3L 1s
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Scale structure
Step pattern
LLLs
sLLL
Equave
2/1 (1200.0¢)
Period
2/1 (1200.0¢)
Generator size
Bright
1\4 to 1\3 (300.0¢ to 400.0¢)
Dark
2\3 to 3\4 (800.0¢ to 900.0¢)
Related MOS scales
Parent
1L 2s
Sister
1L 3s
Daughters
4L 3s, 3L 4s
Neutralized
2L 2s
2-Flought
7L 1s, 3L 5s
Equal tunings
Equalized (L:s = 1:1)
1\4 (300.0¢)
Supersoft (L:s = 4:3)
4\15 (320.0¢)
Soft (L:s = 3:2)
3\11 (327.3¢)
Semisoft (L:s = 5:3)
5\18 (333.3¢)
Basic (L:s = 2:1)
2\7 (342.9¢)
Semihard (L:s = 5:2)
5\17 (352.9¢)
Hard (L:s = 3:1)
3\10 (360.0¢)
Superhard (L:s = 4:1)
4\13 (369.2¢)
Collapsed (L:s = 1:0)
1\3 (400.0¢)
| ← 2L 1s | 3L 1s | 4L 1s → |
| ↙ 2L 2s | ↓ 3L 2s | 4L 2s ↘ |
┌╥╥╥┬┐ │║║║││ ││││││ └┴┴┴┴┘
sLLL
3L 1s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 3 large steps and 1 small step, repeating every octave. Generators that produce this scale range from 300¢ to 400¢, or from 800¢ to 900¢. Scales of this form are always proper because there is only one small step.
Modes
| UDP | Cyclic order |
Step pattern |
Scale degree (mosdegree) | ||||
|---|---|---|---|---|---|---|---|
| 0 | 1 | 2 | 3 | 4 | |||
| 3|0 | 1 | LLLs | Perf. | Perf. | Maj. | Aug. | Perf. |
| 2|1 | 2 | LLsL | Perf. | Perf. | Maj. | Perf. | Perf. |
| 1|2 | 3 | LsLL | Perf. | Perf. | Min. | Perf. | Perf. |
| 0|3 | 4 | sLLL | Perf. | Dim. | Min. | Perf. | Perf. |
Intervals
| 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 300.0¢ |
| Perfect 1-mosstep | P1ms | L | 300.0¢ to 400.0¢ | |
| 2-mosstep | Minor 2-mosstep | m2ms | L + s | 400.0¢ to 600.0¢ |
| Major 2-mosstep | M2ms | 2L | 600.0¢ to 800.0¢ | |
| 3-mosstep | Perfect 3-mosstep | P3ms | 2L + s | 800.0¢ to 900.0¢ |
| Augmented 3-mosstep | A3ms | 3L | 900.0¢ to 1200.0¢ | |
| 4-mosstep | Perfect 4-mosstep | P4ms | 3L + s | 1200.0¢ |
Scale tree
Generator ranges:
- Chroma-positive generator: 300 cents (1\4) to 400 cents (1\3)
- Chroma-negative generator: 800 cents (2\3) to 900 cents (3\4)
| Generator(edo) | Cents | Step ratio | Comments(always proper) | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 1\4 | 300.000 | 900.000 | 1:1 | 1.000 | Equalized 3L 1s | |||||
| 6\23 | 313.043 | 886.957 | 6:5 | 1.200 | ||||||
| 5\19 | 315.789 | 884.211 | 5:4 | 1.250 | ||||||
| 9\34 | 317.647 | 882.353 | 9:7 | 1.286 | Hanson/keemun | |||||
| 4\15 | 320.000 | 880.000 | 4:3 | 1.333 | Supersoft 3L 1s | |||||
| 11\41 | 321.951 | 878.049 | 11:8 | 1.375 | Superkleismic | |||||
| 7\26 | 323.077 | 876.923 | 7:5 | 1.400 | ||||||
| 10\37 | 324.324 | 875.676 | 10:7 | 1.429 | Hyperkleismic | |||||
| 3\11 | 327.273 | 872.727 | 3:2 | 1.500 | Soft 3L 1s | |||||
| 11\40 | 330.000 | 870.000 | 11:7 | 1.571 | ||||||
| 8\29 | 331.034 | 868.966 | 8:5 | 1.600 | ||||||
| 13\47 | 331.915 | 868.085 | 13:8 | 1.625 | Golden dicot (331.672 cents) | |||||
| 5\18 | 333.333 | 866.667 | 5:3 | 1.667 | Semisoft 3L 1s | |||||
| 12\43 | 334.884 | 865.116 | 12:7 | 1.714 | ||||||
| 7\25 | 336.000 | 864.000 | 7:4 | 1.750 | ||||||
| 9\32 | 337.500 | 862.500 | 9:5 | 1.800 | Sixix | |||||
| 2\7 | 342.857 | 857.143 | 2:1 | 2.000 | Basic 3L 1s | |||||
| 9\31 | 348.387 | 851.613 | 9:4 | 2.250 | Mohaha/mohajira | |||||
| 7\24 | 350.000 | 850.000 | 7:3 | 2.333 | ||||||
| 12\41 | 351.220 | 848.780 | 12:5 | 2.400 | Hemif/hemififths | |||||
| 5\17 | 352.941 | 847.059 | 5:2 | 2.500 | Semihard 3L 1s | |||||
| 13\44 | 354.545 | 845.455 | 13:5 | 2.600 | ||||||
| 8\27 | 355.556 | 844.444 | 8:3 | 2.667 | ||||||
| 11\37 | 356.757 | 843.243 | 11:4 | 2.750 | Beatles | |||||
| 3\10 | 360.000 | 840.000 | 3:1 | 3.000 | Hard 3L 1s | |||||
| 10\33 | 363.636 | 836.364 | 10:3 | 3.333 | ||||||
| 7\23 | 365.217 | 834.783 | 7:2 | 3.500 | ||||||
| 11\36 | 366.667 | 833.333 | 11:3 | 3.667 | ||||||
| 4\13 | 369.231 | 830.769 | 4:1 | 4.000 | Superhard 3L 1s | |||||
| 9\29 | 372.414 | 827.586 | 9:2 | 4.500 | Sephiroth | |||||
| 5\16 | 375.000 | 825.000 | 5:1 | 5.000 | ||||||
| 6\19 | 378.947 | 821.053 | 6:1 | 6.000 | Magic↓ | |||||
| 1\3 | 400.000 | 800.000 | 1:0 | → ∞ | Collapsed 3L 1s | |||||