6L 13s
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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¢)
↖ 5L 12s | ↑ 6L 12s | 7L 12s ↗ |
← 5L 13s | 6L 13s | 7L 13s → |
↙ 5L 14s | ↓ 6L 14s | 7L 14s ↘ |
┌╥┬┬╥┬┬╥┬┬╥┬┬╥┬┬╥┬┬┬┐ │║││║││║││║││║││║││││ │││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
sssLssLssLssLssLssL
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
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 |
Scale tree
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 |