6L 13s

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↖ 5L 12s ↑ 6L 12s 7L 12s ↗
← 5L 13s 6L 13s 7L 13s →
↙ 5L 14s ↓ 6L 14s 7L 14s ↘
Scale structure
Step pattern LssLssLssLssLssLsss
sssLssLssLssLssLssL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 3\19 to 1\6 (189.5 ¢ to 200.0 ¢)
Dark 5\6 to 16\19 (1000.0 ¢ to 1010.5 ¢)
TAMNAMS information
Related to 6L 1s (archaeotonic)
With tunings 3:1 to 1:0 (hard)
Related MOS scales
Parent 6L 7s
Sister 13L 6s
Daughters 19L 6s, 6L 19s
Neutralized 12L 7s
2-Flought 25L 13s, 6L 32s
Equal tunings
Equalized (L:s = 1:1) 3\19 (189.5 ¢)
Supersoft (L:s = 4:3) 10\63 (190.5 ¢)
Soft (L:s = 3:2) 7\44 (190.9 ¢)
Semisoft (L:s = 5:3) 11\69 (191.3 ¢)
Basic (L:s = 2:1) 4\25 (192.0 ¢)
Semihard (L:s = 5:2) 9\56 (192.9 ¢)
Hard (L:s = 3:1) 5\31 (193.5 ¢)
Superhard (L:s = 4:1) 6\37 (194.6 ¢)
Collapsed (L:s = 1:0) 1\6 (200.0 ¢)
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6L 13s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 6 large steps and 13 small steps, repeating every octave. 6L 13s is a grandchild scale of 6L 1s, expanding it by 12 tones. Generators that produce this scale range from 189.5 ¢ to 200 ¢, or from 1000 ¢ to 1010.5 ¢.

This MOS divides its small steps 2-2-2-2-2-3, like the hexatonic scale from 13edo. Its generator is a "neutral" whole tone between 3/19edo (189.474 ¢) and 1/6edo (200 ¢), making it index 2 in meantone. ("Neutral" here means neutrality between 10/9 and 9/8.)

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 6L 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 63.2 ¢
Major 1-mosstep M1ms L 63.2 ¢ to 200.0 ¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0 ¢ to 126.3 ¢
Major 2-mosstep M2ms L + s 126.3 ¢ to 200.0 ¢
3-mosstep Diminished 3-mosstep d3ms 3s 0.0 ¢ to 189.5 ¢
Perfect 3-mosstep P3ms L + 2s 189.5 ¢ to 200.0 ¢
4-mosstep Minor 4-mosstep m4ms L + 3s 200.0 ¢ to 252.6 ¢
Major 4-mosstep M4ms 2L + 2s 252.6 ¢ to 400.0 ¢
5-mosstep Minor 5-mosstep m5ms L + 4s 200.0 ¢ to 315.8 ¢
Major 5-mosstep M5ms 2L + 3s 315.8 ¢ to 400.0 ¢
6-mosstep Minor 6-mosstep m6ms L + 5s 200.0 ¢ to 378.9 ¢
Major 6-mosstep M6ms 2L + 4s 378.9 ¢ to 400.0 ¢
7-mosstep Minor 7-mosstep m7ms 2L + 5s 400.0 ¢ to 442.1 ¢
Major 7-mosstep M7ms 3L + 4s 442.1 ¢ to 600.0 ¢
8-mosstep Minor 8-mosstep m8ms 2L + 6s 400.0 ¢ to 505.3 ¢
Major 8-mosstep M8ms 3L + 5s 505.3 ¢ to 600.0 ¢
9-mosstep Minor 9-mosstep m9ms 2L + 7s 400.0 ¢ to 568.4 ¢
Major 9-mosstep M9ms 3L + 6s 568.4 ¢ to 600.0 ¢
10-mosstep Minor 10-mosstep m10ms 3L + 7s 600.0 ¢ to 631.6 ¢
Major 10-mosstep M10ms 4L + 6s 631.6 ¢ to 800.0 ¢
11-mosstep Minor 11-mosstep m11ms 3L + 8s 600.0 ¢ to 694.7 ¢
Major 11-mosstep M11ms 4L + 7s 694.7 ¢ to 800.0 ¢
12-mosstep Minor 12-mosstep m12ms 3L + 9s 600.0 ¢ to 757.9 ¢
Major 12-mosstep M12ms 4L + 8s 757.9 ¢ to 800.0 ¢
13-mosstep Minor 13-mosstep m13ms 4L + 9s 800.0 ¢ to 821.1 ¢
Major 13-mosstep M13ms 5L + 8s 821.1 ¢ to 1000.0 ¢
14-mosstep Minor 14-mosstep m14ms 4L + 10s 800.0 ¢ to 884.2 ¢
Major 14-mosstep M14ms 5L + 9s 884.2 ¢ to 1000.0 ¢
15-mosstep Minor 15-mosstep m15ms 4L + 11s 800.0 ¢ to 947.4 ¢
Major 15-mosstep M15ms 5L + 10s 947.4 ¢ to 1000.0 ¢
16-mosstep Perfect 16-mosstep P16ms 5L + 11s 1000.0 ¢ to 1010.5 ¢
Augmented 16-mosstep A16ms 6L + 10s 1010.5 ¢ to 1200.0 ¢
17-mosstep Minor 17-mosstep m17ms 5L + 12s 1000.0 ¢ to 1073.7 ¢
Major 17-mosstep M17ms 6L + 11s 1073.7 ¢ to 1200.0 ¢
18-mosstep Minor 18-mosstep m18ms 5L + 13s 1000.0 ¢ to 1136.8 ¢
Major 18-mosstep M18ms 6L + 12s 1136.8 ¢ to 1200.0 ¢
19-mosstep Perfect 19-mosstep P19ms 6L + 13s 1200.0 ¢

