9L 5s
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Scale structure
Step pattern
LLsLLsLLsLLsLs
sLsLLsLLsLLsLL
Equave
2/1 (1200.0¢)
Period
2/1 (1200.0¢)
Generator size
Bright
3\14 to 2\9 (257.1¢ to 266.7¢)
Dark
7\9 to 11\14 (933.3¢ to 942.9¢)
TAMNAMS information
Descends from
5L 4s (semiquartal)
Ancestor's step ratio range
1:1 to 2:1 (soft-of-basic)
Related MOS scales
Parent
5L 4s
Sister
5L 9s
Daughters
14L 9s, 9L 14s
Neutralized
4L 10s
2-Flought
23L 5s, 9L 19s
Equal tunings
Equalized (L:s = 1:1)
3\14 (257.1¢)
Supersoft (L:s = 4:3)
11\51 (258.8¢)
Soft (L:s = 3:2)
8\37 (259.5¢)
Semisoft (L:s = 5:3)
13\60 (260.0¢)
Basic (L:s = 2:1)
5\23 (260.9¢)
Semihard (L:s = 5:2)
12\55 (261.8¢)
Hard (L:s = 3:1)
7\32 (262.5¢)
Superhard (L:s = 4:1)
9\41 (263.4¢)
Collapsed (L:s = 1:0)
2\9 (266.7¢)
 |
Todo: confirm Verify temperaments that correspond with 9L 5s |
| ↖ 8L 4s | ↑ 9L 4s | 10L 4s ↗ |
| ← 8L 5s | 9L 5s | 10L 5s → |
| ↙ 8L 6s | ↓ 9L 6s | 10L 6s ↘ |
┌╥╥┬╥╥┬╥╥┬╥╥┬╥┬┐ │║║│║║│║║│║║│║││ ││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
sLsLLsLLsLLsLL
9L 5s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 9 large steps and 5 small steps, repeating every octave. 9L 5s is a child scale of 5L 4s, expanding it by 5 tones. Generators that produce this scale range from 257.1¢ to 266.7¢, or from 933.3¢ to 942.9¢.
The generator can be said to approximate 7/6, but just 7/6 is larger than 2\9edo, so it cannot be used as a generator. The simplest just interval that works as a generator is 36/31. Two generators are said to create a fourth like Godzilla, but in reality it is closer to 27/20, if that is considered a consonance. 9L5s is third smallest MOS of Semiphore.
Modes
| UDP | Cyclic order |
Step pattern |
|---|---|---|
| 13|0 | 1 | LLsLLsLLsLLsLs |
| 12|1 | 4 | LLsLLsLLsLsLLs |
| 11|2 | 7 | LLsLLsLsLLsLLs |
| 10|3 | 10 | LLsLsLLsLLsLLs |
| 9|4 | 13 | LsLLsLLsLLsLLs |
| 8|5 | 2 | LsLLsLLsLLsLsL |
| 7|6 | 5 | LsLLsLLsLsLLsL |
| 6|7 | 8 | LsLLsLsLLsLLsL |
| 5|8 | 11 | LsLsLLsLLsLLsL |
| 4|9 | 14 | sLLsLLsLLsLLsL |
| 3|10 | 3 | sLLsLLsLLsLsLL |
| 2|11 | 6 | sLLsLLsLsLLsLL |
| 1|12 | 9 | sLLsLsLLsLLsLL |
| 0|13 | 12 | sLsLLsLLsLLsLL |
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 85.7¢ |
| Major 1-mosstep | M1ms | L | 85.7¢ to 133.3¢ | |
| 2-mosstep | Minor 2-mosstep | m2ms | L + s | 133.3¢ to 171.4¢ |
| Major 2-mosstep | M2ms | 2L | 171.4¢ to 266.7¢ | |
| 3-mosstep | Diminished 3-mosstep | d3ms | L + 2s | 133.3¢ to 257.1¢ |
| Perfect 3-mosstep | P3ms | 2L + s | 257.1¢ to 266.7¢ | |
| 4-mosstep | Minor 4-mosstep | m4ms | 2L + 2s | 266.7¢ to 342.9¢ |
| Major 4-mosstep | M4ms | 3L + s | 342.9¢ to 400.0¢ | |
| 5-mosstep | Minor 5-mosstep | m5ms | 3L + 2s | 400.0¢ to 428.6¢ |
| Major 5-mosstep | M5ms | 4L + s | 428.6¢ to 533.3¢ | |
| 6-mosstep | Minor 6-mosstep | m6ms | 3L + 3s | 400.0¢ to 514.3¢ |
| Major 6-mosstep | M6ms | 4L + 2s | 514.3¢ to 533.3¢ | |
| 7-mosstep | Minor 7-mosstep | m7ms | 4L + 3s | 533.3¢ to 600.0¢ |
