2L 3s (3/2-equivalent)
| ↖1L 2s⟨3/2⟩ | ↑2L 2s⟨3/2⟩ | 3L 2s⟨3/2⟩↗ |
| ←1L 3s⟨3/2⟩ | 2L 3s⟨3/2⟩ | 3L 3s⟨3/2⟩→ |
| ↙1L 4s⟨3/2⟩ | ↓2L 4s⟨3/2⟩ | 3L 4s⟨3/2⟩↘ |
2L 3s⟨3/2⟩, also called saturnian, is a non-octave moment of symmetry scale containing 2 large steps and 3 small steps, repeating every interval of 3/2 (701.955¢). Modes of this scale are rotations of the step pattern LsLss. Generators that produce this scale range from 280.782¢ to 350.978¢, or from 350.978¢ to 421.173¢.
Due to its minor third generator, this scale contains 2 diminished triads. Basic saturnian is in 7edf, an approximation of 12edo, which allows for playing regular music and saturnian music at the same time. 2L 3s〈3/2〉 is the parent of the 3/2-repeating microdiatonic scale, 5L 2s〈3/2〉, and the sister of 3L 2s〈3/2〉 (uranian) which is generated by a subminor third rather than a minor third.
Notation
The main way of notating the saturnian scale is using a 3/2-repeating notation consisting of 5 naturals. The notation used in this article is J Dionian is the JKLMN.
Intervals
| Scale degree | On J | 7edf (Basic, L:s = 2:1) | 9edf (Hard, L:s = 3:1) | 12edf (Soft, L:s = 3:2) | Approx. JI Ratios | |||
|---|---|---|---|---|---|---|---|---|
| Steps | Cents | Steps | Cents | Steps | Cents | |||
| Perfect 0-mosdegree (unison) | J | 0 | 0 | 0 | 0 | 0 | 0 | 1/1 (exact) |
| Minor 1-mosdegree | K | 1 | 100.3 | 1 | 78 | 2 | 117 | |
| Major 1-mosdegree | K& | 2 | 200.6 | 3 | 234 | 3 | 175.5 | |
| Diminished 2-mosdegree | L@ | 2 | 200.6 | 2 | 156 | 4 | 234 | |
| Perfect 2-mosdegree | L | 3 | 300.8 | 4 | 312 | 5 | 292.5 | |
| Perfect 3-mosdegree | M | 4 | 401.1 | 5 | 390 | 7 | 409.5 | |
| Augmented 3-mosdegree | M& | 5 | 501.4 | 7 | 546 | 8 | 468 | |
| Minor 4-mosdegree | N@ | 5 | 501.4 | 6 | 468 | 9 | 526.5 | |
| Major 4-mosdegree | N | 6 | 601.7 | 8 | 624 | 10 | 585 | |
| Perfect 5-mosdegree (equave) | J | 7 | 702 | 9 | 702 | 12 | 702 | 3/2 (exact) |
Genchain
| -4 | -3 | -2 | -1 | 0 | 1 | 2 | 3 | 4 |
| d2ms | m4ms | m1ms | P3ms | P0ms | P2ms | M4ms | M1ms | A3ms |
Theory
2L 3s〈3/2〉 can be interpreted as the nonoctave regular temperament named pythium by User:CompactStar, tempering out 81/80 in the 3/2.4.5 subgroup. This is the simplest 3/2-equivalent temperament not containing octaves. Because the 3/2-reduced 5th harmonic of 40/27 is conflated with the just perfect fifth, the CTE generator of this temperament is exactly the 32/27 Pythagorean minor third. The best extension of pythium to the 3/2.4.5.7 subgroup adds 64/63 to the comma list, making the CTE generator slightly flatter than 32/27, about 286 cents. Although the most accurate pythium generators are near 32/27, pythium can be tuned with minor thirds as sharp as that of 11edf's (319 cents).
