Swetismic temperaments

This is a collection of rank-3 temperaments tempering out 540/539. Temperaments discussed elsewhere are:

• Terpsichore, {81/80, 540/539} → Didymus rank-3 family
• Big Brother, {99/98, 121/120} → Nuwell family
• Octarod, {100/99, 245/243} → Sensamagic family
• Aplonis, {126/125, 540/539} → Starling family
• Guanyin, {176/175, 540/539} → Orwellismic family
• Marvel, {225/224, 385/384} → Marvel family
• Jove, {243/242, 441/440} → Breed family
• Uni, {540/539, 896/891} → Hemimage family
• Gamel, {540/539, 1029/1024} → Gamelismic family
• Indra, {540/539, 1375/1372} → Mirkwai family
• Claudius, {540/539, 2048/2025} → Diaschismic rank-3 family
• Gariboh, {540/539, 3125/3087} → Gariboh family
• Siebog, {540/539, 3136/3125} → Hemimean family
• Laka, {540/539, 5120/5103} → Hemifamity family
• Jupiter, {540/539, 5632/5625} → Porwell family
• Albus, {540/539, 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