# 6L 19s

 ↖ 5L 18s ↑6L 18s 7L 18s ↗ ← 5L 19s 6L 19s 7L 19s → ↙ 5L 20s ↓6L 20s 7L 20s ↘
```┌╥┬┬┬╥┬┬┬╥┬┬┬╥┬┬┬╥┬┬┬╥┬┬┬┬┐
│║│││║│││║│││║│││║│││║│││││
│││││││││││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘```
Scale structure
Step pattern LsssLsssLsssLsssLsssLssss
ssssLsssLsssLsssLsssLsssL
Equave 2/1 (1200.0¢)
Period 2/1 (1200.0¢)
Generator size
Bright 4\25 to 1\6 (192.0¢ to 200.0¢)
Dark 5\6 to 21\25 (1000.0¢ to 1008.0¢)
TAMNAMS information
Descends from 6L 1s (archaeotonic)
Required step ratio range 4:1 to 1:0 (ultrahard)
Related MOS scales
Parent 6L 13s
Sister 19L 6s
Daughters 25L 6s, 6L 25s
Neutralized 12L 13s
2-Flought 31L 19s, 6L 44s
Equal tunings
Equalized (L:s = 1:1) 4\25 (192.0¢)
Supersoft (L:s = 4:3) 13\81 (192.6¢)
Soft (L:s = 3:2) 9\56 (192.9¢)
Semisoft (L:s = 5:3) 14\87 (193.1¢)
Basic (L:s = 2:1) 5\31 (193.5¢)
Semihard (L:s = 5:2) 11\68 (194.1¢)
Hard (L:s = 3:1) 6\37 (194.6¢)
Superhard (L:s = 4:1) 7\43 (195.3¢)
Collapsed (L:s = 1:0) 1\6 (200.0¢)

6L 19s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 6 large steps and 19 small steps, repeating every octave. 6L 19s is a great-grandchild scale of 6L 1s, expanding it by 18 tones. Generators that produce this scale range from 192¢ to 200¢, or from 1000¢ to 1008¢.

This is the MOS where the large steps divide the small steps into groups of 3-3-3-3-3-4. It is generated by a "neutral" whole tone of no less than 4/25edo (192 cents), laying estimates of the boundary of "practicality" between 37edo (minimum) and 43edo (maximum).

## Modes

Modes of 6L 19s
UDP Rotational order Step pattern
24|0 1 LsssLsssLsssLsssLsssLssss
23|1 5 LsssLsssLsssLsssLssssLsss
22|2 9 LsssLsssLsssLssssLsssLsss
21|3 13 LsssLsssLssssLsssLsssLsss
20|4 17 LsssLssssLsssLsssLsssLsss
19|5 21 LssssLsssLsssLsssLsssLsss
18|6 25 sLsssLsssLsssLsssLsssLsss
17|7 4 sLsssLsssLsssLsssLssssLss
16|8 8 sLsssLsssLsssLssssLsssLss
15|9 12 sLsssLsssLssssLsssLsssLss
14|10 16 sLsssLssssLsssLsssLsssLss
13|11 20 sLssssLsssLsssLsssLsssLss
12|12 24 ssLsssLsssLsssLsssLsssLss
11|13 3 ssLsssLsssLsssLsssLssssLs
10|14 7 ssLsssLsssLsssLssssLsssLs
9|15 11 ssLsssLsssLssssLsssLsssLs
8|16 15 ssLsssLssssLsssLsssLsssLs
7|17 19 ssLssssLsssLsssLsssLsssLs
6|18 23 sssLsssLsssLsssLsssLsssLs
5|19 2 sssLsssLsssLsssLsssLssssL
4|20 6 sssLsssLsssLsssLssssLsssL
3|21 10 sssLsssLsssLssssLsssLsssL
2|22 14 sssLsssLssssLsssLsssLsssL
1|23 18 sssLssssLsssLsssLsssLsssL
0|24 22 ssssLsssLsssLsssLsssLsssL

## Scale tree

Scale Tree and Tuning Spectrum of 6L 19s
Bright Dark L:s Hardness
4\25 192.000 1008.000 1:1 1.000 Equalized 6L 19s
21\131 192.366 1007.634 6:5 1.200
17\106 192.453 1007.547 5:4 1.250
30\187 192.513 1007.487 9:7 1.286
13\81 192.593 1007.407 4:3 1.333 Supersoft 6L 19s
35\218 192.661 1007.339 11:8 1.375
22\137 192.701 1007.299 7:5 1.400
31\193 192.746 1007.254 10:7 1.429
9\56 192.857 1007.143 3:2 1.500 Soft 6L 19s
32\199 192.965 1007.035 11:7 1.571
23\143 193.007 1006.993 8:5 1.600
37\230 193.043 1006.957 13:8 1.625
14\87 193.103 1006.897 5:3 1.667 Semisoft 6L 19s
33\205 193.171 1006.829 12:7 1.714
19\118 193.220 1006.780 7:4 1.750
24\149 193.289 1006.711 9:5 1.800
5\31 193.548 1006.452 2:1 2.000 Basic 6L 19s
Scales with tunings softer than this are proper
21\130 193.846 1006.154 9:4 2.250
16\99 193.939 1006.061 7:3 2.333
27\167 194.012 1005.988 12:5 2.400
11\68 194.118 1005.882 5:2 2.500 Semihard 6L 19s
28\173 194.220 1005.780 13:5 2.600
17\105 194.286 1005.714 8:3 2.667
23\142 194.366 1005.634 11:4 2.750
6\37 194.595 1005.405 3:1 3.000 Hard 6L 19s
19\117 194.872 1005.128 10:3 3.333
13\80 195.000 1005.000 7:2 3.500
20\123 195.122 1004.878 11:3 3.667
7\43 195.349 1004.651 4:1 4.000 Superhard 6L 19s
15\92 195.652 1004.348 9:2 4.500
8\49 195.918 1004.082 5:1 5.000
9\55 196.364 1003.636 6:1 6.000
1\6 200.000 1000.000 1:0 → ∞ Collapsed 6L 19s