meantone[7] vs meantone-7 vs other stuff

I believe the temperament[N] notation is due to Gene, so I'm going to
ask: is there a difference between meantone[7] and meantone-7? Or was
meantone[7] just picked arbitrarily because it's just as good as
anything else?

I'm considering switching it up to meantone-7 from now on when I talk
to newcomers, because it seems to make a psychological difference.
Saying "this is negri temperament, and this 9-note scale is negri-9"
seems to be easier to understand than "this is negri temperament, and
this 9-note scale is negri[9]." I think it's because the latter looks
like it's some sort of mathematical function, so people presume
there's some esoteric arcane math behind it which they don't
understand, so they just shut their brains off.

Yes, it's a silly thing to bring up if you're a h4rdc0re the0r1st
who's used to thinking about much more significant things, but I'm
curious if there's an established difference between meantone-7 and
meantone[7], or if my switching to meantone-7 would confllict with
something else already called meantone-7.

Anyone?

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> I believe the temperament[N] notation is due to Gene, so I'm going to
> ask: is there a difference between meantone[7] and meantone-7? Or was
> meantone[7] just picked arbitrarily because it's just as good as
> anything else?

I don't know what meantone-7 is. Meantone[7] is a generated scale (and in this case a MOS) of meantone with seven notes.

> Anyone?

First step, give a definition of temperament-n, so we can see if it is or is not the same as Temperament[n]. And why in hell do people keep trying to fix things which aint broke?

On Sun, Oct 21, 2012 at 12:46 PM, genewardsmith
<genewardsmith@...> wrote:
>
> First step, give a definition of temperament-n, so we can see if it is or
> is not the same as Temperament[n].

temperament-n is the same as Temperament[n].

-Mike

In keeping with your loathing of relying exclusively on MOS's to utilize temperaments, I'm surprised you even refer to scales by the names of the temperament associated with them. The term "meantone" is meaningless to most n00bs anyway. If you're gonna simplify for the sake of the n00bs, I say drop the temperament names all together. It's not meantone-7, it's just the diatonic scale! I do not discuss temperaments or commas at all in the introductory ET books I'm writing until the appendices, so when I introduce scales, I just name them something that seems intuitive. Like instead of calling it "Porcupine[7]" in 15-ED2, I call it the "quasi-equal heptatonic"...because really, that's just waaaaay more intuitive and transparent than "porcupine". If there's only one scale of a certain size that's of interest in an ET, I don't even give it a qualifier, I just call it the "(penta-, hexa-, hepta-, octa-, ennea-, deca-, etc.)tonic scale".

This only works for small ETs, of course, but if someone's into a larger ET there's no point in simplifying for their benefit, because they're already sold on something complicated.

I do mention the novel enharmonic equivalences of each ET, like how in 15 five perfect fifths gets you back to where you started, or in 14 it's seven of them that does that, or that in 17 you can divide the perfect fifth in half or in five equal parts, etc. This can be construed as a non-mathematical or "conceptual" version of temperament, I suppose, wherein Porcupine, instead of being the 250/243 temperament, is the temperament where two small whole-tones makes a minor 3rd and three makes a perfect 4th. Paul would have a fit about my rampant diatonic centrism, of course, but on the other hand, every ET of interest has at least one regular heptatonic scale with very worthwhile properties.

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> I believe the temperament[N] notation is due to Gene, so I'm going to
> ask: is there a difference between meantone[7] and meantone-7? Or was
> meantone[7] just picked arbitrarily because it's just as good as
> anything else?
>
> I'm considering switching it up to meantone-7 from now on when I talk
> to newcomers, because it seems to make a psychological difference.
> Saying "this is negri temperament, and this 9-note scale is negri-9"
> seems to be easier to understand than "this is negri temperament, and
> this 9-note scale is negri[9]." I think it's because the latter looks
> like it's some sort of mathematical function, so people presume
> there's some esoteric arcane math behind it which they don't
> understand, so they just shut their brains off.
>
> Yes, it's a silly thing to bring up if you're a h4rdc0re the0r1st
> who's used to thinking about much more significant things, but I'm
> curious if there's an established difference between meantone-7 and
> meantone[7], or if my switching to meantone-7 would confllict with
> something else already called meantone-7.
>
> Anyone?
>
> -Mike
>

On Sun, Oct 21, 2012 at 6:24 PM, cityoftheasleep <igliashon@...>
wrote:
>
> In keeping with your loathing of relying exclusively on MOS's to utilize
> temperaments, I'm surprised you even refer to scales by the names of the
> temperament associated with them.

1) It's better than coming up with an entirely new set of names from
scratch so that people have even more stuff to learn
2) Even if you don't care about about ratios, what we're really
interested in is rank-2 tuning systems, not just individual scales.
The something[n] or something-n notation makes it clear that 2L3s and
5L2s and 7L5s aren't completely different scales that have nothing to
do with one another at all.
3) If we're going to name MOS's anything, and it doesn't matter either
way, we might as well just name them after the best temperament that
supports them.
4) Most people do, at least, care about ratios a little bit, in that
Zach Curley is asking about tuning systems that subdivide 5/4, for
instance

> Like instead of
> calling it "Porcupine[7]" in 15-ED2, I call it the "quasi-equal
> heptatonic"...because really, that's just waaaaay more intuitive and
> transparent than "porcupine".

