Yahoo Tuning Groups Ultimate Backup tuning-math A rose by any other name . . .

Let's talk about temperament names. There are also discussions on the
main Tuning list, but the more obscure they get, the more it looks
like mathematics. So let's talk about them on tuning-math.

On this page:

http://xenharmonic.wikispaces.com/Optimal+patent+val

there are two 13-limit entries for "Meantone". As a result, my
website will show two different things as "Meantone" in the 13-limit.
I don't want to hassle anybody who's recovering from surgery, but note
that the second one, 12p&31, is now in my local database as
"Meaningless" and will percolate to the website as such if nothing
else is suggested withing a few days.

This, then, is slated to be Meaningless:

http://x31eq.com/cgi-bin/rt.cgi?limit=13&ets=12p+31

I hope the following will continue to be Meantone because I've been
calling it Meantone (even if I didn't notice) for a few years now and
it makes much more sense as the priveleged 13-limit extension.

http://x31eq.com/cgi-bin/rt.cgi?limit=13&ets=12f+31

In other news, http://www.anaphoria.com/Euler.PDF defines a keyboard
mapping as "Leonhard". It's the second one listed here (Vicentino 2
dimensions higher):

http://x31eq.com/cgi-bin/rt.cgi?limit=2.3.5.7.13&ets=24+31

Period-generator mapping:
2 3 5 7 13
[< 1 1 0 -3 4 ]
< 0 2 8 20 -1 ]>

I've also made the Mohajira variant that comes up with it the
mainstream Mohajira for that subgroup.

As I mentioned in another place, I've been naming Magics. The main
reason to do this is that it helps me think about the 13-limit,
because different 13-limit commas will manifest themselves as unison
vectors in different Magics. Even if the temperament itself isn't up
to much, my notation is based on Magic, so it might make sense to use
an over-complex magic variant even if it would be hopelessly
inefficient when applied to a keyboard.

I noticed that my database has two different entries for "Magic" in
the 13-limit. You can see them both here:

http://x31eq.com/cgi-bin/rt.cgi?limit=13&ets=22+41

It's because I chose one a few years ago and another one's on the
wiki. In this case, the wiki's correct. The more accurate one I
chose (as the best 22&41) is to be killed, and will re-emerge as
Necromancy:

http://x31eq.com/cgi-bin/rt.cgi?limit=13&ets=22p+41

Here's my full list of 13-limit Magic variants, along with defining
equal temperaments according to Herman's names with the "p" and
possible non-defining unison vector ratios:

Magic 41&19p (105:104, 144:143, 196:195)
Witchcraft 41&19e (105:104, 352:351)
Necromancy 41&22p (352:351, 364:363)
Sorcery 19p&22p (78:77, 91:90, 351:350, 625:624)
Telepathy 19e&22p (352:351, 625:624)
Clairvoyance 19e&22f (105:104, 1716:1715)

You can compare them with the output of the following.

http://x31eq.com/cgi-bin/uv.cgi?limit=13&uvs=225/224+245/243

Names are still open to revision, should anybody have more imagination
or a better thesaurus. There's a general tendency for them to become
more evil as the get more complex. "Witchcraft" and "Telepathy" will
move back to the 11-limit. I'm currently of the thinking that
"Technology" and "Queen" would be too clever so I'll keep a
supernatural element.

Graham

🔗Mike Battaglia <battaglia01@gmail.com>

On Mon, Apr 25, 2011 at 2:16 AM, Graham Breed <gbreed@gmail.com> wrote:
>
> Names are still open to revision, should anybody have more imagination
> or a better thesaurus. There's a general tendency for them to become
> more evil as the get more complex. "Witchcraft" and "Telepathy" will
> move back to the 11-limit. I'm currently of the thinking that
> "Technology" and "Queen" would be too clever so I'll keep a
> supernatural element.

If there's a useful way to work 676/675 into it, you might want to
call that one Voodoo, as 676/675 is the "island" comma, and Voodoo is
one of the predominant religions of Haiti. There's also Alchemy,
Wizardry, Divination, and Necromancy. Should you ever come up to a
pair of related temperaments, they should of course be called Hocus
and Pocus. I also know that there's a Harry temperament, but I don't
remember what that is. If you can work some 13-limit extension of
Harry into the magic fold, it should definitely be called Potter.
Hogwarts might also be a good way to go.

