Swetismic temperaments
This is a collection of rank-3 temperaments tempering out 540/539.
Temperaments discussed elsewhere are:
- Terpsichore (+81/80) → Didymus rank-3 family
- Big brother (+99/98 or 121/120) → Nuwell family
- Octarod (+100/99 or 245/243) → Sensamagic family
- Aplonis (+126/125) → Starling family
- Guanyin (+176/175) → Orwellismic family
- Marvel (+225/224 or 385/384) → Marvel family
- Jove (+243/242 or 441/440) → Breed family
- Uni (+896/891) → Hemimage family
- Gamel (+1029/1024) → Gamelismic family
- Indra (+1375/1372) → Mirkwai family
- Claudius (+2048/2025) → Diaschismic rank-3 family
- Gariboh (+3125/3087) → Gariboh family
- Siebog (+3136/3125) → Hemimean family
- Laka (+5120/5103) → Hemifamity family
- Jupiter (+5632/5625) → Porwell family
- Albus (+8019/8000) → Cataharry family
Considered below are hades, minos, persephone and hypnos, but we can begin by looking at the rank-4 temperament.
Swetismic
Subgroup: 2.3.5.7.11
Comma list: 540/539
Mapping: [⟨1 0 0 0 2], ⟨0 1 0 0 3], ⟨0 0 0 1 -2]]
- mapping generators: ~2, ~3, ~5, ~7
Optimal ET sequence: 9, 10, 19, 22, 31, 41, 53, 58, 72, 130, 152, 224, 354, 537, 578
Hades
7-limit (stearnsmic)
Subgroup: 2.3.5.7
Comma list: 118098/117649
Mapping: [⟨2 1 0 2], ⟨0 3 0 5], ⟨0 0 1 0]]
- mapping generators: ~343/243, ~9/7, ~5
Optimal ET sequence: 22, 50, 58, 72, 130, 152, 202, 224, 354
Badness: 0.748 × 10-3
11-limit
Subgroup: 2.3.5.7.11
Comma list: 540/539, 4000/3993
Mapping: [⟨2 1 0 2 3], ⟨0 3 0 5 -1], ⟨0 0 1 0 1]]
Optimal ET sequence: 22, 50, 58, 72, 130, 152, 224, 354, 506e, 578, 730e, 1084de, 1308dee
Badness: 0.361 × 10-3
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 540/539, 729/728, 1575/1573
Mapping: [⟨2 1 0 2 3 -2], ⟨0 3 0 5 -1 13], ⟨0 0 1 0 1 0]]
Optimal ET sequence: 22f, 36, 58, 72, 130, 224, 354, 578
Badness: 0.535 × 10-3
Cerberus
Subgroup: 2.3.5.7.11.13
Comma list: 351/350, 364/363, 540/539
Mapping: [⟨2 1 0 2 3 1], ⟨0 3 0 5 -1 -4], ⟨0 0 1 0 1 2]]
Optimal ET sequence: 22, 50, 58, 72, 130
Badness: 0.766 × 10-3
Minos
Subgroup: 2.3.5.7.11
Comma list: 540/539, 12005/11979
Mapping: [⟨1 0 2 1 2], ⟨0 2 4 3 4], ⟨0 0 -5 -1 -3]]
- mapping generators: ~2, ~121/70, ~49/33
Optimal ET sequence: 9, 49, 58, 72, 130, 193, 202, 467
Badness: 0.886 × 10-3
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 364/363, 540/539, 676/675
Mapping: [⟨1 0 2 1 2 1], ⟨0 2 4 3 4 7], ⟨0 0 -5 -1 -3 -5]]
Optimal ET sequence: 9, 54, 58, 72, 121, 130, 193
Badness: 0.724 × 10-3
Persephone
Subgroup: 2.3.5.7.11
Comma list: 540/539, 88209/87500
Mapping: [⟨1 0 4 -2 10], ⟨0 1 4 0 7], ⟨0 0 -5 3 -11]]
- mapping generators: ~2, ~3, ~100/33
Optimal ET sequence: 50, 53, 58, 103, 108, 111, 161, 214, 272, 375, 1022bcde, 1236bcde, 1397bcde
Badness: 2.015 × 10-3
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 351/350, 540/539, 847/845
Mapping: [⟨1 0 4 -2 10 7], ⟨0 1 4 0 7 5], ⟨0 0 -5 3 -11 -7]]
Optimal ET sequence: 50, 53, 58, 103, 108, 111, 161, 214, 375, 700cdef, 861bcdef, 1075bcdef, 1236bcdef, 1450bcdef
Badness: 0.997 × 10-3
Hypnos
Subgroup: 2.3.5.7.11
Comma list: 540/539, 72171/71680
Mapping: [⟨1 0 0 -3 8], ⟨0 3 0 11 -13], ⟨0 0 1 0 1]]
- mapping generators: ~2, ~81/56, ~5
Optimal ET sequence: 19, 36, 53, 72, 161, 197e, 214, 233, 286, 358, 591be, 663be, 949bce
Badness: 1.629 × 10-3
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 169/168, 540/539, 729/728
Mapping: [⟨1 0 0 -3 8 0], ⟨0 3 0 11 -13 7], ⟨0 0 1 0 1 0]]
Optimal ET sequence: 19, 36, 53, 72, 125f, 197ef
Badness: 1.439 × 10-3