conundrums and you can't obey all the rules at once, so you do the
>> best you can, and sometimes teachers write a lot about how to avoid
>> those pitfalls down the road.
>>
>> I think it's best to take the whole thing with a grain of salt, but
>> FWIW you do get, more or less, the stereotypical classical
>> counterpoint effect by avoiding parallel fifths and octaves, not
>> having voices cross, and doubling roots and fifths more than thirds.
>> So it might be good to at least grab those few things as guidelines
>> without being too OCD about it. You are, of course, always free to
>> leave that style and start mashing on parallel fifths if you want.
>>
>> -Mike
>>
>>
>>
>
>

🔗Jake Freivald <jdfreivald@...>

🔗Keenan Pepper <keenanpepper@...>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> If what you want are rules from the usual common practice freshman 8
> AM theory class, those are
>
> 1) no voices moving in parallel fifth
> 2) no voices moving in parallel octaves
> 3) no voice crossing, e.g. no making the tenor lower than the bass and
> what have you
> 4) in 4 voices with triadic harmony, doubling the root is preferred,
> the fifth second, the third rarely
>
> Those are the basic rules, sometimes with additional nuances and
> exceptions and un-exceptions, and so on. It's not immediately clear to
> me how to generalize them to other systems (no parallel 3/2's? no
> parallel generators? what?).

The correct generalization ought to be no voices moving in exactly parallel consonant intervals.

The "exactly parallel" part is why, in meantone, parallel fifths are avoided, but parallel thirds are a staple. The major third is a simple, otonal consonance, just like the perfect fifth, but if you do parallel thirds in the diatonic scale you never get two major thirds in a row. That's why it sounds so characteristic and good - the voices have independent melodies, but every interval between them is some kind of consonance.

So if you're writing counterpoint in some magic MOS, for example, the main proscription ought to be against parallel 5/4s, because, as the generator, those are almost always going to be exactly parallel. Parallel intervals of the 3/2 class would be fine, because the 3/2s would be mixed up with some other partner interval.

BTW, if you want to hear something amazing, tune up flattone[12], play parallel 3-step intervals, and listen carefully. In 12edo this would be exactly parallel movement, but in flattone[12] it's sometimes 8/7 and sometimes 6/5. The same trick ought to work in meantone[12] with 7/6 and 6/5, but I find it not nearly as striking as flattone.

Keenan

🔗Carl Lumma <carl@...>

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

> Do you have some sort of handy spreadsheet I could use, or
> something?

Sorry, I don't, but it's not hard to compute (it's the RMS
of the Tenney-weighted prime errors).

> > > http://soundcloud.com/cityoftheasleep/stagnant-deity
> > Amazing... that you are being allowed to trade this for
> > a 13-ET axe without having to pay some sort of fine.
>
> LOL. What's more amazing is that I thought at one point
> paying an extra $600 to make triads beat a bit less was a
> worthwhile investment.

$600?

I'm reminded of the South Park episode that discusses
Indiana Jones and the Kingdom of the Crystal Skull...
you're not planning on going back and digitally retuning
all your meantone stuff to machine, are you? ;)

> > > http://soundcloud.com/cityoftheasleep/howling-of-the-holy
> >
> > Hot damn!
>
> So the 13-EDO harmonies have you running screaming from the
> room, but you really enjoy this one? Now I'm really stumped.
> I called this one "howling of the holy" because there is some
> gnarly beating in the 3rds and wolves (among other intervals),
> and a lot of the piece sounds really discordant to me, made
> even more exaggerated by the extremely-pure fifths. You can't
> really "relax into it" because the contrast is so sharp.

It's the contrast that makes it ok. I mean, for contrast,
I'd prefer tonally ambiguous or tense chords with less
outright beating-type discordance to the wolves here, but
it's still the case that you use the contrast with the open
fifths to move the piece along. Not saying it's one of my
favorites, but I liked the organ and the setting, as it
demonstrates your versatility.

-Carl

🔗Mike Battaglia <battaglia01@...>

🔗Carl Lumma <carl@...>

🔗Mike Battaglia <battaglia01@...>

On Thu, Jan 5, 2012 at 4:37 AM, Carl Lumma <carl@...> wrote:
>
> I can't make hide nor tail of that comment in this context.
> Sounds like maybe Paul needs to read Graham's paper on
> weighted prime errors. -C.

For example, if 3 and 5 are both 10 cents sharp, you'll end up getting
the same weighted RMS prime error as you do if 3 is 10 cents flat and
5 is 10 cents sharp, but 5/3 is going to be a lot worse in one of
those, whereas 15/8 will be better in the other one. Note that 15/8
will be just as bad as 15/1, because octaves are pure. 5/3 is much
more important to approximate than 15/8, however, so that's why
looking directly at RMS prime error doesn't work, because it doesn't
take that into account. It doesn't fit Paul's desideratum of having
the weighted prime error give you a good picture of the weighted
overall error of "all intervals" in some meaningful sense, unless you
care equally about 8:12:15 and 4:5:6.

