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 ¢)
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2L 3s⟨3/2⟩ 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 ¢. Due to its minor third generator, this scale has a wealth of diminished triads. Basic saturnian is in 7edf, an approximation of 12edo, which allows for playing regular music and saturnian music at the same time.

Intervals

MOS degrees is deprecated. Please use Template:MOS tunings instead.
Scale degree of 2L 3s⟨3/2⟩
Scale degree 7edf (Basic, L:s = 2:1) Approx. JI Ratios
Steps Cents
Perfect 0-mosdegree (unison) 0 0 1/1 (exact)
Minor 1-mosdegree 1 100.3
Major 1-mosdegree 2 200.6
Diminished 2-mosdegree 2 200.6
Perfect 2-mosdegree 3 300.8
Perfect 3-mosdegree 4 401.1
Augmented 3-mosdegree 5 501.4
Minor 4-mosdegree 5 501.4
Major 4-mosdegree 6 601.7
Perfect 5-mosdegree (equave) 7 702 3/2 (exact)

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. Although the most accurate tunings use near-32/27 generators, pythium can be tuned with minor thirds as high as that of 11edf's (319 cents).

Modes

Modes of 2L 3s⟨3/2⟩
UDP Cyclic
order		 Step
pattern
4|0 1 LsLss
3|1 3 LssLs
2|2 5 sLsLs
1|3 2 sLssL
0|4 4 ssLsL

Scale tree

Template: Scale tree is deprecated. Please use Template: MOS tuning spectrum instead. Details:
Use of a single Comments parameter has become unmaintainable. Existing scale trees should be migrated to the new template, where comments are entered using a step ratio p/q as a parameter: 
{{MOS tuning spectrum
| 3/2 = Example comment
| 4/3 = Another example comment
}}


The parameters tuning and depth have been replaced with Scale Signature and Depth, respectively.


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
13\31 294.368 407.587 8:5 1.600
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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