So what's tetracot[7]?

> I do mention the novel enharmonic equivalences of each ET, like how in 15
> five perfect fifths gets you back to where you started, or in 14 it's seven
> of them that does that, or that in 17 you can divide the perfect fifth in
> half or in five equal parts, etc.

If someone only cares about a tuning system with octaves and which
subdivides the "major third" into three parts, or if this person
specifically identifies a major third with 5/4 as Zach Curley did, you
might point them to this 2.5 contorted temperament:

[<1 2|]
[<0 3|]

So this is literally just a contorted temperament that has nothing in
it but 2/1 and 5/4, and which splits 5/4 into three parts. We could
name these things, if you think that they're the way that people
"naturally" think about things. I'll call it asdf temperament, and pay
no heed to the fact that there's an angry mob outside my door yelling
about contorsion. So then we can define negri as a 2.3.5 extension of
asdf which maps |0 4> to 4/3. Yay, so conceptually tidy!

But the point is, in this case, two seconds of deliberation by anyone
will show that the interval |0 4> is pretty damn close to 4/3. Would
anyone playing this realistically not want to call that |0 4> a
tempered 4/3? I doubt it. So rather than teach people all about asdf
and its wonderful extension negri, why don't we just teach them about
negri temperament first, and just say that asdf is basically a
contorted negri without 4/3?

And while we're at it, rather than call it asdf temperament, why don't
we just call asdf temperament itself negri?

Or if we want to get in the business of naming rank-2 tuning systems
directly, e.g. by generator size and not by mapping, why don't we just
name the tuning system with the generator between 1\9 and 2\19
"negri"?

I don't see any fantastic reason to come up with a new set of names.

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> I don't see any fantastic reason to come up with a new set of names.

Because temperament names are generally nonsensical and semantically opaque, referencing things most people are completely unfamiliar with.

Imagine you're a newly-minted microtonalist. Your first instrument is in 15-ED2. Guru #1 tells you that 15-ED2 has the following scales of interest:

Blackwood[10], Augene[9], Porcupine[8], Porcupine[7], Keemun[7], Triforce[6], Augene[6].

Guru #2 tells you that 15-ED2 has the following scales of interest:
Decatonic, Augmented Enneatonic (Tcherpnin's scale), Quasi-Equal Octatonic, Quasi-Equal Enneatonic, Pseudo-Diminished Heptatonic, Quasi-Equal Hexatonic, Augmented Hexatonic.

Stop and think for a second, and pretend you've *never heard of* regular temperament in your life. Which set of scale names seem more intuitive and/or related to things that might make sense if all you've ever known is 12-TET?

> 1) It's better than coming up with an entirely new set of names from
> scratch so that people have even more stuff to learn

Who says anyone ever has to learn anything about temperament theory? Temperament theory is great for taking a God's-eye view of the tuning world, but it's unnecessarily complicated for dealing with singular ETs. Not everyone wants or needs a God's-eye view of the tuning world, and I think we're doing a lot of people a disservice by trying to force it upon them. Ever think that you could keep peoples' eyes from glazing over if you presented them with something distilled and specialized instead of the Most Generalized and Universal Nomenclature and Theory?

> 2) Even if you don't care about about ratios, what we're really
> interested in is rank-2 tuning systems, not just individual scales.
> The something[n] or something-n notation makes it clear that 2L3s and
> 5L2s and 7L5s aren't completely different scales that have nothing to
> do with one another at all.

Says who? Why are we interested in rank-2 tuning systems? Why is the relationship between 5L2s and 7L5s inherently important? They *are* different scales, and have differnet purposes and applications. If we're talking about using them in the context of a single ET--which is probably where most people want to start, if they're not going straight for JI--why is it easier to give them a name based on the generator, instead of based on their shape?

> 3) If we're going to name MOS's anything, and it doesn't matter either
> way, we might as well just name them after the best temperament that
> supports them.

So how do we pick the best temperament? 7L1s in 15-ED2 is a better Opposum than it is a Porcupine, so should we call it Opposum[8] instead of Porcupine[8]? Is 4L3s in 15-ED2 Keemun[7] or Orgone[7] or something else? Each scale in each ET will, if extended to a large-enough prime-limit, represent a unique temperament. 26 and 31 both support meantone, but 26 is a much better flattone. All temperament families branch out into various extensions with different names, and if we pick the best fit for each scale in each ET, we're gonna end up with no common temperaments between ETs.

> 4) Most people do, at least, care about ratios a little bit, in that
> Zach Curley is asking about tuning systems that subdivide 5/4, for
> instance.

Sure, yeah, most people have drank at least a bit of the JI kool-aid. But caring about ratios isn't the same as caring about temperaments, at least not insofar as caring about temperaments means caring about learning vector or bra-ket notation and the whole attendant lexicon of RMP.

>
> > Like instead of
> > calling it "Porcupine[7]" in 15-ED2, I call it the "quasi-equal
> > heptatonic"...because really, that's just waaaaay more intuitive and
> > transparent than "porcupine".
>
> So what's tetracot[7]?

