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10L 21s

Revision as of 06:52, 15 December 2024 by BudjarnLambeth (talk | contribs) (Stub)

10L 21s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 10 large steps and 21 small steps, repeating every octave. 10L 21s is a great-grandchild scale of 1L 9s, expanding it by 21 tones. Generators that produce this scale range from 116.1 ¢ to 120 ¢, or from 1080 ¢ to 1083.9 ¢.

↖ 9L 20s ↑ 10L 20s 11L 20s ↗
← 9L 21s 10L 21s 11L 21s →
↙ 9L 22s ↓ 10L 22s 11L 22s ↘
Scale structure
Step pattern LssLssLssLssLssLssLssLssLssLsss
sssLssLssLssLssLssLssLssLssLssL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 3\31 to 1\10 (116.1 ¢ to 120.0 ¢)
Dark 9\10 to 28\31 (1080.0 ¢ to 1083.9 ¢)
TAMNAMS information
Related to 1L 9s (antisinatonic)
With tunings 1:1 to 4:3 (ultrasoft)
Related MOS scales
Parent 10L 11s
Sister 21L 10s
Daughters 31L 10s, 10L 31s
Neutralized 20L 11s
2-Flought 41L 21s, 10L 52s
Equal tunings
Equalized (L:s = 1:1) 3\31 (116.1 ¢)
Supersoft (L:s = 4:3) 10\103 (116.5 ¢)
Soft (L:s = 3:2) 7\72 (116.7 ¢)
Semisoft (L:s = 5:3) 11\113 (116.8 ¢)
Basic (L:s = 2:1) 4\41 (117.1 ¢)
Semihard (L:s = 5:2) 9\92 (117.4 ¢)
Hard (L:s = 3:1) 5\51 (117.6 ¢)
Superhard (L:s = 4:1) 6\61 (118.0 ¢)
Collapsed (L:s = 1:0) 1\10 (120.0 ¢)
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Intervals

Intervals of 10L 21s
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 38.7 ¢
Major 1-mosstep M1ms L 38.7 ¢ to 120.0 ¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0 ¢ to 77.4 ¢
Major 2-mosstep M2ms L + s 77.4 ¢ to 120.0 ¢
3-mosstep Diminished 3-mosstep d3ms 3s 0.0 ¢ to 116.1 ¢
Perfect 3-mosstep P3ms L + 2s 116.1 ¢ to 120.0 ¢
4-mosstep Minor 4-mosstep m4ms L + 3s 120.0 ¢ to 154.8 ¢
Major 4-mosstep M4ms 2L + 2s 154.8 ¢ to 240.0 ¢
5-mosstep Minor 5-mosstep m5ms L + 4s 120.0 ¢ to 193.5 ¢
Major 5-mosstep M5ms 2L + 3s 193.5 ¢ to 240.0 ¢
6-mosstep Minor 6-mosstep m6ms L + 5s 120.0 ¢ to 232.3 ¢
Major 6-mosstep M6ms 2L + 4s 232.3 ¢ to 240.0 ¢
7-mosstep Minor 7-mosstep m7ms 2L + 5s 240.0 ¢ to 271.0 ¢
Major 7-mosstep M7ms 3L + 4s 271.0 ¢ to 360.0 ¢
8-mosstep Minor 8-mosstep m8ms 2L + 6s 240.0 ¢ to 309.7 ¢
Major 8-mosstep M8ms 3L + 5s 309.7 ¢ to 360.0 ¢
9-mosstep Minor 9-mosstep m9ms 2L + 7s 240.0 ¢ to 348.4 ¢
Major 9-mosstep M9ms 3L + 6s 348.4 ¢ to 360.0 ¢
10-mosstep Minor 10-mosstep m10ms 3L + 7s 360.0 ¢ to 387.1 ¢
Major 10-mosstep M10ms 4L + 6s 387.1 ¢ to 480.0 ¢
11-mosstep Minor 11-mosstep m11ms 3L + 8s 360.0 ¢ to 425.8 ¢
Major 11-mosstep M11ms 4L + 7s 425.8 ¢ to 480.0 ¢
12-mosstep Minor 12-mosstep m12ms 3L + 9s 360.0 ¢ to 464.5 ¢
Major 12-mosstep M12ms 4L + 8s 464.5 ¢ to 480.0 ¢
13-mosstep Minor 13-mosstep m13ms 4L + 9s 480.0 ¢ to 503.2 ¢
Major 13-mosstep M13ms 5L + 8s 503.2 ¢ to 600.0 ¢
14-mosstep Minor 14-mosstep m14ms 4L + 10s 480.0 ¢ to 541.9 ¢
Major 14-mosstep M14ms 5L + 9s 541.9 ¢ to 600.0 ¢
15-mosstep Minor 15-mosstep m15ms 4L + 11s 480.0 ¢ to 580.6 ¢
Major 15-mosstep M15ms 5L + 10s 580.6 ¢ to 600.0 ¢
16-mosstep Minor 16-mosstep m16ms 5L + 11s 600.0 ¢ to 619.4 ¢
Major 16-mosstep M16ms 6L + 10s 619.4 ¢ to 720.0 ¢
17-mosstep Minor 17-mosstep m17ms 5L + 12s 600.0 ¢ to 658.1 ¢
Major 17-mosstep M17ms 6L + 11s 658.1 ¢ to 720.0 ¢
18-mosstep Minor 18-mosstep m18ms 5L + 13s 600.0 ¢ to 696.8 ¢
Major 18-mosstep M18ms 6L + 12s 696.8 ¢ to 720.0 ¢
19-mosstep Minor 19-mosstep m19ms 6L + 13s 720.0 ¢ to 735.5 ¢
Major 19-mosstep M19ms 7L + 12s 735.5 ¢ to 840.0 ¢
20-mosstep Minor 20-mosstep m20ms 6L + 14s 720.0 ¢ to 774.2 ¢
Major 20-mosstep M20ms 7L + 13s 774.2 ¢ to 840.0 ¢
21-mosstep Minor 21-mosstep m21ms 6L + 15s 720.0 ¢ to 812.9 ¢
Major 21-mosstep M21ms 7L + 14s 812.9 ¢ to 840.0 ¢
22-mosstep Minor 22-mosstep m22ms 7L + 15s 840.0 ¢ to 851.6 ¢
Major 22-mosstep M22ms 8L + 14s 851.6 ¢ to 960.0 ¢
23-mosstep Minor 23-mosstep m23ms 7L + 16s 840.0 ¢ to 890.3 ¢
Major 23-mosstep M23ms 8L + 15s 890.3 ¢ to 960.0 ¢
24-mosstep Minor 24-mosstep m24ms 7L + 17s 840.0 ¢ to 929.0 ¢
Major 24-mosstep M24ms 8L + 16s 929.0 ¢ to 960.0 ¢
25-mosstep Minor 25-mosstep m25ms 8L + 17s 960.0 ¢ to 967.7 ¢
Major 25-mosstep M25ms 9L + 16s 967.7 ¢ to 1080.0 ¢
26-mosstep Minor 26-mosstep m26ms 8L + 18s 960.0 ¢ to 1006.5 ¢
Major 26-mosstep M26ms 9L + 17s 1006.5 ¢ to 1080.0 ¢
27-mosstep Minor 27-mosstep m27ms 8L + 19s 960.0 ¢ to 1045.2 ¢
Major 27-mosstep M27ms 9L + 18s 1045.2 ¢ to 1080.0 ¢
28-mosstep Perfect 28-mosstep P28ms 9L + 19s 1080.0 ¢ to 1083.9 ¢
Augmented 28-mosstep A28ms 10L + 18s 1083.9 ¢ to 1200.0 ¢
29-mosstep Minor 29-mosstep m29ms 9L + 20s 1080.0 ¢ to 1122.6 ¢
Major 29-mosstep M29ms 10L + 19s 1122.6 ¢ to 1200.0 ¢
30-mosstep Minor 30-mosstep m30ms 9L + 21s 1080.0 ¢ to 1161.3 ¢
Major 30-mosstep M30ms 10L + 20s 1161.3 ¢ to 1200.0 ¢
31-mosstep Perfect 31-mosstep P31ms 10L + 21s 1200.0 ¢