Modes
The mode names are based on the 6 largest satellites of Saturn, excluding Titan since the "Titanian" name has been used for the uranian scale.
| UDP | Step pattern | Mode names |
|---|---|---|
| 4|0 | LsLss | Rhean |
| 3|1 | LssLs | Iapetian |
| 2|2 | sLsLs | Dionian |
| 1|3 | sLssL | Tethyian |
| 0|4 | ssLsL | Enceladean |
Scale tree
| Steps of ED | Generator in cents | Step ratio | Comments | ||
|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | ||
| 2\5edf | 280.782 | 421.173 | 1:1 | 1 | Equalized 2L 3s⟨3/2⟩ |
| 11\27edf | 285.982 | 415.973 | 6:5 | 1.2 | |
| 9\22edf | 287.163 | 414.792 | 5:4 | 1.25 | Optimal 3/2.4.5.7 pythium around here |
| 16\39edf | 287.982 | 413.973 | 9:7 | 1.286 | |
| 7\17edf | 289.04 | 412.915 | 4:3 | 1.333 | Supersoft 2L 3s⟨3/2⟩ |
| 19\46edf | 289.938 | 412.017 | 11:8 | 1.375 | |
| 12\29edf | 290.464 | 411.491 | 7:5 | 1.4 | |
| 17\41edf | 291.055 | 410.9 | 10:7 | 1.429 | |
| 5\12edf | 292.481 | 409.474 | 3:2 | 1.5 | Soft 2L 3s⟨3/2⟩ |
| 18\43edf | 293.842 | 408.113 | 11:7 | 1.571 | |
| 13\31edf | 294.368 | 407.587 | 8:5 | 1.6 | Near-just 32/27, optimal 3/2.4.5 pythium around here |
| 21\50edf | 294.821 | 407.134 | 13:8 | 1.625 | |
| 8\19edf | 295.56 | 406.395 | 5:3 | 1.667 | Semisoft 2L 3s⟨3/2⟩ |
| 19\45edf | 296.381 | 405.574 | 12:7 | 1.714 | |
| 11\26edf | 296.981 | 404.974 | 7:4 | 1.75 | |
| 14\33edf | 297.799 | 404.156 | 9:5 | 1.8 | |
| 3\7edf | 300.838 | 401.117 | 2:1 | 2 | Basic 2L 3s⟨3/2⟩ (Generators smaller than this are proper) Augmented 8-mosstep is nearly an octave |
| 13\30edf | 304.181 | 397.775 | 9:4 | 2.25 | |
| 10\23edf | 305.198 | 396.757 | 7:3 | 2.333 | |
| 17\39edf | 305.98 | 395.975 | 12:5 | 2.4 | |
| 7\16edf | 307.105 | 394.85 | 5:2 | 2.5 | Semihard 2L 3s⟨3/2⟩ |
| 18\41edf | 308.175 | 393.78 | 13:5 | 2.6 | |
| 11\25edf | 308.86 | 393.095 | 8:3 | 2.667 | |
| 15\34edf | 309.686 | 392.269 | 11:4 | 2.75 | |
| 4\9edf | 311.98 | 389.975 | 3:1 | 3 | Hard 2L 3s⟨3/2⟩ |
| 13\29edf | 314.669 | 387.286 | 10:3 | 3.333 | |
| 9\20edf | 315.88 | 386.075 | 7:2 | 3.5 | |
| 14\31edf | 317.012 | 384.943 | 11:3 | 3.667 | |
| 5\11edf | 319.07 | 382.885 | 4:1 | 4 | Superhard 2L 3s⟨3/2⟩ |
| 11\24edf | 321.729 | 380.226 | 9:2 | 4.5 | |
| 6\13edf | 323.979 | 377.976 | 5:1 | 5 | |
| 7\15edf | 327.579 | 374.376 | 6:1 | 6 | |
| 1\2edf | 350.978 | 350.978 | 1:0 | → ∞ | Collapsed 2L 3s⟨3/2⟩ Degenerate scale with only 2 tones |