2L 13s

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↖ 1L 12s ↑ 2L 12s 3L 12s ↗
← 1L 13s 2L 13s 3L 13s →
↙ 1L 14s ↓ 2L 14s 3L 14s ↘ 
┌╥┬┬┬┬┬┬╥┬┬┬┬┬┬┬┐
│║││││││║││││││││
│││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LssssssLsssssss
sssssssLssssssL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 7\15 to 1\2 (560.0 ¢ to 600.0 ¢)
Dark 1\2 to 8\15 (600.0 ¢ to 640.0 ¢)
TAMNAMS information
Related to 2L 7s (balzano)
With tunings 4:1 to 1:0 (ultrahard)
Related MOS scales
Parent 2L 11s
Sister 13L 2s
Daughters 15L 2s, 2L 15s
Neutralized 4L 11s
2-Flought 17L 13s, 2L 28s
Equal tunings
Equalized (L:s = 1:1) 7\15 (560.0 ¢)
Supersoft (L:s = 4:3) 22\47 (561.7 ¢)
Soft (L:s = 3:2) 15\32 (562.5 ¢)
Semisoft (L:s = 5:3) 23\49 (563.3 ¢)
Basic (L:s = 2:1) 8\17 (564.7 ¢)
Semihard (L:s = 5:2) 17\36 (566.7 ¢)
Hard (L:s = 3:1) 9\19 (568.4 ¢)
Superhard (L:s = 4:1) 10\21 (571.4 ¢)
Collapsed (L:s = 1:0) 1\2 (600.0 ¢)

2L 13s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 2 large steps and 13 small steps, repeating every octave. 2L 13s is a great-grandchild scale of 2L 7s, expanding it by 6 tones. Generators that produce this scale range from 560 ¢ to 600 ¢, or from 600 ¢ to 640 ¢.

This MOS is the simplest that has a tritone as the only possible size of a generator, since the smallest size for a tritone is defined to be 7/15edo (560 ¢). Since its generator is a tritone, its harmonic entropy minimum is where the generator is 7/5.

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 2L 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 80.0 ¢
Major 1-mosstep M1ms L 80.0 ¢ to 600.0 ¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0 ¢ to 160.0 ¢
Major 2-mosstep M2ms L + s 160.0 ¢ to 600.0 ¢
3-mosstep Minor 3-mosstep m3ms 3s 0.0 ¢ to 240.0 ¢
Major 3-mosstep M3ms L + 2s 240.0 ¢ to 600.0 ¢
4-mosstep Minor 4-mosstep m4ms 4s 0.0 ¢ to 320.0 ¢
Major 4-mosstep M4ms L + 3s 320.0 ¢ to 600.0 ¢
5-mosstep Minor 5-mosstep m5ms 5s 0.0 ¢ to 400.0 ¢
Major 5-mosstep M5ms L + 4s 400.0 ¢ to 600.0 ¢
6-mosstep Minor 6-mosstep m6ms 6s 0.0 ¢ to 480.0 ¢
Major 6-mosstep M6ms L + 5s 480.0 ¢ to 600.0 ¢
7-mosstep Diminished 7-mosstep d7ms 7s 0.0 ¢ to 560.0 ¢
Perfect 7-mosstep P7ms L + 6s 560.0 ¢ to 600.0 ¢
8-mosstep Perfect 8-mosstep P8ms L + 7s 600.0 ¢ to 640.0 ¢
Augmented 8-mosstep A8ms 2L + 6s 640.0 ¢ to 1200.0 ¢
9-mosstep Minor 9-mosstep m9ms L + 8s 600.0 ¢ to 720.0 ¢
Major 9-mosstep M9ms 2L + 7s 720.0 ¢ to 1200.0 ¢
10-mosstep Minor 10-mosstep m10ms L + 9s 600.0 ¢ to 800.0 ¢
Major 10-mosstep M10ms 2L + 8s 800.0 ¢ to 1200.0 ¢
11-mosstep Minor 11-mosstep m11ms L + 10s 600.0 ¢ to 880.0 ¢
Major 11-mosstep M11ms 2L + 9s 880.0 ¢ to 1200.0 ¢
12-mosstep Minor 12-mosstep m12ms L + 11s 600.0 ¢ to 960.0 ¢
Major 12-mosstep M12ms 2L + 10s 960.0 ¢ to 1200.0 ¢
13-mosstep Minor 13-mosstep m13ms L + 12s 600.0 ¢ to 1040.0 ¢
Major 13-mosstep M13ms 2L + 11s 1040.0 ¢ to 1200.0 ¢
14-mosstep Minor 14-mosstep m14ms L + 13s 600.0 ¢ to 1120.0 ¢
Major 14-mosstep M14ms 2L + 12s 1120.0 ¢ to 1200.0 ¢
15-mosstep Perfect 15-mosstep P15ms 2L + 13s 1200.0 ¢

