# 6L 13s

 ↖ 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
Descends from 6L 1s (archaeotonic)
Required 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 13edo hexatonic scale. Its generator is a "neutral" whole tone between 3/19edo (189.474) and 1/6edo (200 cents), making it index 2 in meantone.

## Modes

Modes of 6L 13s
UDP Rotational 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

## Scale tree

Scale Tree and Tuning Spectrum of 6L 13s
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