Yahoo Tuning Groups Ultimate Backup tuning 2D temperament names, part I -- reclassified temperaments from message #101780

Hi again.

In message #101780, I suggested names for an awful lot of 2D temperaments. Soon after that, Gene and Graham warned me that many of them had terribly high "badnesses" when taken in the particular full limit. So I tried to look at them more carefully and I decided to list the temperaments with the "preferred" partial limit.

The names are given in the same order as in message #101780. Temperaments which are not included here can be used in the way suggested in that message. The names marked with ** are the ones which I'm now finding to be completely meaningless extensions of other lower limit temperaments. Those marked with (?) are names chosen to replace those which somehow took into account the excluded primes, like "countdown" instead of "trisedoge" and so on (I welcome any discussion of possible other names for these). The one marked with ! is one which, for some reason, I left out in that message although I was probably aware of the temperament (one line must have escaped me or whatever).

In my next post, I'll list unison vectors for a handful of other purely 5-limit temperaments, by no means as big a list as this one.

----------

Quinmite: 7

Lagaca: 5

Kastro: **

Whoops: 2.3.5.11

Sesesix: 5

Undim: 5

Countdown(?): 2.3.5.11, formerly trisedoge

Zarvo: 7

Tertiosec(?): 5, formerly tertiomar

Quintosec(?): 5, formerly foneth

Misneb: 2.3.5.13

Maquila: 2.3.5.11

Discot: 2.3.5.13

Untriton: **

Trimot: 2.3.5.13

Semaja: 2.3.5.13

Emka: 2.3.5.11.13

Lafa: 5

Sfourth: 5

Amavil: 2.3.5.13

Oquatonic: 2.3.5.7.13

Restles: 2.3.5.13

Tremka: 2.3.5.11.13

Vishnean: 2.3.5.13

Fifives: 2.3.5.13

Cotritone: 11

Ditonic: 2.3.5.11.13

Maja: 2.3.5.13

Fasum: 2.3.5.13

Coheschis: 2.3.5.7.13

Quartemka: 2.3.5.11.13

Metroci: 2.3.5.11.13

Gwazy: 2.3.5.11

Aufo: 5

Majvam: 2.3.5.13

Dodifo: 2.3.5.13

! Twentacufo/Vendequac(?): 2.3.5.11 = 118&111

----------

Petr

🔗genewardsmith <genewardsmith@...>

🔗Petr Parízek <petrparizek2000@...>

Gene wrote:

> |-74 13 23>; pretty awful but I guess Graham is listing all of these, so > I'll quit commenting.

If what you're saying is that sesesix is too complex with regard to the amount of mistuning (or too mistuned with regard to the high complexity), then I would suggest that there are situations in which one or the other attribute may be not of such importance and therefore I'm not exactly sure what is believed to usually set the boundaries.
For example, the best 5-limit temperament I've ever found is the one where |-90 -15 49> vanishes. And yet there are many situations where the almost JI-like behavior of that temperament is impossible to demonstrate or to apply and where temperaments like sesesix still are perfectly noticeable (because the mistuning is no greater than about 0.3 cents if pure octaves are used). Does the fact that it's so much less "in tune" mean we should exclude it from our list while keeping the other one whose rare "in-tune-ness" we are unable to enjoy anyway?
What's more, the complexity matters if we're concerned about things like closed MOS scales. But does it really matter as much if we focus our attention primarily on chord progressions derived from the mapping (which is exactly what I was doing for most of last year)? I'm not sure.

Petr

🔗Herman Miller <hmiller@...>

🔗genewardsmith <genewardsmith@...>

What's the point of sesex? Why is it worth naming?

> For example, the best 5-limit temperament I've ever found is the one where
> |-90 -15 49> vanishes.

Yes, that's pirate, which has been known about for years precisely because it is quite accurate even for its complexity.

And yet there are many situations where the almost
> JI-like behavior of that temperament is impossible to demonstrate or to
> apply and where temperaments like sesesix still are perfectly noticeable
> (because the mistuning is no greater than about 0.3 cents if pure octaves
> are used).

The point of something like pirate is not using it as an actual temperament. In fact, atom, an even more extreme nanotemperament, was in effect discovered in the 18th century, because of applications in theory. Put pirate together with atom, and you get 4296 equal, very interesting as a theory device also. Sesesix needs to pay off either in theory or in practice to we worth noting, but you havn't explained how that is.

