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⟩
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.

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 the diamond MOS notation.

Intervals

Scale degree of 2L 3s⟨3/2⟩
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

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 Rotational 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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