4L 9s
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Scale structure
Step pattern
LssLssLssLsss
sssLssLssLssL
Equave
2/1 (1200.0¢)
Period
2/1 (1200.0¢)
Generator size
Bright
3\13 to 1\4 (276.9¢ to 300.0¢)
Dark
3\4 to 10\13 (900.0¢ to 923.1¢)
TAMNAMS information
Descends from
4L 5s (gramitonic)
Ancestor's step ratio range
2:1 to 1:0 (hard-of-basic)
Related MOS scales
Parent
4L 5s
Sister
9L 4s
Daughters
13L 4s, 4L 13s
Neutralized
8L 5s
2-Flought
17L 9s, 4L 22s
Equal tunings
Equalized (L:s = 1:1)
3\13 (276.9¢)
Supersoft (L:s = 4:3)
10\43 (279.1¢)
Soft (L:s = 3:2)
7\30 (280.0¢)
Semisoft (L:s = 5:3)
11\47 (280.9¢)
Basic (L:s = 2:1)
4\17 (282.4¢)
Semihard (L:s = 5:2)
9\38 (284.2¢)
Hard (L:s = 3:1)
5\21 (285.7¢)
Superhard (L:s = 4:1)
6\25 (288.0¢)
Collapsed (L:s = 1:0)
1\4 (300.0¢)
| ↖ 3L 8s | ↑ 4L 8s | 5L 8s ↗ |
| ← 3L 9s | 4L 9s | 5L 9s → |
| ↙ 3L 10s | ↓ 4L 10s | 5L 10s ↘ |
┌╥┬┬╥┬┬╥┬┬╥┬┬┬┐ │║││║││║││║││││ │││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┘
sssLssLssLssL
4L 9s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 4 large steps and 9 small steps, repeating every octave. 4L 9s is a child scale of 4L 5s, expanding it by 4 tones. Generators that produce this scale range from 276.9¢ to 300¢, or from 900¢ to 923.1¢.
4L 9s represents chromatic scales of Huxley, Lovecraft, gariberttet and subklei temperaments. The harmonic entropy minimum for this pattern maps +2, +3, and +5 bright generators to 7/5, 5/3 and 7/3, respectively.
Modes
| UDP | Cyclic order |
Step pattern |
|---|---|---|
| 12|0 | 1 | LssLssLssLsss |
| 11|1 | 4 | LssLssLsssLss |
| 10|2 | 7 | LssLsssLssLss |
| 9|3 | 10 | LsssLssLssLss |
| 8|4 | 13 | sLssLssLssLss |
| 7|5 | 3 | sLssLssLsssLs |
| 6|6 | 6 | sLssLsssLssLs |
| 5|7 | 9 | sLsssLssLssLs |
| 4|8 | 12 | ssLssLssLssLs |
| 3|9 | 2 | ssLssLssLsssL |
| 2|10 | 5 | ssLssLsssLssL |
| 1|11 | 8 | ssLsssLssLssL |
| 0|12 | 11 | sssLssLssLssL |
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 92.3¢ |
| Major 1-mosstep | M1ms | L | 92.3¢ to 300.0¢ | |
| 2-mosstep | Minor 2-mosstep | m2ms | 2s | 0.0¢ to 184.6¢ |
| Major 2-mosstep | M2ms | L + s | 184.6¢ to 300.0¢ | |
| 3-mosstep | Diminished 3-mosstep | d3ms | 3s | 0.0¢ to 276.9¢ |
| Perfect 3-mosstep | P3ms | L + 2s | 276.9¢ to 300.0¢ | |
| 4-mosstep | Minor 4-mosstep | m4ms | L + 3s | 300.0¢ to 369.2¢ |
| Major 4-mosstep | M4ms | 2L + 2s | 369.2¢ to 600.0¢ | |
| 5-mosstep | Minor 5-mosstep | m5ms | L + 4s | 300.0¢ to 461.5¢ |
| Major 5-mosstep | M5ms | 2L + 3s | 461.5¢ to 600.0¢ | |
| 6-mosstep | Minor 6-mosstep | m6ms | L + 5s | 300.0¢ to 553.8¢ |
| Major 6-mosstep | M6ms | 2L + 4s | 553.8¢ to 600.0¢ | |
| 7-mosstep | Minor 7-mosstep | m7ms | 2L + 5s | 600.0¢ to 646.2¢ |
| Major 7-mosstep | M7ms | 3L + 4s | 646.2¢ to 900.0¢ | |
