9L 9s
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Scale structure
Step pattern
LsLsLsLsLsLsLsLsLs
sLsLsLsLsLsLsLsLsL
Equave
2/1 (1200.0¢)
Period
1\9 (133.3¢)
Generator size
Bright
1\18 to 1\9 (66.7¢ to 133.3¢)
Dark
0\9 to 1\18 (0.0¢ to 66.7¢)
Related MOS scales
Parent
9L 0s
Sister
9L 9s
Daughters
18L 9s, 9L 18s
Neutralized
18L 0s
2-Flought
27L 9s, 9L 27s
Equal tunings
Equalized (L:s = 1:1)
1\18 (66.7¢)
Supersoft (L:s = 4:3)
4\63 (76.2¢)
Soft (L:s = 3:2)
3\45 (80.0¢)
Semisoft (L:s = 5:3)
5\72 (83.3¢)
Basic (L:s = 2:1)
2\27 (88.9¢)
Semihard (L:s = 5:2)
5\63 (95.2¢)
Hard (L:s = 3:1)
3\36 (100.0¢)
Superhard (L:s = 4:1)
4\45 (106.7¢)
Collapsed (L:s = 1:0)
1\9 (133.3¢)
| ↖ 8L 8s | ↑ 9L 8s | 10L 8s ↗ |
| ← 8L 9s | 9L 9s | 10L 9s → |
| ↙ 8L 10s | ↓ 9L 10s | 10L 10s ↘ |
┌╥┬╥┬╥┬╥┬╥┬╥┬╥┬╥┬╥┬┐ │║│║│║│║│║│║│║│║│║││ ││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
sLsLsLsLsLsLsLsLsL
9L 9s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 9 large steps and 9 small steps, with a period of 1 large step and 1 small step that repeats every 133.3¢, or 9 times every octave. Generators that produce this scale range from 66.7¢ to 133.3¢, or from 0¢ to 66.7¢. Scales of the true MOS form, where every period is the same, are proper because there is only one small step per period.
Modes
| UDP | Cyclic order |
Step pattern |
|---|---|---|
| 9|0(9) | 1 | LsLsLsLsLsLsLsLsLs |
| 0|9(9) | 2 | sLsLsLsLsLsLsLsLsL |
Intervals
| 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 66.7¢ |
| Major 1-mosstep | M1ms | L | 66.7¢ to 133.3¢ | |
| 2-mosstep | Perfect 2-mosstep | P2ms | L + s | 133.3¢ |
| 3-mosstep | Minor 3-mosstep | m3ms | L + 2s | 133.3¢ to 200.0¢ |
| Major 3-mosstep | M3ms | 2L + s | 200.0¢ to 266.7¢ | |
| 4-mosstep | Perfect 4-mosstep | P4ms | 2L + 2s | 266.7¢ |
| 5-mosstep | Minor 5-mosstep | m5ms | 2L + 3s | 266.7¢ to 333.3¢ |
| Major 5-mosstep | M5ms | 3L + 2s | 333.3¢ to 400.0¢ | |
| 6-mosstep | Perfect 6-mosstep | P6ms | 3L + 3s | 400.0¢ |
| 7-mosstep | Minor 7-mosstep | m7ms | 3L + 4s | 400.0¢ to 466.7¢ |
| Major 7-mosstep | M7ms | 4L + 3s | 466.7¢ to 533.3¢ | |
| 8-mosstep | Perfect 8-mosstep | P8ms | 4L + 4s | 533.3¢ |
| 9-mosstep | Minor 9-mosstep | m9ms | 4L + 5s | 533.3¢ to 600.0¢ |
| Major 9-mosstep | M9ms | 5L + 4s | 600.0¢ to 666.7¢ | |
| 10-mosstep | Perfect 10-mosstep | P10ms | 5L + 5s | 666.7¢ |
| 11-mosstep | Minor 11-mosstep | m11ms | 5L + 6s | 666.7¢ to 733.3¢ |
| Major 11-mosstep | M11ms | 6L + 5s | 733.3¢ to 800.0¢ | |
| 12-mosstep | Perfect 12-mosstep | P12ms | 6L + 6s | 800.0¢ |