🔗Keenan Pepper <keenanpepper@...>

--- In tuning@yahoogroups.com, Petr Parízek <petrparizek2000@...> wrote:
>
> Gene wrote:
>
> > |-74 13 23>; pretty awful but I guess Graham is listing all of these, so
> > I'll quit commenting.
>
> If what you're saying is that sesesix is too complex with regard to the
> amount of mistuning (or too mistuned with regard to the high complexity),
> then I would suggest that there are situations in which one or the other
> attribute may be not of such importance and therefore I'm not exactly sure
> what is believed to usually set the boundaries.
> For example, the best 5-limit temperament I've ever found is the one where
> |-90 -15 49> vanishes. And yet there are many situations where the almost
> JI-like behavior of that temperament is impossible to demonstrate or to
> apply and where temperaments like sesesix still are perfectly noticeable
> (because the mistuning is no greater than about 0.3 cents if pure octaves
> are used). Does the fact that it's so much less "in tune" mean we should
> exclude it from our list while keeping the other one whose rare
> "in-tune-ness" we are unable to enjoy anyway?
> What's more, the complexity matters if we're concerned about things like
> closed MOS scales. But does it really matter as much if we focus our
> attention primarily on chord progressions derived from the mapping (which is
> exactly what I was doing for most of last year)? I'm not sure.

I'm sure one could compose intelligible comma pumps for 10,000 different commas. Does this mean the corresponding temperaments should all have names?

Keenan

🔗Petr Parízek <petrparizek2000@...>

Keenan wrote:

> I'm sure one could compose intelligible comma pumps for 10,000 different > commas. Does this mean the > corresponding temperaments should all have > names?

Well, that's what I still don't understand -- where the boundaries are between what counts and what doesn't. For example, when Mike first mentioned the temperament which he was calling immunity and which I was calling semaphere/semephere, someone found it objectionable for exactly the same reason (i.e. too complex and too mistuned at the same time). But, on the other hand, 7-limit temperaments like lemba or dominant seem to be perfectly okay to be included, and so do 5-limit ones like father or bug or even something called enipucrop (1125/1024). To me this looks like a rather inconsistent way of making temperament lists because if we include temperaments like lemba or dominant, then we should probably also include the 7-limit temperament of 41&37 which I haven't found mentioned anywhere so far. Honestly, I have tried at least 3 different ways of filtering and sorting and in all the cases, dominant seemed to stick out so much that when I wanted to include that, I also got a bunch of other temperaments which I didn't find worth including -- the same was even more apparent with those like muggles or flattone. And yet you might say that there is a point in including both muggles and flattone (or dominant). And if there are temperaments which are so remarcably in tune, does this mean that we should make a big gap in our list between the ones usable in practice and the ones used for theoretical purposes (without allowing the ones "in-between")? Or does this mean that we should make two completely different lists, one of which includes temperaments like sesquiquartififths and another one which includes temperaments like dominant? Or, in the 5-limit, one which includes temperaments like whoosh and another one which includes temperaments like father? If I want to make a selection of, let's say, 60 5-limit temperaments, I think I should use one particular way of filtering and stick to that for the whole list -- or should I not?

Petr

🔗Petr Parízek <petrparizek2000@...>

🔗genewardsmith <genewardsmith@...>

--- In tuning@yahoogroups.com, Petr Parízek <petrparizek2000@...> wrote:

> Well, that's what I still don't understand -- where the boundaries are
> between what counts and what doesn't.

Boundries, where there are any, only exist for particular listings. On the Xenwiki, the catalogs and Middle Path tables have specific criteria for inclusion. On the Optimal Patent Val page, you'll find a number next to the val pair which is a badness figure. For 7-limit rank two temperaments, that is 1000 times TE logflat badness. For these temperaments, I've been keeping most of the figures below 60. From that point of view, 37&41, with a badness figure of 60.269, is marginal. But of course there might be a good reason to list it anyway.

For example, when Mike first mentioned
> the temperament which he was calling immunity and which I was calling
> semaphere/semephere, someone found it objectionable for exactly the same
> reason (i.e. too complex and too mistuned at the same time). But, on the
> other hand, 7-limit temperaments like lemba or dominant seem to be perfectly
> okay to be included, and so do 5-limit ones like father or bug or even
> something called enipucrop (1125/1024).

Father, bug, and dominant all have one thing in common--they are
not only not complex, they are relatively accurate given their complexity. That's not especially true of lemba and even more of enipucrop, but as I keep trying to tell people, there's more than one reason you might be interested in a comma. Lemba looks better in higher limits and has had music composed in it, and enipucrop, the 1&7 5-limit comma, is useful in studying 7 equal and its associated JI scales. Possibly Mike Battaglia can explain why it is porcupine spelled backwards and what amazing properties it has.

