9L 4s
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Scale structure
Step pattern
LLLsLLsLLsLLs
sLLsLLsLLsLLL
Equave
2/1 (1200.0¢)
Period
2/1 (1200.0¢)
Generator size
Bright
10\13 to 7\9 (923.1¢ to 933.3¢)
Dark
2\9 to 3\13 (266.7¢ to 276.9¢)
TAMNAMS information
Descends from
4L 5s
Ancestor's step ratio range
1:1 to 2:1 (soft-of-basic)
Related MOS scales
Parent
4L 5s
Sister
4L 9s
Daughters
13L 9s, 9L 13s
Neutralized
5L 8s
2-Flought
22L 4s, 9L 17s
Equal tunings
Equalized (L:s = 1:1)
10\13 (923.1¢)
Supersoft (L:s = 4:3)
37\48 (925.0¢)
Soft (L:s = 3:2)
27\35 (925.7¢)
Semisoft (L:s = 5:3)
44\57 (926.3¢)
Basic (L:s = 2:1)
17\22 (927.3¢)
Semihard (L:s = 5:2)
41\53 (928.3¢)
Hard (L:s = 3:1)
24\31 (929.0¢)
Superhard (L:s = 4:1)
31\40 (930.0¢)
Collapsed (L:s = 1:0)
7\9 (933.3¢)
| ↖ 8L 3s | ↑ 9L 3s | 10L 3s ↗ |
| ← 8L 4s | 9L 4s | 10L 4s → |
| ↙ 8L 5s | ↓ 9L 5s | 10L 5s ↘ |
┌╥╥╥┬╥╥┬╥╥┬╥╥┬┐ │║║║│║║│║║│║║││ │││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┘
sLLsLLsLLsLLL
9L 4s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 9 large steps and 4 small steps, repeating every octave. 9L 4s is a child scale of 4L 5s, expanding it by 4 tones. Generators that produce this scale range from 923.1¢ to 933.3¢, or from 266.7¢ to 276.9¢.
It is the chromatic scale of Orwell temperament. The harmonic entropy minimum for this scale has three dark generators map to 8/5 (~813.6¢), where the generator is ~271.2¢.
Modes
| UDP | Cyclic order |
Step pattern |
|---|---|---|
| 12|0 | 1 | LLLsLLsLLsLLs |
| 11|1 | 11 | LLsLLLsLLsLLs |
| 10|2 | 8 | LLsLLsLLLsLLs |
| 9|3 | 5 | LLsLLsLLsLLLs |
| 8|4 | 2 | LLsLLsLLsLLsL |
| 7|5 | 12 | LsLLLsLLsLLsL |
| 6|6 | 9 | LsLLsLLLsLLsL |
| 5|7 | 6 | LsLLsLLsLLLsL |
| 4|8 | 3 | LsLLsLLsLLsLL |
| 3|9 | 13 | sLLLsLLsLLsLL |
| 2|10 | 10 | sLLsLLLsLLsLL |
| 1|11 | 7 | sLLsLLsLLLsLL |
| 0|12 | 4 | sLLsLLsLLsLLL |
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 133.3¢ | |
| 2-mosstep | Minor 2-mosstep | m2ms | L + s | 133.3¢ to 184.6¢ |
| Major 2-mosstep | M2ms | 2L | 184.6¢ to 266.7¢ | |
| 3-mosstep | Perfect 3-mosstep | P3ms | 2L + s | 266.7¢ to 276.9¢ |
| Augmented 3-mosstep | A3ms | 3L | 276.9¢ to 400.0¢ | |
| 4-mosstep | Minor 4-mosstep | m4ms | 2L + 2s | 266.7¢ to 369.2¢ |
| Major 4-mosstep | M4ms | 3L + s | 369.2¢ to 400.0¢ | |
| 5-mosstep | Minor 5-mosstep | m5ms | 3L + 2s | 400.0¢ to 461.5¢ |
| Major 5-mosstep | M5ms | 4L + s | 461.5¢ to 533.3¢ | |
| 6-mosstep | Minor 6-mosstep | m6ms | 4L + 2s | 533.3¢ to 553.8¢ |
| Major 6-mosstep | M6ms | 5L + s | 553.8¢ to 666.7¢ | |
| 7-mosstep | Minor 7-mosstep | m7ms | 4L + 3s | 533.3¢ to 646.2¢ |
| Major 7-mosstep | M7ms | 5L + 2s | 646.2¢ to 666.7¢ | |