| Major 7-mosstep | M7ms | 5L + 2s | 600.0¢ to 666.7¢ | |
| 8-mosstep | Minor 8-mosstep | m8ms | 5L + 3s | 666.7¢ to 685.7¢ |
| Major 8-mosstep | M8ms | 6L + 2s | 685.7¢ to 800.0¢ | |
| 9-mosstep | Minor 9-mosstep | m9ms | 5L + 4s | 666.7¢ to 771.4¢ |
| Major 9-mosstep | M9ms | 6L + 3s | 771.4¢ to 800.0¢ | |
| 10-mosstep | Minor 10-mosstep | m10ms | 6L + 4s | 800.0¢ to 857.1¢ |
| Major 10-mosstep | M10ms | 7L + 3s | 857.1¢ to 933.3¢ | |
| 11-mosstep | Perfect 11-mosstep | P11ms | 7L + 4s | 933.3¢ to 942.9¢ |
| Augmented 11-mosstep | A11ms | 8L + 3s | 942.9¢ to 1066.7¢ | |
| 12-mosstep | Minor 12-mosstep | m12ms | 7L + 5s | 933.3¢ to 1028.6¢ |
| Major 12-mosstep | M12ms | 8L + 4s | 1028.6¢ to 1066.7¢ | |
| 13-mosstep | Minor 13-mosstep | m13ms | 8L + 5s | 1066.7¢ to 1114.3¢ |
| Major 13-mosstep | M13ms | 9L + 4s | 1114.3¢ to 1200.0¢ | |
| 14-mosstep | Perfect 14-mosstep | P14ms | 9L + 5s | 1200.0¢ |
Scale tree
| Generator(edo) | Cents | Step ratio | Comments | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 3\14 | 257.143 | 942.857 | 1:1 | 1.000 | Equalized 9L 5s | |||||
| 17\79 | 258.228 | 941.772 | 6:5 | 1.200 | ||||||
| 14\65 | 258.462 | 941.538 | 5:4 | 1.250 | ||||||
| 25\116 | 258.621 | 941.379 | 9:7 | 1.286 | ||||||
| 11\51 | 258.824 | 941.176 | 4:3 | 1.333 | Supersoft 9L 5s | |||||
| 30\139 | 258.993 | 941.007 | 11:8 | 1.375 | ||||||
| 19\88 | 259.091 | 940.909 | 7:5 | 1.400 | ||||||
| 27\125 | 259.200 | 940.800 | 10:7 | 1.429 | ||||||
| 8\37 | 259.459 | 940.541 | 3:2 | 1.500 | Soft 9L 5s | |||||
| 29\134 | 259.701 | 940.299 | 11:7 | 1.571 | ||||||
| 21\97 | 259.794 | 940.206 | 8:5 | 1.600 | ||||||
| 34\157 | 259.873 | 940.127 | 13:8 | 1.625 | ||||||
| 13\60 | 260.000 | 940.000 | 5:3 | 1.667 | Semisoft 9L 5s | |||||
| 31\143 | 260.140 | 939.860 | 12:7 | 1.714 | ||||||
| 18\83 | 260.241 | 939.759 | 7:4 | 1.750 | ||||||
| 23\106 | 260.377 | 939.623 | 9:5 | 1.800 | ||||||
| 5\23 | 260.870 | 939.130 | 2:1 | 2.000 | Basic 9L 5s Scales with tunings softer than this are proper | |||||
| 22\101 | 261.386 | 938.614 | 9:4 | 2.250 | ||||||
| 17\78 | 261.538 | 938.462 | 7:3 | 2.333 | ||||||
| 29\133 | 261.654 | 938.346 | 12:5 | 2.400 | ||||||
| 12\55 | 261.818 | 938.182 | 5:2 | 2.500 | Semihard 9L 5s | |||||
| 31\142 | 261.972 | 938.028 | 13:5 | 2.600 | ||||||
| 19\87 | 262.069 | 937.931 | 8:3 | 2.667 | ||||||
| 26\119 | 262.185 | 937.815 | 11:4 | 2.750 | ||||||
| 7\32 | 262.500 | 937.500 | 3:1 | 3.000 | Hard 9L 5s | |||||
| 23\105 | 262.857 | 937.143 | 10:3 | 3.333 | ||||||
| 16\73 | 263.014 | 936.986 | 7:2 | 3.500 | ||||||
| 25\114 | 263.158 | 936.842 | 11:3 | 3.667 | ||||||
| 9\41 | 263.415 | 936.585 | 4:1 | 4.000 | Superhard 9L 5s | |||||
| 20\91 | 263.736 | 936.264 | 9:2 | 4.500 | ||||||
| 11\50 | 264.000 | 936.000 | 5:1 | 5.000 | ||||||
| 13\59 | 264.407 | 935.593 | 6:1 | 6.000 | ||||||
| 2\9 | 266.667 | 933.333 | 1:0 | → ∞ | Collapsed 9L 5s | |||||