# 13L 7s

 ↖ 12L 6s ↑13L 6s 14L 6s ↗ ← 12L 7s 13L 7s 14L 7s → ↙ 12L 8s ↓13L 8s 14L 8s ↘
```┌╥╥┬╥╥┬╥╥┬╥╥┬╥╥┬╥╥┬╥┬┐
│║║│║║│║║│║║│║║│║║│║││
││││││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘```
Scale structure
Step pattern LLsLLsLLsLLsLLsLLsLs
sLsLLsLLsLLsLLsLLsLL
Equave 2/1 (1200.0¢)
Period 2/1 (1200.0¢)
Generator size
Bright 3\20 to 2\13 (180.0¢ to 184.6¢)
Dark 11\13 to 17\20 (1015.4¢ to 1020.0¢)
TAMNAMS information
Descends from 6L 1s (archaeotonic)
Descendant's step ratio range 3:2 to 2:1 (hyposoft)
Related MOS scales
Parent 7L 6s
Sister 7L 13s
Daughters 20L 13s, 13L 20s
Neutralized 6L 14s
2-Flought 33L 7s, 13L 27s
Equal tunings
Equalized (L:s = 1:1) 3\20 (180.0¢)
Supersoft (L:s = 4:3) 11\73 (180.8¢)
Soft (L:s = 3:2) 8\53 (181.1¢)
Semisoft (L:s = 5:3) 13\86 (181.4¢)
Basic (L:s = 2:1) 5\33 (181.8¢)
Semihard (L:s = 5:2) 12\79 (182.3¢)
Hard (L:s = 3:1) 7\46 (182.6¢)
Superhard (L:s = 4:1) 9\59 (183.1¢)
Collapsed (L:s = 1:0) 2\13 (184.6¢)

13L 7s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 13 large steps and 7 small steps, repeating every octave. 13L 7s is a grandchild scale of 6L 1s, expanding it by 13 tones. Generators that produce this scale range from 180¢ to 184.6¢, or from 1015.4¢ to 1020¢.

## Modes

Modes of 13L 7s
UDP Rotational order Step pattern
19|0 1 LLsLLsLLsLLsLLsLLsLs
18|1 4 LLsLLsLLsLLsLLsLsLLs
17|2 7 LLsLLsLLsLLsLsLLsLLs
16|3 10 LLsLLsLLsLsLLsLLsLLs
15|4 13 LLsLLsLsLLsLLsLLsLLs
14|5 16 LLsLsLLsLLsLLsLLsLLs
13|6 19 LsLLsLLsLLsLLsLLsLLs
12|7 2 LsLLsLLsLLsLLsLLsLsL
11|8 5 LsLLsLLsLLsLLsLsLLsL
10|9 8 LsLLsLLsLLsLsLLsLLsL
9|10 11 LsLLsLLsLsLLsLLsLLsL
8|11 14 LsLLsLsLLsLLsLLsLLsL
7|12 17 LsLsLLsLLsLLsLLsLLsL
6|13 20 sLLsLLsLLsLLsLLsLLsL
5|14 3 sLLsLLsLLsLLsLLsLsLL
4|15 6 sLLsLLsLLsLLsLsLLsLL
3|16 9 sLLsLLsLLsLsLLsLLsLL
2|17 12 sLLsLLsLsLLsLLsLLsLL
1|18 15 sLLsLsLLsLLsLLsLLsLL
0|19 18 sLsLLsLLsLLsLLsLLsLL

## Scale tree

Scale Tree and Tuning Spectrum of 13L 7s
Bright Dark L:s Hardness
3\20 180.000 1020.000 1:1 1.000 Equalized 13L 7s
17\113 180.531 1019.469 6:5 1.200
14\93 180.645 1019.355 5:4 1.250
25\166 180.723 1019.277 9:7 1.286
11\73 180.822 1019.178 4:3 1.333 Supersoft 13L 7s
30\199 180.905 1019.095 11:8 1.375
19\126 180.952 1019.048 7:5 1.400
27\179 181.006 1018.994 10:7 1.429
8\53 181.132 1018.868 3:2 1.500 Soft 13L 7s
29\192 181.250 1018.750 11:7 1.571
21\139 181.295 1018.705 8:5 1.600
34\225 181.333 1018.667 13:8 1.625
13\86 181.395 1018.605 5:3 1.667 Semisoft 13L 7s
31\205 181.463 1018.537 12:7 1.714
18\119 181.513 1018.487 7:4 1.750
23\152 181.579 1018.421 9:5 1.800
5\33 181.818 1018.182 2:1 2.000 Basic 13L 7s
Scales with tunings softer than this are proper
22\145 182.069 1017.931 9:4 2.250
17\112 182.143 1017.857 7:3 2.333
29\191 182.199 1017.801 12:5 2.400
12\79 182.278 1017.722 5:2 2.500 Semihard 13L 7s
31\204 182.353 1017.647 13:5 2.600
19\125 182.400 1017.600 8:3 2.667
26\171 182.456 1017.544 11:4 2.750
7\46 182.609 1017.391 3:1 3.000 Hard 13L 7s
Mitonic / Minortone
23\151 182.781 1017.219 10:3 3.333
16\105 182.857 1017.143 7:2 3.500
25\164 182.927 1017.073 11:3 3.667
9\59 183.051 1016.949 4:1 4.000 Superhard 13L 7s
20\131 183.206 1016.794 9:2 4.500
11\72 183.333 1016.667 5:1 5.000
13\85 183.529 1016.471 6:1 6.000
2\13 184.615 1015.385 1:0 → ∞ Collapsed 13L 7s