7L 13s

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↖ 6L 12s ↑7L 12s 8L 12s ↗
← 6L 13s7L 13s 8L 13s →
↙ 6L 14s ↓7L 14s 8L 14s ↘
┌╥┬╥┬┬╥┬┬╥┬┬╥┬┬╥┬┬╥┬┬┐
│║│║││║││║││║││║││║│││
││││││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LsLssLssLssLssLssLss
ssLssLssLssLssLssLsL
Equave 2/1 (1200.0¢)
Period 2/1 (1200.0¢)
Generator size
Bright 17\20 to 6\7 (1020.0¢ to 1028.6¢)
Dark 1\7 to 3\20 (171.4¢ to 180.0¢)
TAMNAMS information
Descends from 6L 1s (archaeotonic)
Required step ratio range 1:1 to 3:2 (soft)
Related MOS scales
Parent 7L 6s
Sister 13L 7s
Daughters 20L 7s, 7L 20s
Neutralized 14L 6s
Equal tunings
Equalized (L:s = 1:1) 17\20 (1020.0¢)
Supersoft (L:s = 4:3) 57\67 (1020.9¢)
Soft (L:s = 3:2) 40\47 (1021.3¢)
Semisoft (L:s = 5:3) 63\74 (1021.6¢)
Basic (L:s = 2:1) 23\27 (1022.2¢)
Semihard (L:s = 5:2) 52\61 (1023.0¢)
Hard (L:s = 3:1) 29\34 (1023.5¢)
Superhard (L:s = 4:1) 35\41 (1024.4¢)
Collapsed (L:s = 1:0) 6\7 (1028.6¢)

7L 13s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 7 large steps and 13 small steps, repeating every octave. 7L 13s is a grandchild scale of 6L 1s, expanding it by 13 tones. Generators that produce this scale range from 1020¢ to 1028.6¢, or from 171.4¢ to 180¢.

Modes

Modes of 7L 13s
UDP Rotational order Step pattern
19|0 1 LsLssLssLssLssLssLss
18|1 18 LssLsLssLssLssLssLss
17|2 15 LssLssLsLssLssLssLss
16|3 12 LssLssLssLsLssLssLss
15|4 9 LssLssLssLssLsLssLss
14|5 6 LssLssLssLssLssLsLss
13|6 3 LssLssLssLssLssLssLs
12|7 20 sLsLssLssLssLssLssLs
11|8 17 sLssLsLssLssLssLssLs
10|9 14 sLssLssLsLssLssLssLs
9|10 11 sLssLssLssLsLssLssLs
8|11 8 sLssLssLssLssLsLssLs
7|12 5 sLssLssLssLssLssLsLs
6|13 2 sLssLssLssLssLssLssL
5|14 19 ssLsLssLssLssLssLssL
4|15 16 ssLssLsLssLssLssLssL
3|16 13 ssLssLssLsLssLssLssL
2|17 10 ssLssLssLssLsLssLssL
1|18 7 ssLssLssLssLssLsLssL
0|19 4 ssLssLssLssLssLssLsL

Tuning spectrum

Tetracot / enipucrop range. See also 7L 6s 7L 13s and 13L 7s.

generator L s L/s gen (cents) comment
1\7 1 0 171.429
10\69 8 1 8.000 173.913
9\62 7 1 7.000 174.194 ^ Enipucrop
8\55 6 1 6.000 174.545
15\103 11 2 5.500 174.757
7\48 5 1 5.000 175.000
13\89 9 2 4.500 175.281 Sesquiquartififths
6\41 4 1 4.000 175.610 Monkey
17\116 11 3 3.667 175.862 Bunya
11\75 7 2 3.500 176.000
16\109 10 3 3.333 176.147 Tetracot
5\34 3 1 3.000 176.471
14\95 8 3 2.667 176.842 Modus
9\61 5 2 2.500 177.049
13\88 7 3 2.333 177.273 Ponens
17\115 9 4 2.250 177.391 Wollemia
4\27 2 1 2.000 177.778
15\101 7 4 1.750 178.218
11\74 5 3 1.667 178.378
7\47 3 2 1.500 178.723
17\114 7 5 1.400 178.947
10\67 4 3 1.333 179.104
13\87 5 4 1.250 179.310
16\107 6 5 1.200 179.439
19\127 7 6 1.167 179.528
22\147 8 7 1.143 179.591
3\20 1 1 1.000 180.000