Honestly, I have tried at least 3 different ways of filtering and
> sorting and in all the cases, dominant seemed to stick out so much that when
> I wanted to include that, I also got a bunch of other temperaments which I
> didn't find worth including -- the same was even more apparent with those
> like muggles or flattone. And yet you might say that there is a point in
> including both muggles and flattone (or dominant).

You might claim there's not much point in including muggles, since there isn't much point in distinguishing it from 22 equal. You could make the same claim for dominant and 12 equal, but here you run into the fact that enormous amounts of music has been, in effect, written in dominant temperament and that you really can't ignore. Plus, there's that fairly low badness figure. Flattone I don't understand your objection to. It's a decent temperament and an interesting one, and clearly ought to be listed.

🔗Mike Battaglia <battaglia01@...>

On Sat, Mar 31, 2012 at 1:53 PM, genewardsmith <genewardsmith@...>
wrote:
>
> Father, bug, and dominant all have one thing in common--they are
> not only not complex, they are relatively accurate given their complexity.
> That's not especially true of lemba and even more of enipucrop, but as I
> keep trying to tell people, there's more than one reason you might be
> interested in a comma. Lemba looks better in higher limits and has had music
> composed in it, and enipucrop, the 1&7 5-limit comma, is useful in studying
> 7 equal and its associated JI scales. Possibly Mike Battaglia can explain
> why it is porcupine spelled backwards and what amazing properties it has.

It's porcupine spelled backwards because its 7-note MOS has the
property that the 3/2's are in the same place as porcupine, but the
6/5's and 5/4's switch places, much like mavila[7] does when you
compare it to meantone[7]. It's of interest for those who have
porcupine-based categories and want to mess around with the porcupine
equivalent of mavila. 20b-EDO does it about as well as it can be done;
anyone who can handle the 666 cent 3/2's of 9-EDO will probably also
be able to handle the 660 cent 3/2's of 20b (and there's nothing
stopping you from applying octave stretch, either).

-Mike

🔗Petr Parízek <petrparizek2000@...>

Gene wrote:

> Boundries, where there are any, only exist for particular listings. On the > Xenwiki, the catalogs and Middle Path
> tables have specific criteria for inclusion.

Does it mean that there isn't much of a point in making a list of all temperaments whose complexity, let's say, is lower than "something-x" and whose badness, at the same time, is lower than "something-else-y"?

> On the Optimal Patent Val page, you'll find a number next to the val pair > which is a badness figure. For 7-limit
> rank two temperaments, that is 1000 times TE logflat badness. For these > temperaments, I've been keeping most
> of the figures below 60. From that point of view, 37&41, with a badness > figure of 60.269, is marginal. But of
> course there might be a good reason to list it anyway.

What's TE logflat badness?

> Father, bug, and dominant all have one thing in common--they are
> not only not complex, they are relatively accurate given their complexity.

Then I have no idea what "relatively accurate" means. If I should tolerate the mistuning when 16/15 vanishes, then I could possibly start thinking about tempering out 9/8, FWIW. This is probably not for me.

> You might claim there's not much point in including muggles, since there > isn't much point in distinguishing it from
> 22 equal. You could make the same claim for dominant and 12 equal, but > here you run into the fact that
> enormous amounts of music has been, in effect, written in dominant > temperament and that you really can't
> ignore. Plus, there's that fairly low badness figure.

A) Aha, I see I should really learn more about this "badness" stuff or we don't get anywhere.
B) The problem here seems to be that when I hear 0-700-1000 cents, it always sounds to me like "screwed-up" 18:27:32 or 10:15:18 but never like 4:6:7. If I should simply "take dominant for granted" because 12-equal supports it, then I could also play tetradic harmony in Pythagorean tuning and claim I'm using it as dominant temperament. But (and there's the big but) then the 3rds are mistuned by ~21.5 cents, the 7ths are mistuned by ~27 cents, and at that moment I'm unable to hear the "5-limit-like flavor" in the 3rds or the "7-limit-like flavor" in the 7thes. If a temperament spanning 6 generators for a 7/5 is mistuned as much as that, then the question now arises: Are we supposed to approximate the specified intervals recognizably enough when making music in these temperaments? Or do they only work as some theoretical framework explaining what interval sizes are similar to some others? Something along these lines is the case of the temperament called "schism" whose purpose I can understand from no other point of view than the fact that 17p supports it.

> Flattone I don't understand your objection to. It's a decent temperament > and an interesting one, and clearly
> ought to be listed.

It requires to span as many as 13 generators to get a single 7/5 and at the same time there's not much you can do about the high amount of mistuning.