A scale that doesn't show up in any ET I'd cover. Is tetracot[7] a scale you'd really want to introduce to a n00b?

> If someone only cares about a tuning system with octaves and which
> subdivides the "major third" into three parts, or if this person
> specifically identifies a major third with 5/4 as Zach Curley did, you
> might point them to this 2.5 contorted temperament:
>
> [<1 2|]
> [<0 3|]

Why would you point them to that temperament, when they've already found the tuning system they're looking for? What does knowing that numerical description of the mapping convey that "divides 5/4 into 3 parts" doesn't?

> But the point is, in this case, two seconds of deliberation by anyone
> will show that the interval |0 4> is pretty damn close to 4/3. Would
> anyone playing this realistically not want to call that |0 4> a
> tempered 4/3? I doubt it. So rather than teach people all about asdf
> and its wonderful extension negri, why don't we just teach them about
> negri temperament first, and just say that asdf is basically a
> contorted negri without 4/3?

Well if you want to teach them about negri temperament, then you don't need to teach them about MOS's like negri[9], because MOS's are shitty ways to use temperaments (right?). So now you don't need to worry about scale names at all, because you're dealing with a temperament, not a scale.

> Or if we want to get in the business of naming rank-2 tuning systems
> directly, e.g. by generator size and not by mapping, why don't we just
> name the tuning system with the generator between 1\9 and 2\19
> "negri"?

Because depending on how you tune the generator, you might get a variety of different higher-limit extensions of negri, and it's arbitrary to call them all "negri" just because they have the same 5-limit mapping?

-Igs

On Mon, Oct 22, 2012 at 10:31 PM, cityoftheasleep
<igliashon@...> wrote:
>
> Imagine you're a newly-minted microtonalist. Your first instrument is in 15-ED2. Guru #1 tells you that 15-ED2 has the following scales of interest:
>
> Blackwood[10], Augene[9], Porcupine[8], Porcupine[7], Keemun[7], Triforce[6], Augene[6].
>
> Guru #2 tells you that 15-ED2 has the following scales of interest:
> Decatonic, Augmented Enneatonic (Tcherpnin's scale), Quasi-Equal Octatonic, Quasi-Equal Enneatonic, Pseudo-Diminished Heptatonic, Quasi-Equal Hexatonic, Augmented Hexatonic.
>
> Stop and think for a second, and pretend you've *never heard of* regular temperament in your life. Which set of scale names seem more intuitive and/or related to things that might make sense if all you've ever known is 12-TET?

I'd like Blackwood and Triforce and Porcupine. They're colorful and
interesting. The brackets are weird, so I'd probably go with
Blackwood-10 or whatever instead. "10-note blackwood scale" is fine to
me. I don't think most people will know what the "ennea" in enneatonic
even means, so "Quasi-Equal Enneatonic" isn't much more descriptive
for that crowd. I think "nonatonic" might be more familiar sounding
from what I'd heard in music school, actually. On the other hand,
"pseudo-diminished" is probably better than "keemun."

> Who says anyone ever has to learn anything about temperament theory? Temperament theory is great for taking a God's-eye view of the tuning world, but it's unnecessarily complicated for dealing with singular ETs. Not everyone wants or needs a God's-eye view of the tuning world, and I think we're doing a lot of people a disservice by trying to force it upon them. Ever think that you could keep peoples' eyes from glazing over if you presented them with something distilled and specialized instead of the Most Generalized and Universal Nomenclature and Theory?

I think it'd be a crying shame if people didn't figure out which
tuning systems and scales existed across EDOs. What are you going to
call porcupine[8] in 22-EDO if it's "quasi-equal octatonic" in 15-EDO?
Just assign it a new name?

> Says who? Why are we interested in rank-2 tuning systems? Why is the relationship between 5L2s and 7L5s inherently important? They *are* different scales, and have differnet purposes and applications. If we're talking about using them in the context of a single ET--which is probably where most people want to start, if they're not going straight for JI--why is it easier to give them a name based on the generator, instead of based on their shape?

I guess you could approach it that way. Well, give it a shot and see
how people react to it.

> So how do we pick the best temperament? 7L1s in 15-ED2 is a better Opposum than it is a Porcupine, so should we call it Opposum[8] instead of Porcupine[8]?

It'd be porcupine in the same sense that meanenneadecal in 19-EDO is
also just meantone. Saying "porcupine" also covers opossum just like
saying "meantone" covers "dominatrix" in 12-EDO.

> Is 4L3s in 15-ED2 Keemun[7] or Orgone[7] or something else?

Yes, this is a less clear example. A little while ago, I was working
on a nice simple system for these cases, where you just pick the "most
general" temperament in each case which covers everything else. This
involves being able to cut across subgroups. But, for now, I'm happy
for people to just call it whatever they want. What are they calling
it in 15-EDO now, Orgone? Then orgone it is.

> Sure, yeah, most people have drank at least a bit of the JI kool-aid. But caring about ratios isn't the same as caring about temperaments, at least not insofar as caring about temperaments means caring about learning vector or bra-ket notation and the whole attendant lexicon of RMP.

