5L 21s

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↖ 4L 20s ↑5L 20s 6L 20s ↗
← 4L 21s5L 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
Descends from 5L 1s (machinoid)
Ancestor's step ratio range 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¢)

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 Rotational 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

Scale tree

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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