3L 9s
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Scale structure
Step pattern
LsssLsssLsss
sssLsssLsssL
Equave
2/1 (1200.0¢)
Period
1\3 (400.0¢)
Generator size
Bright
3\12 to 1\3 (300.0¢ to 400.0¢)
Dark
0\3 to 1\12 (0.0¢ to 100.0¢)
TAMNAMS information
Descends from
3L 6s
Ancestor's step ratio range
2:1 to 1:0 (hard-of-basic)
Related MOS scales
Parent
3L 6s
Sister
9L 3s
Daughters
12L 3s, 3L 12s
Neutralized
6L 6s
2-Flought
15L 9s, 3L 21s
Equal tunings
Equalized (L:s = 1:1)
3\12 (300.0¢)
Supersoft (L:s = 4:3)
10\39 (307.7¢)
Soft (L:s = 3:2)
7\27 (311.1¢)
Semisoft (L:s = 5:3)
11\42 (314.3¢)
Basic (L:s = 2:1)
4\15 (320.0¢)
Semihard (L:s = 5:2)
9\33 (327.3¢)
Hard (L:s = 3:1)
5\18 (333.3¢)
Superhard (L:s = 4:1)
6\21 (342.9¢)
Collapsed (L:s = 1:0)
1\3 (400.0¢)
| ↖ 2L 8s | ↑ 3L 8s | 4L 8s ↗ |
| ← 2L 9s | 3L 9s | 4L 9s → |
| ↙ 2L 10s | ↓ 3L 10s | 4L 10s ↘ |
┌╥┬┬┬╥┬┬┬╥┬┬┬┐ │║│││║│││║││││ ││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┘
sssLsssLsssL
3L 9s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 3 large steps and 9 small steps, with a period of 1 large step and 3 small steps that repeats every 400.0¢, or 3 times every octave. 3L 9s is a child scale of 3L 6s, expanding it by 3 tones. Generators that produce this scale range from 300¢ to 400¢, or from 0¢ to 100¢.
This MOS represents, among other chromatic scales, that of the Augene temperament.
Modes
| UDP | Cyclic order |
Step pattern |
|---|---|---|
| 9|0(3) | 1 | LsssLsssLsss |
| 6|3(3) | 4 | sLsssLsssLss |
| 3|6(3) | 3 | ssLsssLsssLs |
| 0|9(3) | 2 | sssLsssLsssL |
Intervals
| Intervals | Steps subtended |
Range in cents | ||
|---|---|---|---|---|
| Generic | Specific | Abbrev. | ||
| 0-mosstep | Perfect 0-mosstep | P0ms | 0 | 0.0¢ |
| 1-mosstep | Perfect 1-mosstep | P1ms | s | 0.0¢ to 100.0¢ |
| Augmented 1-mosstep | A1ms | L | 100.0¢ to 400.0¢ | |
| 2-mosstep | Minor 2-mosstep | m2ms | 2s | 0.0¢ to 200.0¢ |
| Major 2-mosstep | M2ms | L + s | 200.0¢ to 400.0¢ | |
| 3-mosstep | Diminished 3-mosstep | d3ms | 3s | 0.0¢ to 300.0¢ |
| Perfect 3-mosstep | P3ms | L + 2s | 300.0¢ to 400.0¢ | |
| 4-mosstep | Perfect 4-mosstep | P4ms | L + 3s | 400.0¢ |
| 5-mosstep | Perfect 5-mosstep | P5ms | L + 4s | 400.0¢ to 500.0¢ |
| Augmented 5-mosstep | A5ms | 2L + 3s | 500.0¢ to 800.0¢ | |
| 6-mosstep | Minor 6-mosstep | m6ms | L + 5s | 400.0¢ to 600.0¢ |
| Major 6-mosstep | M6ms | 2L + 4s | 600.0¢ to 800.0¢ | |
| 7-mosstep | Diminished 7-mosstep | d7ms | L + 6s | 400.0¢ to 700.0¢ |
| Perfect 7-mosstep | P7ms | 2L + 5s | 700.0¢ to 800.0¢ | |