Scale tree

  Template: Scale tree is deprecated. Please use Template: MOS tuning spectrum instead. Details:
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 10L 21s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
3\31 116.129 1083.871 1:1 1.000 Equalized 10L 21s
16\165 116.364 1083.636 6:5 1.200
13\134 116.418 1083.582 5:4 1.250
23\237 116.456 1083.544 9:7 1.286
10\103 116.505 1083.495 4:3 1.333 Supersoft 10L 21s
27\278 116.547 1083.453 11:8 1.375
17\175 116.571 1083.429 7:5 1.400
24\247 116.599 1083.401 10:7 1.429
7\72 116.667 1083.333 3:2 1.500 Soft 10L 21s
25\257 116.732 1083.268 11:7 1.571
18\185 116.757 1083.243 8:5 1.600
29\298 116.779 1083.221 13:8 1.625
11\113 116.814 1083.186 5:3 1.667 Semisoft 10L 21s
26\267 116.854 1083.146 12:7 1.714
15\154 116.883 1083.117 7:4 1.750
19\195 116.923 1083.077 9:5 1.800
4\41 117.073 1082.927 2:1 2.000 Basic 10L 21s
Scales with tunings softer than this are proper
17\174 117.241 1082.759 9:4 2.250
13\133 117.293 1082.707 7:3 2.333
22\225 117.333 1082.667 12:5 2.400
9\92 117.391 1082.609 5:2 2.500 Semihard 10L 21s
23\235 117.447 1082.553 13:5 2.600
14\143 117.483 1082.517 8:3 2.667
19\194 117.526 1082.474 11:4 2.750
5\51 117.647 1082.353 3:1 3.000 Hard 10L 21s
16\163 117.791 1082.209 10:3 3.333
11\112 117.857 1082.143 7:2 3.500
17\173 117.919 1082.081 11:3 3.667
6\61 118.033 1081.967 4:1 4.000 Superhard 10L 21s
13\132 118.182 1081.818 9:2 4.500
7\71 118.310 1081.690 5:1 5.000
8\81 118.519 1081.481 6:1 6.000
1\10 120.000 1080.000 1:0 → ∞ Collapsed 10L 21s


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