-Mike

🔗Graham Breed <gbreed@gmail.com>

On 25 April 2011 10:57, Mike Battaglia <battaglia01@gmail.com> wrote:
> On Mon, Apr 25, 2011 at 2:16 AM, Graham Breed <gbreed@gmail.com> wrote:
>>
>> Names are still open to revision, should anybody have more imagination
>> or a better thesaurus. There's a general tendency for them to become
>> more evil as the get more complex. "Witchcraft" and "Telepathy" will
>> move back to the 11-limit. I'm currently of the thinking that
>> "Technology" and "Queen" would be too clever so I'll keep a
>> supernatural element.
>
> If there's a useful way to work 676/675 into it, you might want to
> call that one Voodoo, as 676/675 is the "island" comma, and Voodoo is
> one of the predominant religions of Haiti. There's also Alchemy,
> Wizardry, Divination, and Necromancy. Should you ever come up to a
> pair of related temperaments, they should of course be called Hocus
> and Pocus. I also know that there's a Harry temperament, but I don't
> remember what that is. If you can work some 13-limit extension of
> Harry into the magic fold, it should definitely be called Potter.
> Hogwarts might also be a good way to go.

676/675 is profoundly un-Magic. It happens to work with Harry,
though. Here's its entry in my informal comma catalog:

27:26 ~ 26:25 -> 675:676
Greenland, History, Madagascar, Borneo, Baffin
Harry, Tritikleismic, Hemiennealimmal, Mirkat, Quadritikleismic, Catakleismic
Not Orwell or Magic friendly

(What happened to New Guinea?) I'm wary of Voodoo. It could be an
extension of Witchcraft, but it might also be impolite to equate a
living religion with witchcraft. And, in general, I think it's best
to keep religions out of it (even if a few currently worshipped
deities are in there) because they all have a bad image for bigots
from other religions.

We'd really need three related temperaments to bring in Hocus and
Pocus, because one would inherit the previous name. Hocus and Pocus
also happened to be the names of my brother's guinea pigs. There's
already Wizard temperament. Alchemy is good, but I'd prefer it to
relate to Tripod because a tripod can be an alchemical device. The
class consistent with Tripod is the new mainstream Magic. It could
replace Sorcery, which is consistent with 13-limit Marvel, but I like
Sorcery for that. There's a vacancy for a Witchcraft variant, so
maybe Divination. There is a Necromancy.

Muggles already exists, looks like a different 7-limit extension of
5-limit Magic. And there's an Albus, possibly related to Madagascar
and Father in that the mappings start the same.

Graham

🔗Herman Miller <hmiller@IO.COM>

On 4/25/2011 2:16 AM, Graham Breed wrote:
> Let's talk about temperament names. There are also discussions on the
> main Tuning list, but the more obscure they get, the more it looks
> like mathematics. So let's talk about them on tuning-math.
>
> On this page:
>
> http://xenharmonic.wikispaces.com/Optimal+patent+val
>
> there are two 13-limit entries for "Meantone". As a result, my
> website will show two different things as "Meantone" in the 13-limit.
> I don't want to hassle anybody who's recovering from surgery, but note
> that the second one, 12p&31, is now in my local database as
> "Meaningless" and will percolate to the website as such if nothing
> else is suggested withing a few days.
>
> This, then, is slated to be Meaningless:
>
> http://x31eq.com/cgi-bin/rt.cgi?limit=13&ets=12p+31
>
> I hope the following will continue to be Meantone because I've been
> calling it Meantone (even if I didn't notice) for a few years now and
> it makes much more sense as the priveleged 13-limit extension.
>
> http://x31eq.com/cgi-bin/rt.cgi?limit=13&ets=12f+31

Meaningless is my "meantone B" and meantone is my "meantone A". I'm happy with "meantone A" being simply "meantone"; the other one doesn't look all that useful.

> In other news, http://www.anaphoria.com/Euler.PDF defines a keyboard
> mapping as "Leonhard". It's the second one listed here (Vicentino 2
> dimensions higher):
>
> http://x31eq.com/cgi-bin/rt.cgi?limit=2.3.5.7.13&ets=24+31
>
> Period-generator mapping:
> 2 3 5 7 13
> [< 1 1 0 -3 4 ]
> < 0 2 8 20 -1 ]>
>
> I've also made the Mohajira variant that comes up with it the
> mainstream Mohajira for that subgroup.

