5L 21s

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Revision as of 00:30, 16 December 2024 by BudjarnLambeth (talk | contribs) (== Intervals == {{MOS intervals}})
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↖ 4L 20s ↑ 5L 20s 6L 20s ↗
← 4L 21s 5L 21s 6L 21s →
↙ 4L 22s ↓ 5L 22s 6L 22s ↘
Scale structure
Step pattern LssssLssssLssssLssssLsssss
sssssLssssLssssLssssLssssL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 5\26 to 1\5 (230.8 ¢ to 240.0 ¢)
Dark 4\5 to 21\26 (960.0 ¢ to 969.2 ¢)
TAMNAMS information
Related to 5L 1s (machinoid)
With tunings 5:1 to 1:0
Related MOS scales
Parent 5L 16s
Sister 21L 5s
Daughters 26L 5s, 5L 26s
Neutralized 10L 16s
2-Flought 31L 21s, 5L 47s
Equal tunings
Equalized (L:s = 1:1) 5\26 (230.8 ¢)
Supersoft (L:s = 4:3) 16\83 (231.3 ¢)
Soft (L:s = 3:2) 11\57 (231.6 ¢)
Semisoft (L:s = 5:3) 17\88 (231.8 ¢)
Basic (L:s = 2:1) 6\31 (232.3 ¢)
Semihard (L:s = 5:2) 13\67 (232.8 ¢)
Hard (L:s = 3:1) 7\36 (233.3 ¢)
Superhard (L:s = 4:1) 8\41 (234.1 ¢)
Collapsed (L:s = 1:0) 1\5 (240.0 ¢)
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5L 21s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 5 large steps and 21 small steps, repeating every octave. 5L 21s is related to 5L 1s, expanding it by 20 tones. Generators that produce this scale range from 230.8 ¢ to 240 ¢, or from 960 ¢ to 969.2 ¢.

Modes

Modes of 5L 21s
UDP Cyclic
order		 Step
pattern
25|0 1 LssssLssssLssssLssssLsssss
24|1 6 LssssLssssLssssLsssssLssss
23|2 11 LssssLssssLsssssLssssLssss
22|3 16 LssssLsssssLssssLssssLssss
21|4 21 LsssssLssssLssssLssssLssss
20|5 26 sLssssLssssLssssLssssLssss
19|6 5 sLssssLssssLssssLsssssLsss
18|7 10 sLssssLssssLsssssLssssLsss
17|8 15 sLssssLsssssLssssLssssLsss
16|9 20 sLsssssLssssLssssLssssLsss
15|10 25 ssLssssLssssLssssLssssLsss
14|11 4 ssLssssLssssLssssLsssssLss
13|12 9 ssLssssLssssLsssssLssssLss
12|13 14 ssLssssLsssssLssssLssssLss
11|14 19 ssLsssssLssssLssssLssssLss
10|15 24 sssLssssLssssLssssLssssLss
9|16 3 sssLssssLssssLssssLsssssLs
8|17 8 sssLssssLssssLsssssLssssLs
7|18 13 sssLssssLsssssLssssLssssLs
6|19 18 sssLsssssLssssLssssLssssLs
5|20 23 ssssLssssLssssLssssLssssLs
4|21 2 ssssLssssLssssLssssLsssssL
3|22 7 ssssLssssLssssLsssssLssssL
2|23 12 ssssLssssLsssssLssssLssssL
1|24 17 ssssLsssssLssssLssssLssssL
0|25 22 sssssLssssLssssLssssLssssL

