Hemfiness temperaments
Hemfiness rank-two temperaments temper out the hemfiness comma, 4096000/4084101 = [15 -5 3 -5⟩ (saquinru-atriyo), the amount by which a stack of three 5/4s and five 32/21s exceed four octaves.
Temperaments dicussed elsewhere include:
- Hemififths
- Nessafof
- Gamera
- Superkleismic
- Quanharuk
- Merman
- Decipentic
- Oquatonic
- Stockhausenic
- Secant
- Thuja
- Jerome
- Progress
- Witcher
Undesemi
Subgroup: 2.3.5.7
Comma list: 4096000/4084101, 95703125/95551488
Mapping: [⟨1 5 5 1], ⟨0 -51 -40 27]]
Optimal tuning (POTE): ~8575/8192 = 80.347
Optimal ET sequence: 15, …, 194, 209, 224, 463, 687, 1150d
Badness: 0.178777
11-limit
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 4000/3993, 180224/180075
Mapping: [⟨1 5 5 1 5], ⟨0 -51 -40 27 -23]]
POTE generator: ~22/21 = 80.347
Optimal ET sequence: 15, …, 194, 209, 224, 463, 1150de
Badness: 0.042318
Piracy
Subgroup: 2.3.5.7
Comma list: 4096000/4084101, 48828125/48771072
Mapping: [⟨1 -6 0 9], ⟨0 49 15 -40]]
Optimal tuning (POTE): ~4096/3675 = 185.7609
Optimal ET sequence: 71, 84, 155, 239, 323, 885, 1208d, 1531d
Badness: 0.159305
11-limit
Subgroup: 2.3.5.7.11
Comma list: 6250/6237, 12005/11979, 16384/16335
Mapping: [⟨1 -6 0 9 16], ⟨0 49 15 -40 -81]]
Optimal tuning (POTE): ~49/44 = 185.7671
Optimal ET sequence: 84, 155, 239, 562e, 801e
Badness: 0.092173
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 625/624, 2080/2079, 2205/2197, 12005/11979
Mapping: [⟨1 -6 0 9 16 2], ⟨0 49 15 -40 -81 11]]
Optimal tuning (POTE): ~49/44 = 185.7663
Optimal ET sequence: 84, 155, 239f
Badness: 0.063719
Pirateship
Subgroup: 2.3.5.7.11.13
Comma list: 364/363, 1716/1715, 4096/4095, 6250/6237
Mapping: [⟨1 -6 0 9 16 15], ⟨0 49 15 -40 -81 -73]]
Optimal tuning (POTE): ~39/35 = 185.7621
Optimal ET sequence: 84, 155f, 239, 323e
Badness: 0.073523