I've got the full 13-limit 7&24 [<1 1 0 6 2 4|, <0 2 8 -11 5 -1|] as "mohajira A". We could perhaps introduce a distinction between "semififth" and "mohajira" here, with 7&24 getting one name, and 7&24f [<1 1 0 6 2 6|, <0 2 8 -11 5 -8|] getting the other name. But probably no one will remember which is which, and 7&24 does seem to be the better one. 7&24f could be something like "hajiramo" or "morahaji".

> As I mentioned in another place, I've been naming Magics. The main
> reason to do this is that it helps me think about the 13-limit,
> because different 13-limit commas will manifest themselves as unison
> vectors in different Magics. Even if the temperament itself isn't up
> to much, my notation is based on Magic, so it might make sense to use
> an over-complex magic variant even if it would be hopelessly
> inefficient when applied to a keyboard.
>
> I noticed that my database has two different entries for "Magic" in
> the 13-limit. You can see them both here:
>
> http://x31eq.com/cgi-bin/rt.cgi?limit=13&ets=22+41
>
> It's because I chose one a few years ago and another one's on the
> wiki. In this case, the wiki's correct. The more accurate one I
> chose (as the best 22&41) is to be killed, and will re-emerge as
> Necromancy:
>
> http://x31eq.com/cgi-bin/rt.cgi?limit=13&ets=22p+41
>
> Here's my full list of 13-limit Magic variants, along with defining
> equal temperaments according to Herman's names with the "p" and
> possible non-defining unison vector ratios:
>
> Magic 41&19p (105:104, 144:143, 196:195)
> Witchcraft 41&19e (105:104, 352:351)
> Necromancy 41&22p (352:351, 364:363)
> Sorcery 19p&22p (78:77, 91:90, 351:350, 625:624)
> Telepathy 19e&22p (352:351, 625:624)
> Clairvoyance 19e&22f (105:104, 1716:1715)

If I've got this right, it appears that sorcery, magic, and necromancy share an 11-limit mapping (6, -8), while telepathy and clairvoyance share a different 11-limit mapping (-1, 14). That seems like a good split. Witchcraft has its own 11-limit mapping (-7, 33).

> You can compare them with the output of the following.
>
> http://x31eq.com/cgi-bin/uv.cgi?limit=13&uvs=225/224+245/243
>
> Names are still open to revision, should anybody have more imagination
> or a better thesaurus. There's a general tendency for them to become
> more evil as the get more complex. "Witchcraft" and "Telepathy" will
> move back to the 11-limit. I'm currently of the thinking that
> "Technology" and "Queen" would be too clever so I'll keep a
> supernatural element.

🔗Mike Battaglia <battaglia01@gmail.com>

On Mon, Apr 25, 2011 at 3:31 AM, Graham Breed <gbreed@gmail.com> wrote:
>
> (What happened to New Guinea?) I'm wary of Voodoo. It could be an
> extension of Witchcraft, but it might also be impolite to equate a
> living religion with witchcraft. And, in general, I think it's best
> to keep religions out of it (even if a few currently worshipped
> deities are in there) because they all have a bad image for bigots
> from other religions.

That's probably a good point, although as a note beliefs in magic and
the like as part of the Voodoo religion (more properly spelled
"Vodou") are alive and well in Haiti, including beliefs in
zombification and such.

> We'd really need three related temperaments to bring in Hocus and
> Pocus, because one would inherit the previous name. Hocus and Pocus
> also happened to be the names of my brother's guinea pigs. There's
> already Wizard temperament. Alchemy is good, but I'd prefer it to
> relate to Tripod because a tripod can be an alchemical device. The
> class consistent with Tripod is the new mainstream Magic. It could
> replace Sorcery, which is consistent with 13-limit Marvel, but I like
> Sorcery for that. There's a vacancy for a Witchcraft variant, so
> maybe Divination. There is a Necromancy.

You could always go with Abra and Cadabra and Alakazam, but those are
also names of Pokemon, which may not be what we're aiming for here.

> Muggles already exists, looks like a different 7-limit extension of
> 5-limit Magic. And there's an Albus, possibly related to Madagascar
> and Father in that the mappings start the same.