Generator chain

Generator chain of 6L 13s
Bright gens Scale degree Abbrev.
24 Augmented 15-mosdegree A15md
23 Augmented 12-mosdegree A12md
22 Augmented 9-mosdegree A9md
21 Augmented 6-mosdegree A6md
20 Augmented 3-mosdegree A3md
19 Augmented 0-mosdegree A0md
18 Augmented 16-mosdegree A16md
17 Major 13-mosdegree M13md
16 Major 10-mosdegree M10md
15 Major 7-mosdegree M7md
14 Major 4-mosdegree M4md
13 Major 1-mosdegree M1md
12 Major 17-mosdegree M17md
11 Major 14-mosdegree M14md
10 Major 11-mosdegree M11md
9 Major 8-mosdegree M8md
8 Major 5-mosdegree M5md
7 Major 2-mosdegree M2md
6 Major 18-mosdegree M18md
5 Major 15-mosdegree M15md
4 Major 12-mosdegree M12md
3 Major 9-mosdegree M9md
2 Major 6-mosdegree M6md
1 Perfect 3-mosdegree P3md
0 Perfect 0-mosdegree
Perfect 19-mosdegree		 P0md
P19md
−1 Perfect 16-mosdegree P16md
−2 Minor 13-mosdegree m13md
−3 Minor 10-mosdegree m10md
−4 Minor 7-mosdegree m7md
−5 Minor 4-mosdegree m4md
−6 Minor 1-mosdegree m1md
−7 Minor 17-mosdegree m17md
−8 Minor 14-mosdegree m14md
−9 Minor 11-mosdegree m11md
−10 Minor 8-mosdegree m8md
−11 Minor 5-mosdegree m5md
−12 Minor 2-mosdegree m2md
−13 Minor 18-mosdegree m18md
−14 Minor 15-mosdegree m15md
−15 Minor 12-mosdegree m12md
−16 Minor 9-mosdegree m9md
−17 Minor 6-mosdegree m6md
−18 Diminished 3-mosdegree d3md
−19 Diminished 19-mosdegree d19md
−20 Diminished 16-mosdegree d16md
−21 Diminished 13-mosdegree d13md
−22 Diminished 10-mosdegree d10md
−23 Diminished 7-mosdegree d7md
−24 Diminished 4-mosdegree d4md

