A brief detour: some good 11-limit temperaments

Before going back to the rest of the 7-limit temperaments in Paul's "Middle Path" paper, I thought it might be good to look at a comparable list of 11-limit temperaments. But I don't know of a comparable list, so I'm trying to put one together. I've sorted these temperaments by wedgie complexity. Does this look like a good list?

Dominant
[<1, 2, 4, 2, 1], <0, -1, -4, 2, 6]>
TOP P = 1195.035871, G = 495.575856
TOP-RMS P = 1194.104516, G = 494.305885

Injera
[<2, 3, 4, 5, 6], <0, 1, 4, 4, 6]>
TOP P = 600.000000, G = 94.224448) (e.g.)
TOP-RMS P = 600.959942, G = 92.988654

Augene
[<3, 5, 7, 8, 10], <0, -1, 0, 2, 2]>
TOP P = 398.877558, G = 87.095701
TOP-RMS P = 398.505949, G = 88.491624

Hedgehog
[<2, 4, 6, 7, 8], <0, -3, -5, -5, -4]>
TOP P = 599.090477, G = 163.146764
TOP-RMS P = 600.129682, G = 164.649752

Keemun
[<1, 0, 1, 2, 0], <0, 6, 5, 3, 13]>
TOP P = 1202.785732, G = 318.158024) (e.g.)
TOP-RMS P = 1201.710288, G = 318.108390

Porcupine
[<1, 2, 3, 2, 4], <0, -3, -5, 6, -4]>
TOP P = 1198.230132, G = 163.153461
TOP-RMS P = 1198.352019, G = 162.523871

Pajara
[<2, 3, 5, 6, 8], <0, 1, -2, -2, -6]>
TOP P = 598.446711, G = 106.566546
TOP-RMS P = 598.859505, G = 106.681973

Meantone
[<1, 2, 4, 7, 11], <0, -1, -4, -10, -18]>
TOP P = 1201.611156, G = 504.023348
TOP-RMS PI P = 1200.772217, G = 503.355024

Orwell
[<1, 0, 3, 1, 3], <0, 7, -3, 8, 2]>
TOP P = 1201.251092, G = 271.425083
TOP-RMS PI P = 1200.604456, G = 271.562848

Squares
[<1, 3, 8, 6, 7], <0, -4, -16, -9, -10]>
TOP P = 1201.698520, G = 426.458163
TOP-RMS P = 1201.674433, G = 426.551643

Valentine
[<1, 1, 2, 3, 3], <0, 9, 5, -3, 7]>
TOP P = 1200.870043, G = 77.627882
TOP-RMS P = 1200.393486, G = 77.906789

Semififth
[<1, 1, 0, 6, 2], <0, 2, 8, -11, 5]>
TOP P = 1201.698520, G = 348.782195
TOP-RMS P = 1201.165244, G = 348.815068

Magic
[<1, 0, 2, -1, 6], <0, 5, 1, 12, -8]>
TOP P = 1200.749423, G = 380.922404
TOP-RMS P = 1200.143482, G = 380.741936

Meanpop
[<1, 2, 4, 7, -2], <0, -1, -4, -10, 13]>
TOP P = 1201.698520, G = 504.134131
TOP-RMS P = 1201.352803, G = 504.133204

"Schismic" (could use a better name)
[<1, 2, -1, -3, -4], <0, -1, 8, 14, 18]>
TOP P = 1201.362994, G = 497.941436
TOP-RMS P = 1200.198852, G = 497.711073

Cynder/Mothra
[<1, 1, 0, 3, 5], <0, 3, 12, -1, -8]>
TOP P = 1201.698520, G = 232.521463
TOP-RMS P = 1201.405762, G = 232.302506

Superkleismic
[<1, 4, 5, 2, 4], <0, -9, -10, 3, -2]>
TOP P = 1200.048336, G = 321.753163
TOP-RMS P = 1200.176054, G = 321.893777

Myna
[<1, -1, 0, 1, -3], <0, 10, 9, 7, 25]>
TOP P = 1198.828458, G = 309.892661
TOP-RMS P = 1199.347123, G = 309.975532

Sensi
[<1, -1, -1, -2, -8], <0, 7, 9, 13, 31]>
TOP P = 1198.389531, G = 443.160293
TOP-RMS P = 1199.077830, G = 443.285541

