9L 6s
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Scale structure
Step pattern
LLsLsLLsLsLLsLs
sLsLLsLsLLsLsLL
Equave
2/1 (1200.0¢)
Period
1\3 (400.0¢)
Generator size
Bright
3\15 to 2\9 (240.0¢ to 266.7¢)
Dark
1\9 to 2\15 (133.3¢ to 160.0¢)
TAMNAMS information
Descends from
6L 3s (hyrulic)
Ancestor's step ratio range
1:1 to 2:1 (soft-of-basic)
Related MOS scales
Parent
6L 3s
Sister
6L 9s
Daughters
15L 9s, 9L 15s
Neutralized
3L 12s
2-Flought
24L 6s, 9L 21s
Equal tunings
Equalized (L:s = 1:1)
3\15 (240.0¢)
Supersoft (L:s = 4:3)
11\54 (244.4¢)
Soft (L:s = 3:2)
8\39 (246.2¢)
Semisoft (L:s = 5:3)
13\63 (247.6¢)
Basic (L:s = 2:1)
5\24 (250.0¢)
Semihard (L:s = 5:2)
12\57 (252.6¢)
Hard (L:s = 3:1)
7\33 (254.5¢)
Superhard (L:s = 4:1)
9\42 (257.1¢)
Collapsed (L:s = 1:0)
2\9 (266.7¢)
| ↖ 8L 5s | ↑ 9L 5s | 10L 5s ↗ |
| ← 8L 6s | 9L 6s | 10L 6s → |
| ↙ 8L 7s | ↓ 9L 7s | 10L 7s ↘ |
┌╥╥┬╥┬╥╥┬╥┬╥╥┬╥┬┐ │║║│║│║║│║│║║│║││ │││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
sLsLLsLsLLsLsLL
9L 6s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 9 large steps and 6 small steps, with a period of 3 large steps and 2 small steps that repeats every 400.0¢, or 3 times every octave. 9L 6s is a child scale of 6L 3s, expanding it by 6 tones. Generators that produce this scale range from 240¢ to 266.7¢, or from 133.3¢ to 160¢.
The period (400¢) minus one dark generator represents a 23+-limit interval between 23/20 and 7/6 (between ~242¢ to ~267¢).
Modes
| UDP | Cyclic order |
Step pattern |
|---|---|---|
| 12|0(3) | 1 | LLsLsLLsLsLLsLs |
| 9|3(3) | 4 | LsLLsLsLLsLsLLs |
| 6|6(3) | 2 | LsLsLLsLsLLsLsL |
| 3|9(3) | 5 | sLLsLsLLsLsLLsL |
| 0|12(3) | 3 | sLsLLsLsLLsLsLL |
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 80.0¢ |
| Major 1-mosstep | M1ms | L | 80.0¢ to 133.3¢ | |
| 2-mosstep | Perfect 2-mosstep | P2ms | L + s | 133.3¢ to 160.0¢ |
| Augmented 2-mosstep | A2ms | 2L | 160.0¢ to 266.7¢ | |
| 3-mosstep | Diminished 3-mosstep | d3ms | L + 2s | 133.3¢ to 240.0¢ |
| Perfect 3-mosstep | P3ms | 2L + s | 240.0¢ to 266.7¢ | |
| 4-mosstep | Minor 4-mosstep | m4ms | 2L + 2s | 266.7¢ to 320.0¢ |
| Major 4-mosstep | M4ms | 3L + s | 320.0¢ to 400.0¢ | |
| 5-mosstep | Perfect 5-mosstep | P5ms | 3L + 2s | 400.0¢ |
| 6-mosstep | Minor 6-mosstep | m6ms | 3L + 3s | 400.0¢ to 480.0¢ |
| Major 6-mosstep | M6ms | 4L + 2s | 480.0¢ to 533.3¢ | |
| 7-mosstep | Perfect 7-mosstep | P7ms | 4L + 3s | 533.3¢ to 560.0¢ |
| Augmented 7-mosstep | A7ms | 5L + 2s | 560.0¢ to 666.7¢ | |
| 8-mosstep | Diminished 8-mosstep | d8ms | 4L + 4s | 533.3¢ to 640.0¢ |
| Perfect 8-mosstep | P8ms | 5L + 3s | 640.0¢ to 666.7¢ | |
| 9-mosstep | Minor 9-mosstep | m9ms | 5L + 4s | 666.7¢ to 720.0¢ |
| Major 9-mosstep | M9ms | 6L + 3s | 720.0¢ to 800.0¢ | |