If you find any further magic + father temperaments, those that
parallel Albus, then you should probably get Gandalf and Merlin
involved over there, being as they're wise fatherly magicians. Can't
leave them out.

-Mike

🔗Mike Battaglia <battaglia01@gmail.com>

🔗Graham Breed <gbreed@gmail.com>

On 26 April 2011 05:25, Herman Miller <hmiller@io.com> wrote:
> On 4/25/2011 2:16 AM, Graham Breed wrote:

>> In other news, http://www.anaphoria.com/Euler.PDF defines a keyboard
>> mapping as "Leonhard". It's the second one listed here (Vicentino 2
>> dimensions higher):
>>
>> http://x31eq.com/cgi-bin/rt.cgi?limit=2.3.5.7.13&ets=24+31
>>
>> Period-generator mapping:
>> 2 3 5 7 13
>> [< 1 1 0 -3 4 ]
>> < 0 2 8 20 -1 ]>
>>
>> I've also made the Mohajira variant that comes up with it the
>> mainstream Mohajira for that subgroup.
>
> I've got the full 13-limit 7&24 [<1 1 0 6 2 4|, <0 2 8 -11 5 -1|] as
> "mohajira A". We could perhaps introduce a distinction between
> "semififth" and "mohajira" here, with 7&24 getting one name, and 7&24f
> [<1 1 0 6 2 6|, <0 2 8 -11 5 -8|] getting the other name. But probably
> no one will remember which is which, and 7&24 does seem to be the better
> one. 7&24f could be something like "hajiramo" or "morahaji".

I have mohajira A as "mohajira". The -8 fork looks worse by both
error and complexity, so it's an easy choice.

Why do we have to mutilate Arabic words? Mohajira (مهاجر?) could
translate to English as "immigrant", "migratory", or "pilgrim"
according to Jacques. These words can translate back into Arabic as
well. (I'd need to ask somebody how because my dictionary doesn't
have phonetics.)

> If I've got this right, it appears that sorcery, magic, and necromancy
> share an 11-limit mapping (6, -8), while telepathy and clairvoyance
> share a different 11-limit mapping (-1, 14). That seems like a good
> split. Witchcraft has its own 11-limit mapping (-7, 33).

That's the idea. I've jiggled them about now. I brought in
"divination" as 41&38f. It divides the octave into two equal parts,
so you can remember "divination divides". Then, because clairvoyance
is a synonym of telepathy (sometimes, definitions are inconsistent) it
had to go. Also new is "hocus" with a divided generator. That leaves
"pocus" for dividing the generator the other way, however that works .
. .

Here's the family in the 11-limit:

http://x31eq.com/cgi-bin/uv.cgi?limit=11&uvs=225:224+245:243

The currently proposed names are as follows:

Magic 22 & 41
Telepathy 22 & 19e
Witchcraft 41 & 19e
Hocus 22 & 38d
Divination 41 & 3de
Charisma 19p & 3de
Horcrux 19p & 60e

I left some weird non-magic things blank. I've also named the head of
the family:

Supernatural 19e & 22 & 41

Now, back to the 13-limt names:

http://x31eq.com/cgi-bin/uv.cgi?limit=13&uvs=225:224+245:243

These are all extensions, except "intuition" which is the best
alternative I could think of for "telepathy":

Magic 41 & 19p
Witchcraft 41 & 19e
Necromancy 41 & 22p
Sorcery 19p & 22p
Telepathy 19e & 22p
Intuition 19e & 22f
Divination 41 & 38df
Hocus 22f & 38df

Then I went through and named some planar temperaments:

Supernatural 19e & 41 & 19p (extended as magic)
Magician 22p & 41 & 19p (planar magic)
Alchemist 22p & 19p & 19e (supernatural extended as sorcery)
Oberon 22p & 41 & 19e (supernatural extension)
Telepath 22f & 19e & 22p (planar telepathy)
Titania 38df & 41 & 22p (supernatural extension)
Witch 41f & 41 & 19e (planar witchcraft)
Alembic 3de & 41 & 19p (related to tripod)

I decided to go for generic names, except for oberon and titania, who
are at least immortals and so will fit in with the rank 3 deities. If
people want to go through and add literary names for magicians,
witches, and so on, note that there are plenty of scales in each of
these temperaments.

