Yahoo Tuning Groups Ultimate Backup tuning Suggested names for the unclasified temperaments

Hi tuners.

Finally, after a few days of hard work, I've thought of giving some names to the 2D temperaments listed earlier. FYI: This is not a definitive decision, I'm inviting others to take part in the discussion about what might be possible better names for some of them and also if we actually want to strip out some of them for whatever reason. For the last two on the list, I have absolutely no idea what to call them so I'm leaving them nameless for this time.

Trying to make the names contain as much information as possible and at the same time be as short as possible, I've often used the "alphanumeric" conversion which some of you may dislike -- i.e. numbers 1 to 26 are converted to letters "a" to "z". An example of that is "lafa", which actually means that stacking 12 generators makes 6/1 -- "l" for 12, "f" for 6. If you find this too cryptic, you may suggest otherwise. Also, some of my naming schemes are a bit inconsistent so I'll be glad if someone else is capable of making some more order in it. :-)

Note that many of these are also usable as 5-limit temperaments (the one called "ditonic" being a good example), sometimes offering less mistuning than when adjusting towards the higher limit extensions. Therefore, for a lot of them, it's perfectly okay to tune them as well as possible in the 5-limit context, even if we plan to use those extensions in the end.

Unless either stated otherwise or the note says (which one of the two?), these are all pairs of patent vals.

BTW: Once these are classified, I'll probably switch to wedgies; these EDO pairs make me howl even without wolf fifths. :-D

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

15&35: 11-limit - coblack (a counterpart to blacksmith)

4&95: 13-limit - quinmite (5 steps to a minor tenth)

15&103: 11-limit - tritriple (-3*3 generators make an OE of 7/1, 3*3*3 of them make an OE of 3/1)

10&98: 13-limit (possibly without 11/1) - lagaca (12 steps make a 7/3, where "l, g, c" are integers alphabetically converted to letters)

9&109: 13-limit - kastro (an extention to astro, very good up to the 11-limit meant by the "k")

15&167: 11-limit - whoops (an extension to whoosh)

22&105: 11-limit - sesesix? (6*6 generators make an OE of a major sixth)

12&104: 11-limit - undim (some sort of opposite to diminished)

15&80: 11-limit - trisedoge (three semi-diminished octaves add up to 7/1, an octave is made of 5 periods)

72&79: 13-limit - zarvo (similar to marvo but -26 steps are used instead of +46)

75&96: 11-limit - tertiomar (third-octave period, tempers out the "marvel" kleisma)

10&75: 7-limit - foneth (four neutral thirds add up to 7/3)

53&74: 13-limit - misneb (minor seconds, 14 of them get to 5/2)

9&74: 13-limit - maquila? (generators wider than in mavila or mabila)

10&53: 13-limit - discot (which one of the two?)

53&51: 11-limit - untriton (similar to tritonic but not the same)

17c&53: 13-limit - trimot (an extention to tricot)

16&37: 13-limit -- semaja (two steps in a 13/10)

37&50: 13-limit - emka (the primary approximants, in descending order of generator counts, are 5/1, 13/1, 11/1)

14&51: 13-limit - lafa (12 generators add up to 6/1)

45ef&46: 13-limit - sfourth (19 steps to a fourth)

43&52: 13-limit - amavil (similar to mavila in terms of interval sizes but uses a different approach to 3/1)

84&99: 7-limit - nessafof (a neutral second is the generator; a semi-augmented fourth, stacked 5 times, makes 5/1)

84&56: 13-limit - oquatonic (an adjusted abbreviation of the Italian "ottantaquatro")

77&87: 13-limit (possibly without 11/1) - restles (an opposite to beatles)

## Should there be something called "restles", something else could then be called "fites" (along the lines of spelling changes)

50&61: 13-limit (7/1 debatable) - tremka (the "emka" generator split into 3 equal parts)

## Both "emka" and "tremka" are also usable as 5-limit temperaments. However, each of them uses a different approach to 3/1 and therefore the 3 identity can't be used for finding similarities within the temperament family.

31&49: 13-limit - semisept (which one of the two?)

