98 named 7-limit temperaments

Below I give a name and wedgie for 98 rank-two 7-limit temperaments.
In cases where I have more than one name noted down, I just gave one,
which should give plenty of scope for people to make comments or issue
complaints. Note also that just because I know of a name for a
temperament, it does not mean it is better than all nameless
temperaments. The listed temperaments are chosen by no other system
than the fact that I have a name for them. The temperaments are listed
in order of increasing kees badness.

Comments and additions solicted.

Ennealimmal <<18 27 18 1 -22 -34||
Sesquiquartififths <<4 -32 -15 -60 -35 55||
Tertiaseptal <<22 -5 3 -59 -57 21||
Meantone <<1 4 10 4 13 12||
Pontiac <<1 -8 39 -15 59 113||
Magic <<5 1 12 -10 5 25||
Beep <<2 3 1 0 -4 -6||
Augie <<3 0 6 -7 1 14||
Pajara <<2 -4 -4 -11 -12 2||
Dominant <<1 4 -2 4 -6 -16||
Garibaldi <<1 -8 -14 -15 -25 -10||
Miracle <<6 -7 -2 -25 -20 15||
Orwell <<7 -3 8 -21 -7 27||
Hemiwuerschmidt <<16 2 5 -34 -37 6||
Father <<1 -1 3 -4 2 10||
Catakleismic <<6 5 22 -6 18 37||
Blackwood <<0 5 0 8 0 -14||
Neptune <<40 22 21 -58 -79 -13||
Sensi <<7 9 13 -2 1 5||
Hemififths <<2 25 13 35 15 -40||
Amity <<5 13 -17 9 -41 -76||
Diminished <<4 4 4 -3 -5 -2||
Mother <<1 -1 -2 -4 -6 -2||
Parakleismic <<13 14 35 -8 19 42||
Mavila <<1 -3 -4 -7 -9 -1||
Sharptone <<1 4 3 4 2 -4||
Injera <<2 8 8 8 7 -4||
Dicot <<2 1 6 -3 4 11||
Godzilla <<2 8 1 8 -4 -20||
Gamera <<23 40 1 10 -63 -110||
Waage <<0 12 24 19 38 22||
Wizard <<12 -2 20 -31 -2 52||
Keemun <<6 5 3 -6 -12 -7||
Negri <<4 -3 2 -14 -8 13||
Myna <<10 9 7 -9 -17 -9||
Valentine <<9 5 -3 -13 -30 -21||
Augene <<3 0 -6 -7 -18 -14||
Decimal <<4 2 2 -6 -8 -1||
Quasiorwell <<38 -3 8 -93 -94 27||
Unidec <<12 22 -4 7 -40 -71||
Superpyth <<1 9 -2 12 -6 -30||
Mutt <<21 3 -36 -44 -116 -92||
Mothra <<3 12 -1 12 -10 -36||
Rodan <<3 17 -1 20 -10 -50||
Hendecatonic <<11 -11 22 -43 4 82||
Misty <<3 -12 -30 -26 -56 -36||
Quartonic <<11 18 5 3 -23 -39||
Octokaidecal <<2 6 6 5 4 -3||
Hystrix <<3 5 1 1 -7 -12||
Porcupine <<3 5 -6 1 -18 -28||
Hedgehog <<6 10 10 2 -1 -5||
Jamesbond <<0 0 7 0 11 16||
Octacot <<8 18 11 10 -5 -25||
Hemithirds <<15 -2 -5 -38 -50 -6||
Harry <<12 34 20 26 -2 -49||
Flattone <<1 4 -9 4 -17 -32||
Diaschismic <<2 -4 -16 -11 -31 -26||
Superkleismic <<9 10 -3 -5 -30 -35||
Wuerschmidt <<8 1 18 -17 6 39||
Tritonic <<5 -11 -12 -29 -33 3||
Nautilus <<6 10 3 2 -12 -21||
Kwai <<1 33 27 50 40 -30||
Duodec <<0 0 12 0 19 28||
Hemikleismic <<12 10 -9 -12 -48 -49||
Triton <<3 -7 -8 -18 -21 1||
Liese <<3 12 11 12 9 -8||
Semisept <<17 6 15 -30 -24 18||
Nusecond <<11 13 17 -5 -4 3||
Guiron <<3 -24 -1 -45 -10 65||
Grendel <<23 -1 13 -55 -44 33||
Penta <<3 2 4 -4 -2 4||
Beatles <<2 -9 -4 -19 -12 16||
Shrutar <<4 -8 14 -22 11 55||
Clyde <<12 10 25 -12 6 30||
Hemischismic <<2 -16 -40 -30 -69 -48||
Hexe <<6 0 0 -14 -17 0||
Squares <<4 16 9 16 3 -24||
Lemba <<6 -2 -2 -17 -20 1||
Tritikleismic <<18 15 -6 -18 -60 -56||
Gorgo <<3 7 -1 4 -10 -22||
Schism <<1 -8 -2 -15 -6 18||
Doublewide <<8 6 6 -9 -13 -3||
Sidi <<4 2 9 -6 3 15||
Pelogic <<1 -3 5 -7 5 20||
Semiaug <<6 0 15 -14 7 35||
Slender <<13 -10 6 -46 -27 42||
Gidorah <<3 2 -1 -4 -10 -8||
Bisupermajor <<16 -10 34 -53 9 107||
Semififths <<2 8 -11 8 -23 -48||
Undecental <<1 -37 -43 -61 -71 4||
Quasisuper <<1 -13 -2 -23 -6 32||
Bohpier <<13 19 23 0 0 0||
Superpelog <<2 -6 1 -14 -4 19||
Bipelog <<2 -6 -6 -14 -15 3||
Grackle <<1 -8 -26 -15 -44 -38||
Muggles <<5 1 -7 -10 -25 -19||
Keen <<2 -4 18 -11 23 53||
Marvo <<6 17 46 13 56 59||