Petr

🔗genewardsmith <genewardsmith@...>

--- In tuning@yahoogroups.com, Petr Parízek <petrparizek2000@...> wrote:
>
> Gene wrote:
>
> > Boundries, where there are any, only exist for particular listings. On the
> > Xenwiki, the catalogs and Middle Path
> > tables have specific criteria for inclusion.
>
> Does it mean that there isn't much of a point in making a list of all
> temperaments whose complexity, let's say, is lower than "something-x" and
> whose badness, at the same time, is lower than "something-else-y"?

That's a specific criterion also, so if you want to do it I say go for it.

> What's TE logflat badness?

If S is TE relative error aka simple badness, C is TE complexity, n is the rank of the JI group being tempered, and r is the rank of the temperament, then TE logflat badness B is

B = S * C^(r/(n-r))

> > Father, bug, and dominant all have one thing in common--they are
> > not only not complex, they are relatively accurate given their complexity.
>
> Then I have no idea what "relatively accurate" means. If I should tolerate
> the mistuning when 16/15 vanishes, then I could possibly start thinking
> about tempering out 9/8, FWIW. This is probably not for me.

I'm not a fan of it either, but look, for instance, at the least complex independent 7-limit temperaments supported by the patent val for 5edo: father, mother, and beep (ie 7-limit bug.) Even if they are useless as temperaments, and some people don't think so, they are useful for studying pentatonic scales, for one other application.

🔗Petr Parízek <petrparizek2000@...>

Gene wrote:

> That's a specific criterion also, so if you want to do it I say go for it.

Thanx, at least I know I'm not doing nonsense.

> If S is TE relative error aka simple badness, C is TE complexity, n is the > rank of the JI group being tempered,
> and r is the rank of the temperament, then TE logflat badness B is
>
> B = S * C^(r/(n-r))

Okay. Now, let's assume I'm planning to tune some 5-limit temperaments in such a way that octaves are pure and that the temperament uses either the "minimax" version (at least I hope I'm using the right terminology here) or the one where one of the three target intervals (3/1, 5/1, 5/3) is mistuned two times more than the two others (like meantone of 2/7-comma, helmholtz/grovenian of 2/17-schisma, hanson of 2/11-kleisma, semisixth of 1/8-diesis etc.). If I take the number of required generators times the number of periods per octave as a possible measure of complexity (whatever valid that may be), then the size of the vanishing comma can actually work as some sort of "simple badness" measure for pure-octave temperaments. Now the question is how much this idea of badness measure has in common with the "simple badness" you were talking about. But a different question, on the other hand, is how appropriate the prime-related concept of "weighted coordinates" and similar stuff is if pure octaves are desired.

Petr

🔗Petr Parízek <petrparizek2000@...>

🔗genewardsmith <genewardsmith@...>

--- In tuning@yahoogroups.com, Petr Parízek <petrparizek2000@...> wrote:

> > B = S * C^(r/(n-r))
>
> Okay. Now, let's assume I'm planning to tune some 5-limit temperaments in
> such a way that octaves are pure and that the temperament uses either the
> "minimax" version (at least I hope I'm using the right terminology here) or
> the one where one of the three target intervals (3/1, 5/1, 5/3) is mistuned
> two times more than the two others (like meantone of 2/7-comma,
> helmholtz/grovenian of 2/17-schisma, hanson of 2/11-kleisma, semisixth of
> 1/8-diesis etc.). If I take the number of required generators times the
> number of periods per octave as a possible measure of complexity (whatever
> valid that may be), then the size of the vanishing comma can actually work
> as some sort of "simple badness" measure for pure-octave temperaments. Now
> the question is how much this idea of badness measure has in common with the
> "simple badness" you were talking about.

Let's call the maximum error in cents on the 5-limit diamond of the minimax tuning E, and the Graham complexity of the 5-limit diamond C. Then E*C is not the simple badness Graham defined, but it's the same sort of thing. A logflat badness measure is now B = E*C^3. We now have:

Father: 3575
Dicot: 2262
Meantone: 2753
Porcupine: 9833
Magic: 5923
Hanson: 2335
Helmholtz: 1266
Sesesix: 110216
Lagaca: 69338
Countermeantone: 79099
Pirate: 902

Etc. You can see why pirate stands out compared to your other proposals. Of course, one can easily find 5-limit commas even smaller than the atom with low badness figures, but the atom, which has actually seen use, seemed a good place to me to stop.

🔗Petr Parízek <petrparizek2000@...>

Gene wrote:

> A logflat badness measure is now B = E*C^3.

Is it C^3 because the untempered system is 3D? Or what's the 3 doing there?