I don't see why someone should have to learn any of that stuff at all.
One extreme is learning all the math, another extreme is throwing it
all away and starting over without JI, but there's plenty of room in
the middle. For instance, one thing that's in the middle is how Ron
has all of these scale books that just say what the different MOS's in
each EDO are, and (usually) the lowest-badness temperament that refers
to them. Books like that which also had some info about how to
practically use each one, as you do in your paper, that'd also be
another thing in the middle ground.

> > So what's tetracot[7]?
>
> A scale that doesn't show up in any ET I'd cover. Is tetracot[7] a scale you'd really want to introduce to a n00b?

OK, what about maqamic[7] in 17-EDO? What about mavila[7] in 16-EDO or
23-EDO? Are these also quasi-equal hepatonics?

> Why would you point them to that temperament, when they've already found the tuning system they're looking for? What does knowing that numerical description of the mapping convey that "divides 5/4 into 3 parts" doesn't?

You wouldn't realistically do that, this was part one of like a three
part thing about why this is a bad approach.

> Well if you want to teach them about negri temperament, then you don't need to teach them about MOS's like negri[9], because MOS's are shitty ways to use temperaments (right?). So now you don't need to worry about scale names at all, because you're dealing with a temperament, not a scale.

MOS's are great ways to use temperaments, but what I don't like is a
fear of chromaticism.

> > Or if we want to get in the business of naming rank-2 tuning systems
> > directly, e.g. by generator size and not by mapping, why don't we just
> > name the tuning system with the generator between 1\9 and 2\19
> > "negri"?
>
> Because depending on how you tune the generator, you might get a variety of different higher-limit extensions of negri, and it's arbitrary to call them all "negri" just because they have the same 5-limit mapping?

I'm talking about naming ranges of generator sizes directly here.

-Mike

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

> I'd like Blackwood and Triforce and Porcupine. They're colorful and
> interesting. The brackets are weird, so I'd probably go with
> Blackwood-10 or whatever instead. "10-note blackwood scale" is fine to
> me. I don't think most people will know what the "ennea" in enneatonic
> even means, so "Quasi-Equal Enneatonic" isn't much more descriptive
> for that crowd. I think "nonatonic" might be more familiar sounding
> from what I'd heard in music school, actually. On the other hand,
> "pseudo-diminished" is probably better than "keemun."

Sure, "Ionian", "Dorian", "Aeolian", "Mixolydian" (etc.) are all "colorful and interesting" too. Want to guess how long it took me to figure out which one corresponded to which shape on the fretboard in root position? 13 years and counting (I still can never remember what "mixolydian" is). Colorful and interesting is fine if you've got a handful of scales to learn. Transparent and intuitive wins out at some point when you exceed a manageable number of arbitrary words to associate with unfamiliar scales.

> I think it'd be a crying shame if people didn't figure out which
> tuning systems and scales existed across EDOs. What are you going to
> call porcupine[8] in 22-EDO if it's "quasi-equal octatonic" in 15-EDO?
> Just assign it a new name?

Well, my writings only cover ETs 10-18. People who want to deal with 19 and up are probably on a different trip and are going to be more interested in things to do with ratios. The overlap of systems between these is much smaller.

> It'd be porcupine in the same sense that meanenneadecal in 19-EDO is
> also just meantone. Saying "porcupine" also covers opossum just like
> saying "meantone" covers "dominatrix" in 12-EDO.

But why? Why should one temperament name cover others? Why blur the distinctions if they're useful? Why is it okay to group the temperaments with a common mapping for 3 and 5, but not for 7? Is Greeley Porcupine as well? What about Nusecond?

> > Is 4L3s in 15-ED2 Keemun[7] or Orgone[7] or something else?
>
> Yes, this is a less clear example. A little while ago, I was working
> on a nice simple system for these cases, where you just pick the "most
> general" temperament in each case which covers everything else. This
> involves being able to cut across subgroups. But, for now, I'm happy
> for people to just call it whatever they want. What are they calling
> it in 15-EDO now, Orgone? Then orgone it is.

No one's calling it anything, except I guess me, because no one's using it. There's precious little consensus on a lot of important scales, and in some cases, the consensus is only a couple people. What about 5L1s in 16, is it Machine or Slendric? 3L4s in 17, is it Beatles or Maqamic or Mohajira? Is 5L2s in 12-TET Meantone or (gasp) Superpyth? After all, 64/63 vanishes in 12-TET, and if you leave out the mapping for 5 and play a bunch of 0-700-1000 chords, you could make a compelling argument for Superpyth.

In case you can't tell, the reason I don't like your nice, simple system is that temperament names reflect more how a scale will be used than any nice clear objective properties of the scales. Play a bunch of 4:5:9 chords in 6-ED2 and you'd be hard-pressed to say anything but 81/80 is important, but is 6-ED2 meantone in your system?

> I don't see why someone should have to learn any of that stuff at all.
> One extreme is learning all the math, another extreme is throwing it
> all away and starting over without JI, but there's plenty of room in
> the middle. For instance, one thing that's in the middle is how Ron
> has all of these scale books that just say what the different MOS's in
> each EDO are, and (usually) the lowest-badness temperament that refers
> to them. Books like that which also had some info about how to
> practically use each one, as you do in your paper, that'd also be
> another thing in the middle ground.