34&16: 13-limit - vishnean (an extension to vishnu)

34&26: 13-limit - fifives (possibly without 7/1)

35f&37: 13-limit - cotritone (a counterpart to tritonic)

47&50: 13-limit - ditonic (self-explanatory)

50&53: 13-limit - coditone (a counterpart to ditonic)

53&61: 13-limit (possibly 61d) - maja (13/10 generator)

53&14: 13-limit - fasum? (generator as in supermajor but *far* from its accuracy)

53&24: 13-limit (which one of the two?) - coheschis?

26&87: 13-limit - quartemka (the "emka" generator split into 4 equal parts)

87&84: 13-limit - mutt

87&16: 13-limit - metroci (generator = half of what equaves 64/35 and 11/6 which are 385/384 apart -- "me-tr-o-ci" abbreviates the Italian "metà, tre-otto-cinque" meaning "half, 3-8-5")

22&74, 11-limit - gwazy (an extension to kwazy where the 7s introduce more mistuning)

53&55: 13-limit - aufo (the augmented fourth of 45/32 is a possible generator)

47&34d: 13-limit - majvam (two 13/10s equated with 22/13)

47&37: 13-limit - dodifo (a 5-limit microtemperament with a double-diminished fourth as a generator, possibly extended less accurately to higher limits)

53&28: 13-limit - "whatonearthshouldicallthisthing?"

161&183, 11-limit - "noideaaswell"

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

Petr

🔗Graham Breed <gbreed@...>

🔗Petr Pařízek <petrparizek2000@...>

Graham wrote:

> Well, it's taken me about 4 hours of work to add them to my
> database.

Wow, thanks for such a huge contribution; I didn't assume you would do all of it in one "session". Even so, you're pretty lucky; I myself spent almost all day by making that list -- and one more day by actually finding the temperaments and also suitable EDO conbinations in order to avoid listing more labels for a single temperament (like 4&95 vs. 99&103).

> I've had to increase the reverse-lookup search
> size from 300 to 400

I had absolutely no idea you had to do that -- what do you mean by "reverse lookup search"?

> and it still doesn't catch the
> following, in the optimal limits you suggested:
>
> Ditonic, lafa, kastro, tertiomar, tremka, fasum, gwazy,
> majvam, vishnean, maquila, lagaca, sesesix, misneb,
> quinmite, ditonic, vishean, oquatonic, aufo, untriton,
> dodifo.

Well, what I was suggesting was not so much about an optimal limit but rather about the highest limit which I'd consider for taking into account before labeling it as an "extension". A good example for an explanation might be meantone or meanpop; for both of these, the 13-limit is still considered a proper part of the mapping, which actually means that meantone is still "meantone", no matter if you're talking about the 5-limit mapping, 7-limit, 11-limit, or 13-limit. However, trying to map higher primes results in extensions which are not normally considered to belong to the actual meantone mapping. Similarly, meanpop is still "meanpop" both in the 11-limit and 13-limit; but not higher. So, if I go back to the new temperaments, I think vishnean could still be called "vishnean" up to the 13-limit but I'm actually not sure what the optimal limit should be for this particular temperament.

A nice example demonstrating the difference between the highest limit and a possible optimal limit is "kastro" which I think could still be labeled "kastro" as high as in the 13-limit, even though the 13 identity brings significantly more mistuning than all the lower ones do. So I think that an "optimal" limit could be either 7 or 11. At the same time, I still think that the 13-limit extension deserves to be a part of the "kastro" mapping.

What's more, for some temperaments, a quest for the optimal limit would mean to take partial limits into account, which would probably turn the entire concept of temperament families on its head. For example, the one I call "maja" (53&61) is perfectly usable either as a 5-limit temperament or as a 2.3.5.13-limit temperament. But once I add 7 or 11 to the mix, the comparable quality of the temperament is debatable. For 7s, using 61p makes the whole thing much more complex while using 61d brings a lot more mistuning. For 11s, the mistuning isn't so great but it's still recognizably greater than for the other primes. So now I'm facing the question: While calling the 5-limit temperament "maja" even when adding the 13 identity, should I call the 11-limit one "maja" as well? And what'll I do about the 7s at all? Similar situations regarding the 11/1 occur with other temperaments as well -- like lagaca (more mistuned) or restles (more complex). And as an "icing on the cake", I can assure you that when I discovered "emka" back in March 2008, I was using it as a 2.5.11.13-limit temperament -- only a few weeks ago did I actually consider mapping some other primes with it.