-Mike

> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> >
> > > Hm, I don't know why. It's TE error, with the exception that
> > > in this case it's not the error of the TE-optimal tuning.
> >
> > Because it doesn't end up giving you something consistent with
> > the error of all of the intervals in the relevant odd-limit.
> > From Paul
> >
> > "Take a step back and look at meantone. If you just measure the
> > error of prime 5 and the error of prime 3 you'll never get to
> > optimal tunings where 5 is tuned narrow and prime 3 is tempered
> > even more. But most optimal meantones, including POTE meantone,
> > do have this feature. It's largely about getting 6:5 (and 5:3)
> > into your set of target intervals, and probably occupied
> > thousands of posts on the Mills-Yahoo tuning list."
> >
> > -Mike
>
>

🔗Chris Vaisvil <chrisvaisvil@...>

Even though this is in 12 equal I thought posting an example of what I
meant might be valuable to the discussion we are having. There is room for
microtonal songs like this.
This particular one comes from my 4-track cassette days with 3 guitars,
drum machine and vocals.

download

http://alonetone.com/vaisvil/tracks/too-many-years.mp3

Lyrics and online play

http://alonetone.com/vaisvil/tracks/too-many-years

On Wed, Jan 4, 2012 at 9:42 PM, Chris Vaisvil <chrisvaisvil@...>wrote:

> Igs, with all due respect writing 3 part counterpoint doesn't require
> classical training.
>
> There are a number of ways to look at the issue in the context of popular
> music.
>
> 1. Bands like Black Sabbath and Led Zeppelin certainly had many memorable
> moments where bass, guitar, and voice were all playing different but
> interlocking melodies. Heck. What about Jethro Tull.
> 2. If you elevate drums to the level of Peter Thoegersen (a full fledged
> instrument not a time keeper) there is yet another avenue.
>
> If you want to learn how to write fugues, probably college or at least
> composition lessons are a good idea. Otherwise the basic requirement is
> simply 3 independent melodies combining to form harmony.
> I was messing with that with NO clue of theory when I figured out how to
> use two cassette decks to overdub.
> Countless bands have done it in one fashion or another. Is it florid
> Renaissance counterpoint, pretty much no, but it still IS counterpoint.
> Contrapuntal writing is extremely ingrained in western music tradition.
> Its been diluted in many cases but it still is there.
>
> And lets not forget Jazz - where the counterpoint is being made up on the
> spot.
>
> Chris
>
>
>
>

🔗Carl Lumma <carl@...>

Mike wrote:

> For example, if 3 and 5 are both 10 cents sharp, you'll end
> up getting the same weighted RMS prime error as you do if
> 3 is 10 cents flat and 5 is 10 cents sharp, but 5/3 is going
> to be a lot worse in one of those, whereas 15/8 will be
> better in the other one.

It doesn't really affect optimization for rank 1 and rank 2
because the error of ratios whose numerator and denominator
are odd primes is fixed (through a ratio depending on the
val or generator mapping). So RMS will give similar
optimizations to max and Paul's comment about never getting
the right meantone tunings sounds wrong. Here's the

TOP-tuned basis for 31
1201.4675323956367 1899.0938415285873 2790.5052365318015

And here's the TE version
1200.9757470533825 1898.3165034069593 2789.3630254143077

What about comparing different temperaments? Let's
compare <19 30 44| and <440 700 1019|. We'll start with
unweighted error. The former:

(0.0 7.218158760124425 7.366345443781938)
max: 7.37
rms: 5.95

and the latter
(0.0 -7.135908225521462 7.222804773925418)
max: 14.36
rms: 5.86

So it's possible to make an example where max error is
superior. Hold on, let's stretch the tuning of the second
val by 7.135908225521462 cents

(7.135908225521462 0.0 14.35871299944688)

The max is still 14.36 but the RMS is now 9.26. Forget
about weighting, it's simply the case that now RMS
reflects ALL THREE of the intervals we care about while
max only reflects one.

This is the same temperament as before, we just changed
the stretch. What's the TE-optimal error of this val
anyhow?
> (te-val '(440 700 1019) 5lim)
(1199.5281947780031 1908.340309874096 2777.998251088148)
> (te-error '(440 700 1019) 5lim)
3.1240147314501807

And TOP?

> (top-val '(440 700 1019) 5lim)
(1199.3046211341662 1907.984624531628 2777.480474853898)
> (top-damage '(440 700 1019) 5lim)
3.804268973869726

Howabout <19 30 44|?

> (te-val '(19 30 44) 5lim)
(1202.5780456079651 1898.8074404336292 2784.917579302656)
> (te-error '(19 30 44) 5lim)
1.9106383689099584

> (top-val '(19 30 44) 5lim)
(1202.2814046729093 1898.3390600098567 2784.2306213477896)
> (top-damage '(19 30 44) 5lim)
2.281404672909275

Ah, so it still works to compare temperaments when the
*optimal tuning is used*. I think that's because, like
I said at the outset, the error of an interval like 5/3
is simply

700(octave stretch)/1019 + (original error)

and all the business about RMS destroying the signs
of the error is made irrelevant by the optimization.
Maybe Graham can put it better.

-Carl

🔗Mike Battaglia <battaglia01@...>

On Thu, Jan 5, 2012 at 1:03 AM, Keenan Pepper <keenanpepper@...> wrote:
>
> The correct generalization ought to be no voices moving in exactly parallel consonant intervals.
>
> The "exactly parallel" part is why, in meantone, parallel fifths are avoided, but parallel thirds are a staple. The major third is a simple, otonal consonance, just like the perfect fifth, but if you do parallel thirds in the diatonic scale you never get two major thirds in a row. That's why it sounds so characteristic and good - the voices have independent melodies, but every interval between them is some kind of consonance.

