6L 7s

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↖ 5L 6s ↑ 6L 6s 7L 6s ↗
← 5L 7s 6L 7s 7L 7s →
↙ 5L 8s ↓ 6L 8s 7L 8s ↘ 
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└┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LsLsLsLsLsLss
ssLsLsLsLsLsL
Equave 2/1 (1200.0¢)
Period 2/1 (1200.0¢)
Generator size
Bright 2\13 to 1\6 (184.6¢ to 200.0¢)
Dark 5\6 to 11\13 (1000.0¢ to 1015.4¢)
TAMNAMS information
Descends from 6L 1s (archaeotonic)
Ancestor's step ratio range 2:1 to 1:0 (hard-of-basic)
Related MOS scales
Parent 6L 1s
Sister 7L 6s
Daughters 13L 6s, 6L 13s
Neutralized 12L 1s
2-Flought 19L 7s, 6L 20s
Equal tunings
Equalized (L:s = 1:1) 2\13 (184.6¢)
Supersoft (L:s = 4:3) 7\45 (186.7¢)
Soft (L:s = 3:2) 5\32 (187.5¢)
Semisoft (L:s = 5:3) 8\51 (188.2¢)
Basic (L:s = 2:1) 3\19 (189.5¢)
Semihard (L:s = 5:2) 7\44 (190.9¢)
Hard (L:s = 3:1) 4\25 (192.0¢)
Superhard (L:s = 4:1) 5\31 (193.5¢)
Collapsed (L:s = 1:0) 1\6 (200.0¢)

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 (that is, taking every other step of the generator chain) 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

Modes of 6L 7s
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

Intervals

Intervals of 6L 7s
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-mosstep Perfect 0-mosstep P0ms 0 0.0¢
1-mosstep Minor 1-mosstep m1ms s 0.0¢ to 92.3¢
Major 1-mosstep M1ms L 92.3¢ to 200.0¢
2-mosstep Diminished 2-mosstep d2ms 2s 0.0¢ to 184.6¢
Perfect 2-mosstep P2ms L + s 184.6¢ to 200.0¢
3-mosstep Minor 3-mosstep m3ms L + 2s 200.0¢ to 276.9¢
Major 3-mosstep M3ms 2L + s 276.9¢ to 400.0¢
4-mosstep Minor 4-mosstep m4ms L + 3s 200.0¢ to 369.2¢
Major 4-mosstep M4ms 2L + 2s 369.2¢ to 400.0¢
5-mosstep Minor 5-mosstep m5ms 2L + 3s 400.0¢ to 461.5¢
Major 5-mosstep M5ms 3L + 2s 461.5¢ to 600.0¢
6-mosstep Minor 6-mosstep m6ms 2L + 4s 400.0¢ to 553.8¢
Major 6-mosstep M6ms 3L + 3s 553.8¢ to 600.0¢
7-mosstep Minor 7-mosstep m7ms 3L + 4s 600.0¢ to 646.2¢
Major 7-mosstep M7ms 4L + 3s 646.2¢ to 800.0¢
8-mosstep Minor 8-mosstep m8ms 3L + 5s 600.0¢ to 738.5¢
Major 8-mosstep M8ms 4L + 4s 738.5¢ to 800.0¢
9-mosstep Minor 9-mosstep m9ms 4L + 5s 800.0¢ to 830.8¢
Major 9-mosstep M9ms 5L + 4s 830.8¢ to 1000.0¢
10-mosstep Minor 10-mosstep m10ms 4L + 6s 800.0¢ to 923.1¢
Major 10-mosstep M10ms 5L + 5s 923.1¢ to 1000.0¢
11-mosstep Perfect 11-mosstep P11ms 5L + 6s 1000.0¢ to 1015.4¢
Augmented 11-mosstep A11ms 6L + 5s 1015.4¢ to 1200.0¢
12-mosstep Minor 12-mosstep m12ms 5L + 7s 1000.0¢ to 1107.7¢
Major 12-mosstep M12ms 6L + 6s 1107.7¢ to 1200.0¢
13-mosstep Perfect 13-mosstep P13ms 6L + 7s 1200.0¢

Scale tree

Scale Tree and Tuning Spectrum of 6L 7s
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/luna
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/mediantone
7\43 195.349 1004.651 6:1 6.000
1\6 200.000 1000.000 1:0 → ∞ Collapsed 6L 7s
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