| 13-mosstep | Minor 13-mosstep | m13ms | 6L + 7s | 800.0¢ to 866.7¢ |
| Major 13-mosstep | M13ms | 7L + 6s | 866.7¢ to 933.3¢ | |
| 14-mosstep | Perfect 14-mosstep | P14ms | 7L + 7s | 933.3¢ |
| 15-mosstep | Minor 15-mosstep | m15ms | 7L + 8s | 933.3¢ to 1000.0¢ |
| Major 15-mosstep | M15ms | 8L + 7s | 1000.0¢ to 1066.7¢ | |
| 16-mosstep | Perfect 16-mosstep | P16ms | 8L + 8s | 1066.7¢ |
| 17-mosstep | Minor 17-mosstep | m17ms | 8L + 9s | 1066.7¢ to 1133.3¢ |
| Major 17-mosstep | M17ms | 9L + 8s | 1133.3¢ to 1200.0¢ | |
| 18-mosstep | Perfect 18-mosstep | P18ms | 9L + 9s | 1200.0¢ |
Scale tree
| Generator(edo) | Cents | Step ratio | Comments(always proper) | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 1\18 | 66.667 | 66.667 | 1:1 | 1.000 | Equalized 9L 9s | |||||
| 6\99 | 72.727 | 60.606 | 6:5 | 1.200 | ||||||
| 5\81 | 74.074 | 59.259 | 5:4 | 1.250 | ||||||
| 9\144 | 75.000 | 58.333 | 9:7 | 1.286 | ||||||
| 4\63 | 76.190 | 57.143 | 4:3 | 1.333 | Supersoft 9L 9s | |||||
| 11\171 | 77.193 | 56.140 | 11:8 | 1.375 | ||||||
| 7\108 | 77.778 | 55.556 | 7:5 | 1.400 | ||||||
| 10\153 | 78.431 | 54.902 | 10:7 | 1.429 | ||||||
| 3\45 | 80.000 | 53.333 | 3:2 | 1.500 | Soft 9L 9s | |||||
| 11\162 | 81.481 | 51.852 | 11:7 | 1.571 | ||||||
| 8\117 | 82.051 | 51.282 | 8:5 | 1.600 | ||||||
| 13\189 | 82.540 | 50.794 | 13:8 | 1.625 | ||||||
| 5\72 | 83.333 | 50.000 | 5:3 | 1.667 | Semisoft 9L 9s | |||||
| 12\171 | 84.211 | 49.123 | 12:7 | 1.714 | ||||||
| 7\99 | 84.848 | 48.485 | 7:4 | 1.750 | ||||||
| 9\126 | 85.714 | 47.619 | 9:5 | 1.800 | ||||||
| 2\27 | 88.889 | 44.444 | 2:1 | 2.000 | Basic 9L 9s | |||||
| 9\117 | 92.308 | 41.026 | 9:4 | 2.250 | ||||||
| 7\90 | 93.333 | 40.000 | 7:3 | 2.333 | ||||||
| 12\153 | 94.118 | 39.216 | 12:5 | 2.400 | ||||||
| 5\63 | 95.238 | 38.095 | 5:2 | 2.500 | Semihard 9L 9s | |||||
| 13\162 | 96.296 | 37.037 | 13:5 | 2.600 | ||||||
| 8\99 | 96.970 | 36.364 | 8:3 | 2.667 | ||||||
| 11\135 | 97.778 | 35.556 | 11:4 | 2.750 | ||||||
| 3\36 | 100.000 | 33.333 | 3:1 | 3.000 | Hard 9L 9s | |||||
| 10\117 | 102.564 | 30.769 | 10:3 | 3.333 | ||||||
| 7\81 | 103.704 | 29.630 | 7:2 | 3.500 | ||||||
| 11\126 | 104.762 | 28.571 | 11:3 | 3.667 | ||||||
| 4\45 | 106.667 | 26.667 | 4:1 | 4.000 | Superhard 9L 9s | |||||
| 9\99 | 109.091 | 24.242 | 9:2 | 4.500 | ||||||
| 5\54 | 111.111 | 22.222 | 5:1 | 5.000 | ||||||
| 6\63 | 114.286 | 19.048 | 6:1 | 6.000 | ||||||
| 1\9 | 133.333 | 0.000 | 1:0 | → ∞ | Collapsed 9L 9s | |||||
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