So what about porcupine? Are parallel thirds in porcupine[7] OK? There
are a bunch of the same kind all in a row.

Does the generator have to be consonant for this to be true? And are
you talking about like, a harmonic concordance, like 3/2, or this
deeper kind of musical consonance that is independent of an interval's
intonation?

I guess what I'm saying is, what's more important: avoiding parallel
intervals of the same interval class, or avoiding parallel
consonances? Is it only when the two are lumped together that there's
a problem?

> BTW, if you want to hear something amazing, tune up flattone[12], play parallel 3-step intervals, and listen carefully. In 12edo this would be exactly parallel movement, but in flattone[12] it's sometimes 8/7 and sometimes 6/5. The same trick ought to work in meantone[12] with 7/6 and 6/5, but I find it not nearly as striking as flattone.

Yeah man, that's one of the more amazing things about it. John
Moriarty also pointed out that the double harmonic scale of C Db E F G
Ab B C is especially awesome, because it's now Rothenberg proper.
That'll really mess with your head.

-Mike

🔗Mike Battaglia <battaglia01@...>

On Fri, Jan 6, 2012 at 3:35 PM, Carl Lumma <carl@...> wrote:
>
> It doesn't really affect optimization for rank 1 and rank 2
> because the error of ratios whose numerator and denominator
> are odd primes is fixed (through a ratio depending on the
> val or generator mapping).

I don't understand this at all, can you give an example? How is the
error of something like 5/3 fixed?

> So RMS will give similar
> optimizations to max and Paul's comment about never getting
> the right meantone tunings sounds wrong. Here's the
>
> TOP-tuned basis for 31
> 1201.4675323956367 1899.0938415285873 2790.5052365318015
>
> And here's the TE version
> 1200.9757470533825 1898.3165034069593 2789.3630254143077

Yeah, for an EDO like 31, where the octave stretch is dependent on the
other primes, that'd happen. But if you look at the TE version of
5-limit meantone, it has a tuning map of <1201.397 1898.446 2788.196].
If you then multiply everything by 1200/1201.397, you get the POTE
version, which <1200 1896.238 2784.954].

This has both 3/1 and 5/1 flat. Hence, it is -not- the same thing
you'd get if you found the tuning that minimizes weighted RMS error
with the octaves kept pure. That would be a generator of 697.214
cents, which would produce a tuning map of <1200 1897.214 2788.857].
This has a weighted RMS error of 2.252 cents, whereas the actual POTE
version has a weighted RMS error of 2.996 cents.

So why wasn't the POTE version chosen to be the one which minimizes
weighted RMS prime error with octaves kept pure? Because of what
Paul's saying: the only reason one would want to minimize prime error
is if we're assuming that's going to filter through to "all other
intervals" in the limit. And that doesn't happen so well if you just
consider weighted prime RMS error and nothing else when you're working
with pure octaves.

The rest of your post involves only rank-1 tunings, which poses some
complexities I'm not sure about since you can't stretch the octave
without stretching everything else, by definition. I'll leave it for
Graham to weigh in.

-Mike

🔗Carl Lumma <carl@...>

🔗Mike Battaglia <battaglia01@...>

🔗Carl Lumma <carl@...>

🔗Mike Battaglia <battaglia01@...>

🔗Carl Lumma <carl@...>

🔗Mike Battaglia <battaglia01@...>

On Sat, Jan 7, 2012 at 3:47 AM, Carl Lumma <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > It's not at all clear where the constants in that expression came
> > from, nor how that means that the error of a composite ratio is
> > "fixed" in some sense that the error of a prime isn't.
>
> It's not clear that they come from the val given, just like
> the sentence at the top says? You seem to understand anyway,
> since you said the same thing in your initial reply (to which
> I said "Yes").

Oh, it's from that <440 700 1019| val. No, that wasn't clear at all,
because you threw it in at the end after talking about 19p for a
little bit, so it seemed like you were making some kind of general
statement about the nature of composite intervals in TE error with
mystery numbers.

Yes, then everything looks in like with what I said. If you work with
the optimal tuning, everything falls better into place, because if a
lot of primes (other than 2) are all sharp-leaning, meaning things
like 5/3 are better than things like 15/1, there's more room for
optimization by flattening the octave, which yields a lower error. If
you have half the primes flat and half sharp, meaning things like 15/1
are better than 5/3, then there's less room for optimization as pure
octaves are already about the ideal stretch, which yields a higher
error. That's my intuitive understanding of it, anyway, and it also
seemed to be confirmed by your post.

This still doesn't answer the question of what the best error metric
is for pure-octave tunings. Obviously, optimal TE error is better than
pure-octave unweighted TE error in comparing things, but I'm still not
sure it's the perfect solution. Graham suggested using STD error, so I
wonder how that ranks up.