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:

> The temperaments are listed
> in order of increasing kees badness.

Defined using Kees generation complexity and Kees error?

> Comments and additions solicted.

> Meantone <<1 4 10 4 13 12||

For the purposes of my paper, I was naming TOP tuning systems in
order to label horagrams illustrating them. Since this tuning had the
same TOP tuning as 5-limit meantone, I used the same name. But if I
were naming wedgies or tuning maps instead, I'd call this by a
different name, perhaps 'Huygens'.

> Sensi <<7 9 13 -2 1 5||

Even my paper distinguished 'Sensipent' (5-limit) from 'Sensisept' (7-
limit) . . .

> Shrutar <<4 -8 14 -22 11 55||

Really? I thought I proposed Shrutar as an 11-limit temperament; the
Shrutar fretting Dave and I came up with is based on 11-limit ratios,
some of which remain just, and some of which are tempered.

> Pelogic <<1 -3 5 -7 5 20||

I might have trouble with that one :)

--- In tuning-math@yahoogroups.com, "Paul Erlich" <perlich@a...> wrote:
>
> --- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
> wrote:
>
> > The temperaments are listed
> > in order of increasing kees badness.
>
> Defined using Kees generation complexity and Kees error?

Exactly.

> Since this tuning had the
> same TOP tuning as 5-limit meantone, I used the same name. But if I
> were naming wedgies or tuning maps instead, I'd call this by a
> different name, perhaps 'Huygens'.

Wouldn't doing that merely invite confusion?

> > Sensi <<7 9 13 -2 1 5||
>
> Even my paper distinguished 'Sensipent' (5-limit) from 'Sensisept' (7-
> limit) . . .

Couldn't it at least be "sensipent" and "sensi"?

> > Shrutar <<4 -8 14 -22 11 55||
>
> Really? I thought I proposed Shrutar as an 11-limit temperament; the
> Shrutar fretting Dave and I came up with is based on 11-limit ratios,
> some of which remain just, and some of which are tempered.

The 7-limit temperament does not have a very different tuning, and is
the projection of the 11-limit temperament. As the 11-limit
temperament is more central, it makes a good deal of sense to give the
7-limit temperament the same name. The closest I know of to a
cross-limits comparitive badness which could be used to decide which
prime limit is "more central" is L-infinity TOP, but the theoretical
justification for using that to decide what the most important prime
limit is isn't very sound so far as I can see. But it might be worth
considering.

> > Pelogic <<1 -3 5 -7 5 20||
>
> I might have trouble with that one :)

I had two names marked down for that, the other being Hexadecimal.
What's your theory on this?