| 8-mosstep | Perfect 8-mosstep | P8ms | 2L + 6s | 800.0¢ |
| 9-mosstep | Perfect 9-mosstep | P9ms | 2L + 7s | 800.0¢ to 900.0¢ |
| Augmented 9-mosstep | A9ms | 3L + 6s | 900.0¢ to 1200.0¢ | |
| 10-mosstep | Minor 10-mosstep | m10ms | 2L + 8s | 800.0¢ to 1000.0¢ |
| Major 10-mosstep | M10ms | 3L + 7s | 1000.0¢ to 1200.0¢ | |
| 11-mosstep | Diminished 11-mosstep | d11ms | 2L + 9s | 800.0¢ to 1100.0¢ |
| Perfect 11-mosstep | P11ms | 3L + 8s | 1100.0¢ to 1200.0¢ | |
| 12-mosstep | Perfect 12-mosstep | P12ms | 3L + 9s | 1200.0¢ |
Scale tree
 |
Todo: review Review entries from past page revision and enter them into the scale tree. |
| Generator(edo) | Cents | Step ratio | Comments | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 3\12 | 300.000 | 100.000 | 1:1 | 1.000 | Equalized 3L 9s | |||||
| 16\63 | 304.762 | 95.238 | 6:5 | 1.200 | ||||||
| 13\51 | 305.882 | 94.118 | 5:4 | 1.250 | ||||||
| 23\90 | 306.667 | 93.333 | 9:7 | 1.286 | ||||||
| 10\39 | 307.692 | 92.308 | 4:3 | 1.333 | Supersoft 3L 9s | |||||
| 27\105 | 308.571 | 91.429 | 11:8 | 1.375 | ||||||
| 17\66 | 309.091 | 90.909 | 7:5 | 1.400 | ||||||
| 24\93 | 309.677 | 90.323 | 10:7 | 1.429 | ||||||
| 7\27 | 311.111 | 88.889 | 3:2 | 1.500 | Soft 3L 9s | |||||
| 25\96 | 312.500 | 87.500 | 11:7 | 1.571 | ||||||
| 18\69 | 313.043 | 86.957 | 8:5 | 1.600 | ||||||
| 29\111 | 313.514 | 86.486 | 13:8 | 1.625 | ||||||
| 11\42 | 314.286 | 85.714 | 5:3 | 1.667 | Semisoft 3L 9s | |||||
| 26\99 | 315.152 | 84.848 | 12:7 | 1.714 | ||||||
| 15\57 | 315.789 | 84.211 | 7:4 | 1.750 | ||||||
| 19\72 | 316.667 | 83.333 | 9:5 | 1.800 | ||||||
| 4\15 | 320.000 | 80.000 | 2:1 | 2.000 | Basic 3L 9s Scales with tunings softer than this are proper | |||||
| 17\63 | 323.810 | 76.190 | 9:4 | 2.250 | ||||||
| 13\48 | 325.000 | 75.000 | 7:3 | 2.333 | ||||||
| 22\81 | 325.926 | 74.074 | 12:5 | 2.400 | ||||||
| 9\33 | 327.273 | 72.727 | 5:2 | 2.500 | Semihard 3L 9s | |||||
| 23\84 | 328.571 | 71.429 | 13:5 | 2.600 | ||||||
| 14\51 | 329.412 | 70.588 | 8:3 | 2.667 | ||||||
| 19\69 | 330.435 | 69.565 | 11:4 | 2.750 | ||||||
| 5\18 | 333.333 | 66.667 | 3:1 | 3.000 | Hard 3L 9s | |||||
| 16\57 | 336.842 | 63.158 | 10:3 | 3.333 | ||||||
| 11\39 | 338.462 | 61.538 | 7:2 | 3.500 | ||||||
| 17\60 | 340.000 | 60.000 | 11:3 | 3.667 | ||||||
| 6\21 | 342.857 | 57.143 | 4:1 | 4.000 | Superhard 3L 9s | |||||
| 13\45 | 346.667 | 53.333 | 9:2 | 4.500 | ||||||
| 7\24 | 350.000 | 50.000 | 5:1 | 5.000 | ||||||
| 8\27 | 355.556 | 44.444 | 6:1 | 6.000 | ||||||
| 1\3 | 400.000 | 0.000 | 1:0 | → ∞ | Collapsed 3L 9s | |||||