Also note that most of these are very well usable as 5-limit temperaments, as I've said earlier, sometimes tempering out very small intervals -- a good example of that being "dodifo". But do we really want to distinguish 5-limit dodifo and 7|11|13-limit dodifo by calling the former "dodifo" and the latter, let's say, "dodifoan"? I don't think that's necessary. 5-limit meantone and 13-limit meantone are both called the same and we've got used to that as well.

> There are 6 different badness searches for each limit.

I'm afraid I'm not familiar with this topic of badness search -- can you expand on that?

> There will be some overlap, but let's say 400 per search
> gives 1000 distinct rank 2 temperaments overall. If so many
> apparently notable temperaments are failing to make those
> lists, how many am I going to end up cataloging?

I'm not 100% sure myself what methids I should choose for possibly filtering out some "not so good" ones -- or, more precisely, how to decide which ones are worth further examination and which ones are not.

> There could be mistakes, of course. There are too many
> outliers to check right now.

That's understandable, I'm also aware I'll still find more in the future -- as I've said not too long ago, there are many possible methods for finding 2D temperaments ane each of them can give different results. I think that might be a possible explanation for why the 5-limit "fifive" doesn't seem to have been examined before.

Petr

🔗Graham Breed <gbreed@...>

Petr Pařízek <petrparizek2000@...> wrote:

> Wow, thanks for such a huge contribution; I didn't assume
> you would do all of it in one "session". Even so, you're
> pretty lucky; I myself spent almost all day by making
> that list -- and one more day by actually finding the
> temperaments and also suitable EDO conbinations in order
> to avoid listing more labels for a single temperament
> (like 4&95 vs. 99&103).

I should have written a script to parse the original
message. That's how I usually deal with long lists. But
you weren't making it easy for me because your format
wasn't quite consistent. And I'd still have had to deal
with this:

> > I've had to increase the reverse-lookup search
> > size from 300 to 400
>
> I had absolutely no idea you had to do that -- what do
> you mean by "reverse lookup search"?

Originally, I was only keeping a database matching the
Hermite normal form of the mapping to the name. That's
fine when there aren't many names, so the chance of a name
mapping a different temperament in a different prime limit
is slim. But now I record the prime limits as well. So I
wrote a script to search for temperaments that might be in
the database, and see if they match. Because I'm still
using the old code (and I haven't parsed one of the Wiki
pages to get the prime limits) I still run that script for
all the new names. And if it fails to match up a
temperament, I have to add the exceptions in by hand.

Until yesterday, those exceptions were: Leonhard, Bidia,
and Sqrtphi in the 13-limit; Casablanca, Cuboctahedra,
Tritonic, and Semigamera in the 11-limit; and Hemigamera in
the 7-limit. Now there are a lot more and the search is
working harder before it gets to that point.

If I could re-write the scripts, I could make things
simpler, but the names haven't been coming so fast that
that's been an issue. The reverse lookup script takes well
over 10 minutes to run.

> Well, what I was suggesting was not so much about an
> optimal limit but rather about the highest limit which
> I'd consider for taking into account before labeling it
> as an "extension". A good example for an explanation
> might be meantone or meanpop; for both of these, the
> 13-limit is still considered a proper part of the
> mapping, which actually means that meantone is still
> "meantone", no matter if you're talking about the 5-limit
> mapping, 7-limit, 11-limit, or 13-limit. However, trying
> to map higher primes results in extensions which are not
> normally considered to belong to the actual meantone
> mapping. Similarly, meanpop is still "meanpop" both in
> the 11-limit and 13-limit; but not higher. So, if I go
> back to the new temperaments, I think vishnean could
> still be called "vishnean" up to the 13-limit but I'm
> actually not sure what the optimal limit should be for
> this particular temperament.