Great! My recommendation: put it on the Wikipedia.
-C.

At 04:25 PM 10/20/2005, you wrote:
>Below I give a name and wedgie for 98 rank-two 7-limit temperaments.
>In cases where I have more than one name noted down, I just gave one,
>which should give plenty of scope for people to make comments or issue
>complaints. Note also that just because I know of a name for a
>temperament, it does not mean it is better than all nameless
>temperaments. The listed temperaments are chosen by no other system
>than the fact that I have a name for them. The temperaments are listed
>in order of increasing kees badness.
>
>Comments and additions solicted.
>
>Ennealimmal <<18 27 18 1 -22 -34||
>Sesquiquartififths <<4 -32 -15 -60 -35 55||
>Tertiaseptal <<22 -5 3 -59 -57 21||
>Meantone <<1 4 10 4 13 12||
>Pontiac <<1 -8 39 -15 59 113||
>Magic <<5 1 12 -10 5 25||
>Beep <<2 3 1 0 -4 -6||
>Augie <<3 0 6 -7 1 14||
>Pajara <<2 -4 -4 -11 -12 2||
>Dominant <<1 4 -2 4 -6 -16||
>Garibaldi <<1 -8 -14 -15 -25 -10||
>Miracle <<6 -7 -2 -25 -20 15||
>Orwell <<7 -3 8 -21 -7 27||
>Hemiwuerschmidt <<16 2 5 -34 -37 6||
>Father <<1 -1 3 -4 2 10||
>Catakleismic <<6 5 22 -6 18 37||
>Blackwood <<0 5 0 8 0 -14||
>Neptune <<40 22 21 -58 -79 -13||
>Sensi <<7 9 13 -2 1 5||
>Hemififths <<2 25 13 35 15 -40||
>Amity <<5 13 -17 9 -41 -76||
>Diminished <<4 4 4 -3 -5 -2||
>Mother <<1 -1 -2 -4 -6 -2||
>Parakleismic <<13 14 35 -8 19 42||
>Mavila <<1 -3 -4 -7 -9 -1||
>Sharptone <<1 4 3 4 2 -4||
>Injera <<2 8 8 8 7 -4||
>Dicot <<2 1 6 -3 4 11||
>Godzilla <<2 8 1 8 -4 -20||
>Gamera <<23 40 1 10 -63 -110||
>Waage <<0 12 24 19 38 22||
>Wizard <<12 -2 20 -31 -2 52||
>Keemun <<6 5 3 -6 -12 -7||
>Negri <<4 -3 2 -14 -8 13||
>Myna <<10 9 7 -9 -17 -9||
>Valentine <<9 5 -3 -13 -30 -21||
>Augene <<3 0 -6 -7 -18 -14||
>Decimal <<4 2 2 -6 -8 -1||
>Quasiorwell <<38 -3 8 -93 -94 27||
>Unidec <<12 22 -4 7 -40 -71||
>Superpyth <<1 9 -2 12 -6 -30||
>Mutt <<21 3 -36 -44 -116 -92||
>Mothra <<3 12 -1 12 -10 -36||
>Rodan <<3 17 -1 20 -10 -50||
>Hendecatonic <<11 -11 22 -43 4 82||
>Misty <<3 -12 -30 -26 -56 -36||
>Quartonic <<11 18 5 3 -23 -39||
>Octokaidecal <<2 6 6 5 4 -3||
>Hystrix <<3 5 1 1 -7 -12||
>Porcupine <<3 5 -6 1 -18 -28||
>Hedgehog <<6 10 10 2 -1 -5||
>Jamesbond <<0 0 7 0 11 16||
>Octacot <<8 18 11 10 -5 -25||
>Hemithirds <<15 -2 -5 -38 -50 -6||
>Harry <<12 34 20 26 -2 -49||
>Flattone <<1 4 -9 4 -17 -32||
>Diaschismic <<2 -4 -16 -11 -31 -26||
>Superkleismic <<9 10 -3 -5 -30 -35||
>Wuerschmidt <<8 1 18 -17 6 39||
>Tritonic <<5 -11 -12 -29 -33 3||
>Nautilus <<6 10 3 2 -12 -21||
>Kwai <<1 33 27 50 40 -30||
>Duodec <<0 0 12 0 19 28||
>Hemikleismic <<12 10 -9 -12 -48 -49||
>Triton <<3 -7 -8 -18 -21 1||
>Liese <<3 12 11 12 9 -8||
>Semisept <<17 6 15 -30 -24 18||
>Nusecond <<11 13 17 -5 -4 3||
>Guiron <<3 -24 -1 -45 -10 65||
>Grendel <<23 -1 13 -55 -44 33||
>Penta <<3 2 4 -4 -2 4||
>Beatles <<2 -9 -4 -19 -12 16||
>Shrutar <<4 -8 14 -22 11 55||
>Clyde <<12 10 25 -12 6 30||
>Hemischismic <<2 -16 -40 -30 -69 -48||
>Hexe <<6 0 0 -14 -17 0||
>Squares <<4 16 9 16 3 -24||
>Lemba <<6 -2 -2 -17 -20 1||
>Tritikleismic <<18 15 -6 -18 -60 -56||
>Gorgo <<3 7 -1 4 -10 -22||
>Schism <<1 -8 -2 -15 -6 18||
>Doublewide <<8 6 6 -9 -13 -3||
>Sidi <<4 2 9 -6 3 15||
>Pelogic <<1 -3 5 -7 5 20||
>Semiaug <<6 0 15 -14 7 35||
>Slender <<13 -10 6 -46 -27 42||
>Gidorah <<3 2 -1 -4 -10 -8||
>Bisupermajor <<16 -10 34 -53 9 107||
>Semififths <<2 8 -11 8 -23 -48||
>Undecental <<1 -37 -43 -61 -71 4||
>Quasisuper <<1 -13 -2 -23 -6 32||
>Bohpier <<13 19 23 0 0 0||
>Superpelog <<2 -6 1 -14 -4 19||
>Bipelog <<2 -6 -6 -14 -15 3||
>Grackle <<1 -8 -26 -15 -44 -38||
>Muggles <<5 1 -7 -10 -25 -19||
>Keen <<2 -4 18 -11 23 53||
>Marvo <<6 17 46 13 56 59||
>
>
>
>
>
>
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>
>Yahoo! Groups Links
>
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>
>

