6L 5s

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↖ 5L 4s ↑6L 4s 7L 4s ↗
← 5L 5s6L 5s 7L 5s →
↙ 5L 6s ↓6L 6s 7L 6s ↘
┌╥╥┬╥┬╥┬╥┬╥┬┐
│║║│║│║│║│║││
│││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLsLsLsLsLs
sLsLsLsLsLL
Equave 2/1 (1200.0¢)
Period 2/1 (1200.0¢)
Generator size
Bright 9\11 to 5\6 (981.8¢ to 1000.0¢)
Dark 1\6 to 2\11 (200.0¢ to 218.2¢)
TAMNAMS information
Descends from 5L 1s (machinoid)
Required step ratio range 1:1 to 2:1 (soft-of-basic)
Related MOS scales
Parent 5L 1s
Sister 5L 6s
Daughters 11L 6s, 6L 11s
Neutralized 1L 10s
2-Flought 17L 5s, 6L 16s
Equal tunings
Equalized (L:s = 1:1) 9\11 (981.8¢)
Supersoft (L:s = 4:3) 32\39 (984.6¢)
Soft (L:s = 3:2) 23\28 (985.7¢)
Semisoft (L:s = 5:3) 37\45 (986.7¢)
Basic (L:s = 2:1) 14\17 (988.2¢)
Semihard (L:s = 5:2) 33\40 (990.0¢)
Hard (L:s = 3:1) 19\23 (991.3¢)
Superhard (L:s = 4:1) 24\29 (993.1¢)
Collapsed (L:s = 1:0) 5\6 (1000.0¢)

6L 5s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 6 large steps and 5 small steps, repeating every octave. 6L 5s is a child scale of 5L 1s, expanding it by 5 tones. Generators that produce this scale range from 981.8¢ to 1000¢, or from 200¢ to 218.2¢. This MOS has a harmonic entropy minimum (Baldy) which is highly improper (L=8 s=1) in an optimal tuning, However, its saving grace is that it at least has index 2 in syntonic temperaments with wide fifths like superpyth (2.3.7) and pentacircle (2.3.11/7.13/11)[clarification needed].

Modes

Modes of 6L 5s
UDP Rotational order Step pattern
10|0 1 LLsLsLsLsLs
9|1 10 LsLLsLsLsLs
8|2 8 LsLsLLsLsLs
7|3 6 LsLsLsLLsLs
6|4 4 LsLsLsLsLLs
5|5 2 LsLsLsLsLsL
4|6 11 sLLsLsLsLsL
3|7 9 sLsLLsLsLsL
2|8 7 sLsLsLLsLsL
1|9 5 sLsLsLsLLsL
0|10 3 sLsLsLsLsLL

Scale tree

Scale Tree and Tuning Spectrum of 6L 5s
Generator(edo) Cents Step Ratio Comments
Bright Dark L:s Hardness
9\11 981.818 218.182 1:1 1.000 Equalized 6L 5s
50\61 983.607 216.393 6:5 1.200
41\50 984.000 216.000 5:4 1.250
73\89 984.270 215.730 9:7 1.286
32\39 984.615 215.385 4:3 1.333 Supersoft 6L 5s
87\106 984.906 215.094 11:8 1.375
55\67 985.075 214.925 7:5 1.400
78\95 985.263 214.737 10:7 1.429
23\28 985.714 214.286 3:2 1.500 Soft 6L 5s
83\101 986.139 213.861 11:7 1.571
60\73 986.301 213.699 8:5 1.600
97\118 986.441 213.559 13:8 1.625
37\45 986.667 213.333 5:3 1.667 Semisoft 6L 5s
88\107 986.916 213.084 12:7 1.714
51\62 987.097 212.903 7:4 1.750
65\79 987.342 212.658 9:5 1.800
14\17 988.235 211.765 2:1 2.000 Basic 6L 5s
Scales with tunings softer than this are proper
61\74 989.189 210.811 9:4 2.250
47\57 989.474 210.526 7:3 2.333
80\97 989.691 210.309 12:5 2.400
33\40 990.000 210.000 5:2 2.500 Semihard 6L 5s
85\103 990.291 209.709 13:5 2.600
52\63 990.476 209.524 8:3 2.667
71\86 990.698 209.302 11:4 2.750
19\23 991.304 208.696 3:1 3.000 Hard 6L 5s
62\75 992.000 208.000 10:3 3.333
43\52 992.308 207.692 7:2 3.500
67\81 992.593 207.407 11:3 3.667
24\29 993.103 206.897 4:1 4.000 Superhard 6L 5s
53\64 993.750 206.250 9:2 4.500
29\35 994.286 205.714 5:1 5.000
34\41 995.122 204.878 6:1 6.000
5\6 1000.000 200.000 1:0 → ∞ Collapsed 6L 5s