> We now have:
>
> Father: 3575
> Dicot: 2262
> Meantone: 2753
> Porcupine: 9833
> Magic: 5923
> Hanson: 2335
> Helmholtz: 1266
> Sesesix: 110216
> Lagaca: 69338
> Countermeantone: 79099
> Pirate: 902
>
> Etc. You can see why pirate stands out compared to your other proposals.

Okay, now I understand. But if I decide to make a list of all temperaments of complexity less than "whatever-x" and badness less than "whatever-y" and I don't want to miss out some more important ones like valentine or sycamore, don't I run into the danger of inevitably "allowing" unison vectors like 4/3 if I keep the coefficient of C^3 rather than, let's say, C^2?

> Of course, one can easily find 5-limit commas even smaller than the atom > with low badness figures, but
> the atom, which has actually seen use, seemed a good place to me to stop.

Agreed.

Petr

🔗Graham Breed <gbreed@...>

My website's up to date with these changes now.

Petr Parízek <petrparizek2000@...> wrote:
<snip>
> (without allowing the ones "in-between")? Or does this
> mean that we should make two completely different lists,
> one of which includes temperaments like
> sesquiquartififths and another one which includes
> temperaments like dominant? Or, in the 5-limit, one which
> includes temperaments like whoosh and another one which
> includes temperaments like father? If I want to make a
> selection of, let's say, 60 5-limit temperaments, I think
> I should use one particular way of filtering and stick to
> that for the whole list -- or should I not?

I certainly think we should use different lists. Those
lists can be merged, of course. But there are some
temperaments that aren't likely to come up on any lists.

With my new code, to assign prime limits to mappings I'm
checking 7 different lists of 2,000 temperament classes for
each consecutive prime limit, or 400 for other bases. It
seems reasonable that any temperament notable enough to
have a name would sit on one of these lists. But I'm still
missing some.

Currently these are: Flourine in the 7-limit; Leonhard,
Injera, and Novemkleismic in the 13-limit; and Fasum and
Misneb in the 2.3.5.13-limit.

If such apparently obscure temperaments are really useful,
then there's a deficiency in the theory we need to fix.
Alternatively, there may be tens of thousands of notable
temperament classes that all deserve a name. I don't
relish keeping track of them all.

Graham

🔗Petr Parízek <petrparizek2000@...>

Gene wrote:

> A logflat badness measure is now B = E*C^3.
The following 5-limit unison vectors which weren't included in the older lists survived even after applying a different filtering scheme (the figures preceded by # refer to footnotes)

[10,4,-7> (#1)

[-13,-2,7> (#2)

[-27,-2,13> = ditonic

[19,10,-15> = countdown

[-36,11,8> = discot

[47,-15,-10> = quintosec

[61,4,-29> = squarschmidt

[22,33,-32> (#3)

[-52,-17,34> (#4)

[-67,-9,35> = dodifo

-- Notes:

#1. The least complex temperament I know of which uses a "semitone" as a generator and at the same time is tempered out in 12-equal. Also an octave inversion of ripple. Suggests something like invrip, semitonic, dodecal.

#2. Five generators in 10/3. What about some higher limits? Name?

#3. Halfway between parakleismic and egads on the spiral of minor thirds. As I'm not sure where egads comes from, I'm not sure what name could understandably reflect this fact.

#4. Equates an octave with (25/24)^17, similarly as enealimmal equates an octave with (27/25)^9. Something like heptadecalimmal or heptadecachrom is quite a mouthful.

----------

Petr

2D temperament names, part I -- reclassified temperaments from message #101780

🔗Petr Pařízek <petrparizek2000@...>

🔗genewardsmith <genewardsmith@...>

🔗Petr Parízek <petrparizek2000@...>

🔗Herman Miller <hmiller@...>

🔗genewardsmith <genewardsmith@...>

🔗Keenan Pepper <keenanpepper@...>

🔗Petr Parízek <petrparizek2000@...>

🔗Petr Parízek <petrparizek2000@...>

🔗genewardsmith <genewardsmith@...>

🔗Mike Battaglia <battaglia01@...>

🔗Petr Parízek <petrparizek2000@...>

🔗genewardsmith <genewardsmith@...>

🔗Petr Parízek <petrparizek2000@...>

🔗Petr Parízek <petrparizek2000@...>

🔗genewardsmith <genewardsmith@...>

🔗Petr Parízek <petrparizek2000@...>

🔗Graham Breed <gbreed@...>

🔗Petr Parízek <petrparizek2000@...>

🔗genewardsmith <genewardsmith@...>