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2L 3s (3/2-equivalent)

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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.

↖ 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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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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