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'.
| 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 | |||||