5L 22s

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↖4L 21s ↑5L 21s 6L 21s↗
←4L 22s5L 22s 6L 22s→
↙4L 23s ↓5L 23s 6L 23s↘
┌╥┬┬┬┬╥┬┬┬┬╥┬┬┬┬┬╥┬┬┬┬╥┬┬┬┬┬┐
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│││││││││││││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LssssLssssLsssssLssssLsssss
sssssLssssLsssssLssssLssssL
Equave 2/1 (1200.0¢)
Period 2/1 (1200.0¢)
Generator size
Bright 16\27 to 3\5 (711.1¢ to 720.0¢)
Dark 2\5 to 11\27 (480.0¢ to 488.9¢)
TAMNAMS information
Descends from 5L 2s (diatonic)
Required step ratio range 5:1 to 1:0
Related MOS scales
Parent 5L 17s
Sister 22L 5s
Daughters 27L 5s, 5L 27s
Neutralized 10L 17s
Equal tunings
Equalized (L:s = 1:1) 16\27 (711.1¢)
Supersoft (L:s = 4:3) 51\86 (711.6¢)
Soft (L:s = 3:2) 35\59 (711.9¢)
Semisoft (L:s = 5:3) 54\91 (712.1¢)
Basic (L:s = 2:1) 19\32 (712.5¢)
Semihard (L:s = 5:2) 41\69 (713.0¢)
Hard (L:s = 3:1) 22\37 (713.5¢)
Superhard (L:s = 4:1) 25\42 (714.3¢)
Collapsed (L:s = 1:0) 3\5 (720.0¢)

5L 22s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 5 large steps and 22 small steps, repeating every octave. 5L 22s is related to 5L 2s, expanding it by 20 tones. Generators that produce this scale range from 711.1¢ to 720¢, or from 480¢ to 488.9¢.

Modes

Modes of 5L 22s
UDP Rotational order Step pattern
26|0 1 LssssLssssLsssssLssssLsssss
25|1 17 LssssLsssssLssssLssssLsssss
24|2 6 LssssLsssssLssssLsssssLssss
23|3 22 LsssssLssssLssssLsssssLssss
22|4 11 LsssssLssssLsssssLssssLssss
21|5 27 sLssssLssssLsssssLssssLssss
20|6 16 sLssssLsssssLssssLssssLssss
19|7 5 sLssssLsssssLssssLsssssLsss
18|8 21 sLsssssLssssLssssLsssssLsss
17|9 10 sLsssssLssssLsssssLssssLsss
16|10 26 ssLssssLssssLsssssLssssLsss
15|11 15 ssLssssLsssssLssssLssssLsss
14|12 4 ssLssssLsssssLssssLsssssLss
13|13 20 ssLsssssLssssLssssLsssssLss
12|14 9 ssLsssssLssssLsssssLssssLss
11|15 25 sssLssssLssssLsssssLssssLss
10|16 14 sssLssssLsssssLssssLssssLss
9|17 3 sssLssssLsssssLssssLsssssLs
8|18 19 sssLsssssLssssLssssLsssssLs
7|19 8 sssLsssssLssssLsssssLssssLs
6|20 24 ssssLssssLssssLsssssLssssLs
5|21 13 ssssLssssLsssssLssssLssssLs
4|22 2 ssssLssssLsssssLssssLsssssL
3|23 18 ssssLsssssLssssLssssLsssssL
2|24 7 ssssLsssssLssssLsssssLssssL
1|25 23 sssssLssssLssssLsssssLssssL
0|26 12 sssssLssssLsssssLssssLssssL

Scale tree

Scale Tree and Tuning Spectrum of 5L 22s
Generator(edo) Cents Step Ratio Comments
Bright Dark L:s Hardness
16\27 711.111 488.889 1:1 1.000 Equalized 5L 22s
83\140 711.429 488.571 6:5 1.200
67\113 711.504 488.496 5:4 1.250
118\199 711.558 488.442 9:7 1.286
51\86 711.628 488.372 4:3 1.333 Supersoft 5L 22s
137\231 711.688 488.312 11:8 1.375
86\145 711.724 488.276 7:5 1.400
121\204 711.765 488.235 10:7 1.429
35\59 711.864 488.136 3:2 1.500 Soft 5L 22s
124\209 711.962 488.038 11:7 1.571
89\150 712.000 488.000 8:5 1.600
143\241 712.033 487.967 13:8 1.625
54\91 712.088 487.912 5:3 1.667 Semisoft 5L 22s
127\214 712.150 487.850 12:7 1.714
73\123 712.195 487.805 7:4 1.750
92\155 712.258 487.742 9:5 1.800
19\32 712.500 487.500 2:1 2.000 Basic 5L 22s
Scales with tunings softer than this are proper
79\133 712.782 487.218 9:4 2.250
60\101 712.871 487.129 7:3 2.333
101\170 712.941 487.059 12:5 2.400
41\69 713.043 486.957 5:2 2.500 Semihard 5L 22s
104\175 713.143 486.857 13:5 2.600
63\106 713.208 486.792 8:3 2.667
85\143 713.287 486.713 11:4 2.750
22\37 713.514 486.486 3:1 3.000 Hard 5L 22s
69\116 713.793 486.207 10:3 3.333
47\79 713.924 486.076 7:2 3.500
72\121 714.050 485.950 11:3 3.667
25\42 714.286 485.714 4:1 4.000 Superhard 5L 22s
53\89 714.607 485.393 9:2 4.500
28\47 714.894 485.106 5:1 5.000
31\52 715.385 484.615 6:1 6.000
3\5 720.000 480.000 1:0 → ∞ Collapsed 5L 22s
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