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5L 13s

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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 ¢.

↖ 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
Related to 5L 3s (oneirotonic)
With tunings 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 ¢)
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Scale properties

This article uses TAMNAMS conventions for the names of this scale's intervals and scale degrees. The use of 1-indexed ordinal names is reserved for interval regions.

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 ¢

Generator chain

Generator chain of 5L 13s
Bright gens Scale degree Abbrev.
22 Augmented 10-mosdegree A10md
21 Augmented 3-mosdegree A3md
20 Augmented 14-mosdegree A14md
19 Augmented 7-mosdegree A7md
18 Augmented 0-mosdegree A0md
17 Augmented 11-mosdegree A11md
16 Major 4-mosdegree M4md
15 Major 15-mosdegree M15md
14 Major 8-mosdegree M8md
13 Major 1-mosdegree M1md
12 Major 12-mosdegree M12md
11 Major 5-mosdegree M5md
10 Major 16-mosdegree M16md
9 Major 9-mosdegree M9md
8 Major 2-mosdegree M2md
7 Major 13-mosdegree M13md
6 Major 6-mosdegree M6md
5 Major 17-mosdegree M17md
4 Major 10-mosdegree M10md
3 Major 3-mosdegree M3md
2 Major 14-mosdegree M14md
1 Perfect 7-mosdegree P7md
0 Perfect 0-mosdegree
Perfect 18-mosdegree		 P0md
P18md
−1 Perfect 11-mosdegree P11md
−2 Minor 4-mosdegree m4md
−3 Minor 15-mosdegree m15md
−4 Minor 8-mosdegree m8md
−5 Minor 1-mosdegree m1md
−6 Minor 12-mosdegree m12md
−7 Minor 5-mosdegree m5md
−8 Minor 16-mosdegree m16md
−9 Minor 9-mosdegree m9md
−10 Minor 2-mosdegree m2md
−11 Minor 13-mosdegree m13md
−12 Minor 6-mosdegree m6md
−13 Minor 17-mosdegree m17md
−14 Minor 10-mosdegree m10md
−15 Minor 3-mosdegree m3md
−16 Minor 14-mosdegree m14md
−17 Diminished 7-mosdegree d7md
−18 Diminished 18-mosdegree d18md
−19 Diminished 11-mosdegree d11md
−20 Diminished 4-mosdegree d4md
−21 Diminished 15-mosdegree d15md
−22 Diminished 8-mosdegree d8md

Modes

Scale degrees of the modes of 5L 13s
UDP Cyclic
order 		Step
pattern 		Scale degree (mosdegree)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
17|0 1 LssLsssLssLsssLsss Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Aug. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
16|1 8 LssLsssLsssLssLsss Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
15|2 15 LsssLssLsssLssLsss Perf. Maj. Maj. Maj. Min. Maj. Maj. Perf. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
14|3 4 LsssLssLsssLsssLss Perf. Maj. Maj. Maj. Min. Maj. Maj. Perf. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Min. Maj. Maj. Perf.
13|4 11 LsssLsssLssLsssLss Perf. Maj. Maj. Maj. Min. Maj. Maj. Perf. Min. Maj. Maj. Perf. Maj. Maj. Maj. Min. Maj. Maj. Perf.
12|5 18 sLssLsssLssLsssLss Perf. Min. Maj. Maj. Min. Maj. Maj. Perf. Min. Maj. Maj. Perf. Maj. Maj. Maj. Min. Maj. Maj. Perf.
11|6 7 sLssLsssLsssLssLss Perf. Min. Maj. Maj. Min. Maj. Maj. Perf. Min. Maj. Maj. Perf. Min. Maj. Maj. Min. Maj. Maj. Perf.
10|7 14 sLsssLssLsssLssLss Perf. Min. Maj. Maj. Min. Min. Maj. Perf. Min. Maj. Maj. Perf. Min. Maj. Maj. Min. Maj. Maj. Perf.
9|8 3 sLsssLssLsssLsssLs Perf. Min. Maj. Maj. Min. Min. Maj. Perf. Min. Maj. Maj. Perf. Min. Maj. Maj. Min. Min. Maj. Perf.
8|9 10 sLsssLsssLssLsssLs Perf. Min. Maj. Maj. Min. Min. Maj. Perf. Min. Min. Maj. Perf. Min. Maj. Maj. Min. Min. Maj. Perf.
7|10 17 ssLssLsssLssLsssLs Perf. Min. Min. Maj. Min. Min. Maj. Perf. Min. Min. Maj. Perf. Min. Maj. Maj. Min. Min. Maj. Perf.
6|11 6 ssLssLsssLsssLssLs Perf. Min. Min. Maj. Min. Min. Maj. Perf. Min. Min. Maj. Perf. Min. Min. Maj. Min. Min. Maj. Perf.
5|12 13 ssLsssLssLsssLssLs Perf. Min. Min. Maj. Min. Min. Min. Perf. Min. Min. Maj. Perf. Min. Min. Maj. Min. Min. Maj. Perf.
4|13 2 ssLsssLssLsssLsssL Perf. Min. Min. Maj. Min. Min. Min. Perf. Min. Min. Maj. Perf. Min. Min. Maj. Min. Min. Min. Perf.
3|14 9 ssLsssLsssLssLsssL Perf. Min. Min. Maj. Min. Min. Min. Perf. Min. Min. Min. Perf. Min. Min. Maj. Min. Min. Min. Perf.
2|15 16 sssLssLsssLssLsssL Perf. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Perf. Min. Min. Maj. Min. Min. Min. Perf.
1|16 5 sssLssLsssLsssLssL Perf. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Perf.
0|17 12 sssLsssLssLsssLssL Perf. Min. Min. Min. Min. Min. Min. Dim. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Perf.

Scale tree

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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