Swetismic temperaments
- This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.
This is a collection of rank-3 temperaments tempering out the swetisma (ratio: 540/539, monzo: [2 3 1 -2 -1⟩). For the rank-4 swetismic temperament, see Catalog of rank-4 temperaments #Swetismic (540/539).
Temperaments discussed elsewhere are:
- Terpsichore (+81/80) → Didymus rank-3 family
- Big brother (+99/98 or 121/120) → Biyatismic clan
- 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
- Octasand (+2200/2187) → Octagar 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.
Hades
- For the 7-limit version, see Miscellaneous 7-limit temperaments #Stearnsmic.
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]]
- mapping generators: ~99/70, ~9/7, ~5
- WE: ~99/70 = 599.9486 ¢, ~9/7 = 433.9084 ¢, ~5/4 = 386.2290 ¢
- error map: ⟨-0.103 -0.281 -0.290 +0.613 +0.643]
- CWE: ~99/70 = 600.0000 ¢, ~9/7 = 433.9204 ¢, ~5/4 = 386.1272 ¢
- error map: ⟨0.000 -0.194 -0.187 +0.776 +0.889]
Optimal ET sequence: 22, 50, 58, 72, 130, 152, 224, 354, 506e, 578, 730e, 1084de, 1308dee
Badness (Sintel): 0.434
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 tunings:
- WE: ~99/70 = 599.9598 ¢, ~9/7 = 433.8891 ¢, ~5/4 = 386.1680 ¢
- CWE: ~99/70 = 600.0000 ¢, ~9/7 = 433.9059 ¢, ~5/4 = 386.1014 ¢
Optimal ET sequence: 22f, 36ce, 58, 72, 130, 224, 354, 578
Badness (Sintel): 0.501
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 tunings:
- WE: ~55/39 = 599.9565 ¢, ~9/7 = 433.8372 ¢, ~5/4 = 387.1905 ¢
- CWE: ~55/39 = 600.0000 ¢, ~9/7 = 433.8475 ¢, ~5/4 = 387.1030 ¢
Optimal ET sequence: 8d, 14cf, 22, 36f, 44ceff, 50, 58, 72, 130
Badness (Sintel): 0.716
Minos
Subgroup: 2.3.5.7.11
Comma list: 540/539, 12005/11979
Mapping: [⟨1 0 -3 0 -1], ⟨0 2 4 3 4], ⟨0 0 5 1 3]]
- mapping generators: ~2, ~121/70, ~66/49
- WE: ~2 = 1199.8923 ¢, ~121/70 = 950.8327 ¢, ~66/49 = 516.4492 ¢
- error map: ⟨-0.108 -0.290 -0.414 +0.121 +1.468]
- CWE: ~2 = 1200.0000 ¢, ~121/70 = 950.8712 ¢, ~66/49 = 516.5067 ¢
- error map: ⟨0.000 -0.213 -0.295 +0.294 +1.687]
Optimal ET sequence: 9, …, 49, 58, 72, 130, 193, 202, 323e, 395e, 525e *
Badness (Sintel): 1.06
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 364/363, 540/539, 676/675
Mapping: [⟨1 0 -3 0 -1 -4], ⟨0 2 4 3 4 7], ⟨0 0 5 1 3 5]]
Optimal tunings:
- WE: ~2 = 1199.7669 ¢, ~26/15 = 950.9360 ¢, ~66/49 = 516.3652 ¢
- CWE: ~2 = 1200.0000 ¢, ~26/15 = 951.0324 ¢, ~66/49 = 516.4883 ¢
Optimal ET sequence: 9, …, 49f, 58, 72, 121, 130, 193, 251e, 323e
Badness (Sintel): 0.677
Persephone
Subgroup: 2.3.5.7.11
Comma list: 540/539, 88209/87500
Mapping: [⟨1 0 -6 4 -12], ⟨0 1 4 0 7], ⟨0 0 5 -3 11]]
- mapping generators: ~2, ~3, ~33/25
- WE: ~2 = 1200.0185 ¢, ~3/2 = 700.9179 ¢, ~33/25 = 476.7538 ¢
- error map: ⟨+0.019 -1.019 +1.090 +0.987 -0.694]
- CWE: ~2 = 1200.0000 ¢, ~3/2 = 700.9220 ¢, ~33/25 = 476.7393 ¢
- error map: ⟨0.000 -1.033 +1.071 +0.956 -0.732]
Optimal ET sequence: 8d, …, 45e, 50, 53, 58, 103, 161, 214, 272, 375
Badness (Sintel): 2.42
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 351/350, 540/539, 847/845
Mapping: [⟨1 0 -6 4 -12 -7], ⟨0 1 4 0 7 5], ⟨0 0 5 -3 11 7]]
Optimal tunings:
- WE: ~2 = 1199.9553 ¢, ~3/2 = 700.9477 ¢, ~33/25 = 476.6709 ¢
- CWE: ~2 = 1200.0000 ¢, ~3/2 = 700.9378 ¢, ~33/25 = 476.7054 ¢
Optimal ET sequence: 8d, …, 45ef, 50, 53, 58, 103, 111, 161, 214, 375
Badness (Sintel): 0.933
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
- WE: ~2 = 1200.3393 ¢, ~81/56 = 633.6837 ¢, ~5/4 = 385.6892 ¢
- error map: ⟨+0.339 -0.904 +0.054 +0.677 -0.124]
- CWE: ~2 = 1200.0000 ¢, ~81/56 = 633.5228 ¢, ~5/4 = 385.9359 ¢
- error map: ⟨0.000 -1.387 -0.378 -0.075 -1.178]
Optimal ET sequence: 17c, 19, …, 36, 53, 72, 161, 214, 233, 286, 358, 591be
Badness (Sintel): 1.96
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 tunings:
- WE: ~2 = 1200.6306 ¢, ~81/56 = 633.8505 ¢, ~5/4 = 385.0539 ¢
- CWE: ~2 = 1200.0000 ¢, ~81/56 = 633.5546 ¢, ~5/4 = 385.4668 ¢
Optimal ET sequence: 17c, 19, 36ce, 53, 72, 125f, 197ef
Badness (Sintel): 1.35