-Mike

🔗Carl Lumma <carl@...>

Keenan and Mike wrote:

>> The correct generalization ought to be no voices moving
>> in exactly parallel consonant intervals.
>> The "exactly parallel" part is why, in meantone, parallel
>> fifths are avoided, but parallel thirds are a staple.
>
> So what about porcupine? Are parallel thirds in
> porcupine[7] OK? There are a bunch of the same kind
> all in a row.

I call this "timbre-breaking harmony"; scales that can do
it have the "diatonic property". I applied it in my first
generalized diatonic scale search in 2000:
/tuning/topicId_8379.html#8379

Actually I think I did one before this but I can't find
it now. I explain it in connection with a later search
attempt in 2002:
/tuning-math/message/4015
(scroll down to the section beginning
"the simultaneity of two or more series")

Finally in 2003 it wound up here:
http://lumma.org/music/theory/gd/gd3-spec.txt

""Diatonic Property (higher values are better)
There is at least one generic interval at which a melody
may be harmonized without the voices becoming timbre-fused.
Such a harmony is parallel with respect to generic
intervals but not with respect to actual intervals.

(k+1-c)(d^2)/(k^3) for a given interval class
where d is the number of times it produces a consonant
triad with the interval of equivalence and c is the length
of the longest consecutive run of some specific interval
through it.""

The spreadsheet and Scala files used are in the parent
directory: http://lumma.org/music/theory/gd/

On the spreadsheet you can see that porpupine[7] has a
score of 0.429, for sixths that can be 5:3 or 8:5.
This compares to a score of 0.857 for the diatonic scale,
for the same interval class and intervals. That's due
to the fact that they don't alternate as much.

Kalle Aho later pointed out that the diatonic property
is ideally fulfilled by rank 2 scales with a chromatic
unison vector (L-s) that is the difference of two
consonances. E.g. 25/24 separates 6/5 and 5/4 in the
diatonic scale. It remains an open problem to do a
search with this insight from RMP in mind.

> I guess what I'm saying is, what's more important: avoiding
> parallel intervals of the same interval class, or avoiding
> parallel consonances? Is it only when the two are lumped
> together that there's a problem?

Singing vocal harmony is so easy in the diatonic scale
because you can simply sing thirds and have it come out
right. The category of the third makes this easy.
Any good scale lets you create alternating harmony by
mixing scale degrees... the diatonic property, on the
other hand, is quite rare (at least if you want good
tuning accuracy).

-Carl

🔗Carl Lumma <carl@...>

I wrote:
> I call this "timbre-breaking harmony"; scales that can do
> it have the "diatonic property". I applied it in my first
> generalized diatonic scale search in 2000:
> /tuning/topicId_8379.html#8379
> Actually I think I did one before this but I can't find
> it now.

Here's where I first hit on it:

---------------------------------------------------------------------
11/21/1998

[Paul Erlich]
>a given consonant interval is always approximated by the same
>number of scale steps.

[me]
>I think agree...

Okay, I've thought it over. I still agree that this may be
responsible for an important effect, but it is not the rule I'd
give if I had to give only one rule telling where the goodness
of diatonicity comes from.

That rule is almost the inverse: that a given number of scale
steps be able to represent different consonances.

For example, 12tET, used like a diatonic scale, gives a complete
tetrad on every scale degree. It is strictly proper, maximally
even, and a MOS between the two most fundamental intervals known.
And it is a very resourceful scale! But it lacks the ability to
produce different harmonies using the same number of scale
degrees. And this is the thing that gives (7 tone) diatonic
music much of its punch.

-C.

🔗Mike Battaglia <battaglia01@...>

On Sat, Jan 7, 2012 at 4:11 AM, Carl Lumma <carl@...> wrote:
>
> Keenan and Mike wrote:
>
> >> The correct generalization ought to be no voices moving
> >> in exactly parallel consonant intervals.
> >> The "exactly parallel" part is why, in meantone, parallel
> >> fifths are avoided, but parallel thirds are a staple.
> >
> > So what about porcupine? Are parallel thirds in
> > porcupine[7] OK? There are a bunch of the same kind
> > all in a row.
>
> I call this "timbre-breaking harmony"; scales that can do
> it have the "diatonic property". I applied it in my first
> generalized diatonic scale search in 2000:

I'll respond when I have more functioning brain cells, but I've seen
this before. Or at least I saw the thing on your lumma.org site. I
thought it was a neat idea.

One triad pair I've been trying to find in a scale is 4:6:7 and
6:9:11. I'm not sure if timbral fusion is the way I was thinking of
it, but it is definitely a neat major/minor sort of pair. But I so far
haven't been able to find this in many tunings - the only one I've
sort of seen it in is mavila[7], and not even really that.

The chroma involved is 22/21, so we can look in the 2.3.7.11 subgroup
and find some EDOs that temper it out. Graham's finder is saying 5,
3de, 2p, 1e, 2de, 4e, 7p, 3p, 8d, and 6p. So we can click one of those
and look at random combinations of unison vectors that include 22/21,
and see what Fokker blocks come up. But no time to do it now, need
sleep...

