2L 1s (3/2-equivalent)

From Xenharmonic Wiki
Jump to navigation Jump to search
← 1L 1s⟨3/2⟩ 2L 1s (3/2-equivalent) 3L 1s⟨3/2⟩ →
↙ 1L 2s⟨3/2⟩ ↓ 2L 2s⟨3/2⟩ 3L 2s⟨3/2⟩ ↘ 
┌╥╥┬┐
│║║││
│││││
└┴┴┴┘
Scale structure
Step pattern LLs
sLL
Equave 3/2 (702.0 ¢)
Period 3/2 (702.0 ¢)
Generator size(edf)
Bright 1\3 to 1\2 (234.0 ¢ to 351.0 ¢)
Dark 1\2 to 2\3 (351.0 ¢ to 468.0 ¢)
Related MOS scales
Parent 1L 1s⟨3/2⟩
Sister 1L 2s⟨3/2⟩
Daughters 3L 2s⟨3/2⟩, 2L 3s⟨3/2⟩
Neutralized 1L 2s⟨3/2⟩
2-Flought 5L 1s⟨3/2⟩, 2L 4s⟨3/2⟩
Equal tunings(edf)
Equalized (L:s = 1:1) 1\3 (234.0 ¢)
Supersoft (L:s = 4:3) 4\11 (255.3 ¢)
Soft (L:s = 3:2) 3\8 (263.2 ¢)
Semisoft (L:s = 5:3) 5\13 (270.0 ¢)
Basic (L:s = 2:1) 2\5 (280.8 ¢)
Semihard (L:s = 5:2) 5\12 (292.5 ¢)
Hard (L:s = 3:1) 3\7 (300.8 ¢)
Superhard (L:s = 4:1) 4\9 (312.0 ¢)
Collapsed (L:s = 1:0) 1\2 (351.0 ¢)

2L 1s⟨3/2⟩ is a 3/2-equivalent (fifth-equivalent) moment of symmetry scale containing 2 large steps and 1 small step, repeating every interval of 3/2 (702.0 ¢). Generators that produce this scale range from 234 ¢ to 351 ¢, or from 351 ¢ to 468 ¢. Scales of this form are always proper because there is only one small step.

Scale properties

This article uses TAMNAMS conventions for the names of this scale's intervals and scale degrees. The use of 1-indexed ordinal names is reserved for diatonic interval categories.

Intervals

Intervals of 2L 1s⟨3/2⟩
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-mosstep Perfect 0-mosstep P0ms 0 0.0 ¢
1-mosstep Diminished 1-mosstep d1ms s 0.0 ¢ to 234.0 ¢
Perfect 1-mosstep P1ms L 234.0 ¢ to 351.0 ¢
2-mosstep Perfect 2-mosstep P2ms L + s 351.0 ¢ to 468.0 ¢
Augmented 2-mosstep A2ms 2L 468.0 ¢ to 702.0 ¢
3-mosstep Perfect 3-mosstep P3ms 2L + s 702.0 ¢

Generator chain

Generator chain of 2L 1s⟨3/2⟩
Bright gens Scale degree Abbrev.
4 Augmented 1-mosdegree A1md
3 Augmented 0-mosdegree A0md
2 Augmented 2-mosdegree A2md
1 Perfect 1-mosdegree P1md
0 Perfect 0-mosdegree
Perfect 3-mosdegree		 P0md
P3md
−1 Perfect 2-mosdegree P2md
−2 Diminished 1-mosdegree d1md
−3 Diminished 3-mosdegree d3md
−4 Diminished 2-mosdegree d2md

Modes

Scale degrees of the modes of 2L 1s⟨3/2⟩
UDP Cyclic
order		 Step
pattern		 Scale degree (mosdegree)
0 1 2 3
2|0 1 LLs Perf. Perf. Aug. Perf.
1|1 2 LsL Perf. Perf. Perf. Perf.
0|2 3 sLL Perf. Dim. Perf. Perf.

Scale tree

Scale tree and tuning spectrum of 2L 1s⟨3/2⟩
Generator(edf) Cents Step ratio Comments(always proper)
Bright Dark L:s Hardness
1\3 233.985 467.970 1:1 1.000 Equalized 2L 1s⟨3/2⟩
6\17 247.749 454.206 6:5 1.200
5\14 250.698 451.257 5:4 1.250
9\25 252.704 449.251 9:7 1.286
4\11 255.256 446.699 4:3 1.333 Supersoft 2L 1s⟨3/2⟩
11\30 257.384 444.572 11:8 1.375
7\19 258.615 443.340 7:5 1.400
10\27 259.983 441.972 10:7 1.429
3\8 263.233 438.722 3:2 1.500 Soft 2L 1s⟨3/2⟩
11\29 266.259 435.696 11:7 1.571
8\21 267.411 434.544 8:5 1.600
13\34 268.395 433.560 13:8 1.625
5\13 269.983 431.972 5:3 1.667 Semisoft 2L 1s⟨3/2⟩
12\31 271.725 430.230 12:7 1.714
7\18 272.983 428.973 7:4 1.750
9\23 274.678 427.277 9:5 1.800
2\5 280.782 421.173 2:1 2.000 Basic 2L 1s⟨3/2⟩
9\22 287.163 414.792 9:4 2.250
7\17 289.040 412.915 7:3 2.333
12\29 290.464 411.491 12:5 2.400
5\12 292.481 409.474 5:2 2.500 Semihard 2L 1s⟨3/2⟩
13\31 294.368 407.587 13:5 2.600
8\19 295.560 406.395 8:3 2.667
11\26 296.981 404.974 11:4 2.750
3\7 300.838 401.117 3:1 3.000 Hard 2L 1s⟨3/2⟩
10\23 305.198 396.757 10:3 3.333
7\16 307.105 394.850 7:2 3.500
11\25 308.860 393.095 11:3 3.667
4\9 311.980 389.975 4:1 4.000 Superhard 2L 1s⟨3/2⟩
9\20 315.880 386.075 9:2 4.500
5\11 319.070 382.885 5:1 5.000
6\13 323.979 377.976 6:1 6.000
1\2 350.978 350.978 1:0 → ∞ Collapsed 2L 1s⟨3/2⟩
Icon-Stub.png This page is a stub. You can help the Xenharmonic Wiki by expanding it.
Retrieved from "https://en.xen.wiki/index.php?title=2L_1s_(3/2-equivalent)&oldid=184247"