Sure, Ron's a good sport about just playing along with whatever the naming consensus is, but I'm not. I'll include that stuff in an appendix or a sidebar describing "some theorists who discovered this scale independently", but what I care about is the simplest, clearest, least-threatening presentation possible. There should be a reason for everything, and it should be obvious. I can't change history, but I reckon I can change the state of discourse if I ever succeed in finishing these blasted books and get them out to people.

> OK, what about maqamic[7] in 17-EDO? What about mavila[7] in 16-EDO or
> 23-EDO? Are these also quasi-equal hepatonics?

Mavila[7] in 16 is just the 16-tone diatonic scale; maqamic[7] is certainly a quasi-equal heptatonic (IIRC, that's exactly how it's described in scala), but I could call the neutral heptatonic or the neutral diatonic as well. Of course no text on 17 would be complete without a comprehensive list of maqamat, since 17's the smallest ET that supports all of them in general outline.

> > Why would you point them to that temperament, when they've already found the tuning system they're looking for? What does knowing that numerical description of the mapping convey that "divides 5/4 into 3 parts" doesn't?
>
> You wouldn't realistically do that, this was part one of like a three
> part thing about why this is a bad approach.

Can we keep this in the realm of things you'd realistically do?

> I'm talking about naming ranges of generator sizes directly here.

...yeah, but which ranges? Apparently, the ones that can share a common mapping for some arbitrary selection of basis intervals.

-Igs

On Tue, Oct 23, 2012 at 12:47 AM, cityoftheasleep
<igliashon@...> wrote:
>
> Sure, "Ionian", "Dorian", "Aeolian", "Mixolydian" (etc.) are all "colorful and interesting" too. Want to guess how long it took me to figure out which one corresponded to which shape on the fretboard in root position? 13 years and counting (I still can never remember what "mixolydian" is). Colorful and interesting is fine if you've got a handful of scales to learn. Transparent and intuitive wins out at some point when you exceed a manageable number of arbitrary words to associate with unfamiliar scales.

I think that "augmented enneatonic" is going to go over for people
about as well as "mixolydian" does.

> Well, my writings only cover ETs 10-18. People who want to deal with 19 and up are probably on a different trip and are going to be more interested in things to do with ratios. The overlap of systems between these is much smaller.

OK, so say orgone in 11-EDO, 15-EDO, and 18-EDO then.

> > It'd be porcupine in the same sense that meanenneadecal in 19-EDO is
> > also just meantone. Saying "porcupine" also covers opossum just like
> > saying "meantone" covers "dominatrix" in 12-EDO.
>
> But why? Why should one temperament name cover others? Why blur the distinctions if they're useful? Why is it okay to group the temperaments with a common mapping for 3 and 5, but not for 7? Is Greeley Porcupine as well? What about Nusecond?

Because what limit are we supposed to talk in? If I can't say "12-EDO
supports meantone" and leave it at that, am I always supposed to say
"12-EDO supports dominatrix?" Why not go even higher to the 17-limit
or the 31-limit?

> No one's calling it anything, except I guess me, because no one's using it. There's precious little consensus on a lot of important scales, and in some cases, the consensus is only a couple people. What about 5L1s in 16, is it Machine or Slendric? 3L4s in 17, is it Beatles or Maqamic or Mohajira? Is 5L2s in 12-TET Meantone or (gasp) Superpyth? After all, 64/63 vanishes in 12-TET, and if you leave out the mapping for 5 and play a bunch of 0-700-1000 chords, you could make a compelling argument for Superpyth.

No argument there.

> In case you can't tell, the reason I don't like your nice, simple system is that temperament names reflect more how a scale will be used than any nice clear objective properties of the scales. Play a bunch of 4:5:9 chords in 6-ED2 and you'd be hard-pressed to say anything but 81/80 is important, but is 6-ED2 meantone in your system?

No, the 2.9.5 81/80 temperament isn't called "meantone" under Keenan's
naming system, because the generator mappings don't agree. I believe I
suggested a while ago that it be called wholetone temperament. I don't
remember where I posted that suggestion, but if it wasn't here, then
I'm posting it here now.

> Sure, Ron's a good sport about just playing along with whatever the naming consensus is, but I'm not. I'll include that stuff in an appendix or a sidebar describing "some theorists who discovered this scale independently", but what I care about is the simplest, clearest, least-threatening presentation possible. There should be a reason for everything, and it should be obvious. I can't change history, but I reckon I can change the state of discourse if I ever succeed in finishing these blasted books and get them out to people.

OK, so do it your way. But if you're saying -I- should adopt your
system of naming, then it would be useful if you could at least
outline what it is. What do I call the MOS's in 22-EDO?

> > OK, what about maqamic[7] in 17-EDO? What about mavila[7] in 16-EDO or
> > 23-EDO? Are these also quasi-equal hepatonics?
>
> Mavila[7] in 16 is just the 16-tone diatonic scale

I'd at least recommend you call it the "anti-diatonic scale," but
whatever. Are you at least calling mavila[9] the superdiatonic scale?