-Mike

🔗Carl Lumma <carl@...>

🔗cityoftheasleep <igliashon@...>

🔗Keenan Pepper <keenanpepper@...>

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
> I call this "timbre-breaking harmony"; scales that can do
> it have the "diatonic property". I applied it in my first
> generalized diatonic scale search in 2000:
> /tuning/topicId_8379.html#8379

Seems like the scales you came up with are

meantone[7]
negri[10]
blackwood[10]
Two scales that don't have enough consonant relationships to pin down specific temperaments (i.e. they work in 5-limit JI)
pajara[10] pentachordal MODMOS

> Actually I think I did one before this but I can't find
> it now. I explain it in connection with a later search
> attempt in 2002:
> /tuning-math/message/4015
> (scroll down to the section beginning
> "the simultaneity of two or more series")
>
> Finally in 2003 it wound up here:
> http://lumma.org/music/theory/gd/gd3-spec.txt
>
> ""Diatonic Property (higher values are better)
> There is at least one generic interval at which a melody
> may be harmonized without the voices becoming timbre-fused.
> Such a harmony is parallel with respect to generic
> intervals but not with respect to actual intervals.
>
> (k+1-c)(d^2)/(k^3) for a given interval class
> where d is the number of times it produces a consonant
> triad with the interval of equivalence and c is the length
> of the longest consecutive run of some specific interval
> through it.""
>
> The spreadsheet and Scala files used are in the parent
> directory: http://lumma.org/music/theory/gd/
>
> On the spreadsheet you can see that porpupine[7] has a
> score of 0.429, for sixths that can be 5:3 or 8:5.
> This compares to a score of 0.857 for the diatonic scale,
> for the same interval class and intervals. That's due
> to the fact that they don't alternate as much.
>
> Kalle Aho later pointed out that the diatonic property
> is ideally fulfilled by rank 2 scales with a chromatic
> unison vector (L-s) that is the difference of two
> consonances. E.g. 25/24 separates 6/5 and 5/4 in the
> diatonic scale. It remains an open problem to do a
> search with this insight from RMP in mind.
>
> > I guess what I'm saying is, what's more important: avoiding
> > parallel intervals of the same interval class, or avoiding
> > parallel consonances? Is it only when the two are lumped
> > together that there's a problem?
>
> Singing vocal harmony is so easy in the diatonic scale
> because you can simply sing thirds and have it come out
> right. The category of the third makes this easy.
> Any good scale lets you create alternating harmony by
> mixing scale degrees... the diatonic property, on the
> other hand, is quite rare (at least if you want good
> tuning accuracy).

I started this a while ago: http://xenharmonic.wikispaces.com/Consonant+class+scale

Keenan

🔗Carl Lumma <carl@...>

🔗cityoftheasleep <igliashon@...>

🔗Jake Freivald <jdfreivald@...>

Keenan, I saw that a while ago and thought it was a superb idea.
Another hidden gem on the wiki. Now if I just had time to play with
all those parallel runs in different tunings!

Regards,
Jake

On 1/7/12, Keenan Pepper <keenanpepper@...> wrote:
>
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>> I call this "timbre-breaking harmony"; scales that can do
>> it have the "diatonic property". I applied it in my first
>> generalized diatonic scale search in 2000:
>> /tuning/topicId_8379.html#8379
>
> Seems like the scales you came up with are
>
> meantone[7]
> negri[10]
> blackwood[10]
> Two scales that don't have enough consonant relationships to pin down
> specific temperaments (i.e. they work in 5-limit JI)
> pajara[10] pentachordal MODMOS
>
>> Actually I think I did one before this but I can't find
>> it now. I explain it in connection with a later search
>> attempt in 2002:
>> /tuning-math/message/4015
>> (scroll down to the section beginning
>> "the simultaneity of two or more series")
>>
>> Finally in 2003 it wound up here:
>> http://lumma.org/music/theory/gd/gd3-spec.txt
>>
>> ""Diatonic Property (higher values are better)
>> There is at least one generic interval at which a melody
>> may be harmonized without the voices becoming timbre-fused.
>> Such a harmony is parallel with respect to generic
>> intervals but not with respect to actual intervals.
>>
>> (k+1-c)(d^2)/(k^3) for a given interval class
>> where d is the number of times it produces a consonant
>> triad with the interval of equivalence and c is the length
>> of the longest consecutive run of some specific interval
>> through it.""
>>
>> The spreadsheet and Scala files used are in the parent
>> directory: http://lumma.org/music/theory/gd/
>>
>> On the spreadsheet you can see that porpupine[7] has a
>> score of 0.429, for sixths that can be 5:3 or 8:5.
>> This compares to a score of 0.857 for the diatonic scale,
>> for the same interval class and intervals. That's due
>> to the fact that they don't alternate as much.
>>
>> Kalle Aho later pointed out that the diatonic property
>> is ideally fulfilled by rank 2 scales with a chromatic
>> unison vector (L-s) that is the difference of two
>> consonances. E.g. 25/24 separates 6/5 and 5/4 in the
>> diatonic scale. It remains an open problem to do a
>> search with this insight from RMP in mind.
>>
>> > I guess what I'm saying is, what's more important: avoiding
>> > parallel intervals of the same interval class, or avoiding
>> > parallel consonances? Is it only when the two are lumped
>> > together that there's a problem?
>>
>> Singing vocal harmony is so easy in the diatonic scale
>> because you can simply sing thirds and have it come out
>> right. The category of the third makes this easy.
>> Any good scale lets you create alternating harmony by
>> mixing scale degrees... the diatonic property, on the
>> other hand, is quite rare (at least if you want good
>> tuning accuracy).
>
> I started this a while ago:
> http://xenharmonic.wikispaces.com/Consonant+class+scale
>
> Keenan
>
>
>
>
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🔗Keenan Pepper <keenanpepper@...>

🔗Carl Lumma <carl@...>

🔗Chris Vaisvil <chrisvaisvil@...>

🔗Keenan Pepper <keenanpepper@...>

🔗Carl Lumma <carl@...>

🔗Mike Battaglia <battaglia01@...>

🔗genewardsmith <genewardsmith@...>

🔗Carl Lumma <carl@...>

🔗gbreed@...

