5L 13s

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↖ 4L 12s ↑ 5L 12s 6L 12s ↗
← 4L 13s 5L 13s 6L 13s →
↙ 4L 14s ↓ 5L 14s 6L 14s ↘ 
┌╥┬┬╥┬┬┬╥┬┬╥┬┬┬╥┬┬┬┐
│║││║│││║││║│││║││││
││││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LssLsssLssLsssLsss
sssLsssLssLsssLssL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 7\18 to 2\5 (466.7 ¢ to 480.0 ¢)
Dark 3\5 to 11\18 (720.0 ¢ to 733.3 ¢)
TAMNAMS information
Descends from 5L 3s (oneirotonic)
Ancestor's step ratio range 3:1 to 1:0 (hard)
Related MOS scales
Parent 5L 8s
Sister 13L 5s
Daughters 18L 5s, 5L 18s
Neutralized 10L 8s
2-Flought 23L 13s, 5L 31s
Equal tunings
Equalized (L:s = 1:1) 7\18 (466.7 ¢)
Supersoft (L:s = 4:3) 23\59 (467.8 ¢)
Soft (L:s = 3:2) 16\41 (468.3 ¢)
Semisoft (L:s = 5:3) 25\64 (468.8 ¢)
Basic (L:s = 2:1) 9\23 (469.6 ¢)
Semihard (L:s = 5:2) 20\51 (470.6 ¢)
Hard (L:s = 3:1) 11\28 (471.4 ¢)
Superhard (L:s = 4:1) 13\33 (472.7 ¢)
Collapsed (L:s = 1:0) 2\5 (480.0 ¢)

5L 13s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 5 large steps and 13 small steps, repeating every octave. 5L 13s is a grandchild scale of 5L 3s, expanding it by 10 tones. Generators that produce this scale range from 466.7 ¢ to 480 ¢, or from 720 ¢ to 733.3 ¢.

Modes

Modes of 5L 13s
UDP Cyclic
order		 Step
pattern
17|0 1 LssLsssLssLsssLsss
16|1 8 LssLsssLsssLssLsss
15|2 15 LsssLssLsssLssLsss
14|3 4 LsssLssLsssLsssLss
13|4 11 LsssLsssLssLsssLss
12|5 18 sLssLsssLssLsssLss
11|6 7 sLssLsssLsssLssLss
10|7 14 sLsssLssLsssLssLss
9|8 3 sLsssLssLsssLsssLs
8|9 10 sLsssLsssLssLsssLs
7|10 17 ssLssLsssLssLsssLs
6|11 6 ssLssLsssLsssLssLs
5|12 13 ssLsssLssLsssLssLs
4|13 2 ssLsssLssLsssLsssL
3|14 9 ssLsssLsssLssLsssL
2|15 16 sssLssLsssLssLsssL
1|16 5 sssLssLsssLsssLssL
0|17 12 sssLsssLssLsssLssL