Intervals

Intervals of 5L 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 46.2 ¢
Major 1-mosstep M1ms L 46.2 ¢ to 240.0 ¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0 ¢ to 92.3 ¢
Major 2-mosstep M2ms L + s 92.3 ¢ to 240.0 ¢
3-mosstep Minor 3-mosstep m3ms 3s 0.0 ¢ to 138.5 ¢
Major 3-mosstep M3ms L + 2s 138.5 ¢ to 240.0 ¢
4-mosstep Minor 4-mosstep m4ms 4s 0.0 ¢ to 184.6 ¢
Major 4-mosstep M4ms L + 3s 184.6 ¢ to 240.0 ¢
5-mosstep Diminished 5-mosstep d5ms 5s 0.0 ¢ to 230.8 ¢
Perfect 5-mosstep P5ms L + 4s 230.8 ¢ to 240.0 ¢
6-mosstep Minor 6-mosstep m6ms L + 5s 240.0 ¢ to 276.9 ¢
Major 6-mosstep M6ms 2L + 4s 276.9 ¢ to 480.0 ¢
7-mosstep Minor 7-mosstep m7ms L + 6s 240.0 ¢ to 323.1 ¢
Major 7-mosstep M7ms 2L + 5s 323.1 ¢ to 480.0 ¢
8-mosstep Minor 8-mosstep m8ms L + 7s 240.0 ¢ to 369.2 ¢
Major 8-mosstep M8ms 2L + 6s 369.2 ¢ to 480.0 ¢
9-mosstep Minor 9-mosstep m9ms L + 8s 240.0 ¢ to 415.4 ¢
Major 9-mosstep M9ms 2L + 7s 415.4 ¢ to 480.0 ¢
10-mosstep Minor 10-mosstep m10ms L + 9s 240.0 ¢ to 461.5 ¢
Major 10-mosstep M10ms 2L + 8s 461.5 ¢ to 480.0 ¢
11-mosstep Minor 11-mosstep m11ms 2L + 9s 480.0 ¢ to 507.7 ¢
Major 11-mosstep M11ms 3L + 8s 507.7 ¢ to 720.0 ¢
12-mosstep Minor 12-mosstep m12ms 2L + 10s 480.0 ¢ to 553.8 ¢
Major 12-mosstep M12ms 3L + 9s 553.8 ¢ to 720.0 ¢
13-mosstep Minor 13-mosstep m13ms 2L + 11s 480.0 ¢ to 600.0 ¢
Major 13-mosstep M13ms 3L + 10s 600.0 ¢ to 720.0 ¢
14-mosstep Minor 14-mosstep m14ms 2L + 12s 480.0 ¢ to 646.2 ¢
Major 14-mosstep M14ms 3L + 11s 646.2 ¢ to 720.0 ¢
15-mosstep Minor 15-mosstep m15ms 2L + 13s 480.0 ¢ to 692.3 ¢
Major 15-mosstep M15ms 3L + 12s 692.3 ¢ to 720.0 ¢
16-mosstep Minor 16-mosstep m16ms 3L + 13s 720.0 ¢ to 738.5 ¢
Major 16-mosstep M16ms 4L + 12s 738.5 ¢ to 960.0 ¢
17-mosstep Minor 17-mosstep m17ms 3L + 14s 720.0 ¢ to 784.6 ¢
Major 17-mosstep M17ms 4L + 13s 784.6 ¢ to 960.0 ¢
18-mosstep Minor 18-mosstep m18ms 3L + 15s 720.0 ¢ to 830.8 ¢
Major 18-mosstep M18ms 4L + 14s 830.8 ¢ to 960.0 ¢
19-mosstep Minor 19-mosstep m19ms 3L + 16s 720.0 ¢ to 876.9 ¢
Major 19-mosstep M19ms 4L + 15s 876.9 ¢ to 960.0 ¢
20-mosstep Minor 20-mosstep m20ms 3L + 17s 720.0 ¢ to 923.1 ¢
Major 20-mosstep M20ms 4L + 16s 923.1 ¢ to 960.0 ¢
21-mosstep Perfect 21-mosstep P21ms 4L + 17s 960.0 ¢ to 969.2 ¢
Augmented 21-mosstep A21ms 5L + 16s 969.2 ¢ to 1200.0 ¢
22-mosstep Minor 22-mosstep m22ms 4L + 18s 960.0 ¢ to 1015.4 ¢
Major 22-mosstep M22ms 5L + 17s 1015.4 ¢ to 1200.0 ¢
23-mosstep Minor 23-mosstep m23ms 4L + 19s 960.0 ¢ to 1061.5 ¢
Major 23-mosstep M23ms 5L + 18s 1061.5 ¢ to 1200.0 ¢
24-mosstep Minor 24-mosstep m24ms 4L + 20s 960.0 ¢ to 1107.7 ¢
Major 24-mosstep M24ms 5L + 19s 1107.7 ¢ to 1200.0 ¢
25-mosstep Minor 25-mosstep m25ms 4L + 21s 960.0 ¢ to 1153.8 ¢
Major 25-mosstep M25ms 5L + 20s 1153.8 ¢ to 1200.0 ¢
26-mosstep Perfect 26-mosstep P26ms 5L + 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 5L 21s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
5\26 230.769 969.231 1:1 1.000 Equalized 5L 21s
26\135 231.111 968.889 6:5 1.200
21\109 231.193 968.807 5:4 1.250
37\192 231.250 968.750 9:7 1.286
16\83 231.325 968.675 4:3 1.333 Supersoft 5L 21s
43\223 231.390 968.610 11:8 1.375
27\140 231.429 968.571 7:5 1.400
38\197 231.472 968.528 10:7 1.429
11\57 231.579 968.421 3:2 1.500 Soft 5L 21s
39\202 231.683 968.317 11:7 1.571
28\145 231.724 968.276 8:5 1.600
45\233 231.760 968.240 13:8 1.625
17\88 231.818 968.182 5:3 1.667 Semisoft 5L 21s
40\207 231.884 968.116 12:7 1.714
23\119 231.933 968.067 7:4 1.750
29\150 232.000 968.000 9:5 1.800
6\31 232.258 967.742 2:1 2.000 Basic 5L 21s
Scales with tunings softer than this are proper
25\129 232.558 967.442 9:4 2.250
19\98 232.653 967.347 7:3 2.333
32\165 232.727 967.273 12:5 2.400
13\67 232.836 967.164 5:2 2.500 Semihard 5L 21s
33\170 232.941 967.059 13:5 2.600
20\103 233.010 966.990 8:3 2.667
27\139 233.094 966.906 11:4 2.750
7\36 233.333 966.667 3:1 3.000 Hard 5L 21s
22\113 233.628 966.372 10:3 3.333
15\77 233.766 966.234 7:2 3.500
23\118 233.898 966.102 11:3 3.667
8\41 234.146 965.854 4:1 4.000 Superhard 5L 21s
17\87 234.483 965.517 9:2 4.500
9\46 234.783 965.217 5:1 5.000
10\51 235.294 964.706 6:1 6.000
1\5 240.000 960.000 1:0 → ∞ Collapsed 5L 21s


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