It was always obvious that Pajara was the same kind of thing as a linear temperament. There was some debate about the terminology because linear temperaments were originally octave equivalent, like MOS.
Pajara was well known since Paul's 22all paper. The name was standardized with the Middle Path.
Systematic rank two temperament searches were 2001. TOP was late 2003. TOP searches may have been codimension one because that's an easy special case. It's a problem with TOP not temperament searches

Graham

------Original message------
From: Carl Lumma <carl@...>
To: <tuning@yahoogroups.com>
Date: Monday, January 9, 2012 2:34:27 AM GMT-0000
Subject: [tuning] Re: The Elusive "Meantone Killer"

--- "genewardsmith" <genewardsmith@...> wrote:

> As far as I can tell from searching, I started talking about
> ranks of temperaments and wedge products back in August, 2001.

I posted those rules in May 2002, and they were nearly identical
to rules I used in early 2000. "Pajara" had been named only
three months earlier; the MOS hypothesis had been proven six
months earlier. It wasn't yet clear whether temperaments with
fractional-octave periods would be called linear or planar or
what, and I think the only top-n temperament searches that had
been done were codimension 1. The pieces were all there, but
it was still a time when the things people were naming at a clip
were Scala files, not temperaments -- you can see I scored
several of yours in the ranking. Maybe others understood it,
but AFAIK Kalle Aho was the first to point out the relationship
between rank 2 temperaments and the diatonic property.

-Carl

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

🔗Carl Lumma <carl@...>

🔗gbreed@...

I called diaschismic "a kind of linear temperament" on my website. Paul identified the symmetric decatonics as being maximally even in that landmark paper. Why do you insist we didn't know what we were talking about?

Graham

------Original message------
From: Carl Lumma <carl@...>
To: <tuning@yahoogroups.com>
Date: Monday, January 9, 2012 9:37:29 AM GMT-0000
Subject: [tuning] Re: The Elusive "Meantone Killer"

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

> Pajara was well known since Paul's 22all paper.

That paper was written in '92 or something. The decatonic
scales were not recognized as MOS of a temperament.
Paul first posted their Fokker block interpretation in 1999.
Twintone wasn't identified as a temperament until after Gene
showed up in 2001.

> Systematic rank two temperament searches were 2001.

You're right - at least Gene posted some. You had the
something at microtonal.co.uk/temper in May 2001, when
you were apparently working on implementing the two-ETs
method for it.

> TOP was late 2003.

January 2004, though Paul apparently did think of it in
a fever the week before the New Year.

-Carl

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

🔗Chris Vaisvil <chrisvaisvil@...>

Hello Igs....???????????

On Thu, Jan 5, 2012 at 6:05 PM, Chris Vaisvil <chrisvaisvil@...>wrote:

> Even though this is in 12 equal I thought posting an example of what I
> meant might be valuable to the discussion we are having. There is room for
> microtonal songs like this.
> This particular one comes from my 4-track cassette days with 3 guitars,
> drum machine and vocals.
>
> download
>
> http://alonetone.com/vaisvil/tracks/too-many-years.mp3
>
> Lyrics and online play
>
> http://alonetone.com/vaisvil/tracks/too-many-years
>
>
> On Wed, Jan 4, 2012 at 9:42 PM, Chris Vaisvil <chrisvaisvil@...>wrote:
>
>> Igs, with all due respect writing 3 part counterpoint doesn't require
>> classical training.
>>
>> There are a number of ways to look at the issue in the context of popular
>> music.
>>
>> 1. Bands like Black Sabbath and Led Zeppelin certainly had many memorable
>> moments where bass, guitar, and voice were all playing different but
>> interlocking melodies. Heck. What about Jethro Tull.
>> 2. If you elevate drums to the level of Peter Thoegersen (a full fledged
>> instrument not a time keeper) there is yet another avenue.
>>
>> If you want to learn how to write fugues, probably college or at least
>> composition lessons are a good idea. Otherwise the basic requirement is
>> simply 3 independent melodies combining to form harmony.
>> I was messing with that with NO clue of theory when I figured out how to
>> use two cassette decks to overdub.
>> Countless bands have done it in one fashion or another. Is it florid
>> Renaissance counterpoint, pretty much no, but it still IS counterpoint.
>> Contrapuntal writing is extremely ingrained in western music tradition.
>> Its been diluted in many cases but it still is there.
>>
>> And lets not forget Jazz - where the counterpoint is being made up on the
>> spot.
>>
>> Chris
>>
>>
>>
>>

🔗cityoftheasleep <igliashon@...>

Sorry Chris, saw it but haven't had a chance to listen. Will listen to it tomorrow sometime.