Intervals

Intervals of 5L 13s
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 66.7 ¢
Major 1-mosstep M1ms L 66.7 ¢ to 240.0 ¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0 ¢ to 133.3 ¢
Major 2-mosstep M2ms L + s 133.3 ¢ to 240.0 ¢
3-mosstep Minor 3-mosstep m3ms 3s 0.0 ¢ to 200.0 ¢
Major 3-mosstep M3ms L + 2s 200.0 ¢ to 240.0 ¢
4-mosstep Minor 4-mosstep m4ms L + 3s 240.0 ¢ to 266.7 ¢
Major 4-mosstep M4ms 2L + 2s 266.7 ¢ to 480.0 ¢
5-mosstep Minor 5-mosstep m5ms L + 4s 240.0 ¢ to 333.3 ¢
Major 5-mosstep M5ms 2L + 3s 333.3 ¢ to 480.0 ¢
6-mosstep Minor 6-mosstep m6ms L + 5s 240.0 ¢ to 400.0 ¢
Major 6-mosstep M6ms 2L + 4s 400.0 ¢ to 480.0 ¢
7-mosstep Diminished 7-mosstep d7ms L + 6s 240.0 ¢ to 466.7 ¢
Perfect 7-mosstep P7ms 2L + 5s 466.7 ¢ to 480.0 ¢
8-mosstep Minor 8-mosstep m8ms 2L + 6s 480.0 ¢ to 533.3 ¢
Major 8-mosstep M8ms 3L + 5s 533.3 ¢ to 720.0 ¢
9-mosstep Minor 9-mosstep m9ms 2L + 7s 480.0 ¢ to 600.0 ¢
Major 9-mosstep M9ms 3L + 6s 600.0 ¢ to 720.0 ¢
10-mosstep Minor 10-mosstep m10ms 2L + 8s 480.0 ¢ to 666.7 ¢
Major 10-mosstep M10ms 3L + 7s 666.7 ¢ to 720.0 ¢
11-mosstep Perfect 11-mosstep P11ms 3L + 8s 720.0 ¢ to 733.3 ¢
Augmented 11-mosstep A11ms 4L + 7s 733.3 ¢ to 960.0 ¢
12-mosstep Minor 12-mosstep m12ms 3L + 9s 720.0 ¢ to 800.0 ¢
Major 12-mosstep M12ms 4L + 8s 800.0 ¢ to 960.0 ¢
13-mosstep Minor 13-mosstep m13ms 3L + 10s 720.0 ¢ to 866.7 ¢
Major 13-mosstep M13ms 4L + 9s 866.7 ¢ to 960.0 ¢
14-mosstep Minor 14-mosstep m14ms 3L + 11s 720.0 ¢ to 933.3 ¢
Major 14-mosstep M14ms 4L + 10s 933.3 ¢ to 960.0 ¢
15-mosstep Minor 15-mosstep m15ms 4L + 11s 960.0 ¢ to 1000.0 ¢
Major 15-mosstep M15ms 5L + 10s 1000.0 ¢ to 1200.0 ¢
16-mosstep Minor 16-mosstep m16ms 4L + 12s 960.0 ¢ to 1066.7 ¢
Major 16-mosstep M16ms 5L + 11s 1066.7 ¢ to 1200.0 ¢
17-mosstep Minor 17-mosstep m17ms 4L + 13s 960.0 ¢ to 1133.3 ¢
Major 17-mosstep M17ms 5L + 12s 1133.3 ¢ to 1200.0 ¢
18-mosstep Perfect 18-mosstep P18ms 5L + 13s 1200.0 ¢

Scale tree

Icon-Deprecated.png Scale tree is deprecated. Please use Template: MOS tuning spectrum instead.
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 13s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
7\18 466.667 733.333 1:1 1.000 Equalized 5L 13s
37\95 467.368 732.632 6:5 1.200
30\77 467.532 732.468 5:4 1.250
53\136 467.647 732.353 9:7 1.286
23\59 467.797 732.203 4:3 1.333 Supersoft 5L 13s
62\159 467.925 732.075 11:8 1.375
39\100 468.000 732.000 7:5 1.400
55\141 468.085 731.915 10:7 1.429
16\41 468.293 731.707 3:2 1.500 Soft 5L 13s
57\146 468.493 731.507 11:7 1.571
41\105 468.571 731.429 8:5 1.600
66\169 468.639 731.361 13:8 1.625
25\64 468.750 731.250 5:3 1.667 Semisoft 5L 13s
59\151 468.874 731.126 12:7 1.714
34\87 468.966 731.034 7:4 1.750
43\110 469.091 730.909 9:5 1.800
9\23 469.565 730.435 2:1 2.000 Basic 5L 13s
Scales with tunings softer than this are proper
38\97 470.103 729.897 9:4 2.250
29\74 470.270 729.730 7:3 2.333
49\125 470.400 729.600 12:5 2.400
20\51 470.588 729.412 5:2 2.500 Semihard 5L 13s
51\130 470.769 729.231 13:5 2.600
31\79 470.886 729.114 8:3 2.667
42\107 471.028 728.972 11:4 2.750
11\28 471.429 728.571 3:1 3.000 Hard 5L 13s
35\89 471.910 728.090 10:3 3.333
24\61 472.131 727.869 7:2 3.500
37\94 472.340 727.660 11:3 3.667
13\33 472.727 727.273 4:1 4.000 Superhard 5L 13s
28\71 473.239 726.761 9:2 4.500
15\38 473.684 726.316 5:1 5.000
17\43 474.419 725.581 6:1 6.000
2\5 480.000 720.000 1:0 → ∞ Collapsed 5L 13s


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