Generator chain

Generator chain of 2L 13s
Bright gens Scale degree Abbrev.
16 Augmented 7-mosdegree A7md
15 Augmented 0-mosdegree A0md
14 Augmented 8-mosdegree A8md
13 Major 1-mosdegree M1md
12 Major 9-mosdegree M9md
11 Major 2-mosdegree M2md
10 Major 10-mosdegree M10md
9 Major 3-mosdegree M3md
8 Major 11-mosdegree M11md
7 Major 4-mosdegree M4md
6 Major 12-mosdegree M12md
5 Major 5-mosdegree M5md
4 Major 13-mosdegree M13md
3 Major 6-mosdegree M6md
2 Major 14-mosdegree M14md
1 Perfect 7-mosdegree P7md
0 Perfect 0-mosdegree
Perfect 15-mosdegree		 P0md
P15md
−1 Perfect 8-mosdegree P8md
−2 Minor 1-mosdegree m1md
−3 Minor 9-mosdegree m9md
−4 Minor 2-mosdegree m2md
−5 Minor 10-mosdegree m10md
−6 Minor 3-mosdegree m3md
−7 Minor 11-mosdegree m11md
−8 Minor 4-mosdegree m4md
−9 Minor 12-mosdegree m12md
−10 Minor 5-mosdegree m5md
−11 Minor 13-mosdegree m13md
−12 Minor 6-mosdegree m6md
−13 Minor 14-mosdegree m14md
−14 Diminished 7-mosdegree d7md
−15 Diminished 15-mosdegree d15md
−16 Diminished 8-mosdegree d8md

Modes

Scale degrees of the modes of 2L 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
14|0 1 LssssssLsssssss Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Aug. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
13|1 8 LsssssssLssssss Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
12|2 15 sLssssssLssssss Perf. Min. Maj. Maj. Maj. Maj. Maj. Perf. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
11|3 7 sLsssssssLsssss Perf. Min. Maj. Maj. Maj. Maj. Maj. Perf. Perf. Min. Maj. Maj. Maj. Maj. Maj. Perf.
10|4 14 ssLssssssLsssss Perf. Min. Min. Maj. Maj. Maj. Maj. Perf. Perf. Min. Maj. Maj. Maj. Maj. Maj. Perf.
9|5 6 ssLsssssssLssss Perf. Min. Min. Maj. Maj. Maj. Maj. Perf. Perf. Min. Min. Maj. Maj. Maj. Maj. Perf.
8|6 13 sssLssssssLssss Perf. Min. Min. Min. Maj. Maj. Maj. Perf. Perf. Min. Min. Maj. Maj. Maj. Maj. Perf.
7|7 5 sssLsssssssLsss Perf. Min. Min. Min. Maj. Maj. Maj. Perf. Perf. Min. Min. Min. Maj. Maj. Maj. Perf.
6|8 12 ssssLssssssLsss Perf. Min. Min. Min. Min. Maj. Maj. Perf. Perf. Min. Min. Min. Maj. Maj. Maj. Perf.
5|9 4 ssssLsssssssLss Perf. Min. Min. Min. Min. Maj. Maj. Perf. Perf. Min. Min. Min. Min. Maj. Maj. Perf.
4|10 11 sssssLssssssLss Perf. Min. Min. Min. Min. Min. Maj. Perf. Perf. Min. Min. Min. Min. Maj. Maj. Perf.
3|11 3 sssssLsssssssLs Perf. Min. Min. Min. Min. Min. Maj. Perf. Perf. Min. Min. Min. Min. Min. Maj. Perf.
2|12 10 ssssssLssssssLs Perf. Min. Min. Min. Min. Min. Min. Perf. Perf. Min. Min. Min. Min. Min. Maj. Perf.
1|13 2 ssssssLsssssssL Perf. Min. Min. Min. Min. Min. Min. Perf. Perf. Min. Min. Min. Min. Min. Min. Perf.
0|14 9 sssssssLssssssL Perf. Min. Min. Min. Min. Min. Min. Dim. Perf. Min. Min. Min. Min. Min. Min. Perf.

Scale tree

Scale tree and tuning spectrum of 2L 13s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
7\15 560.000 640.000 1:1 1.000 Equalized 2L 13s
36\77 561.039 638.961 6:5 1.200
29\62 561.290 638.710 5:4 1.250
51\109 561.468 638.532 9:7 1.286
22\47 561.702 638.298 4:3 1.333 Supersoft 2L 13s
59\126 561.905 638.095 11:8 1.375
37\79 562.025 637.975 7:5 1.400
52\111 562.162 637.838 10:7 1.429
15\32 562.500 637.500 3:2 1.500 Soft 2L 13s
53\113 562.832 637.168 11:7 1.571
38\81 562.963 637.037 8:5 1.600
61\130 563.077 636.923 13:8 1.625
23\49 563.265 636.735 5:3 1.667 Semisoft 2L 13s
54\115 563.478 636.522 12:7 1.714
31\66 563.636 636.364 7:4 1.750
39\83 563.855 636.145 9:5 1.800
8\17 564.706 635.294 2:1 2.000 Basic 2L 13s
Scales with tunings softer than this are proper
33\70 565.714 634.286 9:4 2.250
25\53 566.038 633.962 7:3 2.333
42\89 566.292 633.708 12:5 2.400
17\36 566.667 633.333 5:2 2.500 Semihard 2L 13s
43\91 567.033 632.967 13:5 2.600
26\55 567.273 632.727 8:3 2.667
35\74 567.568 632.432 11:4 2.750
9\19 568.421 631.579 3:1 3.000 Hard 2L 13s
28\59 569.492 630.508 10:3 3.333
19\40 570.000 630.000 7:2 3.500
29\61 570.492 629.508 11:3 3.667
10\21 571.429 628.571 4:1 4.000 Superhard 2L 13s
21\44 572.727 627.273 9:2 4.500
11\23 573.913 626.087 5:1 5.000
12\25 576.000 624.000 6:1 6.000
1\2 600.000 600.000 1:0 → ∞ Collapsed 2L 13s
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