Also, in the realm of lower complexity:

http://x31eq.com/cgi-bin/uv.cgi?limit=13&uvs=225:224+245:243&page=5

Charisma 19p & 3def
Devotion 19p & 3de

Graham

🔗Herman Miller <hmiller@IO.COM>

On 4/25/2011 9:46 PM, Mike Battaglia wrote:
> On Mon, Apr 25, 2011 at 3:31 AM, Graham Breed<gbreed@gmail.com> wrote:
>>
>> (What happened to New Guinea?) I'm wary of Voodoo. It could be an
>> extension of Witchcraft, but it might also be impolite to equate a
>> living religion with witchcraft. And, in general, I think it's best
>> to keep religions out of it (even if a few currently worshipped
>> deities are in there) because they all have a bad image for bigots
>> from other religions.
>
> That's probably a good point, although as a note beliefs in magic and
> the like as part of the Voodoo religion (more properly spelled
> "Vodou") are alive and well in Haiti, including beliefs in
> zombification and such.

It's also worth pointing out that "voodoo" was proposed for a temperament with mapping [<1 9 2 7|, <0 -23 1 -13|], also known as "grendel".

>> We'd really need three related temperaments to bring in Hocus and
>> Pocus, because one would inherit the previous name. Hocus and Pocus
>> also happened to be the names of my brother's guinea pigs. There's
>> already Wizard temperament. Alchemy is good, but I'd prefer it to
>> relate to Tripod because a tripod can be an alchemical device. The
>> class consistent with Tripod is the new mainstream Magic. It could
>> replace Sorcery, which is consistent with 13-limit Marvel, but I like
>> Sorcery for that. There's a vacancy for a Witchcraft variant, so
>> maybe Divination. There is a Necromancy.
>
> You could always go with Abra and Cadabra and Alakazam, but those are
> also names of Pokemon, which may not be what we're aiming for here.

I wouldn't be opposed in principle to using Pokï¿½mon names, if they make sense, particularly how they have evolution chains that would be nice for representing higher limits, but I'd be wary of using trademarked names in general. On the other hand, there's all sorts of possibilities with Pokï¿½mon names. There are 17 elemental types and 14 different egg groups, which could represent different commas or other similarities.

>> Muggles already exists, looks like a different 7-limit extension of
>> 5-limit Magic. And there's an Albus, possibly related to Madagascar
>> and Father in that the mappings start the same.
>
> If you find any further magic + father temperaments, those that
> parallel Albus, then you should probably get Gandalf and Merlin
> involved over there, being as they're wise fatherly magicians. Can't
> leave them out.
>
> -Mike

Yes, there's muggles. You could always claim it's named after a Louis Armstrong song, but that explanation would convince no one. So we've already got a temperament name that's potentially trademarked. I don't know if that would be a problem, since it would be trademarked for specific uses (and it happens to be a real word, an old slang word for marijuana). I wasn't aware of Albus.

🔗Herman Miller <hmiller@IO.COM>

🔗Graham Breed <gbreed@gmail.com>

On 27 April 2011 04:25, Herman Miller <hmiller@io.com> wrote:

> I'm not too fond of hocus by itself; either find a pocus to go with it,
> or just call it hocuspocus. Charisma doesn't especially sound magical.
> And I wouldn't name anything horcrux, you'd have to commit a murder in
> order to use it!

I kept on jiggling them around, so this is the current 11-limit list:

Magic 22 & 41
Telepathy 22 & 19e
Witchcraft 41 & 19e
Divination 22 & 38d
Hocus 41 & 3de
Charisma 19p & 3de
Horcrux 19p & 60e

At least, I think it's right. I forgot to copy the latest one over.
Hocus is correctly named now so that there is a pocus. It doesn't
rank highly in the 11-limit, and has a better 7-limit partner that
I've called "spell". (Not a good name, but not a good temperament, so
it doesn't matter.) Divination also has a better 7-limit partner, and
that's called "astrology". That covers the whole magic family.

Charisma is magical in origin, but it's good magic because it comes
from God, so it has low complexity. (I'm mapping evil to complexity,
which is the real problem in making voodoo a partner of witchcraft.
But if anybody doesn't care about that, witchcraft's partner is still
unnamed, primarily because it isn't much use.) I've changed
charisma's 13-limit partner from "devotion" to "glamor". Both of them
are pretty useless but I happen to like the names. Check a dictionary
if you don't think glamor is related to magic. (Google tells me
"Glamor is a fictional character in the Marvel Universe". That ties
into the other sub-thread. But, yes, I believe glamor, as an ultimate
descendant of 7-limit magic, can be placed in the marvel universe.)