>> Pelogic <<1 -3 5 -7 5 20||
>
>I might have trouble with that one :)

My recommendation: fix it on the wikipedia.
-Carl

>>> Pelogic <<1 -3 5 -7 5 20||
>>
>>I might have trouble with that one :)
>
>My recommendation: fix it on the wikipedia.
>-Carl

Oops, the Wikipedia isn't for unfinished research. Damnit.

Too bad Graham's Wiki isn't running on MediaWiki...

-Carl

--- In tuning-math@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
>
> Great! My recommendation: put it on the Wikipedia.

I don't think so, but I think it would be fair to put up a Wikipedia
article on miracle, as mentioned in New Yorker Magazine. What I'm
hoping is to get some feedback, and then put up a web page. That could
then be the publically available information you wanted. A five and
eleven limit page would also make sense.

Here are some more names from an old list I was keeping (probably nowhere near being complete). Most of these alternate names are no longer in use (except for a few like the ones in Paul's "Middle Path" paper, which I've marked with "MP"), but this could be useful for reference when reading through the archives.

Gene Ward Smith wrote:

> Pontiac <<1 -8 39 -15 59 113||
aka "infraschismic"

> Beep <<2 3 1 0 -4 -6||
compare with the 5-limit temperament also known as "bug"; this 7-limit one is different enough that I think it should keep the name "beep", and we can keep the older name "bug" for the 5-limit 27/25 temperament.

> Augie <<3 0 6 -7 1 14||
aka "augmented", "august" (MP). There are so many "aug-" names it gets confusing to remember which is which.