| 8-mosstep | Minor 8-mosstep | m8ms | 2L + 6s | 600.0¢ to 738.5¢ |
| Major 8-mosstep | M8ms | 3L + 5s | 738.5¢ to 900.0¢ | |
| 9-mosstep | Minor 9-mosstep | m9ms | 2L + 7s | 600.0¢ to 830.8¢ |
| Major 9-mosstep | M9ms | 3L + 6s | 830.8¢ to 900.0¢ | |
| 10-mosstep | Perfect 10-mosstep | P10ms | 3L + 7s | 900.0¢ to 923.1¢ |
| Augmented 10-mosstep | A10ms | 4L + 6s | 923.1¢ to 1200.0¢ | |
| 11-mosstep | Minor 11-mosstep | m11ms | 3L + 8s | 900.0¢ to 1015.4¢ |
| Major 11-mosstep | M11ms | 4L + 7s | 1015.4¢ to 1200.0¢ | |
| 12-mosstep | Minor 12-mosstep | m12ms | 3L + 9s | 900.0¢ to 1107.7¢ |
| Major 12-mosstep | M12ms | 4L + 8s | 1107.7¢ to 1200.0¢ | |
| 13-mosstep | Perfect 13-mosstep | P13ms | 4L + 9s | 1200.0¢ |
Scale tree
| Generator(edo) | Cents | Step ratio | Comments | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 3\13 | 276.923 | 923.077 | 1:1 | 1.000 | Equalized 4L 9s | |||||
| 16\69 | 278.261 | 921.739 | 6:5 | 1.200 | ||||||
| 13\56 | 278.571 | 921.429 | 5:4 | 1.250 | ||||||
| 23\99 | 278.788 | 921.212 | 9:7 | 1.286 | ||||||
| 10\43 | 279.070 | 920.930 | 4:3 | 1.333 | Supersoft 4L 9s | |||||
| 27\116 | 279.310 | 920.690 | 11:8 | 1.375 | ||||||
| 17\73 | 279.452 | 920.548 | 7:5 | 1.400 | ||||||
| 24\103 | 279.612 | 920.388 | 10:7 | 1.429 | ||||||
| 7\30 | 280.000 | 920.000 | 3:2 | 1.500 | Soft 4L 9s | |||||
| 25\107 | 280.374 | 919.626 | 11:7 | 1.571 | ||||||
| 18\77 | 280.519 | 919.481 | 8:5 | 1.600 | ||||||
| 29\124 | 280.645 | 919.355 | 13:8 | 1.625 | ||||||
| 11\47 | 280.851 | 919.149 | 5:3 | 1.667 | Semisoft 4L 9s | |||||
| 26\111 | 281.081 | 918.919 | 12:7 | 1.714 | ||||||
| 15\64 | 281.250 | 918.750 | 7:4 | 1.750 | ||||||
| 19\81 | 281.481 | 918.519 | 9:5 | 1.800 | ||||||
| 4\17 | 282.353 | 917.647 | 2:1 | 2.000 | Basic 4L 9s Scales with tunings softer than this are proper | |||||
| 17\72 | 283.333 | 916.667 | 9:4 | 2.250 | ||||||
| 13\55 | 283.636 | 916.364 | 7:3 | 2.333 | ||||||
| 22\93 | 283.871 | 916.129 | 12:5 | 2.400 | ||||||
| 9\38 | 284.211 | 915.789 | 5:2 | 2.500 | Semihard 4L 9s | |||||
| 23\97 | 284.536 | 915.464 | 13:5 | 2.600 | ||||||
| 14\59 | 284.746 | 915.254 | 8:3 | 2.667 | ||||||
| 19\80 | 285.000 | 915.000 | 11:4 | 2.750 | ||||||
| 5\21 | 285.714 | 914.286 | 3:1 | 3.000 | Hard 4L 9s | |||||
| 16\67 | 286.567 | 913.433 | 10:3 | 3.333 | ||||||
| 11\46 | 286.957 | 913.043 | 7:2 | 3.500 | ||||||
| 17\71 | 287.324 | 912.676 | 11:3 | 3.667 | ||||||
| 6\25 | 288.000 | 912.000 | 4:1 | 4.000 | Superhard 4L 9s | |||||
| 13\54 | 288.889 | 911.111 | 9:2 | 4.500 | ||||||
| 7\29 | 289.655 | 910.345 | 5:1 | 5.000 | ||||||
| 8\33 | 290.909 | 909.091 | 6:1 | 6.000 | ||||||
| 1\4 | 300.000 | 900.000 | 1:0 | → ∞ | Collapsed 4L 9s | |||||