"Horcrux" is the most complex mapping here, and so is named after the
most evil form of magic. It isn't the most efficient. I don't think
it makes the top 100 for any badness parameter. If anybody does want
to use it, they only have to murder a temperament class. It happens
that hocus and horcrux are related through 105:104 and 196:195.

Graham

🔗Graham Breed <gbreed@gmail.com>

On 27 April 2011 04:16, Herman Miller <hmiller@io.com> wrote:

> Yes, there's muggles. You could always claim it's named after a Louis
> Armstrong song, but that explanation would convince no one. So we've
> already got a temperament name that's potentially trademarked. I don't
> know if that would be a problem, since it would be trademarked for
> specific uses (and it happens to be a real word, an old slang word for
> marijuana). I wasn't aware of Albus.

I don't think it's a problem, as if there is a trademark it would
indeed be for specific uses. In that case, the Louis Armstrong song
would cause more trouble, as would "beatles". Albus is, in fact a
real word, connected with geomancy. (Oh, "geomancy", I missed that
one.) As is "Minerva" that's also the name of a character in Harry
Potter. Probably coincidentally, but maybe Gene checked that Albus
and Minerva were related. (But not too closely, because Hogwarts
appears to be a celibate institution.)

In other news, "deecee" is in there, and I'm sure it's related to
"marvel". "Godzilla" isn't in my list, but will probably get in one
day, and is sure to be trademarked. The other monster names may be as
well. "Jamesbond" clearly evokes a trademark. I wondered if the
Blair estate had trademarked "Orwell" given that it wasn't his real
name. Apparently not, but Google uncovers "Orwell® is a registered
trademark used for Overcoats, Raincoats, Jackets, Anoraks, Waistcoats,
Blouse Jackets, Pants, Slacks, Trousers, Jeans, Shorts, ..."

There's no escape.

If there was anything else I meant to say, I forgot.

Graham

🔗Daniel Nielsen <nielsed@uah.edu>

🔗genewardsmith <genewardsmith@sbcglobal.net>

🔗Graham Breed <gbreed@gmail.com>

"genewardsmith" <genewardsmith@sbcglobal.net> wrote:
>
> --- In tuning-math@yahoogroups.com, Graham Breed
> <gbreed@...> wrote:
>
> > I hope the following will continue to be Meantone
> > because I've been calling it Meantone (even if I didn't
> > notice) for a few years now and it makes much more
> > sense as the priveleged 13-limit extension.
> >
> > http://x31eq.com/cgi-bin/rt.cgi?limit=13&ets=12f+31
>
> Then let's call it meantone, and give another name to the
> other extension. What name?

Currently it's "Meaningless". If you can think of
something better, put it on the wiki and I'll pick it up.

While you're there, I found some other mappings that look
wrong. This is what I have as Squares in the 11-limit:

http://x31eq.com/cgi-bin/rt.cgi?limit=11&ets=31+14

I got another Squares from the wiki and can't work out why.

If I'm correctly guessing what an "Sval name" is, Nestoria,
in "chromatic pairs", should be:

http://x31eq.com/cgi-bin/rt.cgi?limit=2.3.5.19&ets=12+29

Whether that's right or not, the commas certainly disagree
with the mapping.

Athene is wrong, somewhere, probably a typo. It starts 0,
1, 2, 2, 4 instead of 0, 1 2, 4, 4. If I find where, I can
fix it, of course.

The other things on my problem list that I haven't tracked
down yet (with abbreviated Hermite normal forms):

Casablanca (19, 14, 4, 1, 12, 10, 5)
Sensis (8, 9, 13, 4, 10, 1, 6, 8, 11, 6, 10)
Roulette (2, 5, 9, -8, 1, 0, -3, -7, -13)
Casablanca (19, 14, 4, 1, 1, 12, 10, 5, 4)
Semigamera (46, 80, 2, 89, 1, 6, 10, 3, 12)
Gammic (20, 11, 96, 1, 2, 2, 0) not found
Bidia (1, -2, -5, -9, 8, 4, 0, 22, 43, 71, -36)
Escaped (9, -7, 26, 1, 2, 2, 3)
Baldy (1, -4, -7, 10, 1, 0, 15, 25, -8)
Gammic (20, 11, 1, 2, 2)
Tritonic (5, -11, -12, 28, 1, 4, -3, -3, 17)
Undecental (1, -37, -43, 1, 0, 61, 71)

The names I have and can assign a prime limit and equal
temperaments to are here:

http://x31eq.com/catalog2.html

Graham

🔗Graham Breed <gbreed@gmail.com>

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

> If you must worry, worry about Snape.