> Garibaldi <<1 -8 -14 -15 -25 -10||
aka "schismic"

> Blackwood <<0 5 0 8 0 -14||
aka "quintal", "blacksmith" (MP)

> Sensi <<7 9 13 -2 1 5||
aka "semisixths", "tiny diesic", "sensisept" (MP)

> Diminished <<4 4 4 -3 -5 -2||
aka "dimisept" (MP)

> Mavila <<1 -3 -4 -7 -9 -1||
aka "pelogic"

> Injera <<2 8 8 8 7 -4||
aka "double diatonic"

> Godzilla <<2 8 1 8 -4 -20||
aka "hemifourths", "semaphore" (MP)

> Waage <<0 12 24 19 38 22||
aka "compton" (MP), "duodecimal"

> Keemun <<6 5 3 -6 -12 -7||
aka "kleismic", "keenan"

> Negri <<4 -3 2 -14 -8 13||
aka "tertiathirds", "negrisept" (MP)

> Myna <<10 9 7 -9 -17 -9||
aka "nonkleismic", "small diesic"

> Valentine <<9 5 -3 -13 -30 -21||
aka "quartaminorthirds"

> Augene <<3 0 -6 -7 -18 -14||
aka "tripletone" (a name that I prefer, to avoid confusion with all those "aug-" names)

> Superpyth <<1 9 -2 12 -6 -30||
aka "superpythagorean"

> Mothra <<3 12 -1 12 -10 -36||
aka "supermajor seconds", "cynder" (MP)

> Rodan <<3 17 -1 20 -10 -50||
aka "supersupermajor"

> Octokaidecal <<2 6 6 5 4 -3||
aka "supersharp"

> Octacot <<8 18 11 10 -5 -25||
aka "octafifths"

> Duodec <<0 0 12 0 19 28||
aka "catler" (MP)

> Liese <<3 12 11 12 9 -8||
aka "gawel"

> Beatles <<2 -9 -4 -19 -12 16||
aka "neutral thirds"

> Pelogic <<1 -3 5 -7 5 20||
aka "hexadecimal"

"Pelogic" vs. "mavila" vs. "hexadecimal"... before we started using "mavila" for the 5-limit temperament, I recommended calling this one "pelogic" as opposed to <<1 -3 -4 -7 -9 -1||. Now I almost think we'd be better off keeping "hexadecimal" for this one; at least it's not been used for anything else. I don't know what would be a good name for the other one, though.

> Semififths <<2 8 -11 8 -23 -48||
Confusingly similar to "hemififths".... (but I don't know of another name for it)

> Keen <<2 -4 18 -11 23 53||
may have been called "diaschismic", but that name is probably better for <<2 -4 -16 -11 -31 -26||.

A couple more names from my list:

vulture <<4, 21, -3, 24, -16, -66||
septimin <<11, -6, 10, -35, -15, 40||

"Vulture" is familiar, but not "septimin". I don't remember where I got that, but it must be in the archive somewhere.

>I don't think so, but I think it would be fair to put up a Wikipedia
>article on miracle, as mentioned in New Yorker Magazine.

Whaat??

-Carl

--- In tuning-math@yahoogroups.com, Herman Miller <hmiller@I...> wrote:
>
> Here are some more names from an old list I was keeping (probably
> nowhere near being complete). Most of these alternate names are no
> longer in use (except for a few like the ones in Paul's "Middle Path"
> paper, which I've marked with "MP"), but this could be useful for
> reference when reading through the archives.

> > Augie <<3 0 6 -7 1 14||
> aka "augmented", "august" (MP). There are so many "aug-" names it gets
> confusing to remember which is which.

I'm OK with "August". It puts me in mind of my grandfather August
Smith, so I'll just assume we are naming the temperament in his honor.

> > Blackwood <<0 5 0 8 0 -14||
> aka "quintal", "blacksmith" (MP)

What should this be?

> > Sensi <<7 9 13 -2 1 5||
> aka "semisixths", "tiny diesic", "sensisept" (MP)
>
> > Diminished <<4 4 4 -3 -5 -2||
> aka "dimisept" (MP)

Dimisept will do. I'd rather just call "sensisept" "sensi".

> > Waage <<0 12 24 19 38 22||
> aka "compton" (MP), "duodecimal"

Is "Compton" the latest theory on what this should be called, and who
is Compton?

> > Negri <<4 -3 2 -14 -8 13||
> aka "tertiathirds", "negrisept" (MP)

I'm OK with "negrisept".

> > Augene <<3 0 -6 -7 -18 -14||
> aka "tripletone" (a name that I prefer, to avoid confusion with all
> those "aug-" names)

"Tripletone" was my original name for it. Paul?

