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Welcome to Orgonia, the commatic realm of the orgonisma, the 11-limit comma 65536/65219!

Orgonismic temperament

Comma: 65536/65219

Minimax tuning subgroup: 2.3.5.11/7. The minimax tuning makes 7 and 11 both sharp by (65536/65219)^(1/5), which is 1.679 cents, and the 5-limit just.

Map: <<1 0 0 2 4]
[0 1 0 0 0]
[0 0 1 0 0]
[0 0 0 3 -2]||

EDOs: 15, 19, 22, 37, 41, 89, 111, 130, 152, 282
Spectrum: 4/3, 11/8, 12/11, 5/4, 8/7, 6/5, 11/10, 7/6, 9/8, 7/5, 11/9, 10/9, 9/7, 14/11

Subgroup temperaments


Orgone

Commas:65536/65219
Subgroup: 2.7.11

POTE generator: ~77/64 = 323.372

Sval map: [<1 2 4|, <0 3 -2|]
EDOs: 7, 11, 15, 26, 37, 63, 89, 115, 141, 167, 308, 475bc, 783bc

orgone_heptatonic.jpg

Oregon

Commas: 55/54, 64/63, 100/99
Subgroup: 2.9.15.7.11

POTE generator: ~6/5 = 326.139

Sval map: [<1 1 1 5 2|, <0 3 4 -3 2|]
EDOs: 7, 11, 59b, 70bc, 81bcd, 92bcd

The subgroup 2.9.15.7.11 is the 11-limit 2*11 subgroup, the largest subgroup of the 11-limit on which 11edo acts like 22edo, in the sense that it gives the same tuning to intervals and has the same commas. Oregon temperament is just 11-limit porcupine temperament restricted to this subgroup.

Orca

Commas: 55/54, 64/63, 100/99, 85/84
Subgroup: 2.9.15.7.11.17

POTE generator: ~6/5 = 326.644

Sval map: [<1 1 1 5 2 7|, <0 3 4 -3 2 -4|]
EDOs: 7, 11, 92bcd, 103bcd

Ork

Commas: 99/98, 121/120, 136/135, 256/255
Subgroup: 2.9.15.7.11.17

POTE generator: ~17/14 = 325.714

Sval map: [<1 1 5 2 4 3|, <0 8 -4 3 -2 4|]
EDOs: 11, 37, 48, 59, 70c