Why, would Britten fans object? Anyway, there's no Snape
on my list but there is a Luna.

I've reconciled a few more temperaments. Here are the ones
I'm still having trouble with:

Squares (4, 16, 9, -21, 1, 3, 8, 6, -4)
Sensis (8, 9, 13, 4, 10, 1, 6, 8, 11, 6, 10)
Roulette (2, 5, 9, -8, 1, 0, -3, -7, -13)
Semigamera (46, 80, 2, 89, 1, 6, 10, 3, 12)
Gammic (20, 11, 96, 1, 2, 2, 0)
Bidia (1, -2, -5, -9, 8, 4, 0, 22, 43, 71, -36)
Escaped (9, -7, 26, 1, 2, 2, 3)
Baldy (1, -4, -7, 10, 1, 0, 15, 25, -8)
Gammic (20, 11, 1, 2, 2)
Tritonic (5, -11, -12, 28, 1, 4, -3, -3, 17)
Hemigamera (23, 40, 1, 2, 12, 20, 6)

I don't think Hemigamera's a big problem because I used to
have it. I remember not being able to make sense of Baldy
or Tritonic.

Graham

🔗Herman Miller <hmiller@IO.COM>

On 4/28/2011 8:12 AM, Graham Breed wrote:
> "genewardsmith"<genewardsmith@sbcglobal.net> wrote:
>>
>> --- In tuning-math@yahoogroups.com, Graham Breed
>> <gbreed@...> wrote:
>>
>>> I hope the following will continue to be Meantone
>>> because I've been calling it Meantone (even if I didn't
>>> notice) for a few years now and it makes much more
>>> sense as the priveleged 13-limit extension.
>>>
>>> http://x31eq.com/cgi-bin/rt.cgi?limit=13&ets=12f+31
>>
>> Then let's call it meantone, and give another name to the
>> other extension. What name?
>
> Currently it's "Meaningless". If you can think of
> something better, put it on the wiki and I'll pick it up.
>
> While you're there, I found some other mappings that look
> wrong. This is what I have as Squares in the 11-limit:
>
> http://x31eq.com/cgi-bin/rt.cgi?limit=11&ets=31+14
>
> I got another Squares from the wiki and can't work out why.

That agrees with what I've got provisionally as squares.

[<1 3 8 6 7|, <0 -4 -16 -9 -10|]

> If I'm correctly guessing what an "Sval name" is, Nestoria,
> in "chromatic pairs", should be:
>
> http://x31eq.com/cgi-bin/rt.cgi?limit=2.3.5.19&ets=12+29
>
> Whether that's right or not, the commas certainly disagree
> with the mapping.
>
> Athene is wrong, somewhere, probably a typo. It starts 0,
> 1, 2, 2, 4 instead of 0, 1 2, 4, 4. If I find where, I can
> fix it, of course.
>
> The other things on my problem list that I haven't tracked
> down yet (with abbreviated Hermite normal forms):
>
> Casablanca (19, 14, 4, 1, 12, 10, 5)

I don't know how to interpret those numbers, but it's a temperament with a 19/42 generator. It came up in a discussion a few months ago on the tuning list, hmm almost a year ago actually, in a thread "Re: Two more 31-tet MOS's" in June 2010.

31&42 [<1 -7 -4 1|, <0 19 14 4|]

Gene suggested an 11-limit extension:

31&42 [<1 -7 -4 1 3|, <0 19 14 4 1|]

My temperament finder prefers this one, which however is inconsistent with the 19/42 generator:

31&73 [<1 -7 -4 1 -11|, <0 19 14 4 32|]

The 14/31 MOS could be considered as either of these. I'll suggest "marrakesh" for 31&73, leaving "casablanca" for 31&42.

