5L 11s

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↖ 4L 10s ↑ 5L 10s 6L 10s ↗
← 4L 11s 5L 11s 6L 11s →
↙ 4L 12s ↓ 5L 12s 6L 12s ↘ 
┌╥┬┬╥┬┬╥┬┬╥┬┬╥┬┬┬┐
│║││║││║││║││║││││
││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LssLssLssLssLsss
sssLssLssLssLssL
Equave 2/1 (1200.0¢)
Period 2/1 (1200.0¢)
Generator size
Bright 3\16 to 1\5 (225.0¢ to 240.0¢)
Dark 4\5 to 13\16 (960.0¢ to 975.0¢)
TAMNAMS information
Descends from 5L 1s
Ancestor's step ratio range 3:1 to 1:0 (hard)
Related MOS scales
Parent 5L 6s
Sister 11L 5s
Daughters 16L 5s, 5L 16s
Neutralized 10L 6s
2-Flought 21L 11s, 5L 27s
Equal tunings
Equalized (L:s = 1:1) 3\16 (225.0¢)
Supersoft (L:s = 4:3) 10\53 (226.4¢)
Soft (L:s = 3:2) 7\37 (227.0¢)
Semisoft (L:s = 5:3) 11\58 (227.6¢)
Basic (L:s = 2:1) 4\21 (228.6¢)
Semihard (L:s = 5:2) 9\47 (229.8¢)
Hard (L:s = 3:1) 5\26 (230.8¢)
Superhard (L:s = 4:1) 6\31 (232.3¢)
Collapsed (L:s = 1:0) 1\5 (240.0¢)

5L 11s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 5 large steps and 11 small steps, repeating every octave. 5L 11s is a grandchild scale of 5L 1s, expanding it by 10 tones. Generators that produce this scale range from 225¢ to 240¢, or from 960¢ to 975¢.

This mos has a large "diatonic" whole tone of 3\16edo (225 cents) to 1\5edo (240 cents) as a generator. Converging to 5edo as it becomes ever more improper, it moves from gorgo into slendric (the 2.3.7-subgroup temperament which tempers out the gamelisma of 1029/1024).

Modes

Modes of 5L 11s
UDP Cyclic
order		 Step
pattern
15|0 1 LssLssLssLssLsss
14|1 4 LssLssLssLsssLss
13|2 7 LssLssLsssLssLss
12|3 10 LssLsssLssLssLss
11|4 13 LsssLssLssLssLss
10|5 16 sLssLssLssLssLss
9|6 3 sLssLssLssLsssLs
8|7 6 sLssLssLsssLssLs
7|8 9 sLssLsssLssLssLs
6|9 12 sLsssLssLssLssLs
5|10 15 ssLssLssLssLssLs
4|11 2 ssLssLssLssLsssL
3|12 5 ssLssLssLsssLssL
2|13 8 ssLssLsssLssLssL
1|14 11 ssLsssLssLssLssL
0|15 14 sssLssLssLssLssL