| 10-mosstep | Perfect 10-mosstep | P10ms | 6L + 4s | 800.0¢ |
| 11-mosstep | Minor 11-mosstep | m11ms | 6L + 5s | 800.0¢ to 880.0¢ |
| Major 11-mosstep | M11ms | 7L + 4s | 880.0¢ to 933.3¢ | |
| 12-mosstep | Perfect 12-mosstep | P12ms | 7L + 5s | 933.3¢ to 960.0¢ |
| Augmented 12-mosstep | A12ms | 8L + 4s | 960.0¢ to 1066.7¢ | |
| 13-mosstep | Diminished 13-mosstep | d13ms | 7L + 6s | 933.3¢ to 1040.0¢ |
| Perfect 13-mosstep | P13ms | 8L + 5s | 1040.0¢ to 1066.7¢ | |
| 14-mosstep | Minor 14-mosstep | m14ms | 8L + 6s | 1066.7¢ to 1120.0¢ |
| Major 14-mosstep | M14ms | 9L + 5s | 1120.0¢ to 1200.0¢ | |
| 15-mosstep | Perfect 15-mosstep | P15ms | 9L + 6s | 1200.0¢ |
Scale tree
| Generator(edo) | Cents | Step ratio | Comments | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 3\15 | 240.000 | 160.000 | 1:1 | 1.000 | Equalized 9L 6s | |||||
| 17\84 | 242.857 | 157.143 | 6:5 | 1.200 | ||||||
| 14\69 | 243.478 | 156.522 | 5:4 | 1.250 | ||||||
| 25\123 | 243.902 | 156.098 | 9:7 | 1.286 | ||||||
| 11\54 | 244.444 | 155.556 | 4:3 | 1.333 | Supersoft 9L 6s | |||||
| 30\147 | 244.898 | 155.102 | 11:8 | 1.375 | ||||||
| 19\93 | 245.161 | 154.839 | 7:5 | 1.400 | ||||||
| 27\132 | 245.455 | 154.545 | 10:7 | 1.429 | ||||||
| 8\39 | 246.154 | 153.846 | 3:2 | 1.500 | Soft 9L 6s | |||||
| 29\141 | 246.809 | 153.191 | 11:7 | 1.571 | ||||||
| 21\102 | 247.059 | 152.941 | 8:5 | 1.600 | ||||||
| 34\165 | 247.273 | 152.727 | 13:8 | 1.625 | ||||||
| 13\63 | 247.619 | 152.381 | 5:3 | 1.667 | Semisoft 9L 6s | |||||
| 31\150 | 248.000 | 152.000 | 12:7 | 1.714 | ||||||
| 18\87 | 248.276 | 151.724 | 7:4 | 1.750 | ||||||
| 23\111 | 248.649 | 151.351 | 9:5 | 1.800 | ||||||
| 5\24 | 250.000 | 150.000 | 2:1 | 2.000 | Basic 9L 6s Scales with tunings softer than this are proper | |||||
| 22\105 | 251.429 | 148.571 | 9:4 | 2.250 | ||||||
| 17\81 | 251.852 | 148.148 | 7:3 | 2.333 | ||||||
| 29\138 | 252.174 | 147.826 | 12:5 | 2.400 | ||||||
| 12\57 | 252.632 | 147.368 | 5:2 | 2.500 | Semihard 9L 6s | |||||
| 31\147 | 253.061 | 146.939 | 13:5 | 2.600 | ||||||
| 19\90 | 253.333 | 146.667 | 8:3 | 2.667 | ||||||
| 26\123 | 253.659 | 146.341 | 11:4 | 2.750 | ||||||
| 7\33 | 254.545 | 145.455 | 3:1 | 3.000 | Hard 9L 6s | |||||
| 23\108 | 255.556 | 144.444 | 10:3 | 3.333 | ||||||
| 16\75 | 256.000 | 144.000 | 7:2 | 3.500 | ||||||
| 25\117 | 256.410 | 143.590 | 11:3 | 3.667 | ||||||
| 9\42 | 257.143 | 142.857 | 4:1 | 4.000 | Superhard 9L 6s | |||||
| 20\93 | 258.065 | 141.935 | 9:2 | 4.500 | ||||||
| 11\51 | 258.824 | 141.176 | 5:1 | 5.000 | ||||||
| 13\60 | 260.000 | 140.000 | 6:1 | 6.000 | ||||||
| 2\9 | 266.667 | 133.333 | 1:0 | → ∞ | Collapsed 9L 6s | |||||
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