13-limit meantone is the second best 13-limit rank 2
temperament for a target of 7.6 cents (the TE error of
meantone). It's the best for a 7 cent target. Vishnean
comes in at number 582 when you target it's TE error.
There's a big difference between them. To the extent that
Vishnean doesn't look like it should have a name in the
13-limit -- or, at least, the 581 temperaments ahead of it
should also have names because there are so many 13-limit
temperament classes that might be musically useful.
Vishnean, as it happens, doesn't get picked up in the 7- to
11-limits either. Neither does it make the shortlist of
13-limit Vishnu extensions with the lowest target error I
thought was plausible when I wrote the website:

http://x31eq.com/cgi-bin/uv.cgi?uvs=[23%2C6%2C-14>&page=13&limit=13

It looks like Vishnean isn't notable at all. If there's a
reason it is, scholars can puzzle it out when they analyze
this database of named temperaments I'm building up.

> A nice example demonstrating the difference between the
> highest limit and a possible optimal limit is "kastro"
> which I think could still be labeled "kastro" as high as
> in the 13-limit, even though the 13 identity brings
> significantly more mistuning than all the lower ones do.
> So I think that an "optimal" limit could be either 7 or
> 11. At the same time, I still think that the 13-limit
> extension deserves to be a part of the "kastro" mapping.

Kastro does seem to get picked up in the 11-limit. It
isn't in the 7- or 13-limits.

If there's no other plausible 13-limit extension, the name
doesn't have to go in. It'll show up as Kastro+.

> What's more, for some temperaments, a quest for the
> optimal limit would mean to take partial limits into
> account, which would probably turn the entire concept of
> temperament families on its head. For example, the one I
> call "maja" (53&61) is perfectly usable either as a
> 5-limit temperament or as a 2.3.5.13-limit temperament.
> But once I add 7 or 11 to the mix, the comparable quality
> of the temperament is debatable. For 7s, using 61p makes
> the whole thing much more complex while using 61d brings
> a lot more mistuning. For 11s, the mistuning isn't so
> great but it's still recognizably greater than for the
> other primes. So now I'm facing the question: While
> calling the 5-limit temperament "maja" even when adding
> the 13 identity, should I call the 11-limit one "maja" as
> well? And what'll I do about the 7s at all? Similar
> situations regarding the 11/1 occur with other
> temperaments as well -- like lagaca (more mistuned) or
> restles (more complex). And as an "icing on the cake", I
> can assure you that when I discovered "emka" back in
> March 2008, I was using it as a 2.5.11.13-limit
> temperament -- only a few weeks ago did I actually
> consider mapping some other primes with it.

I don't have Maja. It can go in, but it's another thing
that doesn't look notable:

http://31eq.com/cgi-bin/rt.cgi?ets=53%2661&limit=2.3.5.13

http://31eq.com/cgi-bin/rt.cgi?ets=53%2661&limit=5

Lagaca gets found in the 5-limit, and in the 7-limit now
that I've increased the search size. Emka is one of the
few that got picked up in all applicable limits. According
to this search, it's an outstanding 2.5.11.13-limit
temperament:

http://x31eq.com/cgi-bin/pregular.cgi?limit=2.5.11.13&error=.3

So now it's listed as one.

> Also note that most of these are very well usable as
> 5-limit temperaments, as I've said earlier, sometimes
> tempering out very small intervals -- a good example of
> that being "dodifo". But do we really want to distinguish
> 5-limit dodifo and 7|11|13-limit dodifo by calling the
> former "dodifo" and the latter, let's say, "dodifoan"? I
> don't think that's necessary. 5-limit meantone and
> 13-limit meantone are both called the same and we've got
> used to that as well.

Dodifo gets picked up in the 5-limit, but it isn't
outstanding. I'm all for sharing names between limits.
Then maybe we can keep it to less than 1000 total names
instead of tens of thousands. But the other issues whether
lower scoring temperaments should have names at all.

> > There are 6 different badness searches for each limit.
>
> I'm afraid I'm not familiar with this topic of badness
> search -- can you expand on that?

Badness searches are what my website gives you. The result
is a list of temperaments sorted by badness, which is a
balance of error and complexity. There are ways of
comparing Meantone and Ennealimmal with the same badness
function, but I use one with a free parameter corresponding
to the target error. So if you search for 1 cent
temperaments, the results should have a TE error of around
1 cent (scaled up to the relative limit) and be more
outstanding the further they deviate from it.

