15L 6s

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↖ 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

Intervals

Intervals of 15L 6s
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 57.1 ¢
Major 1-mosstep M1ms L 57.1 ¢ to 80.0 ¢
2-mosstep Minor 2-mosstep m2ms L + s 80.0 ¢ to 114.3 ¢
Major 2-mosstep M2ms 2L 114.3 ¢ to 160.0 ¢
3-mosstep Perfect 3-mosstep P3ms 2L + s 160.0 ¢ to 171.4 ¢
Augmented 3-mosstep A3ms 3L 171.4 ¢ to 240.0 ¢
4-mosstep Diminished 4-mosstep d4ms 2L + 2s 160.0 ¢ to 228.6 ¢
Perfect 4-mosstep P4ms 3L + s 228.6 ¢ to 240.0 ¢
5-mosstep Minor 5-mosstep m5ms 3L + 2s 240.0 ¢ to 285.7 ¢
Major 5-mosstep M5ms 4L + s 285.7 ¢ to 320.0 ¢
6-mosstep Minor 6-mosstep m6ms 4L + 2s 320.0 ¢ to 342.9 ¢
Major 6-mosstep M6ms 5L + s 342.9 ¢ to 400.0 ¢
7-mosstep Perfect 7-mosstep P7ms 5L + 2s 400.0 ¢
8-mosstep Minor 8-mosstep m8ms 5L + 3s 400.0 ¢ to 457.1 ¢
Major 8-mosstep M8ms 6L + 2s 457.1 ¢ to 480.0 ¢
9-mosstep Minor 9-mosstep m9ms 6L + 3s 480.0 ¢ to 514.3 ¢
Major 9-mosstep M9ms 7L + 2s 514.3 ¢ to 560.0 ¢
10-mosstep Perfect 10-mosstep P10ms 7L + 3s 560.0 ¢ to 571.4 ¢
Augmented 10-mosstep A10ms 8L + 2s 571.4 ¢ to 640.0 ¢
11-mosstep Diminished 11-mosstep d11ms 7L + 4s 560.0 ¢ to 628.6 ¢
Perfect 11-mosstep P11ms 8L + 3s 628.6 ¢ to 640.0 ¢
12-mosstep Minor 12-mosstep m12ms 8L + 4s 640.0 ¢ to 685.7 ¢
Major 12-mosstep M12ms 9L + 3s 685.7 ¢ to 720.0 ¢
13-mosstep Minor 13-mosstep m13ms 9L + 4s 720.0 ¢ to 742.9 ¢
Major 13-mosstep M13ms 10L + 3s 742.9 ¢ to 800.0 ¢
14-mosstep Perfect 14-mosstep P14ms 10L + 4s 800.0 ¢
15-mosstep Minor 15-mosstep m15ms 10L + 5s 800.0 ¢ to 857.1 ¢
Major 15-mosstep M15ms 11L + 4s 857.1 ¢ to 880.0 ¢
16-mosstep Minor 16-mosstep m16ms 11L + 5s 880.0 ¢ to 914.3 ¢
Major 16-mosstep M16ms 12L + 4s 914.3 ¢ to 960.0 ¢
17-mosstep Perfect 17-mosstep P17ms 12L + 5s 960.0 ¢ to 971.4 ¢
Augmented 17-mosstep A17ms 13L + 4s 971.4 ¢ to 1040.0 ¢
18-mosstep Diminished 18-mosstep d18ms 12L + 6s 960.0 ¢ to 1028.6 ¢
Perfect 18-mosstep P18ms 13L + 5s 1028.6 ¢ to 1040.0 ¢
19-mosstep Minor 19-mosstep m19ms 13L + 6s 1040.0 ¢ to 1085.7 ¢
Major 19-mosstep M19ms 14L + 5s 1085.7 ¢ to 1120.0 ¢
20-mosstep Minor 20-mosstep m20ms 14L + 6s 1120.0 ¢ to 1142.9 ¢
Major 20-mosstep M20ms 15L + 5s 1142.9 ¢ to 1200.0 ¢
21-mosstep Perfect 21-mosstep P21ms 15L + 6s 1200.0 ¢

Scale tree

Icon-Deprecated.png Scale tree is deprecated. Please use Template: MOS tuning spectrum instead.
Use of a single Comments parameter has become unmaintainable. Existing scale trees should be migrated to the new template, where comments are entered using a step ratio p/q as a parameter: 
{{MOS tuning spectrum
| 3/2 = Example comment
| 4/3 = Another example comment
}}


The parameters tuning and depth have been replaced with Scale Signature and Depth, respectively.


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


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