15L 8s

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↖14L 7s ↑15L 7s 16L 7s↗
←14L 8s15L 8s 16L 8s→
↙14L 9s ↓15L 9s 16L 9s↘
┌╥╥┬╥╥┬╥╥┬╥╥┬╥╥┬╥╥┬╥╥┬╥┬┐
│║║│║║│║║│║║│║║│║║│║║│║││
│││││││││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLsLLsLLsLLsLLsLLsLLsLs
sLsLLsLLsLLsLLsLLsLLsLL
Equave 2/1 (1200.0¢)
Period 2/1 (1200.0¢)
Step size ranges
Large 1\23 to 1\15 (52.2¢ to 80.0¢)
Small 0\15 to 1\23 (0.0¢ to 52.2¢)
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)
Related MOS scales
Parent 8L 7s
Sister 8L 15s
Daughters 23L 15s
15L 23s
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¢)

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'.

Scale tree and tuning spectrum of 15L 8s
Generator (in steps of 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