Currently I'm searching from 0.01 cent/octave to 10
cent/octave. At the 13-limit, where the primes are taken
from the first 4 octaves, that'll be around 0.04 to 40
cents.

> > There will be some overlap, but let's say 400 per search
> > gives 1000 distinct rank 2 temperaments overall. If so
> > many apparently notable temperaments are failing to
> > make those lists, how many am I going to end up
> > cataloging?
>
> I'm not 100% sure myself what methids I should choose for
> possibly filtering out some "not so good" ones -- or,
> more precisely, how to decide which ones are worth
> further examination and which ones are not.

Yes, that's an open question. The TE measures aren't
perfect. You can run the searches yourself, using a
temperament's actual error as the target for a search (there
are links to take you straight there now) and if it doesn't
come up in the top 30 decide why it's more notable than
those that do. (30 is all you get on the web, because the
searches are more processor intensive the more results you
aim for. I was assuming 30 would be all anybody would
want, fool that I was.)

> > There could be mistakes, of course. There are too many
> > outliers to check right now.
>
> That's understandable, I'm also aware I'll still find
> more in the future -- as I've said not too long ago,
> there are many possible methods for finding 2D
> temperaments ane each of them can give different results.
> I think that might be a possible explanation for why the
> 5-limit "fifive" doesn't seem to have been examined
> before.

They'll give different results, but I hope they aren't so
different that notable temperaments don't make a top 400.

I managed to find Fifive in a top 30:

http://x31eq.com/cgi-bin/more.cgi?r=2&limit=2_3_5_13&error=1.18

You can see that there are a lot of entries ahead of it
without names. But also Majvam, that being the only name
you originally gave in the top 30 for a limit you
originally suggested.

Probably Fifive hasn't been examined in the 5-limit before
because there are at least 30 things (some of them
contorted) that appear to be more worthy of examination:

http://x31eq.com/cgi-bin/more.cgi?r=2&limit=5&error=2.09

Although you can't tell from the link, Fifive would have
been the 31st entry in that list.

The conclusion may be that there are more 5-limit
temperaments worthy of examination than I'd bargained
for. That worries me, given that I'm trying to keep this
list comprehensive. Hopefully I can keep up with the deluge
with ever more sophisticated electronic aids.

Graham

🔗genewardsmith <genewardsmith@...>

🔗Petr Pařízek <petrparizek2000@...>

Graham wrote:

> It looks like Vishnean isn't notable at all. If there's a
> reason it is, scholars can puzzle it out when they analyze
> this database of named temperaments I'm building up.

From what you've just said it really seems it isn't. You made me "re-ask myself" why I picked that one in the first place. And I'll tell you why. Because my very first idea for extending both vishnu and fifive was to map the 13/1, which seemed to work okay. Later I thought: "Hell, there must be a way there to map those 7s and 11s as well." And that's where vishnean and fifives came from. Although the 7/1 isn't particularly "in tune" in vishnean, I still think its fairly good in fifives.

> Kastro does seem to get picked up in the 11-limit. It
> isn't in the 7- or 13-limits.

Interesting.

> If there's no other plausible 13-limit extension, the name
> doesn't have to go in. It'll show up as Kastro+.

I'll be damned ... You're right, actually, I should have written different suggestions for the limits to avoid confusion ... No, one more day rewriting the same list. :-(

> I don't have Maja. It can go in, but it's another thing
> that doesn't look notable:

Hmmm ... Then it seems I'll never properly understand what the criteria are that tell which ones are more "worth it" and which ones are less.

> Dodifo gets picked up in the 5-limit, but it isn't
> outstanding. I'm all for sharing names between limits.
> Then maybe we can keep it to less than 1000 total names
> instead of tens of thousands. But the other issues whether
> lower scoring temperaments should have names at all.

Same for this.

> Badness searches are what my website gives you. The result
> is a list of temperaments sorted by badness, which is a
> balance of error and complexity. There are ways of
> comparing Meantone and Ennealimmal with the same badness
> function, but I use one with a free parameter corresponding
> to the target error. So if you search for 1 cent
> temperaments, the results should have a TE error of around
> 1 cent (scaled up to the relative limit) and be more
> outstanding the further they deviate from it.