Miracle
[<1, 1, 3, 3, 2], <0, 6, -7, -2, 15]>
TOP P = 1200.631014, G = 116.720642
TOP-RMS P = 1200.763536, G = 116.706954

Shrutar
[<2, 3, 5, 5, 7], <0, 2, -4, 7, -1]>
TOP P = 599.822848, G = 52.372763
TOP-RMS P = 599.774873, G = 52.660207

Tritonic
[<1, 4, -3, -3, 2], <0, -5, 11, 12, 3]>
TOP P = 1201.417748, G = 581.192614
TOP-RMS P = 1201.715717, G = 581.096970

Bohpier
[<1, 0, 0, 0, 2], <0, 13, 19, 23, 12]>
TOP P = 1198.828896, G = 146.475959 (e.g.)
TOP-RMS P = 1199.236235, G = 146.451310

Diaschismic
[<2, 3, 5, 7, 9], <0, 1, -2, -8, -12]>
TOP P = 599.366202, G = 103.787012
TOP-RMS P = 599.448788, G = 103.618927

Rodan
[<1, 1, -1, 3, 6], <0, 3, 17, -1, -13]>
TOP P = 1200.230389, G = 234.381795
TOP-RMS P = 1200.057139, G = 234.469894

Wizard
[<2, 1, 5, 2, 8], <0, 6, -1, 10, -3]>
TOP P = 600.319786, G = 216.770253)
TOP-RMS P = 600.305522, G = 216.878315

For "schismic", one problem is that both "schismic" and "schismatic" have been used -- for different temperaments! "Schismic" is obviously some variety of garibaldi, but [<1, 2, -1, -3, 13], <0, -1, 8, 14, -23]> is closer to 7-limit garibaldi. There are still other versions of garibaldi, like [<1, 2, -1, -3, -9], <0, -1, 8, 14, 30]>. We could name them after other fish in the damselfish family or related species.... I know, garibaldi the temperament isn't named after the fish, but....

