15L 6s

From Xenharmonic Wiki
Jump to navigation Jump to search
↖ 14L 5s ↑ 15L 5s 16L 5s ↗
← 14L 6s 15L 6s 16L 6s →
↙ 14L 7s ↓ 15L 7s 16L 7s ↘
┌╥╥╥┬╥╥┬╥╥╥┬╥╥┬╥╥╥┬╥╥┬┐
│║║║│║║│║║║│║║│║║║│║║││
│││││││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLLsLLsLLLsLLsLLLsLLs
sLLsLLLsLLsLLLsLLsLLL
Equave 2/1 (1200.0¢)
Period 1\3 (400.0¢)
Generator size
Bright 4\21 to 3\15 (228.6¢ to 240.0¢)
Dark 2\15 to 3\21 (160.0¢ to 171.4¢)
TAMNAMS information
Descends from 6L 3s (hyrulic)
Ancestor's step ratio range 2:1 to 3:1 (hypohard)
Related MOS scales
Parent 6L 9s
Sister 6L 15s
Daughters 21L 15s, 15L 21s
Neutralized 9L 12s
2-Flought 36L 6s, 15L 27s
Equal tunings
Equalized (L:s = 1:1) 4\21 (228.6¢)
Supersoft (L:s = 4:3) 15\78 (230.8¢)
Soft (L:s = 3:2) 11\57 (231.6¢)
Semisoft (L:s = 5:3) 18\93 (232.3¢)
Basic (L:s = 2:1) 7\36 (233.3¢)
Semihard (L:s = 5:2) 17\87 (234.5¢)
Hard (L:s = 3:1) 10\51 (235.3¢)
Superhard (L:s = 4:1) 13\66 (236.4¢)
Collapsed (L:s = 1:0) 3\15 (240.0¢)

15L 6s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 15 large steps and 6 small steps, with a period of 5 large steps and 2 small steps that repeats every 400.0¢, or 3 times every octave. 15L 6s is a grandchild scale of 6L 3s, expanding it by 12 tones. Generators that produce this scale range from 228.6¢ to 240¢, or from 160¢ to 171.4¢.

Modes

Modes of 15L 6s
UDP Cyclic
order
Step
pattern
18|0(3) 1 LLLsLLsLLLsLLsLLLsLLs
15|3(3) 5 LLsLLLsLLsLLLsLLsLLLs
12|6(3) 2 LLsLLsLLLsLLsLLLsLLsL
9|9(3) 6 LsLLLsLLsLLLsLLsLLLsL
6|12(3) 3 LsLLsLLLsLLsLLLsLLsLL
3|15(3) 7 sLLLsLLsLLLsLLsLLLsLL
0|18(3) 4 sLLsLLLsLLsLLLsLLsLLL

Scale tree

Scale Tree and Tuning Spectrum of 15L 6s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
4\21 228.571 171.429 1:1 1.000 Equalized 15L 6s
23\120 230.000 170.000 6:5 1.200
19\99 230.303 169.697 5:4 1.250
34\177 230.508 169.492 9:7 1.286
15\78 230.769 169.231 4:3 1.333 Supersoft 15L 6s
41\213 230.986 169.014 11:8 1.375
26\135 231.111 168.889 7:5 1.400
37\192 231.250 168.750 10:7 1.429
11\57 231.579 168.421 3:2 1.500 Soft 15L 6s
40\207 231.884 168.116 11:7 1.571
29\150 232.000 168.000 8:5 1.600
47\243 232.099 167.901 13:8 1.625
18\93 232.258 167.742 5:3 1.667 Semisoft 15L 6s
43\222 232.432 167.568 12:7 1.714
25\129 232.558 167.442 7:4 1.750
32\165 232.727 167.273 9:5 1.800
7\36 233.333 166.667 2:1 2.000 Basic 15L 6s
Scales with tunings softer than this are proper
31\159 233.962 166.038 9:4 2.250
24\123 234.146 165.854 7:3 2.333
41\210 234.286 165.714 12:5 2.400
17\87 234.483 165.517 5:2 2.500 Semihard 15L 6s
44\225 234.667 165.333 13:5 2.600
27\138 234.783 165.217 8:3 2.667
37\189 234.921 165.079 11:4 2.750
10\51 235.294 164.706 3:1 3.000 Hard 15L 6s
33\168 235.714 164.286 10:3 3.333
23\117 235.897 164.103 7:2 3.500
36\183 236.066 163.934 11:3 3.667
13\66 236.364 163.636 4:1 4.000 Superhard 15L 6s
29\147 236.735 163.265 9:2 4.500
16\81 237.037 162.963 5:1 5.000
19\96 237.500 162.500 6:1 6.000
3\15 240.000 160.000 1:0 → ∞ Collapsed 15L 6s