🔗Graham Breed <gbreed@gmail.com>

Herman Miller <hmiller@IO.COM> wrote:
> On 4/28/2011 8:12 AM, Graham Breed wrote:

> > Casablanca (19, 14, 4, 1, 12, 10, 5)
>
> I don't know how to interpret those numbers, but it's a
> temperament with a 19/42 generator. It came up in a
> discussion a few months ago on the tuning list, hmm
> almost a year ago actually, in a thread "Re: Two more
> 31-tet MOS's" in June 2010.
>
> 31&42 [<1 -7 -4 1|, <0 19 14 4|]

That's it. It comes up in the search when I use 100 seed
ETs instead of 50.

> Gene suggested an 11-limit extension:
>
> 31&42 [<1 -7 -4 1 3|, <0 19 14 4 1|]

This is 526th in the 1-cent 11-limit list. (800
seeds.) I don't search that deep, so it's in a table of
exceptions instead.

> My temperament finder prefers this one, which however is
> inconsistent with the 19/42 generator:
>
> 31&73 [<1 -7 -4 1 -11|, <0 19 14 4 32|]
>
> The 14/31 MOS could be considered as either of these.
> I'll suggest "marrakesh" for 31&73, leaving "casablanca"
> for 31&42.

It's as consistent with 19/42 as anything else, because 42
is ambiguous. It happens to use the optimal mapping. It
comes 119th in the 1-cent list and is better than casablanca
in both error and complexity.

Here are the options:

http://x31eq.com/cgi-bin/rt.cgi?limit=11&ets=31+42

Graham

🔗genewardsmith <genewardsmith@sbcglobal.net>

🔗Graham Breed <gbreed@gmail.com>

I've now reconciles every name on the wiki with a pair of equal
temperaments. Where I think the mappings on the wiki were wrong, I've
corrected them. This affects:

Optimal patent val -- Sensis

Chromatic pairs -- Roulette, Baldy

Proposed names . . . -- Gammic, Escaped

Tritonic is listed with two different 11-limit mappings. In Proposed
names . . . it's 31&91e and in Optimal patent val it's 31&91p. 31&91e
looks better.

Changes to my website won't be visible until I connect with my laptop.
I do have a local copy of catalog2 that I can look to adding to the
files here.

Now I know what "Sensis" is, I've added it to the 11- and no-11-limits.

I made some rank 3 additions, but I lost the diffs, so I may not have
all of them here. But let's have a go.

To honor her new position as patron deity of tripod notation, Hecate
is added as a 13-limit Marvel:

<1, 0, 0, -5, 12, 2]
<0, 1, 0, 2, -1, 4]
<0, 0, 1, 2, -3, -2]

Artemis is an 11-limit Marvel permutation that tends to show up near
Apollo on the lists:

<1, 0, 1, -3, 2]
<0, 1, 1, 4, 1]
<0, 0, 2, 4, 1]

Isis is a 13-limit Marvel that extends will into the 17-limit, related
to Minerva and Necromancy:

<1, 0, 0, -5, 12, 17]
<0, 1, 0, 2, -1, -4]
<0, 0, 1, 2, -3, -3]

<0, 0, 1, 2, -3, -3, -1]
<0, 1, 0, 2, -1, -4, -1]
<1, 0, 0, -5, 12, 17, 8]

Aphrodite comes up in the 11-limit lists and so may as well have a name:

<0, 0, 4, 3, 2]
<0, 1, 1, 0, 1]
<1, 0, 1, 3, 2]

Zeus+ comes up in the 13-limit lists, so I've called it Zeus. There
are other possible extensions of Zeus, so see if this looks right:

<0, 0, 2, -3, 1, -1
<0, 1, 1, -1, 1, 1]
<1, 0, 1, 4, 2, 2]

Erato is extended to the 13-limit.

<0, 0, 0, 0, 1, 0]
<0, 1, 4, 10, 0, 15]
<1, 0, -4, -13, 0, -20]

Octagari extensions come up looking good in the 11- and 13-limit
lists, so they're now official:

<0, 0, 2, 3, 4]
<0, 1, 0, -2, -2]
<1, 0, 1, 4, 4]

<0, 0, 2, 3, 4, 5]
<0, 1, 0, -2, -2, -1]
<1, 0, 1, 4, 4, 2]

Graham