6L 13s

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↖ 5L 12s ↑ 6L 12s 7L 12s ↗
← 5L 13s 6L 13s 7L 13s →
↙ 5L 14s ↓ 6L 14s 7L 14s ↘ 
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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
Descends from 6L 1s (archaeotonic)
Ancestor's step ratio range 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¢)

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 cents) and 1/6edo (200 cents), making it index 2 in meantone. ("Neutral" as in neutrality between 10/9 and 9/8.)

Modes

Modes of 6L 13s
UDP Cyclic
order		 Step
pattern
18|0 1 LssLssLssLssLssLsss
17|1 4 LssLssLssLssLsssLss
16|2 7 LssLssLssLsssLssLss
15|3 10 LssLssLsssLssLssLss
14|4 13 LssLsssLssLssLssLss
13|5 16 LsssLssLssLssLssLss
12|6 19 sLssLssLssLssLssLss
11|7 3 sLssLssLssLssLsssLs
10|8 6 sLssLssLssLsssLssLs
9|9 9 sLssLssLsssLssLssLs
8|10 12 sLssLsssLssLssLssLs
7|11 15 sLsssLssLssLssLssLs
6|12 18 ssLssLssLssLssLssLs
5|13 2 ssLssLssLssLssLsssL
4|14 5 ssLssLssLssLsssLssL
3|15 8 ssLssLssLsssLssLssL
2|16 11 ssLssLsssLssLssLssL
1|17 14 ssLsssLssLssLssLssL
0|18 17 sssLssLssLssLssLssL

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¢

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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