Xenharmonic Wiki

5L 22s

Revision as of 00:37, 15 December 2024 by BudjarnLambeth (talk | contribs) (-todo:expand, already stub which is more accurate; add intervals)

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 ¢.

↖ 4L 21s ↑ 5L 21s 6L 21s ↗
← 4L 22s 5L 22s 6L 22s →
↙ 4L 23s ↓ 5L 23s 6L 23s ↘
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
Related to 5L 2s (diatonic)
With tunings 5:1 to 1:0
Related MOS scales
Parent 5L 17s
Sister 22L 5s
Daughters 27L 5s, 5L 27s
Neutralized 10L 17s
2-Flought 32L 22s, 5L 49s
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 ¢)
View • Talk • Edit

Modes

Modes of 5L 22s
UDP Cyclic
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

Intervals

Intervals of 5L 22s
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 44.4 ¢
Major 1-mosstep M1ms L 44.4 ¢ to 240.0 ¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0 ¢ to 88.9 ¢
Major 2-mosstep M2ms L + s 88.9 ¢ to 240.0 ¢
3-mosstep Minor 3-mosstep m3ms 3s 0.0 ¢ to 133.3 ¢
Major 3-mosstep M3ms L + 2s 133.3 ¢ to 240.0 ¢
4-mosstep Minor 4-mosstep m4ms 4s 0.0 ¢ to 177.8 ¢
Major 4-mosstep M4ms L + 3s 177.8 ¢ to 240.0 ¢
5-mosstep Minor 5-mosstep m5ms 5s 0.0 ¢ to 222.2 ¢
Major 5-mosstep M5ms L + 4s 222.2 ¢ to 240.0 ¢
6-mosstep Minor 6-mosstep m6ms L + 5s 240.0 ¢ to 266.7 ¢
Major 6-mosstep M6ms 2L + 4s 266.7 ¢ to 480.0 ¢
7-mosstep Minor 7-mosstep m7ms L + 6s 240.0 ¢ to 311.1 ¢
Major 7-mosstep M7ms 2L + 5s 311.1 ¢ to 480.0 ¢
8-mosstep Minor 8-mosstep m8ms L + 7s 240.0 ¢ to 355.6 ¢
Major 8-mosstep M8ms 2L + 6s 355.6 ¢ to 480.0 ¢
9-mosstep Minor 9-mosstep m9ms L + 8s 240.0 ¢ to 400.0 ¢
Major 9-mosstep M9ms 2L + 7s 400.0 ¢ to 480.0 ¢
10-mosstep Minor 10-mosstep m10ms L + 9s 240.0 ¢ to 444.4 ¢
Major 10-mosstep M10ms 2L + 8s 444.4 ¢ to 480.0 ¢
11-mosstep Perfect 11-mosstep P11ms 2L + 9s 480.0 ¢ to 488.9 ¢
Augmented 11-mosstep A11ms 3L + 8s 488.9 ¢ to 720.0 ¢
12-mosstep Minor 12-mosstep m12ms 2L + 10s 480.0 ¢ to 533.3 ¢
Major 12-mosstep M12ms 3L + 9s 533.3 ¢ to 720.0 ¢
13-mosstep Minor 13-mosstep m13ms 2L + 11s 480.0 ¢ to 577.8 ¢
Major 13-mosstep M13ms 3L + 10s 577.8 ¢ to 720.0 ¢
14-mosstep Minor 14-mosstep m14ms 2L + 12s 480.0 ¢ to 622.2 ¢
Major 14-mosstep M14ms 3L + 11s 622.2 ¢ to 720.0 ¢
15-mosstep Minor 15-mosstep m15ms 2L + 13s 480.0 ¢ to 666.7 ¢
Major 15-mosstep M15ms 3L + 12s 666.7 ¢ to 720.0 ¢
16-mosstep Diminished 16-mosstep d16ms 2L + 14s 480.0 ¢ to 711.1 ¢
Perfect 16-mosstep P16ms 3L + 13s 711.1 ¢ to 720.0 ¢
17-mosstep Minor 17-mosstep m17ms 3L + 14s 720.0 ¢ to 755.6 ¢
Major 17-mosstep M17ms 4L + 13s 755.6 ¢ to 960.0 ¢
18-mosstep Minor 18-mosstep m18ms 3L + 15s 720.0 ¢ to 800.0 ¢
Major 18-mosstep M18ms 4L + 14s 800.0 ¢ to 960.0 ¢
19-mosstep Minor 19-mosstep m19ms 3L + 16s 720.0 ¢ to 844.4 ¢
Major 19-mosstep M19ms 4L + 15s 844.4 ¢ to 960.0 ¢
20-mosstep Minor 20-mosstep m20ms 3L + 17s 720.0 ¢ to 888.9 ¢
Major 20-mosstep M20ms 4L + 16s 888.9 ¢ to 960.0 ¢
21-mosstep Minor 21-mosstep m21ms 3L + 18s 720.0 ¢ to 933.3 ¢
Major 21-mosstep M21ms 4L + 17s 933.3 ¢ to 960.0 ¢
22-mosstep Minor 22-mosstep m22ms 4L + 18s 960.0 ¢ to 977.8 ¢
Major 22-mosstep M22ms 5L + 17s 977.8 ¢ to 1200.0 ¢
23-mosstep Minor 23-mosstep m23ms 4L + 19s 960.0 ¢ to 1022.2 ¢
Major 23-mosstep M23ms 5L + 18s 1022.2 ¢ to 1200.0 ¢
24-mosstep Minor 24-mosstep m24ms 4L + 20s 960.0 ¢ to 1066.7 ¢
Major 24-mosstep M24ms 5L + 19s 1066.7 ¢ to 1200.0 ¢
25-mosstep Minor 25-mosstep m25ms 4L + 21s 960.0 ¢ to 1111.1 ¢
Major 25-mosstep M25ms 5L + 20s 1111.1 ¢ to 1200.0 ¢
26-mosstep Minor 26-mosstep m26ms 4L + 22s 960.0 ¢ to 1155.6 ¢
Major 26-mosstep M26ms 5L + 21s 1155.6 ¢ to 1200.0 ¢
27-mosstep Perfect 27-mosstep P27ms 5L + 22s 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 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


  This page is a stub. You can help the Xenharmonic Wiki by expanding it.
Retrieved from "https://en.xen.wiki/index.php?title=5L_22s&oldid=170406"