Temperament ideas: A cuckoo, and two oracles

Hi list,

here are some suggestions for temperaments related to 31-EDO which I
think could need a name.

The first one is a rank three temperament, defined in the 11- and 13-limit:

Cuckoo

Commas: 126/125, 243/242

Map: [<1 1 0 -3 2|, <0 2 0 -4 5|, <0 0 1 3 0|]
EDOs: 31 34 58 65 89 154 185 216

13-limit
Commas: 126/125, 196/195, 243/242

Map: [<1 1 0 -3 2 -5|, <0 2 0 -4 5 -10|, <0 0 1 3 0 5|]
EDOs: 31 58 65f 89f 92e 154 185 216f

Cuckoo tempers out the rastma 243/242, which means the fifth is split in
two neutral thirds 11/9. It also tempers out the starling comma 126/125,
so stacking three minor thirds 6/5 gives 12/7.

Possible generators for cuckoo are 2/1, 11/9, 6/5, or 2/1, 11/9, 5/4. One
way to look at it would be 7-limit starling with generators 2/1, 3/2, 6/5,
except that the 3/2 generator is split in two neutral thirds 11/9, extending
it to the 11-limit.
Another useful way to look at it would be as a variant of 11-limit mandos,
but with a different mapping for 7.

Related linear temperaments include myna, migration, wollemia,
worschmidt, cypress, hemisensi and monocerus.
The respective temperament finder links are here:
http://x31eq.com/cgi-bin/rt.cgi?ets=7d_31_27e&limit=11
http://x31eq.com/cgi-bin/rt.cgi?ets=38df_31_27e&limit=13

I gave it the name "cuckoo" because (a) a bird name would be appropriate
for a starling temperament, and (b) the intervals 6/5, 11/9, 5/4 and 4/3,
which are typical for a cuckoo, are within close reach of each other in this
temperament.

The other two (linear) temperaments are named after two oracles from
Epirus. The first one is an extension of 5-limit cypress:

Necromanteion
Commas: 1029/1024, 5103/5000

POTE generator: ~48/35 = 541.779

Map: [<1 7 10 1|, <0 -12 -17 4|]
EDOs: 11c, 20c, 31, 51c, 82c, 113c, 144c

11-limit
Commas: 176/175, 243/242, 1029/1024

POTE generator: ~15/11 = 541.729

Map: [<1 7 10 1 17|, <0 -12 -17 4 -30|]
EDOs: 31, 82c, 113c, 144c

13-limit
Commas: 144/143, 176/175, 243/242, 343/338

POTE generator: ~15/11 = 541.606

Map: [<1 7 10 1 17 1|, <0 -12 -17 4 -30 6|]
EDOs: 31, 51ce, 82cf, 113cf, 144cf

This temperament is very closely related to 31-EDO, and I think there is
no other important EDO that supports it using the patent val.
Like oracle, it tempers out the gamelisma 1029/1024, meaning the fifth 3/2
is split into three septimal wholetones 8/7. Unlike oracle, it uses 5103/5000
(instead of 225/224) to split the 8/7 into two secor-like semitones 27/25.
27/25^2 * 7/8. This semitone plus an octave is further split into two intervals
of 35/24 (or 22/15 in the 11-limit), the generator for this temperament.
In the 11-limit, it tempers out the valinorsma 176/175, equating the generator
35/24 with 22/15 (or 48/35 with 15/11, if you prefer), and 35/32 with 11/10.
It also tempers out the rastma 243/242, meaning 6 stacked generators
make a neutral third 11/9.

Tempering out 176/175, 243/242 and 144/143, necromanteion is strongly
related to mandos. It is identical to cypress in the 2.3.5.11-limit, and to
miracle in the (contorted) 2.3.7.11-limit if unmapped intervals are ignored.

Since I already named a temperament 'oracle', which splits 8/7 into four
approximate 540 cent steps and is related to miracle (or orwell) temperament,
I thought I could use specific oracle names for similar temperaments, and
choosing greek oracles somehow fits with the mediterranean theme of
other similar temperaments like 'casablanca' or 'cypress'.
'Necromanteion', the "Oracle of Death" (or "Oracle of the Dead") seemed
to go well with the mandos theme. I also read that cypresses are related to
the deceased; firstly, its "noble" wood seems to have been used for sarcophagi
by egypts, and secondly, they were apparently typical for roman cemeteries
or tombs.
However, I didn't verify the credibility of these claims, which I found here:
http://www.slowtuscany.it/tuscany/pisa/cypresses_1.htm

The second temperament which I decided to name after an oracle is simply
2.9.15.7.11-limit orwell, i.e. the subgroup orwell that results from doubling
its generator:

Dodona
Subgroup: 2.9.15.7.11
Commas: 99/98, 121/120, 176/175
Svalname: 11&31 (?)

Generator: ~11/8

Map: [<1 0 3 1 3|, <0 7 2 4 1|]
EDOs: 11, 22, 31, 42, 53, 84e

Dodona is an oracle where Zeus was worshipped, and this was the closest I
got to zeus temperament while fulfilling the above criteria.
(8/7 split into four ~540 cent intervals; related to miracle or orwell)
In the 11-limit, orwell tempers out all intervals which zeus does, so dodona
does the same in the 2.9.15.7.11-limit.

I'm not too familiar with subgroup temperaments, so the 'Svalname' might not
be what I assume it is, and I don't know how to calculate a POT2 generator.
Also, I don't know if the EDOs I listed for the temperaments are a good choice,
I just listed some which I think are worth mentioning. And I still don't know how
to calculate badness, so if those temperaments get approved, I'd be glad if
someone could calculate it for those (and for oracle). :)

Best
- Geddy

Ok, Graham has put the data for cuckoo and necromanteion in the temperament finder
database (many thanks!), and none complaint yet, so I assume there are no problems
with those suggestions.
If there should be any concerns about names or classification nonetheless, we can
discuss them, and maybe find a better compromise.

Speaking of classification: Where should I put necromanteion? I see only three more
or less reasonable options:

(1) Create a new page "Rastmic Temperaments" for linear temperaments that temper
out the rastma 243:242, and add cypress and necromanteion.
(2) Create a new page "Cypress Temperaments" for linear temperaments that temper
out 258280326/244140625, and add cypress and necromanteion.
(3) Keep cypress as a starling temperament, and add necromanteion to the gamelismic
clan.

#3 is possible, but I'm not very fond of the idea. #2 looks to me like the most solid solution.
#1 is interesting, but also a little unconventional, and I'm not sure how well it would work.

I'd love to get some feedback; if there's none I'll simply go for option #2.

- Geddy

P.S.: Here are the temperament finder links for necromanteion, seems I forgot them
in my previous post: http://x31eq.com/cgi-bin/rt.cgi?ets=31_51c&limit=7
http://x31eq.com/cgi-bin/rt.cgi?ets=31_51ce&limit=11

http://x31eq.com/cgi-bin/rt.cgi?ets=31_51ce&limit=13