1L 1s (3/2-equivalent)

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1L 1s (3/2-equivalent) 2L 1s⟨3/2⟩ →
↓ 1L 2s⟨3/2⟩ 2L 2s⟨3/2⟩ ↘ 
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Scale structure
Step pattern Ls
sL
Equave 3/2 (702.0¢)
Period 3/2 (702.0¢)
Generator size(edf)
Bright 1\2 to 1\1 (351.0¢ to 702.0¢)
Dark 0\1 to 1\2 (0.0¢ to 351.0¢)
Related MOS scales
Parent 1L 0s⟨3/2⟩
Sister 1L 1s⟨3/2⟩
Daughters 2L 1s⟨3/2⟩, 1L 2s⟨3/2⟩
Neutralized 2L 0s⟨3/2⟩
2-Flought 3L 1s⟨3/2⟩, 1L 3s⟨3/2⟩
Equal tunings(edf)
Equalized (L:s = 1:1) 1\2 (351.0¢)
Supersoft (L:s = 4:3) 4\7 (401.1¢)
Soft (L:s = 3:2) 3\5 (421.2¢)
Semisoft (L:s = 5:3) 5\8 (438.7¢)
Basic (L:s = 2:1) 2\3 (468.0¢)
Semihard (L:s = 5:2) 5\7 (501.4¢)
Hard (L:s = 3:1) 3\4 (526.5¢)
Superhard (L:s = 4:1) 4\5 (561.6¢)
Collapsed (L:s = 1:0) 1\1 (702.0¢)

1L 1s<3/2> is a fifth-repeating MOS scale. The notation "<3/2>" means the period of the MOS is perfect fifth of 3/2, disambiguating it from octave-repeating 1L 1s.

This MOS scale makes root-3rd-P5 triads with pure perfect fifth (e.g. 4:5:6, 6:7:9, 10:12:15 and 14:18:21).

The chroma-positive generator is between 351 cents (square root of 3/2) and 702 cents (pure 3/2), which makes various major triads such as 4:5:6, 10:13:15 and 14:18:21.

Tuning ranges

Soft tunings (hyposoft, parasoft and ultrasoft) make root-3rd-P5 triads including 4:5:6, 6:7:9, 10:12:15, 10:13:15, 14:17:21, 14:18:21, 16:19:24, 18:22:27 and 18:23:27. The chroma-positive generator is a major third (or hemisixth), and the chroma-negative generator is a minor third (or hemifourth).

Hypohard tuning makes root-4th-P5 triads including 6:8:9, 16:21:24 and 20:27:30. The chroma-positive generator is a fourth and the chroma-negative generator is a whole tone.

Modes

Modes of 1L 1s⟨3/2⟩
UDP Cyclic
order		 Step
pattern
1|0 1 Ls
0|1 2 sL

Intervals

Intervals of 1L 1s⟨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 351.0¢
Major 1-mosstep M1ms L 351.0¢ to 702.0¢
2-mosstep Perfect 2-mosstep P2ms L + s 702.0¢

Scale tree

Generator ranges:

  • Chroma-positive generator: 350.9775 cents (1\2ed3/2) to 701.9550 cents (1\1ed3/2)
  • Chroma-negative generator: 0 cents (0\1ed3/2) to 350.9775 cents (1\2ed3/2)
Generator Cents L s L/s Comments
1\2 350.978 1 1 1.000
6\11 382.885 6 5 1.200 Carlos Beta
5\9 389.975 5 4 1.250 Carlos Alpha
9\16 394.850 9 7 1.286
4\7 401.117 4 3 1.333 12edo-esque triad
11\19 406.395 11 8 1.375
7\12 409.474 7 5 1.400
10\17 412.915 10 7 1.429
3\5 421.173 3 2 1.500
11\18 428.973 11 7 1.571
8\13 431.972 8 5 1.600
13\21 434.544 13 8 1.625 Unnamed golden tuning (433.8320¢)
5\8 438.722 5 3 1.667
12\19 443.340 12 7 1.714
7\11 446.699 7 4 1.750
9\14 451.257 9 5 1.800
2\3 467.970 2 1 2.000 Gamelan tuning
(Basic 1L 1s<3/2>)
9\13 485.969 9 4 2.250
7\10 491.369 7 3 2.333
12\17 495.498 12 5 2.400
5\7 501.396 5 2 2.500 Sus4 chord
13\18 506.968 13 5 2.600 Unnamed golden tuning (507.9394¢)
8\11 510.513 8 3 2.667
11\15 514.767 11 4 2.750
3\4 526.466 3 1 3.000
10\13 539.965 10 3 3.333
7\9 545.965 7 2 3.500
11\14 551.536 11 3 3.667
4\5 561.564 4 1 4.000
9\11 574.327 9 2 4.500
5\6 584.963 5 1 5.000
6\7 601.676 6 1 6.000
1\1 701.955 1 0 → inf

See also

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