> > Godzilla <<2 8 1 8 -4 -20||
> aka "hemifourths", "semaphore" (MP)
>
> > Mothra <<3 12 -1 12 -10 -36||
> aka "supermajor seconds", "cynder" (MP)
>
> > Rodan <<3 17 -1 20 -10 -50||
> aka "supersupermajor"

The Japanese monster names flag an 8/7 generator; "semaphore" is cute
but I like the idea of the generator flag.

> > Octacot <<8 18 11 10 -5 -25||
> aka "octafifths"

Octacot, which goes with tetracot and dicot, makes it into a family
affair.

> > Duodec <<0 0 12 0 19 28||
> aka "catler" (MP)

I think if Paul uses Catler we may as well make that the name.

> > Beatles <<2 -9 -4 -19 -12 16||
> aka "neutral thirds"

It's got a 49/40 generator, and 2401/2400 is a comma of the system,
but it isn't a very accurate temperament in comparison to 2401/2400.
Hemififths would be more logical for the name.

> > Pelogic <<1 -3 5 -7 5 20||
> aka "hexadecimal"

> "Pelogic" vs. "mavila" vs. "hexadecimal"... before we started using
> "mavila" for the 5-limit temperament, I recommended calling this one
> "pelogic" as opposed to <<1 -3 -4 -7 -9 -1||. Now I almost think
we'd be
> better off keeping "hexadecimal" for this one; at least it's not been
> used for anything else. I don't know what would be a good name for the
> other one, though.

I'm OK with "hexadecimal" for this one, if Paul objects to "pelogic",
but Paul didn't explain what was wrong with "pelogic".

> > Semififths <<2 8 -11 8 -23 -48||
> Confusingly similar to "hemififths".... (but I don't know of another
> name for it)

Anyone else have an idea about this?

> vulture <<4, 21, -3, 24, -16, -66||

It should get another name than "vulture" if we follow the ideas that
differing TOP tunings and a low Linf badness for the 5-limit than the
7-limit suggest this. "Buzzard" would be one possibility, and

> septimin <<11, -6, 10, -35, -15, 40||

I've added it to my list, where for some reason it was omitted.

Gene Ward Smith wrote:
>>>Blackwood <<0 5 0 8 0 -14||
>>
>>aka "quintal", "blacksmith" (MP)
> > > What should this be? I would've just called it "blackwood" (or "7-limit blackwood" if the distinction is necessary), but the TOP tuning is a bit different from 5-limit blackwood, so I don't have any problem with naming it something different.

> The Japanese monster names flag an 8/7 generator; "semaphore" is cute
> but I like the idea of the generator flag.

I also like the Japanese monster names (and in general, families of related names for similar temperaments like "porcupine" and "hystrix", or "grackle" and "myna", or as you mentioned, the "dicot", "tetracot", "octacot" series).

>>>Beatles <<2 -9 -4 -19 -12 16||
>>
>>aka "neutral thirds"
> > > It's got a 49/40 generator, and 2401/2400 is a comma of the system,
> but it isn't a very accurate temperament in comparison to 2401/2400.
> Hemififths would be more logical for the name.

But hemififths is already used. I don't like "neutral thirds" either, because the first thing that comes to mind is dicot (since it obliterates the distinction between major and minor thirds by tempering out 25/24). Two 7-limit "neutral third"-based temperaments are <<2, 1, 6, -3, 4, 11|| and <<2, 1, -4, -3, -12, -12||, but neither of these is very close to 5-limit dicot.

>>vulture <<4, 21, -3, 24, -16, -66||
> > > It should get another name than "vulture" if we follow the ideas that
> differing TOP tunings and a low Linf badness for the 5-limit than the
> 7-limit suggest this. "Buzzard" would be one possibility, and Does 5-limit vulture really need a different name? I thought this was one of the ones that only becomes interesting in higher limits. The TOP tuning for the octave is only 0.66 cents different between the 5 and 7 limit. To me that's not a very big difference, but it might be to someone who'd be interested in a temperament as complex as vulture. But yes, "buzzard" would be one possibility, and "condor" for another related temperament if one turns up.