| 8-mosstep | Minor 8-mosstep | m8ms | 5L + 3s | 666.7¢ to 738.5¢ |
| Major 8-mosstep | M8ms | 6L + 2s | 738.5¢ to 800.0¢ | |
| 9-mosstep | Minor 9-mosstep | m9ms | 6L + 3s | 800.0¢ to 830.8¢ |
| Major 9-mosstep | M9ms | 7L + 2s | 830.8¢ to 933.3¢ | |
| 10-mosstep | Diminished 10-mosstep | d10ms | 6L + 4s | 800.0¢ to 923.1¢ |
| Perfect 10-mosstep | P10ms | 7L + 3s | 923.1¢ to 933.3¢ | |
| 11-mosstep | Minor 11-mosstep | m11ms | 7L + 4s | 933.3¢ to 1015.4¢ |
| Major 11-mosstep | M11ms | 8L + 3s | 1015.4¢ to 1066.7¢ | |
| 12-mosstep | Minor 12-mosstep | m12ms | 8L + 4s | 1066.7¢ to 1107.7¢ |
| Major 12-mosstep | M12ms | 9L + 3s | 1107.7¢ to 1200.0¢ | |
| 13-mosstep | Perfect 13-mosstep | P13ms | 9L + 4s | 1200.0¢ |
Scale tree
| Generator(edo) | Cents | Step ratio | Comments | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 10\13 | 923.077 | 276.923 | 1:1 | 1.000 | Equalized 9L 4s | |||||
| 57\74 | 924.324 | 275.676 | 6:5 | 1.200 | ||||||
| 47\61 | 924.590 | 275.410 | 5:4 | 1.250 | ||||||
| 84\109 | 924.771 | 275.229 | 9:7 | 1.286 | ||||||
| 37\48 | 925.000 | 275.000 | 4:3 | 1.333 | Supersoft 9L 4s | |||||
| 101\131 | 925.191 | 274.809 | 11:8 | 1.375 | ||||||
| 64\83 | 925.301 | 274.699 | 7:5 | 1.400 | ||||||
| 91\118 | 925.424 | 274.576 | 10:7 | 1.429 | ||||||
| 27\35 | 925.714 | 274.286 | 3:2 | 1.500 | Soft 9L 4s | |||||
| 98\127 | 925.984 | 274.016 | 11:7 | 1.571 | ||||||
| 71\92 | 926.087 | 273.913 | 8:5 | 1.600 | ||||||
| 115\149 | 926.174 | 273.826 | 13:8 | 1.625 | ||||||
| 44\57 | 926.316 | 273.684 | 5:3 | 1.667 | Semisoft 9L 4s | |||||
| 105\136 | 926.471 | 273.529 | 12:7 | 1.714 | ||||||
| 61\79 | 926.582 | 273.418 | 7:4 | 1.750 | ||||||
| 78\101 | 926.733 | 273.267 | 9:5 | 1.800 | ||||||
| 17\22 | 927.273 | 272.727 | 2:1 | 2.000 | Basic 9L 4s Scales with tunings softer than this are proper | |||||
| 75\97 | 927.835 | 272.165 | 9:4 | 2.250 | ||||||
| 58\75 | 928.000 | 272.000 | 7:3 | 2.333 | ||||||
| 99\128 | 928.125 | 271.875 | 12:5 | 2.400 | ||||||
| 41\53 | 928.302 | 271.698 | 5:2 | 2.500 | Semihard 9L 4s | |||||
| 106\137 | 928.467 | 271.533 | 13:5 | 2.600 | ||||||
| 65\84 | 928.571 | 271.429 | 8:3 | 2.667 | ||||||
| 89\115 | 928.696 | 271.304 | 11:4 | 2.750 | ||||||
| 24\31 | 929.032 | 270.968 | 3:1 | 3.000 | Hard 9L 4s | |||||
| 79\102 | 929.412 | 270.588 | 10:3 | 3.333 | ||||||
| 55\71 | 929.577 | 270.423 | 7:2 | 3.500 | ||||||
| 86\111 | 929.730 | 270.270 | 11:3 | 3.667 | ||||||
| 31\40 | 930.000 | 270.000 | 4:1 | 4.000 | Superhard 9L 4s | |||||
| 69\89 | 930.337 | 269.663 | 9:2 | 4.500 | ||||||
| 38\49 | 930.612 | 269.388 | 5:1 | 5.000 | ||||||
| 45\58 | 931.034 | 268.966 | 6:1 | 6.000 | ||||||
| 7\9 | 933.333 | 266.667 | 1:0 | → ∞ | Collapsed 9L 4s | |||||