6L 7s

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Todo: cleanup
Clean up intro

↖5L 6s ↑6L 6s 7L 6s↗
←5L 7s6L 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¢)
Step size ranges
Large 1\13 to 1\6 (92.3¢ to 200.0¢)
Small 0\6 to 1\13 (0.0¢ to 92.3¢)
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)
Related MOS scales
Parent 6L 1s
Sister 7L 6s
Daughters 13L 6s
6L 13s
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 of various meantone temperaments. It is a great early step into un-syntonic temperaments by virtue of this property, though admittedly Neutral thirds/Mohajira is greater in this respect if you don't mind essentially giving up major and minor seconds/sevenths and thirds/sixths (syntonic temperaments are index 2 subtemperaments of them) because it at least has an albitonic sized MOS which feels like a division of the octave, which cannot be said for the temperaments which this scale belongs to (Happy and Grumpy scales have a very strong period dysphoric feeling due to the common practice use of the equally divided chromatic scale, and Grumpy scales have it stronger because their small step is the the odd step out).

Modes

Modes of 6L 7s
UDP Rotational 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

Scale tree and tuning spectrum of 6L 7s
Generator (in steps of 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
5\31 193.548 1006.452 4:1 4.000 Superhard 6L 7s
11\68 194.118 1005.882 9:2 4.500
6\37 194.595 1005.405 5:1 5.000
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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