-Igs

--- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
>
> Hello Igs....???????????
>
>
>
> On Thu, Jan 5, 2012 at 6:05 PM, Chris Vaisvil <chrisvaisvil@...>wrote:
>
> > Even though this is in 12 equal I thought posting an example of what I
> > meant might be valuable to the discussion we are having. There is room for
> > microtonal songs like this.
> > This particular one comes from my 4-track cassette days with 3 guitars,
> > drum machine and vocals.
> >
> > download
> >
> > http://alonetone.com/vaisvil/tracks/too-many-years.mp3
> >
> > Lyrics and online play
> >
> > http://alonetone.com/vaisvil/tracks/too-many-years
> >
> >
> > On Wed, Jan 4, 2012 at 9:42 PM, Chris Vaisvil <chrisvaisvil@...>wrote:
> >
> >> Igs, with all due respect writing 3 part counterpoint doesn't require
> >> classical training.
> >>
> >> There are a number of ways to look at the issue in the context of popular
> >> music.
> >>
> >> 1. Bands like Black Sabbath and Led Zeppelin certainly had many memorable
> >> moments where bass, guitar, and voice were all playing different but
> >> interlocking melodies. Heck. What about Jethro Tull.
> >> 2. If you elevate drums to the level of Peter Thoegersen (a full fledged
> >> instrument not a time keeper) there is yet another avenue.
> >>
> >> If you want to learn how to write fugues, probably college or at least
> >> composition lessons are a good idea. Otherwise the basic requirement is
> >> simply 3 independent melodies combining to form harmony.
> >> I was messing with that with NO clue of theory when I figured out how to
> >> use two cassette decks to overdub.
> >> Countless bands have done it in one fashion or another. Is it florid
> >> Renaissance counterpoint, pretty much no, but it still IS counterpoint.
> >> Contrapuntal writing is extremely ingrained in western music tradition.
> >> Its been diluted in many cases but it still is there.
> >>
> >> And lets not forget Jazz - where the counterpoint is being made up on the
> >> spot.
> >>
> >> Chris
> >>
> >>
> >>
> >>
>

🔗Carl Lumma <carl@...>

Graham wrote:

> I called diaschismic "a kind of linear temperament" on
> my website. Paul identified the symmetric decatonics as
> being maximally even in that landmark paper. Why do you
> insist we didn't know what we were talking about?

Did I say you didn't know what you were talking about?
I think I said it wasn't clear how rank 2 temperaments
related to the diatonic property. (It still isn't entirely
clear since the important comma isn't in the kernel of the
temperament, but rather depends on the particular scale.
And then there's the matter of how to get rapid alternation.
I think that has to do with how many times the generator
will go into the period.)

It was obvious that linear temperaments of low Graham
complexity should do well, which is why I included a bunch
of them in the comparison. But AFAIK Kalle Aho was the
first to point out the connection explicitly, in Dec. 2002
/tuning/topicId_41347.html#41360

You commented on gd3.xls when it came out but you didn't
make such a remark. That was spring 2002 because I was
headed to Reno. After the search came out I had people
sending me scales to include in the next one. Gene did
this using a bunch of different methods, not the chroma-
based one suggested by Kalle.

I said Paul was surprised when it became clear the scales
in his paper were only examples of the class of things
that included the linear temperaments we already knew about
(like meantone, schismic, kleismic, and miracle). I didn't
find the exact moment in the archives, but it must have
been after this
/tuning-math/message/6

Until the Hypothesis, nobody thought of things like maximal
evenness in terms of temperament -- it was just one of many
proposed properties that applied to arbitrary scales. That
fits with it having come out of academic theory, which
wasn't concerned with approximating concordances.

-Carl

🔗Mike Battaglia <battaglia01@...>

🔗Carl Lumma <carl@...>

Mike wrote:

> I think what we want are two vals, V1 and V2, which satisfy the
> property that <V1|C> = 0 and <V2|C> = 1, for C = the chroma you're
> looking for.

Do you mean two vals to wedge to get a rank 2 temperament?
If so, I think you're on to something, except I think <V2|C>
just has to be greater than 0. V1 will correspond to the
scale size, e.g. <7 11 16|-3 -1 2> = 0. If V2 is <12 19 28|
we get the diatonic scale in 12. But <31 49 72|-3 -1 2> = 2,
because the chromatic semitone is 2 steps in 31, but that's
no problem.

> The former ought to be a sublattice of val space, and I
> believe the latter is a coset of the same lattice, so you
> get a set of two parallel lattices.

Lost me here.

> I believe the scales with the most "alternating property"
> will be the ones that have generators of round(size/2).
> I think that's the same thing you meant by how many times
> the generator goes into the period.

Do you mean the generator should be close to half a period?
I agree. The octave is involved too -- things like
octatonic and blackwood benefit. Something like

(octave/period)/(period/generator) = oct*gen/period^2

would go up as the alternating got better. -Carl

🔗Carl Lumma <carl@...>

🔗Mike Battaglia <battaglia01@...>

On Tue, Jan 10, 2012 at 2:18 AM, Carl Lumma <carl@...> wrote:
>
> Mike wrote:
>
> > I think what we want are two vals, V1 and V2, which satisfy the
> > property that <V1|C> = 0 and <V2|C> = 1, for C = the chroma you're
> > looking for.
>
> Do you mean two vals to wedge to get a rank 2 temperament?