--- In tuning-math@yahoogroups.com, Herman Miller <hmiller@...> wrote:
>
> Before going back to the rest of the 7-limit temperaments in Paul's
> "Middle Path" paper, I thought it might be good to look at a
comparable
> list of 11-limit temperaments. But I don't know of a comparable
list, so
> I'm trying to put one together. I've sorted these temperaments by
wedgie
> complexity. Does this look like a good list?
>
> Dominant
> [<1, 2, 4, 2, 1], <0, -1, -4, 2, 6]>
> TOP P = 1195.035871, G = 495.575856
> TOP-RMS P = 1194.104516, G = 494.305885
>
> Injera
> [<2, 3, 4, 5, 6], <0, 1, 4, 4, 6]>
> TOP P = 600.000000, G = 94.224448) (e.g.)
> TOP-RMS P = 600.959942, G = 92.988654
>
> Augene
> [<3, 5, 7, 8, 10], <0, -1, 0, 2, 2]>
> TOP P = 398.877558, G = 87.095701
> TOP-RMS P = 398.505949, G = 88.491624
>
> Hedgehog
> [<2, 4, 6, 7, 8], <0, -3, -5, -5, -4]>
> TOP P = 599.090477, G = 163.146764
> TOP-RMS P = 600.129682, G = 164.649752
>
> Keemun
> [<1, 0, 1, 2, 0], <0, 6, 5, 3, 13]>
> TOP P = 1202.785732, G = 318.158024) (e.g.)
> TOP-RMS P = 1201.710288, G = 318.108390
>
> Porcupine
> [<1, 2, 3, 2, 4], <0, -3, -5, 6, -4]>
> TOP P = 1198.230132, G = 163.153461
> TOP-RMS P = 1198.352019, G = 162.523871
>
> Pajara
> [<2, 3, 5, 6, 8], <0, 1, -2, -2, -6]>
> TOP P = 598.446711, G = 106.566546
> TOP-RMS P = 598.859505, G = 106.681973
>
> Meantone
> [<1, 2, 4, 7, 11], <0, -1, -4, -10, -18]>
> TOP P = 1201.611156, G = 504.023348
> TOP-RMS PI P = 1200.772217, G = 503.355024
>
> Orwell
> [<1, 0, 3, 1, 3], <0, 7, -3, 8, 2]>
> TOP P = 1201.251092, G = 271.425083
> TOP-RMS PI P = 1200.604456, G = 271.562848
>
> Squares
> [<1, 3, 8, 6, 7], <0, -4, -16, -9, -10]>
> TOP P = 1201.698520, G = 426.458163
> TOP-RMS P = 1201.674433, G = 426.551643
>
> Valentine
> [<1, 1, 2, 3, 3], <0, 9, 5, -3, 7]>
> TOP P = 1200.870043, G = 77.627882
> TOP-RMS P = 1200.393486, G = 77.906789
>
> Semififth
> [<1, 1, 0, 6, 2], <0, 2, 8, -11, 5]>
> TOP P = 1201.698520, G = 348.782195
> TOP-RMS P = 1201.165244, G = 348.815068
>
> Magic
> [<1, 0, 2, -1, 6], <0, 5, 1, 12, -8]>
> TOP P = 1200.749423, G = 380.922404
> TOP-RMS P = 1200.143482, G = 380.741936
>
> Meanpop
> [<1, 2, 4, 7, -2], <0, -1, -4, -10, 13]>
> TOP P = 1201.698520, G = 504.134131
> TOP-RMS P = 1201.352803, G = 504.133204
>
> "Schismic" (could use a better name)
> [<1, 2, -1, -3, -4], <0, -1, 8, 14, 18]>
> TOP P = 1201.362994, G = 497.941436
> TOP-RMS P = 1200.198852, G = 497.711073
>
> Cynder/Mothra
> [<1, 1, 0, 3, 5], <0, 3, 12, -1, -8]>
> TOP P = 1201.698520, G = 232.521463
> TOP-RMS P = 1201.405762, G = 232.302506
>
> Superkleismic
> [<1, 4, 5, 2, 4], <0, -9, -10, 3, -2]>
> TOP P = 1200.048336, G = 321.753163
> TOP-RMS P = 1200.176054, G = 321.893777
>
> Myna
> [<1, -1, 0, 1, -3], <0, 10, 9, 7, 25]>
> TOP P = 1198.828458, G = 309.892661
> TOP-RMS P = 1199.347123, G = 309.975532
>
> Sensi
> [<1, -1, -1, -2, -8], <0, 7, 9, 13, 31]>
> TOP P = 1198.389531, G = 443.160293
> TOP-RMS P = 1199.077830, G = 443.285541
>
> Miracle
> [<1, 1, 3, 3, 2], <0, 6, -7, -2, 15]>
> TOP P = 1200.631014, G = 116.720642
> TOP-RMS P = 1200.763536, G = 116.706954
>
> Shrutar
> [<2, 3, 5, 5, 7], <0, 2, -4, 7, -1]>
> TOP P = 599.822848, G = 52.372763
> TOP-RMS P = 599.774873, G = 52.660207
>
> Tritonic
> [<1, 4, -3, -3, 2], <0, -5, 11, 12, 3]>
> TOP P = 1201.417748, G = 581.192614
> TOP-RMS P = 1201.715717, G = 581.096970
>
> Bohpier
> [<1, 0, 0, 0, 2], <0, 13, 19, 23, 12]>
> TOP P = 1198.828896, G = 146.475959 (e.g.)
> TOP-RMS P = 1199.236235, G = 146.451310
>
> Diaschismic
> [<2, 3, 5, 7, 9], <0, 1, -2, -8, -12]>
> TOP P = 599.366202, G = 103.787012
> TOP-RMS P = 599.448788, G = 103.618927
>
> Rodan
> [<1, 1, -1, 3, 6], <0, 3, 17, -1, -13]>
> TOP P = 1200.230389, G = 234.381795
> TOP-RMS P = 1200.057139, G = 234.469894
>
> Wizard
> [<2, 1, 5, 2, 8], <0, 6, -1, 10, -3]>
> TOP P = 600.319786, G = 216.770253)
> TOP-RMS P = 600.305522, G = 216.878315
>
> For "schismic", one problem is that both "schismic"
and "schismatic"
> have been used -- for different temperaments! "Schismic" is
obviously
> some variety of garibaldi, but [<1, 2, -1, -3, 13], <0, -1, 8, 14, -
23]>
> is closer to 7-limit garibaldi. There are still other versions of
> garibaldi, like [<1, 2, -1, -3, -9], <0, -1, 8, 14, 30]>. We could
name
> them after other fish in the damselfish family or related
species.... I
> know, garibaldi the temperament isn't named after the fish, but....

I like it, and that brings up "diaschimic" temperament (is there a
diaschismatic temperament?) I like using fish, then you can fish for
temperaments, so to speak

PGH