> > > Why would you point them to that temperament, when they've already found the tuning system they're looking for? What does knowing that numerical description of the mapping convey that "divides 5/4 into 3 parts" doesn't?
> >
> > You wouldn't realistically do that, this was part one of like a three
> > part thing about why this is a bad approach.
>
> Can we keep this in the realm of things you'd realistically do?

Try reading the whole thing before responding.

> > I'm talking about naming ranges of generator sizes directly here.
>
> ...yeah, but which ranges? Apparently, the ones that can share a common mapping for some arbitrary selection of basis intervals.

Right. You keep saying that just unsystematically naming things after
popular temperaments and what the average person seems to care about
is a bad idea, but I'm not seeing you suggest anything better. All
you've suggested is unsystematically naming things after... something
else, I'm not quite sure what.

-Mike

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

> I think that "augmented enneatonic" is going to go over for people
> about as well as "mixolydian" does.

Alright, so I'll give up the proper Greek and go with "nonatonic", or just call it "Tcherpnin's scale", since that's what most people would know it as, if they know it at all. I'd say that for any scale an ET shares with 12-TET, just call it by its 12-TET name, regardless of if it corresponds to a different temperament.

> OK, so say orgone in 11-EDO, 15-EDO, and 18-EDO then.

Orgone's the only heptatonic of interest in 11, so it doesn't need a designation. But yeah, it's more or less a pseudo-diminished scale in all of them, because it's as close to a diminished scale as you could get in any of those ETs. 18's weird, though, and I might have to come up with a more involved naming scheme for it. I'm not sure yet, it's at the bottom of my priority list.

> > But why? Why should one temperament name cover others? Why blur
> > the distinctions if they're useful? Why is it okay to group the
> > temperaments with a common mapping for 3 and 5, but not for 7? Is
> > Greeley Porcupine as well? What about Nusecond?
>
> Because what limit are we supposed to talk in? If I can't say "12-EDO
> supports meantone" and leave it at that, am I always supposed to say
> "12-EDO supports dominatrix?" Why not go even higher to the 17-limit
> or the 31-limit?

Well, that's precisely my point. I don't think it makes sense to privilege the 5-limit, especially when several ETs of interest--11, 13, 14, 17, and 18--don't really support the 5-limit in very meaningful ways. And other ETs of interest--15, 16, 19, 21, 22, 24, and pretty much everything above 25--are primarily of interest because of what they do in limits above 5. How many people, at a guess, would you say are interested in microtonality solely for the purpose of playing 5-limit music in alternative temperaments? I.e., they have ZERO interest in the 7-limit or higher?

I'd say we should deal with at least the 13-limit, if not the 17-limit, but it's tricky because in all honesty, I think of almost every small ET (5 to about 25 or 26) as having a particular subgroup that describes the most sensible way of getting consonant harmony out of it. I could make you a list of my favorite subgroups to use with each of those ETs if you like, but suffice to say some include primes up to 17, and nothing includes the full complement of the 17-limit until you get to 26.

> > Is 5L2s in 12-TET Meantone or (gasp) Superpyth? After all, 64/63 > > vanishes in 12-TET, and if you leave out the mapping for 5 and
> > play a bunch of 0-700-1000 chords, you could make a compelling
> > argument for Superpyth.
>
> No argument there.

So, what's 5L2s in 12-TET then?

> > Play a bunch of 4:5:9 chords in 6-ED2 and you'd be hard-pressed
> > to say anything but 81/80 is important, but is 6-ED2 meantone in
> > your system?
>
> No, the 2.9.5 81/80 temperament isn't called "meantone" under Keenan's
> naming system, because the generator mappings don't agree.

So is it mappings you're naming, then?

> OK, so do it your way. But if you're saying -I- should adopt your
> system of naming, then it would be useful if you could at least
> outline what it is. What do I call the MOS's in 22-EDO?

I'm not saying that you should adopt my system. I don't deal with 22, because I don't see a point in anyone learning anything about 22 unless they want to learn about it as an 11-limit temperament. In which case, to go back to the OP, I doubt such people are really going to be very concerned whether it's Porcupine[7] or Porcupine-7. What I am saying is, the kind of people who are so scared of math that anything with brackets makes their eyes glaze over are not going to want to learn about temperaments, period, and are not going to care about JI, either, and are therefore not going to be interested in the merits of large accurate temperaments like 22, 26, 27, or 31. They probably just like microtonality because it's "weird", and they probably don't care about the specific ways in which it's "better" than 12, and will probably be about equally interested in a bunch of low ETs. They want to know why each one is cool, what kind of weird stuff you can do with each one.

> > Mavila[7] in 16 is just the 16-tone diatonic scale
>
> I'd at least recommend you call it the "anti-diatonic scale," but
> whatever. Are you at least calling mavila[9] the superdiatonic
> scale?

Paul gave me no end of crap about "anti-diatonic", because that's apparently what some jackass decided to call mohajira[7] in 24-TET. I've settled on calling it the "bizarro diatonic", but it's a diatonic scale at heart. And yeah, mavila[9] is totally superdiatonic, that's the only name that makes sense for it. It's a diatonic scale that comes from a circle of fifths, but it has two extra whole-tones.