Right.

> If so, I think you're on to something, except I think <V2|C>
> just has to be greater than 0. V1 will correspond to the
> scale size, e.g. <7 11 16|-3 -1 2> = 0. If V2 is <12 19 28|
> we get the diatonic scale in 12. But <31 49 72|-3 -1 2> = 2,
> because the chromatic semitone is 2 steps in 31, but that's
> no problem.

I was thinking along the lines that V1 would correspond to the scale
in which C is the chroma, which means that it'd have to be tempered
out under that val. But then I was also thinking that, for any MOS in
which c is some chroma, the next MOS down will have c be either the
large or small step - but either way it's one step. So there's some
other val, which I called V2, in which <V2|C> = 1.

If we're going to look outside of setting <V2|C> = 1, we can find
things that work in which it's not positive: For example, if you wedge
7 ^ 16cc, you end up getting meantone, despite that <16 25 36|-3 -1 2>
= -1.

On the other hand, consider 7&12bbb: now <12 21 28|-3 -1 2> = -1, but
it doesn't work; it looks like you get something in which 5/4 and 6/5
no longer share an interval class.

One thing to note about setting V2 to <16 25 36| is that if you add
linear combinations of V2 and V1, you can get to some other V2* with
only positive coefficients such that <V2*|C> = 1. Is that true for
12bbb?

-Mike

🔗Kalle Aho <kalleaho@...>

🔗cityoftheasleep <igliashon@...>

🔗Carl Lumma <carl@...>

Igs wrote:

> Wow. Primitive, yet effective. I haven't seen people talk
> much about organizational properties of scales (like having
> root-position otonal and utonal tetrads fit the same pattern
> of scale degrees) in a loooooooong time, which is a shame,
> because I think such properties are very important.

I've always felt strongly that the diatonic property is
the most important thing after raw consonances/note, for
those looking to make something that behaves like the
diatonic scale. AFAIK I am the first author to discuss
its importance, and explain the rule against parallel
4ths & 5ths (but not 3rds & 6ths) as avoiding timbre-fusion.
However it seems so obvious it must have been discussed
before. But I've read a couple or more papers that try to
derive the rules of voice leading but resort to arcane and
totally unconvincing explanations for that rule, IMO.

> Interesting that Kalle came up with temperaments tempering
> out either 25/24, 49/48, or 50/49.

The scale, taken as rank 1, must temper out 25/24 and 49/48.
Since 25/24 - 49/48 = 50/49, the latter is not an independent
element of the kernel basis.

The host temperament must temper out 50/49 but NOT 25/24
or 49/48. Another way to say that is that it must map
the two larger commas to the same number of nonzero steps.

-Carl

🔗Herman Miller <hmiller@...>

🔗Mike Battaglia <battaglia01@...>

🔗genewardsmith <genewardsmith@...>

🔗Carl Lumma <carl@...>

Herman wrote:
> > The host temperament must temper out 50/49 but NOT 25/24
> > or 49/48. Another way to say that is that it must map
> > the two larger commas to the same number of nonzero steps.
>
> That narrows it down a bit. Some of the best options
> appear to be:
>
> 4&12 diminished [<4 6 9 11|, <0 1 1 1|]
> 2&10 pajara [<2 3 5 6|, <0 1 -2 -2|]
> 6&16 astrology [<2 5 5 6|, <0 -5 -1 -1|]
> 10&18 octokaidecal [<2 3 4 5|, <0 1 3 3|]
> 12&26 injera [<2 3 4 5|, <0 1 4 4|]
> 4&18 doublewide [<2 5 6 7|, <0 -4 -3 -3|]
> 12&20 [<4 6 10 12|, <0 1 -2 -2|]
> 8d&26 fifive [<2 2 3 4|, <0 5 7 7|]
> 6&12 hexe [<6 10 14 17|, <0 -1 0 0|]
> 10&16 lemba [<2 2 5 6|, <0 3 -1 -1|]
> 8d&22 hedgehog [<2 4 6 7|, <0 -3 -5 -5|]
> 12&48 [<12 19 28 34|, <0 0 -1 -1|]
> 12&54 [<6 10 13 16|, <0 -1 2 2|]
> 2b&22 [<2 4 5 6|, <0 -9 -4 -4|]

Thanks Herman. The complexities show the only really
attractive generalized diatonic system besides pajara is
octokaidecal, where the fifths are really out of whack.
Lemba, with 4/10 modes containing a target chord, and
Injera with its rather large scale size, deserve honorable
mention. Your Lemba Galatsia is really nice by the way...
great proof that this sort of theory leads to exactly the
kind of music predicted... something that sounds both
foreign and familiar (or 'correct') at the same time.
In the soundtrack when our heroes land on Endor, I think

1. Nobody would notice something about the tuning
2. Everyone would remember the music as being important to
the scene, and the culture of the Ewoks being especially
tangible and convincing

-Carl

🔗Chris Vaisvil <chrisvaisvil@...>

bump

On Thu, Jan 5, 2012 at 6:05 PM, Chris Vaisvil <chrisvaisvil@...>wrote: