15L 8s
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Scale structure
Step pattern
LLsLLsLLsLLsLLsLLsLLsLs
sLsLLsLLsLLsLLsLLsLLsLL
Equave
2/1 (1200.0¢)
Period
2/1 (1200.0¢)
Generator size
Bright
3\23 to 2\15 (156.5¢ to 160.0¢)
Dark
13\15 to 20\23 (1040.0¢ to 1043.5¢)
TAMNAMS information
Descends from
7L 1s (pine)
Ancestor's step ratio range
3:2 to 2:1 (hyposoft)
Related MOS scales
Parent
8L 7s
Sister
8L 15s
Daughters
23L 15s, 15L 23s
Neutralized
7L 16s
2-Flought
38L 8s, 15L 31s
Equal tunings
Equalized (L:s = 1:1)
3\23 (156.5¢)
Supersoft (L:s = 4:3)
11\84 (157.1¢)
Soft (L:s = 3:2)
8\61 (157.4¢)
Semisoft (L:s = 5:3)
13\99 (157.6¢)
Basic (L:s = 2:1)
5\38 (157.9¢)
Semihard (L:s = 5:2)
12\91 (158.2¢)
Hard (L:s = 3:1)
7\53 (158.5¢)
Superhard (L:s = 4:1)
9\68 (158.8¢)
Collapsed (L:s = 1:0)
2\15 (160.0¢)
| ↖ 14L 7s | ↑ 15L 7s | 16L 7s ↗ |
| ← 14L 8s | 15L 8s | 16L 8s → |
| ↙ 14L 9s | ↓ 15L 9s | 16L 9s ↘ |
┌╥╥┬╥╥┬╥╥┬╥╥┬╥╥┬╥╥┬╥╥┬╥┬┐ │║║│║║│║║│║║│║║│║║│║║│║││ │││││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
sLsLLsLLsLLsLLsLLsLLsLL
15L 8s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 15 large steps and 8 small steps, repeating every octave. 15L 8s is a grandchild scale of 7L 1s, expanding it by 15 tones. Generators that produce this scale range from 156.5¢ to 160¢, or from 1040¢ to 1043.5¢.
It is the quarter tone scale of Hemikleismic temperament, generated by a 'neutral whole tone'.
Modes
| UDP | Cyclic order |
Step pattern |
|---|---|---|
| 22|0 | 1 | LLsLLsLLsLLsLLsLLsLLsLs |
| 21|1 | 4 | LLsLLsLLsLLsLLsLLsLsLLs |
| 20|2 | 7 | LLsLLsLLsLLsLLsLsLLsLLs |
| 19|3 | 10 | LLsLLsLLsLLsLsLLsLLsLLs |
| 18|4 | 13 | LLsLLsLLsLsLLsLLsLLsLLs |
| 17|5 | 16 | LLsLLsLsLLsLLsLLsLLsLLs |
| 16|6 | 19 | LLsLsLLsLLsLLsLLsLLsLLs |
| 15|7 | 22 | LsLLsLLsLLsLLsLLsLLsLLs |
| 14|8 | 2 | LsLLsLLsLLsLLsLLsLLsLsL |
| 13|9 | 5 | LsLLsLLsLLsLLsLLsLsLLsL |
| 12|10 | 8 | LsLLsLLsLLsLLsLsLLsLLsL |
| 11|11 | 11 | LsLLsLLsLLsLsLLsLLsLLsL |
| 10|12 | 14 | LsLLsLLsLsLLsLLsLLsLLsL |
| 9|13 | 17 | LsLLsLsLLsLLsLLsLLsLLsL |
| 8|14 | 20 | LsLsLLsLLsLLsLLsLLsLLsL |
| 7|15 | 23 | sLLsLLsLLsLLsLLsLLsLLsL |
| 6|16 | 3 | sLLsLLsLLsLLsLLsLLsLsLL |
| 5|17 | 6 | sLLsLLsLLsLLsLLsLsLLsLL |
| 4|18 | 9 | sLLsLLsLLsLLsLsLLsLLsLL |
| 3|19 | 12 | sLLsLLsLLsLsLLsLLsLLsLL |
| 2|20 | 15 | sLLsLLsLsLLsLLsLLsLLsLL |
| 1|21 | 18 | sLLsLsLLsLLsLLsLLsLLsLL |
| 0|22 | 21 | sLsLLsLLsLLsLLsLLsLLsLL |
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 52.2¢ |
| Major 1-mosstep | M1ms | L | 52.2¢ to 80.0¢ | |
| 2-mosstep | Minor 2-mosstep | m2ms | L + s | 80.0¢ to 104.3¢ |
| Major 2-mosstep | M2ms | 2L | 104.3¢ to 160.0¢ | |
| 3-mosstep | Diminished 3-mosstep | d3ms | L + 2s | 80.0¢ to 156.5¢ |
| Perfect 3-mosstep | P3ms | 2L + s | 156.5¢ to 160.0¢ | |
| 4-mosstep | Minor 4-mosstep | m4ms | 2L + 2s | 160.0¢ to 208.7¢ |
| Major 4-mosstep | M4ms | 3L + s | 208.7¢ to 240.0¢ | |
| 5-mosstep | Minor 5-mosstep | m5ms | 3L + 2s | 240.0¢ to 260.9¢ |
| Major 5-mosstep | M5ms | 4L + s | 260.9¢ to 320.0¢ | |
| 6-mosstep | Minor 6-mosstep | m6ms | 3L + 3s | 240.0¢ to 313.0¢ |
| Major 6-mosstep | M6ms | 4L + 2s | 313.0¢ to 320.0¢ | |
| 7-mosstep | Minor 7-mosstep | m7ms | 4L + 3s | 320.0¢ to 365.2¢ |
| Major 7-mosstep | M7ms | 5L + 2s | 365.2¢ to 400.0¢ | |
| 8-mosstep | Minor 8-mosstep | m8ms | 5L + 3s | 400.0¢ to 417.4¢ |
| Major 8-mosstep | M8ms | 6L + 2s | 417.4¢ to 480.0¢ | |
| 9-mosstep | Minor 9-mosstep | m9ms | 5L + 4s | 400.0¢ to 469.6¢ |
| Major 9-mosstep | M9ms | 6L + 3s | 469.6¢ to 480.0¢ | |
| 10-mosstep | Minor 10-mosstep | m10ms | 6L + 4s | 480.0¢ to 521.7¢ |
| Major 10-mosstep | M10ms | 7L + 3s | 521.7¢ to 560.0¢ | |
| 11-mosstep | Minor 11-mosstep | m11ms | 7L + 4s | 560.0¢ to 573.9¢ |
| Major 11-mosstep | M11ms | 8L + 3s | 573.9¢ to 640.0¢ | |
| 12-mosstep | Minor 12-mosstep | m12ms | 7L + 5s | 560.0¢ to 626.1¢ |
| Major 12-mosstep | M12ms | 8L + 4s | 626.1¢ to 640.0¢ | |
| 13-mosstep | Minor 13-mosstep | m13ms | 8L + 5s | 640.0¢ to 678.3¢ |
| Major 13-mosstep | M13ms | 9L + 4s | 678.3¢ to 720.0¢ | |
| 14-mosstep | Minor 14-mosstep | m14ms | 9L + 5s | 720.0¢ to 730.4¢ |
| Major 14-mosstep | M14ms | 10L + 4s | 730.4¢ to 800.0¢ | |
| 15-mosstep | Minor 15-mosstep | m15ms | 9L + 6s | 720.0¢ to 782.6¢ |
| Major 15-mosstep | M15ms | 10L + 5s | 782.6¢ to 800.0¢ | |
| 16-mosstep | Minor 16-mosstep | m16ms | 10L + 6s | 800.0¢ to 834.8¢ |
| Major 16-mosstep | M16ms | 11L + 5s | 834.8¢ to 880.0¢ | |
| 17-mosstep | Minor 17-mosstep | m17ms | 11L + 6s | 880.0¢ to 887.0¢ |
| Major 17-mosstep | M17ms | 12L + 5s | 887.0¢ to 960.0¢ | |
| 18-mosstep | Minor 18-mosstep | m18ms | 11L + 7s | 880.0¢ to 939.1¢ |
| Major 18-mosstep | M18ms | 12L + 6s | 939.1¢ to 960.0¢ | |
| 19-mosstep | Minor 19-mosstep | m19ms | 12L + 7s | 960.0¢ to 991.3¢ |
| Major 19-mosstep | M19ms | 13L + 6s | 991.3¢ to 1040.0¢ | |
| 20-mosstep | Perfect 20-mosstep | P20ms | 13L + 7s | 1040.0¢ to 1043.5¢ |
| Augmented 20-mosstep | A20ms | 14L + 6s | 1043.5¢ to 1120.0¢ | |
| 21-mosstep | Minor 21-mosstep | m21ms | 13L + 8s | 1040.0¢ to 1095.7¢ |
| Major 21-mosstep | M21ms | 14L + 7s | 1095.7¢ to 1120.0¢ | |
| 22-mosstep | Minor 22-mosstep | m22ms | 14L + 8s | 1120.0¢ to 1147.8¢ |
| Major 22-mosstep | M22ms | 15L + 7s | 1147.8¢ to 1200.0¢ | |
| 23-mosstep | Perfect 23-mosstep | P23ms | 15L + 8s | 1200.0¢ |
Scale tree
| Generator(edo) | Cents | Step ratio | Comments | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 3\23 | 156.522 | 1043.478 | 1:1 | 1.000 | Equalized 15L 8s | |||||
| 17\130 | 156.923 | 1043.077 | 6:5 | 1.200 | ||||||
| 14\107 | 157.009 | 1042.991 | 5:4 | 1.250 | ||||||
| 25\191 | 157.068 | 1042.932 | 9:7 | 1.286 | ||||||
| 11\84 | 157.143 | 1042.857 | 4:3 | 1.333 | Supersoft 15L 8s | |||||
| 30\229 | 157.205 | 1042.795 | 11:8 | 1.375 | ||||||
| 19\145 | 157.241 | 1042.759 | 7:5 | 1.400 | ||||||
| 27\206 | 157.282 | 1042.718 | 10:7 | 1.429 | ||||||
| 8\61 | 157.377 | 1042.623 | 3:2 | 1.500 | Soft 15L 8s | |||||
| 29\221 | 157.466 | 1042.534 | 11:7 | 1.571 | ||||||
| 21\160 | 157.500 | 1042.500 | 8:5 | 1.600 | ||||||
| 34\259 | 157.529 | 1042.471 | 13:8 | 1.625 | ||||||
| 13\99 | 157.576 | 1042.424 | 5:3 | 1.667 | Semisoft 15L 8s | |||||
| 31\236 | 157.627 | 1042.373 | 12:7 | 1.714 | ||||||
| 18\137 | 157.664 | 1042.336 | 7:4 | 1.750 | ||||||
| 23\175 | 157.714 | 1042.286 | 9:5 | 1.800 | ||||||
| 5\38 | 157.895 | 1042.105 | 2:1 | 2.000 | Basic 15L 8s Scales with tunings softer than this are proper | |||||
| 22\167 | 158.084 | 1041.916 | 9:4 | 2.250 | ||||||
| 17\129 | 158.140 | 1041.860 | 7:3 | 2.333 | ||||||
| 29\220 | 158.182 | 1041.818 | 12:5 | 2.400 | ||||||
| 12\91 | 158.242 | 1041.758 | 5:2 | 2.500 | Semihard 15L 8s | |||||
| 31\235 | 158.298 | 1041.702 | 13:5 | 2.600 | ||||||
| 19\144 | 158.333 | 1041.667 | 8:3 | 2.667 | ||||||
| 26\197 | 158.376 | 1041.624 | 11:4 | 2.750 | ||||||
| 7\53 | 158.491 | 1041.509 | 3:1 | 3.000 | Hard 15L 8s | |||||
| 23\174 | 158.621 | 1041.379 | 10:3 | 3.333 | ||||||
| 16\121 | 158.678 | 1041.322 | 7:2 | 3.500 | Hemikleismic (includes 38edo and 53edo) | |||||
| 25\189 | 158.730 | 1041.270 | 11:3 | 3.667 | ||||||
| 9\68 | 158.824 | 1041.176 | 4:1 | 4.000 | Superhard 15L 8s | |||||
| 20\151 | 158.940 | 1041.060 | 9:2 | 4.500 | ||||||
| 11\83 | 159.036 | 1040.964 | 5:1 | 5.000 | ||||||
| 13\98 | 159.184 | 1040.816 | 6:1 | 6.000 | ||||||
| 2\15 | 160.000 | 1040.000 | 1:0 | → ∞ | Collapsed 15L 8s | |||||