24 7-limit temperaments with 245/243 as a comma

"Clyde" comes from the kleisma; I was thinking bi and clyde was sort
of like Bonnie and Clyde, but it isn't a bi, it's a semi. "Sidi" is
short for "semidicot", and "semiaug" for "semiaugmented". "Bohpier",
of course, comes from Bohlen and Pierce.

The numbers on the third line are Graham complexity, TOP error, TOP
badness and Graham-TOP badness. I used TOP l-infinity badness to sort
since that is more intrinsic than Graham, but it seems to make no
difference.

magic
[5, 1, 12, -10, 5, 25]
[[1, 0, 2, -1], [0, 5, 1, 12]]
12 1.276744 183.851136 23.327687

father
[1, -1, 3, -4, 2, 10]
[[1, 2, 2, 4], [0, -1, 1, -3]]
4 14.130875 226.094010 33.256527

sensi/semisixths
[7, 9, 13, -2, 1, 5]
[[1, -1, -1, -2], [0, 7, 9, 13]]
13 1.610469 272.169318 34.533812

godzilla/hemifourths
[2, 8, 1, 8, -4, -20]
[[1, 2, 4, 3], [0, -2, -8, -1]]
8 3.668842 234.805888 43.552336

superpythagorean
[1, 9, -2, 12, -6, -30]
[[1, 2, 6, 2], [0, -1, -9, 2]]
11 2.403879 290.869402 50.917023

rodan/supersupermajor
[3, 17, -1, 20, -10, -50]
[[1, 1, -1, 3], [0, 3, 17, -1]]
18 .894655 289.868296 52.638504

hedgehog
[6, 10, 10, 2, -1, -5]
[[2, 4, 6, 7], [0, -3, -5, -5]]
10 3.106578 310.657834 57.621529

octacot
[8, 18, 11, 10, -5, -25]
[[1, 1, 1, 2], [0, 8, 18, 11]]
18 .968741 313.872084 58.217715

shrutar
[4, -8, 14, -22, 11, 55]
[[2, 3, 5, 5], [0, 2, -4, 7]]
22 1.079127 522.297520 76.825572

clyde Number 78 {245/243, 3136/3125}
[12, 10, 25, -12, 6, 30]
[[1, 6, 6, 12], [0, -12, -10, -25]]
25 .971298 607.061287 77.026097

sidi Number 93 {25/24, 245/243}
[4, 2, 9, -6, 3, 15]
[[1, 3, 3, 6], [0, -4, -2, -9]]
9 8.170435 661.805266 83.972208

semiaug Number 95 {128/125, 245/243}
[6, 0, 15, -14, 7, 35]
[[3, 5, 7, 9], [0, -2, 0, -5]]
15 2.939961 661.491318 84.758945

bohpier Number 106 {245/243, 3125/3087}
[13, 19, 23, 0, 0, 0]
[[1, 0, 0, 0], [0, 13, 19, 23]]
23 1.408527 745.110689 94.757554

[2, -16, 13, -30, 15, 75]
[[1, 1, 7, -1], [0, 2, -16, 13]]
29 .894655 752.405053 118.436634

[3, -7, 11, -18, 9, 45]
[[1, 3, -1, 8], [0, -3, 7, -11]]
18 2.563758 830.657592 122.182745

[9, -7, 26, -32, 16, 80]
[[1, 2, 2, 4], [0, -9, 7, -26]]
33 .894655 974.279552 134.754571

[15, 27, 24, 8, -4, -20]
[[3, 7, 11, 12], [0, -5, -9, -8]]
27 1.015676 740.428092 137.336304

[9, 17, 14, 6, -3, -15]
[[1, 3, 5, 5], [0, -9, -17, -14]]
17 2.747484 794.022876 147.277188

[17, 11, 37, -22, 11, 55]
[[1, -2, 0, -5], [0, 17, 11, 37]]
37 .894655 1224.783018 155.404830

[8, 8, 16, -6, 3, 15]
[[8, 13, 19, 23], [0, -1, -1, -2]]
16 4.953617 1268.126009 160.904343

[5, 11, 7, 6, -3, -15]
[[1, 1, 1, 2], [0, 5, 11, 7]]
11 7.195870 870.700224 161.499478

[2, -6, 8, -14, 7, 35]
[[2, 3, 5, 5], [0, 1, -3, 4]]
14 7.149508 1401.303568 206.119969

[0, 10, -5, 16, -8, -40]
[[5, 8, 12, 14], [0, 0, -2, 1]]
15 5.665687 1274.779496 213.343963

[22, 36, 37, 6, -3, -15]
[[1, -9, -15, -15], [0, 22, 36, 37]]
37 1.149341 1573.448359 276.284496

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

> godzilla/hemifourths
> [2, 8, 1, 8, -4, -20]
> [[1, 2, 4, 3], [0, -2, -8, -1]]

Herman's chart calls this "mothra". My paper calls it "semaphore".
Let's call the whole thing off :)

Paul Erlich wrote:

> --- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> > wrote:
> > >>godzilla/hemifourths
>>[2, 8, 1, 8, -4, -20]
>>[[1, 2, 4, 3], [0, -2, -8, -1]]
> > > Herman's chart calls this "mothra". My paper calls it "semaphore". > Let's call the whole thing off :)

"Mothra" is <<3, 12, -1, 12, -10, -36|| (formerly known as "supermajor seconds"). I've added "Cynder" to my list of names, but I haven't decided yet which one I prefer.

Actually, I think I prefer calling it "5&26" until I get more familiar with it. Godzilla/hemifourths/semaphore would be "5&19". In fact, almost all the useful temperaments can be named this way (if you specify the prime limit). Miracle is 10&31, porcupine is 7&8 in the 5-limit version, 15&22 in the 7-limit version (avoiding the 7-limit inconsistent ET's 7 and 8), negri is 9&10 (no surprise there), orwell is 9&22. This can be extended to naming planar temperaments, with starling as an example being 4&12&15; this immediately lets you know that 4&12 (diminished), 4&15 (kleismic) and 12&15 (tripletone) are starling temperaments.

As an added bonus, if the ET's are consistent in a higher limit, there's no question which ET should get the name; in the case of porcupine, 15&22 in the 11-limit is <<3, 5, -6, 4, 1, -18, -4, -28, -8, 32|| (map [<1, 2, 3, 2, 4|, <0, -3, -5, 6, -4|]). By that logic, 7-limit 12&29 <<1, -8, -14, -15, -25, -10|| should have the same name as 5-limit 12&29 <<1, -8, -15|| (schismic). But once you get to the 11-limit, 12-ET is inconsistent.