--- In tuning-math@yahoogroups.com, Herman Miller <hmiller@I...> wrote:
>
> Gene Ward Smith wrote:
> >>>Blackwood <<0 5 0 8 0 -14||
> >>
> >>aka "quintal", "blacksmith" (MP)
> >
> >
> > What should this be?
>
> I would've just called it "blackwood" (or "7-limit blackwood" if the
> distinction is necessary), but the TOP tuning is a bit different from
> 5-limit blackwood, so I don't have any problem with naming it something
> different.

Paul seems to want to call it "blacksmith", which would link it to the
5-limit name at any rate.

> But hemififths is already used.

I just meant that "neutral thirds" would have made more sense for the
hemififths temperament name, but I don't much like it because it is
associated to dicot in my mind. Graham has a planar temperament in
mind for it.

> > It should get another name than "vulture" if we follow the ideas that
> > differing TOP tunings and a low Linf badness for the 5-limit than the
> > 7-limit suggest this. "Buzzard" would be one possibility, and
>
> Does 5-limit vulture really need a different name? I thought this was
> one of the ones that only becomes interesting in higher limits. The TOP
> tuning for the octave is only 0.66 cents different between the 5 and 7
> limit. To me that's not a very big difference, but it might be to
> someone who'd be interested in a temperament as complex as vulture.

There's a good case for it. "Buzzard" is a microtemperament, whereas
"vulture" is a nanotemperament. "Vulture" is not more interesting in
higher limits; it turned up first in the 5-limit as a nanotemperament.

Gene Ward Smith wrote:

>>But hemififths is already used.
> > I just meant that "neutral thirds" would have made more sense for the
> hemififths temperament name, but I don't much like it because it is
> associated to dicot in my mind. Graham has a planar temperament in
> mind for it.

If I say "neutral thirds scale" I'll usually mean an MOS with two generators to a perfect fifth, or variations like the quartertonal Arabic Rast. Typically, that means the generator is identified with 11:9 and so 243:242 is tempered out. The mappings to other primes would depend on what tuning you look at and in what context, so "neutral thirds" is a family of families, like "meantone", "schismic" or "diaschismic" in higher limits. Except that it's defined by a 1.3.11 comma instead of a 1.3.5 one.

I also have a "7-limit neutral thirds lattice" which requires 2401:2400 to be tempered out and so could represent a planar temperament (usually with 243:242 tempered out as well). But the "7-limit" is as important as "neutral thirds" for that.

I don't have any designs on "hemififths".

Graham

--- In tuning-math@yahoogroups.com, Graham Breed <gbreed@g...> wrote:

> I also have a "7-limit neutral thirds lattice" which requires 2401:2400
> to be tempered out and so could represent a planar temperament (usually
> with 243:242 tempered out as well). But the "7-limit" is as important
> as "neutral thirds" for that.

I've been calling the lattice of pitch classes with generators 10/7
and 49/40 the "breed plane". Is that how you do things?

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
>
> --- In tuning-math@yahoogroups.com, "Paul Erlich" <perlich@a...>
wrote:
> >
> > --- In tuning-math@yahoogroups.com, "Gene Ward Smith"
<gwsmith@s...>
> > wrote:
> >
> > > The temperaments are listed
> > > in order of increasing kees badness.
> >
> > Defined using Kees generation complexity and Kees error?
>
> Exactly.
>
> > Since this tuning had the
> > same TOP tuning as 5-limit meantone, I used the same name. But if
I
> > were naming wedgies or tuning maps instead, I'd call this by a
> > different name, perhaps 'Huygens'.
>
> Wouldn't doing that merely invite confusion?

If you're using "meantone" to refer both to a tuning system and to a
wedgie/map, yes, that could be confusing. In my paper, though, I only
named the former.

:)

(Quite a cop-out, I know . . .)

>> > > Sensi <<7 9 13 -2 1 5||
>> >
>> > Even my paper distinguished 'Sensipent' (5-limit)
from 'Sensisept' (7-
>> > limit) . . .
>
>> Couldn't it at least be "sensipent" and "sensi"?

Why is 7-limit the default?

