6L 7s
↖ 5L 6s | ↑ 6L 6s | 7L 6s ↗ |
← 5L 7s | 6L 7s | 7L 7s → |
↙ 5L 8s | ↓ 6L 8s | 7L 8s ↘ |
┌╥┬╥┬╥┬╥┬╥┬╥┬┬┐ │║│║│║│║│║│║│││ │││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┘
ssLsLsLsLsLsL
6L 7s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 6 large steps and 7 small steps, repeating every octave. 6L 7s is a child scale of 6L 1s, expanding it by 6 tones. Generators that produce this scale range from 184.6¢ to 200¢, or from 1000¢ to 1015.4¢. This MOS is the chromatic scale of a family of temperaments which are index 2 subtemperaments of various meantone temperaments: that is, those that are generated by a mean tone, that being specifically a whole tone of tunings with a fifth in between that of 26edo and 12edo, and roughly speaking between 10/9 and 9/8. The most notable temperaments generating this scale are didacus in the 2.5.7 subgroup and its extensions, with its generator identified with ~28/25, whose optimum makes a superhard tuning, similarly to the situation with 5L 6s and slendric.
Modes
UDP | Cyclic order |
Step pattern |
---|---|---|
12|0 | 1 | LsLsLsLsLsLss |
11|1 | 3 | LsLsLsLsLssLs |
10|2 | 5 | LsLsLsLssLsLs |
9|3 | 7 | LsLsLssLsLsLs |
8|4 | 9 | LsLssLsLsLsLs |
7|5 | 11 | LssLsLsLsLsLs |
6|6 | 13 | sLsLsLsLsLsLs |
5|7 | 2 | sLsLsLsLsLssL |
4|8 | 4 | sLsLsLsLssLsL |
3|9 | 6 | sLsLsLssLsLsL |
2|10 | 8 | sLsLssLsLsLsL |
1|11 | 10 | sLssLsLsLsLsL |
0|12 | 12 | ssLsLsLsLsLsL |
Scale tree
Generator(edo) | Cents | Step ratio | Comments | |||||||
---|---|---|---|---|---|---|---|---|---|---|
Bright | Dark | L:s | Hardness | |||||||
2\13 | 184.615 | 1015.385 | 1:1 | 1.000 | Equalized 6L 7s | |||||
11\71 | 185.915 | 1014.085 | 6:5 | 1.200 | ||||||
9\58 | 186.207 | 1013.793 | 5:4 | 1.250 | ||||||
16\103 | 186.408 | 1013.592 | 9:7 | 1.286 | ||||||
7\45 | 186.667 | 1013.333 | 4:3 | 1.333 | Supersoft 6L 7s | |||||
19\122 | 186.885 | 1013.115 | 11:8 | 1.375 | ||||||
12\77 | 187.013 | 1012.987 | 7:5 | 1.400 | ||||||
17\109 | 187.156 | 1012.844 | 10:7 | 1.429 | ||||||
5\32 | 187.500 | 1012.500 | 3:2 | 1.500 | Soft 6L 7s | |||||
18\115 | 187.826 | 1012.174 | 11:7 | 1.571 | ||||||
13\83 | 187.952 | 1012.048 | 8:5 | 1.600 | ||||||
21\134 | 188.060 | 1011.940 | 13:8 | 1.625 | ||||||
8\51 | 188.235 | 1011.765 | 5:3 | 1.667 | Semisoft 6L 7s | |||||
19\121 | 188.430 | 1011.570 | 12:7 | 1.714 | ||||||
11\70 | 188.571 | 1011.429 | 7:4 | 1.750 | ||||||
14\89 | 188.764 | 1011.236 | 9:5 | 1.800 | ||||||
3\19 | 189.474 | 1010.526 | 2:1 | 2.000 | Basic 6L 7s Scales with tunings softer than this are proper | |||||
13\82 | 190.244 | 1009.756 | 9:4 | 2.250 | ||||||
10\63 | 190.476 | 1009.524 | 7:3 | 2.333 | ||||||
17\107 | 190.654 | 1009.346 | 12:5 | 2.400 | ||||||
7\44 | 190.909 | 1009.091 | 5:2 | 2.500 | Semihard 6L 7s | |||||
18\113 | 191.150 | 1008.850 | 13:5 | 2.600 | ||||||
11\69 | 191.304 | 1008.696 | 8:3 | 2.667 | ||||||
15\94 | 191.489 | 1008.511 | 11:4 | 2.750 | ||||||
4\25 | 192.000 | 1008.000 | 3:1 | 3.000 | Hard 6L 7s | |||||
13\81 | 192.593 | 1007.407 | 10:3 | 3.333 | ||||||
9\56 | 192.857 | 1007.143 | 7:2 | 3.500 | ||||||
14\87 | 193.103 | 1006.897 | 11:3 | 3.667 | Hemithirds | |||||
5\31 | 193.548 | 1006.452 | 4:1 | 4.000 | Superhard 6L 7s Didacus/hemiwürschmidt | |||||
11\68 | 194.118 | 1005.882 | 9:2 | 4.500 | ||||||
6\37 | 194.595 | 1005.405 | 5:1 | 5.000 | Roulette | |||||
7\43 | 195.349 | 1004.651 | 6:1 | 6.000 | ||||||
1\6 | 200.000 | 1000.000 | 1:0 | → ∞ | Collapsed 6L 7s |