> Right. You keep saying that just unsystematically naming things
> after popular temperaments and what the average person seems to
> care about
> is a bad idea, but I'm not seeing you suggest anything better. All
> you've suggested is unsystematically naming things after...
> something else, I'm not quite sure what.

Alright, tell you what. I tried to do exactly what you are trying to do at one time, and I failed. Here's what happened:
I decided that I would name generator ranges according to generators that would produce the same MOS up to 15 notes. I came up with this spreadsheet to demonstrate the ranges: /tuning/files/IgliashonJones/MOS Spreadsheet.pdf

That gives 29 different MOS families, excluding multi-MOS scales, each of which should have a unique name under my system. Frankly, I could probably have gone narrower, 1\10 was the smallest generator I covered (because I couldn't imagine anyone caring about something smaller), but you could take it down to 1\16 probably, since people like Valentine temperament. But that's not important.

Wanna know the problem with this, which ultimately caused me to abandon this project? Let's say we call 1\7--2\13 "Tetracot", and 2\13--1\6 "Roulette". Well, what's the scale in 13-ED2 that's generated by 2\13? Is it Tetracot or Roulette? Well, it's apparently both. But that's stupid, now we have two names for the same scale, which creates more problems and more confusion than it solves.

And there's no way out of it. This happens in every ET up to 15 notes. If we try to say "okay, we'll narrow the ranges, such that we're grouping scales that make the same MOS up to 22 notes", the problem gets worse instead of better, because now every ET up to 22 has a boundary case. If we try to widen the ranges and say we're just going to name the generators that produce the same MOS up to 10 notes, then we start lumping scales together that are actually very different from each other--2\9 to 1\4 becomes one MOS family, despite the massive harmonic differences in scales with (say) a 272-cent generator and a 282-cent generator. It's hopeless. And mappings don't make it any better, either, because you'll always run into ETs that can use multiple mappings for the same scale. Like 12-TET and its superpyth meantone.

I guess what I'm hoping you'll take a way from this is that naming things according to how you intuitively group scales across tunings is actually impossible to systematize, and is going to be fraught with problems no matter what you try to do. The only solution is not to use names to group scales across tunings, and just accept that however similar two tunings of a scale might be in one regard, they're different in another regard and you shouldn't gloss over those differences.

-Igs

On Tue, Oct 23, 2012 at 1:00 PM, cityoftheasleep
<igliashon@...> wrote:
>
> > Because what limit are we supposed to talk in? If I can't say "12-EDO
> > supports meantone" and leave it at that, am I always supposed to say
> > "12-EDO supports dominatrix?" Why not go even higher to the 17-limit
> > or the 31-limit?
>
> Well, that's precisely my point. I don't think it makes sense to privilege the 5-limit, especially when several ETs of interest--11, 13, 14, 17, and 18--don't really support the 5-limit in very meaningful ways.

You don't have to privilege the 5-limit. But if you say that some
equal temperament supports some other rank-2 temperament, this doesn't
mean it doesn't also support some higher-limit extension of that
temperament. For instance, one can say that 11-EDO supports orgone
without having to always say it supports "oregon," and one can say
that 12-EDO supports meantone without always having to say it supports
"dominatrix," and so on. The 5-limit isn't the default limit; it's
just a matter of building a nice family structure. For instance, I'd
like it if we could just name the 2.3.11 243/242 temperament and get
it overwith, so that instead of always talking about mohajira, or
maqamic, or whatever, we can just say that all of these tunings
support that (and then, if they support some extension of it, ok,
whatever, people don't need to worry about the names of every single
extension that exists).

> > > Is 5L2s in 12-TET Meantone or (gasp) Superpyth? After all, 64/63 > > vanishes in 12-TET, and if you leave out the mapping for 5 and
> > > play a bunch of 0-700-1000 chords, you could make a compelling
> > > argument for Superpyth.
> >
> > No argument there.
>
> So, what's 5L2s in 12-TET then?

If I were presenting this, I'd say it's meantone first and foremost,
and have a little blurb about the 7-limit and dominant and superpyth
as well.

> > No, the 2.9.5 81/80 temperament isn't called "meantone" under Keenan's
> > naming system, because the generator mappings don't agree.
>
> So is it mappings you're naming, then?

We're naming limits + mappings, which is the same thing as naming
limits + kernels (assuming you're ignoring contorsion).

> > I'd at least recommend you call it the "anti-diatonic scale," but
> > whatever. Are you at least calling mavila[9] the superdiatonic
> > scale?
>
> Paul gave me no end of crap about "anti-diatonic", because that's apparently what some jackass decided to call mohajira[7] in 24-TET.

Alright, someone around here needs to fess up. Who was it?

> I've settled on calling it the "bizarro diatonic", but it's a diatonic scale at heart. And yeah, mavila[9] is totally superdiatonic, that's the only name that makes sense for it. It's a diatonic scale that comes from a circle of fifths, but it has two extra whole-tones.

I don't see a problem with "mavila diatonic." I think you're
underestimating the power of some of these names. I mean, this is an
actual scale that balafon musicians from the village of Mavila play.
That's cool. Who wouldn't find that interesting? I mean, I agree that
"triforce" is probably tacky for a certain audience, but when the
names are good, you should sell it. Or "pelogic diatonic", that's
another good one.