> > > Shrutar <<4 -8 14 -22 11 55||
> >
> > Really? I thought I proposed Shrutar as an 11-limit temperament;
the
> > Shrutar fretting Dave and I came up with is based on 11-limit
ratios,
> > some of which remain just, and some of which are tempered.
>
> The 7-limit temperament does not have a very different tuning, and
is
> the projection of the 11-limit temperament. As the 11-limit
> temperament is more central, it makes a good deal of sense to give
the
> 7-limit temperament the same name.

?

> > > Pelogic <<1 -3 5 -7 5 20||
> >
> > I might have trouble with that one :)
>
> I had two names marked down for that, the other being Hexadecimal.
> What's your theory on this?

Is Gamelan music in Pelog 7-limit in any sense?

:)

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:

> Is "Compton" the latest theory on what this should be called, and
who
> is Compton?

I got it from here:

http://www.freelists.org/archives/tuning-math/07-2002/msg00058.html

>
> > > Godzilla <<2 8 1 8 -4 -20||
> > aka "hemifourths", "semaphore" (MP)
> >
> > > Mothra <<3 12 -1 12 -10 -36||
> > aka "supermajor seconds", "cynder" (MP)
> >
> > > Rodan <<3 17 -1 20 -10 -50||
> > aka "supersupermajor"
>
> The Japanese monster names flag an 8/7 generator; "semaphore" is
cute
> but I like the idea of the generator flag.

Thanks. "Semaphore" means talking with flags and it also tells you
(flags you?) that the generator is a semifourth.

> > > Octacot <<8 18 11 10 -5 -25||
> > aka "octafifths"
>
> Octacot, which goes with tetracot and dicot, makes it into a family
> affair.

But are they really comparable in terms of complexity? Or do other
things really deserve the same names?

>
> > > Beatles <<2 -9 -4 -19 -12 16||
> > aka "neutral thirds"
>
> It's got a 49/40 generator, and 2401/2400 is a comma of the system,
> but it isn't a very accurate temperament in comparison to 2401/2400.

So?

> Hemififths would be more logical for the name.
>
> > > Semififths <<2 8 -11 8 -23 -48||
> > Confusingly similar to "hemififths".... (but I don't know of
another
> > name for it)
>
> Anyone else have an idea about this?
>
> > vulture <<4, 21, -3, 24, -16, -66||
>
> It should get another name than "vulture" if we follow the ideas
that
> differing TOP tunings and a low

Lower?

> Linf

Could we use L1 instead?

--- In tuning-math@yahoogroups.com, "Paul Erlich" <perlich@a...> wrote:

> Why is 7-limit the default?

It strikes me as marginally more significant, but that really depends
on what kind of temperament interests you. The 7-limit version is not
as well in tune, but still pretty good in that department--comperable
to meantone but a bit better.

> > > > Pelogic <<1 -3 5 -7 5 20||
> > >
> > > I might have trouble with that one :)
> >
> > I had two names marked down for that, the other being Hexadecimal.
> > What's your theory on this?
>
> Is Gamelan music in Pelog 7-limit in any sense?

I imagine you could tune a gamelan orchestra to a lot of things,
including this, with good success. But another idea for naming it
might be to use the fact that 23 steps of 41edo is a generator.

Gene Ward Smith wrote:
> --- In tuning-math@yahoogroups.com, "Paul Erlich" <perlich@a...> wrote:
>>
>>Is Gamelan music in Pelog 7-limit in any sense?
> > > I imagine you could tune a gamelan orchestra to a lot of things,
> including this, with good success. But another idea for naming it
> might be to use the fact that 23 steps of 41edo is a generator.

Generally I've found that selecting 7 notes from a 9-note MOS/DE scale tends to produce good pelog scales. You could even do something like 7 out of 9 out of 16 (as I've done when playing around with lemba[16] on the keyboard). Occasionally you might hear some harmonic progressions in gamelan music that make sense as 5-limit mavila, but I don't think that's very common. The tuning is so variable from one place to another that in the general case, I don't think it makes a whole lot of sense to think of pelog as a 7-limit scale. Jegog is a special case; essentially the 4-note scale sounds like a 4:5:6:7 tetrad.

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
>
> --- In tuning-math@yahoogroups.com, "Paul Erlich" <perlich@a...>
wrote:
>
> > Why is 7-limit the default?
>
> It strikes me as marginally more significant, but that really depends
> on what kind of temperament interests you. The 7-limit version is not
> as well in tune,

?