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

The intervals of 2L 3s⟨3/2⟩ are named after the number of mossteps (L and s) they subtend. Each interval, apart from the root and equave (perfect 0-mosstep and perfect 5-mosstep), has two varieties, or sizes, each. Interval varieties are named major and minor for the large and small sizes, respectively, and augmented, perfect, and diminished for the scale's generators.

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

A chain of bright generators, each a perfect 2-mosstep, produces the following scale degrees. A chain of 5 bright generators contains the scale degrees of one of the modes of 2L 3s⟨3/2⟩. Expanding the chain to 7 scale degrees produces the modes of either 5L 2s⟨3/2⟩ (for soft-of-basic tunings) or 2L 5s⟨3/2⟩ (for hard-of-basic tunings).

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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