2L 3s (3/2-equivalent)

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↖ 1L 2s⟨3/2⟩ ↑ 2L 2s⟨3/2⟩ 3L 2s⟨3/2⟩ ↗
← 1L 3s⟨3/2⟩ 2L 3s (3/2-equivalent) 3L 3s⟨3/2⟩ →
↙ 1L 4s⟨3/2⟩ ↓ 2L 4s⟨3/2⟩ 3L 4s⟨3/2⟩ ↘ 
┌╥┬╥┬┬┐
│║│║│││
│││││││
└┴┴┴┴┴┘
Scale structure
Step pattern LsLss
ssLsL
Equave 3/2 (702.0 ¢)
Period 3/2 (702.0 ¢)
Generator size(edf)
Bright 2\5 to 1\2 (280.8 ¢ to 351.0 ¢)
Dark 1\2 to 3\5 (351.0 ¢ to 421.2 ¢)
Related MOS scales
Parent 2L 1s⟨3/2⟩
Sister 3L 2s⟨3/2⟩
Daughters 5L 2s⟨3/2⟩, 2L 5s⟨3/2⟩
Neutralized 4L 1s⟨3/2⟩
2-Flought 7L 3s⟨3/2⟩, 2L 8s⟨3/2⟩
Equal tunings(edf)
Equalized (L:s = 1:1) 2\5 (280.8 ¢)
Supersoft (L:s = 4:3) 7\17 (289.0 ¢)
Soft (L:s = 3:2) 5\12 (292.5 ¢)
Semisoft (L:s = 5:3) 8\19 (295.6 ¢)
Basic (L:s = 2:1) 3\7 (300.8 ¢)
Semihard (L:s = 5:2) 7\16 (307.1 ¢)
Hard (L:s = 3:1) 4\9 (312.0 ¢)
Superhard (L:s = 4:1) 5\11 (319.1 ¢)
Collapsed (L:s = 1:0) 1\2 (351.0 ¢)

2L 3s⟨3/2⟩, also called saturnian, is a 3/2-equivalent (fifth-equivalent) moment of symmetry scale containing 2 large steps and 3 small steps, repeating every interval of 3/2 (702.0 ¢). Generators that produce this scale range from 280.8 ¢ to 351 ¢, or from 351 ¢ to 421.2 ¢. The name saturnian was coined by CompactStar, referring to this MOS being the sister MOS of uranian.

This scale contains 2 diminished triads represented by stacks of the minor third generator. Basic saturnian is in 7edf, a very close approximation of 12edo, which allows for playing diatonic 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.

Scale characteristics

Intervals

Intervals of 2L 3s⟨3/2⟩
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-mosstep Perfect 0-mosstep P0ms 0 0.0 ¢
1-mosstep Minor 1-mosstep m1ms s 0.0 ¢ to 140.4 ¢
Major 1-mosstep M1ms L 140.4 ¢ to 351.0 ¢
2-mosstep Diminished 2-mosstep d2ms 2s 0.0 ¢ to 280.8 ¢
Perfect 2-mosstep P2ms L + s 280.8 ¢ to 351.0 ¢
3-mosstep Perfect 3-mosstep P3ms L + 2s 351.0 ¢ to 421.2 ¢
Augmented 3-mosstep A3ms 2L + s 421.2 ¢ to 702.0 ¢
4-mosstep Minor 4-mosstep m4ms L + 3s 351.0 ¢ to 561.6 ¢
Major 4-mosstep M4ms 2L + 2s 561.6 ¢ to 702.0 ¢
5-mosstep Perfect 5-mosstep P5ms 2L + 3s 702.0 ¢

Generator chain

Generator chain of 2L 3s⟨3/2⟩
Bright gens Scale degree Abbrev.
6 Augmented 2-mosdegree A2md
5 Augmented 0-mosdegree A0md
4 Augmented 3-mosdegree A3md
3 Major 1-mosdegree M1md
2 Major 4-mosdegree M4md
1 Perfect 2-mosdegree P2md
0 Perfect 0-mosdegree
Perfect 5-mosdegree		 P0md
P5md
−1 Perfect 3-mosdegree P3md
−2 Minor 1-mosdegree m1md
−3 Minor 4-mosdegree m4md
−4 Diminished 2-mosdegree d2md
−5 Diminished 5-mosdegree d5md
−6 Diminished 3-mosdegree d3md