Intervals

Intervals of 5L 11s
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 75.0¢
Major 1-mosstep M1ms L 75.0¢ to 240.0¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0¢ to 150.0¢
Major 2-mosstep M2ms L + s 150.0¢ to 240.0¢
3-mosstep Diminished 3-mosstep d3ms 3s 0.0¢ to 225.0¢
Perfect 3-mosstep P3ms L + 2s 225.0¢ to 240.0¢
4-mosstep Minor 4-mosstep m4ms L + 3s 240.0¢ to 300.0¢
Major 4-mosstep M4ms 2L + 2s 300.0¢ to 480.0¢
5-mosstep Minor 5-mosstep m5ms L + 4s 240.0¢ to 375.0¢
Major 5-mosstep M5ms 2L + 3s 375.0¢ to 480.0¢
6-mosstep Minor 6-mosstep m6ms L + 5s 240.0¢ to 450.0¢
Major 6-mosstep M6ms 2L + 4s 450.0¢ to 480.0¢
7-mosstep Minor 7-mosstep m7ms 2L + 5s 480.0¢ to 525.0¢
Major 7-mosstep M7ms 3L + 4s 525.0¢ to 720.0¢
8-mosstep Minor 8-mosstep m8ms 2L + 6s 480.0¢ to 600.0¢
Major 8-mosstep M8ms 3L + 5s 600.0¢ to 720.0¢
9-mosstep Minor 9-mosstep m9ms 2L + 7s 480.0¢ to 675.0¢
Major 9-mosstep M9ms 3L + 6s 675.0¢ to 720.0¢
10-mosstep Minor 10-mosstep m10ms 3L + 7s 720.0¢ to 750.0¢
Major 10-mosstep M10ms 4L + 6s 750.0¢ to 960.0¢
11-mosstep Minor 11-mosstep m11ms 3L + 8s 720.0¢ to 825.0¢
Major 11-mosstep M11ms 4L + 7s 825.0¢ to 960.0¢
12-mosstep Minor 12-mosstep m12ms 3L + 9s 720.0¢ to 900.0¢
Major 12-mosstep M12ms 4L + 8s 900.0¢ to 960.0¢
13-mosstep Perfect 13-mosstep P13ms 4L + 9s 960.0¢ to 975.0¢
Augmented 13-mosstep A13ms 5L + 8s 975.0¢ to 1200.0¢
14-mosstep Minor 14-mosstep m14ms 4L + 10s 960.0¢ to 1050.0¢
Major 14-mosstep M14ms 5L + 9s 1050.0¢ to 1200.0¢
15-mosstep Minor 15-mosstep m15ms 4L + 11s 960.0¢ to 1125.0¢
Major 15-mosstep M15ms 5L + 10s 1125.0¢ to 1200.0¢
16-mosstep Perfect 16-mosstep P16ms 5L + 11s 1200.0¢

Scale tree

Scale Tree and Tuning Spectrum of 5L 11s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
3\16 225.000 975.000 1:1 1.000 Equalized 5L 11s
16\85 225.882 974.118 6:5 1.200
13\69 226.087 973.913 5:4 1.250
23\122 226.230 973.770 9:7 1.286
10\53 226.415 973.585 4:3 1.333 Supersoft 5L 11s
27\143 226.573 973.427 11:8 1.375
17\90 226.667 973.333 7:5 1.400
24\127 226.772 973.228 10:7 1.429
7\37 227.027 972.973 3:2 1.500 Soft 5L 11s
25\132 227.273 972.727 11:7 1.571
18\95 227.368 972.632 8:5 1.600
29\153 227.451 972.549 13:8 1.625
11\58 227.586 972.414 5:3 1.667 Semisoft 5L 11s
26\137 227.737 972.263 12:7 1.714
15\79 227.848 972.152 7:4 1.750
19\100 228.000 972.000 9:5 1.800
4\21 228.571 971.429 2:1 2.000 Basic 5L 11s
Scales with tunings softer than this are proper
17\89 229.213 970.787 9:4 2.250
13\68 229.412 970.588 7:3 2.333
22\115 229.565 970.435 12:5 2.400
9\47 229.787 970.213 5:2 2.500 Semihard 5L 11s
23\120 230.000 970.000 13:5 2.600
14\73 230.137 969.863 8:3 2.667
19\99 230.303 969.697 11:4 2.750
5\26 230.769 969.231 3:1 3.000 Hard 5L 11s
16\83 231.325 968.675 10:3 3.333
11\57 231.579 968.421 7:2 3.500
17\88 231.818 968.182 11:3 3.667
6\31 232.258 967.742 4:1 4.000 Superhard 5L 11s
13\67 232.836 967.164 9:2 4.500
7\36 233.333 966.667 5:1 5.000
8\41 234.146 965.854 6:1 6.000
1\5 240.000 960.000 1:0 → ∞ Collapsed 5L 11s
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