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
Related to 5L 1s (machinoid)
With tunings 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 ¢) to 1\5edo (240 ¢) 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).

Scale properties

This article uses TAMNAMS conventions for the names of this scale's intervals and scale degrees. The use of 1-indexed ordinal names is reserved for diatonic interval categories.

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 ¢

Generator chain

Generator chain of 5L 11s
Bright gens Scale degree Abbrev.
20 Augmented 12-mosdegree A12md
19 Augmented 9-mosdegree A9md
18 Augmented 6-mosdegree A6md
17 Augmented 3-mosdegree A3md
16 Augmented 0-mosdegree A0md
15 Augmented 13-mosdegree A13md
14 Major 10-mosdegree M10md
13 Major 7-mosdegree M7md
12 Major 4-mosdegree M4md
11 Major 1-mosdegree M1md
10 Major 14-mosdegree M14md
9 Major 11-mosdegree M11md
8 Major 8-mosdegree M8md
7 Major 5-mosdegree M5md
6 Major 2-mosdegree M2md
5 Major 15-mosdegree M15md
4 Major 12-mosdegree M12md
3 Major 9-mosdegree M9md
2 Major 6-mosdegree M6md
1 Perfect 3-mosdegree P3md
0 Perfect 0-mosdegree
Perfect 16-mosdegree		 P0md
P16md
−1 Perfect 13-mosdegree P13md
−2 Minor 10-mosdegree m10md
−3 Minor 7-mosdegree m7md
−4 Minor 4-mosdegree m4md
−5 Minor 1-mosdegree m1md
−6 Minor 14-mosdegree m14md
−7 Minor 11-mosdegree m11md
−8 Minor 8-mosdegree m8md
−9 Minor 5-mosdegree m5md
−10 Minor 2-mosdegree m2md
−11 Minor 15-mosdegree m15md
−12 Minor 12-mosdegree m12md
−13 Minor 9-mosdegree m9md
−14 Minor 6-mosdegree m6md
−15 Diminished 3-mosdegree d3md
−16 Diminished 16-mosdegree d16md
−17 Diminished 13-mosdegree d13md
−18 Diminished 10-mosdegree d10md
−19 Diminished 7-mosdegree d7md
−20 Diminished 4-mosdegree d4md

Modes

Scale degrees of the modes of 5L 11s
UDP Cyclic
order 		Step
pattern 		Scale degree (mosdegree)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
15|0 1 LssLssLssLssLsss Perf. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Aug. Maj. Maj. Perf.
14|1 4 LssLssLssLsssLss Perf. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Perf.
13|2 7 LssLssLsssLssLss Perf. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Min. Maj. Maj. Perf. Maj. Maj. Perf.
12|3 10 LssLsssLssLssLss Perf. Maj. Maj. Perf. Maj. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Perf. Maj. Maj. Perf.
11|4 13 LsssLssLssLssLss Perf. Maj. Maj. Perf. Min. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Perf. Maj. Maj. Perf.
10|5 16 sLssLssLssLssLss Perf. Min. Maj. Perf. Min. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Perf. Maj. Maj. Perf.
9|6 3 sLssLssLssLsssLs Perf. Min. Maj. Perf. Min. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Perf. Min. Maj. Perf.
8|7 6 sLssLssLsssLssLs Perf. Min. Maj. Perf. Min. Maj. Maj. Min. Maj. Maj. Min. Min. Maj. Perf. Min. Maj. Perf.
7|8 9 sLssLsssLssLssLs Perf. Min. Maj. Perf. Min. Maj. Maj. Min. Min. Maj. Min. Min. Maj. Perf. Min. Maj. Perf.
6|9 12 sLsssLssLssLssLs Perf. Min. Maj. Perf. Min. Min. Maj. Min. Min. Maj. Min. Min. Maj. Perf. Min. Maj. Perf.
5|10 15 ssLssLssLssLssLs Perf. Min. Min. Perf. Min. Min. Maj. Min. Min. Maj. Min. Min. Maj. Perf. Min. Maj. Perf.
4|11 2 ssLssLssLssLsssL Perf. Min. Min. Perf. Min. Min. Maj. Min. Min. Maj. Min. Min. Maj. Perf. Min. Min. Perf.
3|12 5 ssLssLssLsssLssL Perf. Min. Min. Perf. Min. Min. Maj. Min. Min. Maj. Min. Min. Min. Perf. Min. Min. Perf.
2|13 8 ssLssLsssLssLssL Perf. Min. Min. Perf. Min. Min. Maj. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Perf.
1|14 11 ssLsssLssLssLssL Perf. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Perf.
0|15 14 sssLssLssLssLssL Perf. Min. Min. Dim. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Perf.

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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