Modes

Scale degrees of the modes of 2L 3s⟨3/2⟩
UDP Cyclic
order		 Step
pattern		 Scale degree (mosdegree)
0 1 2 3 4 5
4|0 1 LsLss Perf. Maj. Perf. Aug. Maj. Perf.
3|1 3 LssLs Perf. Maj. Perf. Perf. Maj. Perf.
2|2 5 sLsLs Perf. Min. Perf. Perf. Maj. Perf.
1|3 2 sLssL Perf. Min. Perf. Perf. Min. Perf.
0|4 4 ssLsL Perf. Min. Dim. Perf. Min. Perf.

Theory

Temperament interpretations

From a half-prime subgroup point of view, 2L 3s⟨3/2⟩ can be interpreted as the Sirius B temperament in the 3/2.5/2.7/2 subgroup, where the generator is represented by the minor third ~25/21 and 2 of them make ~7/5. It may also be interpreted as meanquad temperament using a period of 3/2 rather than 4/1, where the generator is represented by 32/27~6/5 (in the CTE tuning, it is exactly 32/27). Both temperaments have very similar generators.

Modes

The mode names were coined by CompactStar, based on the 6 largest satellites of Saturn, excluding Titan since the "Titanian" name has been used for the uranian scale.

Modes of 2L 3s⟨3/2⟩
UDP Cyclic
order		 Step
pattern		 Mode names
4|0 1 LsLss Rhean
3|1 3 LssLs Iapetian
2|2 5 sLsLs Dionian
1|3 2 sLssL Tethyian
0|4 4 ssLsL Enceladean

Scale tree

Scale tree and tuning spectrum of 2L 3s⟨3/2⟩
Generator(edf) Cents Step ratio Comments
Bright Dark L:s Hardness
2\5 280.782 421.173 1:1 1.000 Equalized 2L 3s⟨3/2⟩
11\27 285.982 415.973 6:5 1.200
9\22 287.163 414.792 5:4 1.250
16\39 287.982 413.973 9:7 1.286
7\17 289.040 412.915 4:3 1.333 Supersoft 2L 3s⟨3/2⟩
19\46 289.938 412.017 11:8 1.375
12\29 290.464 411.491 7:5 1.400
17\41 291.055 410.900 10:7 1.429
5\12 292.481 409.474 3:2 1.500 Soft 2L 3s⟨3/2⟩
18\43 293.842 408.113 11:7 1.571 CTE tuning for Sirius B temperament (293.825 ¢)
13\31 294.368 407.587 8:5 1.600 Just 32/27 (294.135 ¢)
21\50 294.821 407.134 13:8 1.625
8\19 295.560 406.395 5:3 1.667 Semisoft 2L 3s⟨3/2⟩
19\45 296.381 405.574 12:7 1.714
11\26 296.981 404.974 7:4 1.750
14\33 297.799 404.156 9:5 1.800
3\7 300.838 401.117 2:1 2.000 Basic 2L 3s⟨3/2⟩
Scales with tunings softer than this are proper
13\30 304.181 397.775 9:4 2.250
10\23 305.198 396.757 7:3 2.333
17\39 305.980 395.975 12:5 2.400
7\16 307.105 394.850 5:2 2.500 Semihard 2L 3s⟨3/2⟩
18\41 308.175 393.780 13:5 2.600
11\25 308.860 393.095 8:3 2.667
15\34 309.686 392.269 11:4 2.750
4\9 311.980 389.975 3:1 3.000 Hard 2L 3s⟨3/2⟩
13\29 314.669 387.286 10:3 3.333
9\20 315.880 386.075 7:2 3.500
14\31 317.012 384.943 11:3 3.667
5\11 319.070 382.885 4:1 4.000 Superhard 2L 3s⟨3/2⟩
11\24 321.729 380.226 9:2 4.500
6\13 323.979 377.976 5:1 5.000
7\15 327.579 374.376 6:1 6.000
1\2 350.978 350.978 1:0 → ∞ Collapsed 2L 3s⟨3/2⟩
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