> Wanna know the problem with this, which ultimately caused me to abandon this project? Let's say we call 1\7--2\13 "Tetracot", and 2\13--1\6 "Roulette". Well, what's the scale in 13-ED2 that's generated by 2\13? Is it Tetracot or Roulette? Well, it's apparently both. But that's stupid, now we have two names for the same scale, which creates more problems and more confusion than it solves.

It's neither; "glacial" is the name you want.

Here's what I want. I want to come up with some sort of "superbadness"
measure which takes into account the subgroup, as well as the kernel,
and which hence allows us to compare temperaments across subgroups. If
we had something like that, then it'd be easy enough for us to see
which temperament is the lowest-superbadness one generated by 2\13. If
you design the measure correctly, it won't ever yield a ridiculous
result like tetracot, because something like glacial will be so much
lower in superbadness that it'd come up first. So you won't have to
try and force-fit full-limit temperaments to these various EDOs, you
can just find the best overall subgroup that does the trick and go
with that.

Doing this allows you to come up with a sort of "family" structure
like what we have now, except instead of 5-limit temperaments
extending to 7-limit ones and so on, you can have things like 2.3.7
superpyth extending to 2.3.5.7 superpyth, and 2.9/7.5/3 sensi
extending to 7-limit sensi, and so on. The 2.3.11 243/242 temperament
can extend to 2.3.5.11 mohajira if you temper out 81/80, and 2.3.7.11
maqamic if you temper out 64/63, and so on.

So in effect, I'm talking about a temperament finder like Graham's
that doesn't require you to put in any limit, but searches across all
temperaments. So I would expect that if you do this, you'll end up
with, I dunno, maybe 25 temperament families that most people agree
are kickass. These are all the names that people will ever have to
learn, and they're guaranteed to be the most musically useful.
Theorists may continue to come up with different names for the
extensions of these, like sorcery and astrology and so on for magic
temperament, and that's fine. Theorists can continue to do that,
musicians can continue to just refer to the name of the base
temperament in the family, and life goes on. Again, it's the same as
how people say that 12-EDO supports meantone temperament instead of
dominatrix or whatever, because the latter implies the former.

This is what I was working on a while ago, but then I got sidetracked
with Weil tuning stuff. I'll probably get back to it soon. But, I
don't have it done, so there's really nothing for me to defend other
than the above idea. If you hate it and you like your own system, go
ahead and use it, and I'll keep working on this in parallel.

-Mike

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

> So in effect, I'm talking about a temperament finder like Graham's
> that doesn't require you to put in any limit, but searches across all
> temperaments. So I would expect that if you do this, you'll end up
> with, I dunno, maybe 25 temperament families that most people agree
> are kickass. These are all the names that people will ever have to
> learn, and they're guaranteed to be the most musically useful.

I think 25 is far too conservative of a guess, but honestly I've been after precisely the same goal, and rather than bicker over speculations, I'll just say "let's make it happen" and see what comes out. I don't think everyone will agree, because there will have to be a free error parameter and we're never gonna stop quibbling about what a sensible value is for that, and we're also never gonna agree on a proper superbadness cut-off, but holy crap would I love to be able to feed in a scale (even just a pair of ETs) and get an ordered list of temperaments of decreasing superbadness.

> This is what I was working on a while ago, but then I got sidetracked
> with Weil tuning stuff. I'll probably get back to it soon. But, I
> don't have it done, so there's really nothing for me to defend other
> than the above idea. If you hate it and you like your own system, go
> ahead and use it, and I'll keep working on this in parallel.

Dude, forget the Weil stuff, if you can make superbadness happen, do it! What can I offer you to incentivize this??

-Igs

I should also add: this is way better than just trying to name MOS's by generator ranges.

-Igs

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
>
> > So in effect, I'm talking about a temperament finder like Graham's
> > that doesn't require you to put in any limit, but searches across all
> > temperaments. So I would expect that if you do this, you'll end up
> > with, I dunno, maybe 25 temperament families that most people agree
> > are kickass. These are all the names that people will ever have to
> > learn, and they're guaranteed to be the most musically useful.
>
> I think 25 is far too conservative of a guess, but honestly I've been after precisely the same goal, and rather than bicker over speculations, I'll just say "let's make it happen" and see what comes out. I don't think everyone will agree, because there will have to be a free error parameter and we're never gonna stop quibbling about what a sensible value is for that, and we're also never gonna agree on a proper superbadness cut-off, but holy crap would I love to be able to feed in a scale (even just a pair of ETs) and get an ordered list of temperaments of decreasing superbadness.
>
> > This is what I was working on a while ago, but then I got sidetracked
> > with Weil tuning stuff. I'll probably get back to it soon. But, I
> > don't have it done, so there's really nothing for me to defend other
> > than the above idea. If you hate it and you like your own system, go
> > ahead and use it, and I'll keep working on this in parallel.
>
> Dude, forget the Weil stuff, if you can make superbadness happen, do it! What can I offer you to incentivize this??
>
> -Igs
>