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.

Intervals

Scale degree of 2L 1s⟨3/2⟩
Scale degree 5edf (Basic, L:s = 2:1) Approx. JI Ratios
Steps Cents
Perfect 0-mosdegree (unison) 0 0 1/1 (exact)
Diminished 1-mosdegree 1 140.4
Perfect 1-mosdegree 2 280.8
Perfect 2-mosdegree 3 421.2
Augmented 2-mosdegree 4 561.6
Perfect 3-mosdegree (equave) 5 702 3/2 (exact)

Modes

Modes of 2L 1s⟨3/2⟩
UDP Rotational order Step pattern
2|0 1 LLs
1|1 2 LsL
0|2 3 sLL

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⟩