Modes

Scale degrees of the modes of 6L 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 19
18|0 1 LssLssLssLssLssLsss Perf. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Aug. Maj. Maj. Perf.
17|1 4 LssLssLssLssLsssLss Perf. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Perf.
16|2 7 LssLssLssLsssLssLss Perf. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Min. Maj. Maj. Perf. Maj. Maj. Perf.
15|3 10 LssLssLsssLssLssLss Perf. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Perf. Maj. Maj. Perf.
14|4 13 LssLsssLssLssLssLss Perf. Maj. Maj. Perf. Maj. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Perf. Maj. Maj. Perf.
13|5 16 LsssLssLssLssLssLss Perf. Maj. Maj. Perf. Min. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Perf. Maj. Maj. Perf.
12|6 19 sLssLssLssLssLssLss Perf. Min. Maj. Perf. Min. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Perf. Maj. Maj. Perf.
11|7 3 sLssLssLssLssLsssLs Perf. Min. Maj. Perf. Min. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Perf. Min. Maj. Perf.
10|8 6 sLssLssLssLsssLssLs Perf. Min. Maj. Perf. Min. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Min. Min. Maj. Perf. Min. Maj. Perf.
9|9 9 sLssLssLsssLssLssLs Perf. Min. Maj. Perf. Min. Maj. Maj. Min. Maj. Maj. Min. Min. Maj. Min. Min. Maj. Perf. Min. Maj. Perf.
8|10 12 sLssLsssLssLssLssLs Perf. Min. Maj. Perf. Min. Maj. Maj. Min. Min. Maj. Min. Min. Maj. Min. Min. Maj. Perf. Min. Maj. Perf.
7|11 15 sLsssLssLssLssLssLs Perf. Min. Maj. Perf. Min. Min. Maj. Min. Min. Maj. Min. Min. Maj. Min. Min. Maj. Perf. Min. Maj. Perf.
6|12 18 ssLssLssLssLssLssLs Perf. Min. Min. Perf. Min. Min. Maj. Min. Min. Maj. Min. Min. Maj. Min. Min. Maj. Perf. Min. Maj. Perf.
5|13 2 ssLssLssLssLssLsssL Perf. Min. Min. Perf. Min. Min. Maj. Min. Min. Maj. Min. Min. Maj. Min. Min. Maj. Perf. Min. Min. Perf.
4|14 5 ssLssLssLssLsssLssL Perf. Min. Min. Perf. Min. Min. Maj. Min. Min. Maj. Min. Min. Maj. Min. Min. Min. Perf. Min. Min. Perf.
3|15 8 ssLssLssLsssLssLssL Perf. Min. Min. Perf. Min. Min. Maj. Min. Min. Maj. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Perf.
2|16 11 ssLssLsssLssLssLssL Perf. Min. Min. Perf. Min. Min. Maj. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Perf.
1|17 14 ssLsssLssLssLssLssL Perf. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Perf.
0|18 17 sssLssLssLssLssLssL Perf. Min. Min. Dim. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Perf.

Scale tree

Scale tree and tuning spectrum of 6L 13s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
3\19 189.474 1010.526 1:1 1.000 Equalized 6L 13s
16\101 190.099 1009.901 6:5 1.200
13\82 190.244 1009.756 5:4 1.250
23\145 190.345 1009.655 9:7 1.286
10\63 190.476 1009.524 4:3 1.333 Supersoft 6L 13s
27\170 190.588 1009.412 11:8 1.375
17\107 190.654 1009.346 7:5 1.400
24\151 190.728 1009.272 10:7 1.429
7\44 190.909 1009.091 3:2 1.500 Soft 6L 13s
25\157 191.083 1008.917 11:7 1.571
18\113 191.150 1008.850 8:5 1.600
29\182 191.209 1008.791 13:8 1.625
11\69 191.304 1008.696 5:3 1.667 Semisoft 6L 13s
26\163 191.411 1008.589 12:7 1.714
15\94 191.489 1008.511 7:4 1.750
19\119 191.597 1008.403 9:5 1.800
4\25 192.000 1008.000 2:1 2.000 Basic 6L 13s
Scales with tunings softer than this are proper
17\106 192.453 1007.547 9:4 2.250
13\81 192.593 1007.407 7:3 2.333
22\137 192.701 1007.299 12:5 2.400
9\56 192.857 1007.143 5:2 2.500 Semihard 6L 13s
23\143 193.007 1006.993 13:5 2.600
14\87 193.103 1006.897 8:3 2.667
19\118 193.220 1006.780 11:4 2.750
5\31 193.548 1006.452 3:1 3.000 Hard 6L 13s
16\99 193.939 1006.061 10:3 3.333
11\68 194.118 1005.882 7:2 3.500
17\105 194.286 1005.714 11:3 3.667
6\37 194.595 1005.405 4:1 4.000 Superhard 6L 13s
13\80 195.000 1005.000 9:2 4.500
7\43 195.349 1004.651 5:1 5.000
8\49 195.918 1004.082 6:1 6.000
1\6 200.000 1000.000 1:0 → ∞ Collapsed 6L 13s
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