Is that the same thing you talk about in the PDF you're linking to?

> Yes, that's an open question. The TE measures aren't
> perfect. You can run the searches yourself, using a
> temperament's actual error as the target for a search (there
> are links to take you straight there now) and if it doesn't
> come up in the top 30 decide why it's more notable than
> those that do. (30 is all you get on the web, because the
> searches are more processor intensive the more results you
> aim for. I was assuming 30 would be all anybody would
> want, fool that I was.)

Are you talking about the "pregular.html" now?

> They'll give different results, but I hope they aren't so
> different that notable temperaments don't make a top 400.

So do I.

> I managed to find Fifive in a top 30:
>
> http://x31eq.com/cgi-bin/more.cgi?r=2&limit=2_3_5_13&error=1.18
>
> You can see that there are a lot of entries ahead of it
> without names.

I hope this question isn't answered with something like "that would mean rewriting like half the code": Would it be possible, in a future version, to allow the user to somehow switch on/off inclusion of contorted temperaments?

> But also Majvam, that being the only name
> you originally gave in the top 30 for a limit you
> originally suggested.

Now, THIS is weird; it's calling the temperament "majvam", even though 34&183 clearly doesn't do majvam since 34&183 maps the 13/1 to -40 generators rather than -6.

> Probably Fifive hasn't been examined in the 5-limit before
> because there are at least 30 things (some of them
> contorted) that appear to be more worthy of examination:

I'm still not getting the point why a temperament like a contorted hanson (using as many as 12 generators for a 3/1) should be more "worthwhile" than fifive.

Anyway, I'm realizing I have to seriously rethink my methods of filtering, that's all I can say in conclusion so far.

Petr

🔗Mike Battaglia <battaglia01@...>

🔗Petr Parízek <petrparizek2000@...>

🔗Graham Breed <gbreed@...>

Petr Pařízek <petrparizek2000@...> wrote:
> Graham wrote:

> > Badness searches are what my website gives you. The
> > result is a list of temperaments sorted by badness,
> > which is a balance of error and complexity. There are
> > ways of comparing Meantone and Ennealimmal with the
> > same badness function, but I use one with a free
> > parameter corresponding to the target error. So if you
> > search for 1 cent temperaments, the results should have
> > a TE error of around 1 cent (scaled up to the relative
> > limit) and be more outstanding the further they deviate
> > from it.
>
> Is that the same thing you talk about in the PDF you're
> linking to?

Yes!

> > Yes, that's an open question. The TE measures aren't
> > perfect. You can run the searches yourself, using a
> > temperament's actual error as the target for a search
> > (there are links to take you straight there now) and if
> > it doesn't come up in the top 30 decide why it's more
> > notable than those that do. (30 is all you get on the
> > web, because the searches are more processor intensive
> > the more results you aim for. I was assuming 30 would
> > be all anybody would want, fool that I was.)
>
> Are you talking about the "pregular.html" now?

Yes.

> I hope this question isn't answered with something like
> "that would mean rewriting like half the code": Would it
> be possible, in a future version, to allow the user to
> somehow switch on/off inclusion of contorted temperaments?

I could do, very easily. But it wouldn't make the
interface any simpler. Crucially, showing results without
contorsion wouldn't be any harder than showing more
results. So I've done that. The "show more of these"
pages are now listing 50 results for the 5-limit and 40 for
the 7-limit.

> > But also Majvam, that being the only name
> > you originally gave in the top 30 for a limit you
> > originally suggested.
>
> Now, THIS is weird; it's calling the temperament
> "majvam", even though 34&183 clearly doesn't do majvam
> since 34&183 maps the 13/1 to -40 generators rather than
> -6.

47p&34d is where I got majvam from.

> > Probably Fifive hasn't been examined in the 5-limit
> > before because there are at least 30 things (some of
> > them contorted) that appear to be more worthy of
> > examination:
>
> I'm still not getting the point why a temperament like a
> contorted hanson (using as many as 12 generators for a
> 3/1) should be more "worthwhile" than fifive.

Hanson (with or without contorsion) is a lot more
accurate. Hanson with contorsion is only twice as complex
as Hanson without.

Graham