11L 5s

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↖ 10L 4s ↑ 11L 4s 12L 4s ↗
← 10L 5s 11L 5s 12L 5s →
↙ 10L 6s ↓ 11L 6s 12L 6s ↘ 
┌╥╥╥┬╥╥┬╥╥┬╥╥┬╥╥┬┐
│║║║│║║│║║│║║│║║││
││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLLsLLsLLsLLsLLs
sLLsLLsLLsLLsLLL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 13\16 to 9\11 (975.0 ¢ to 981.8 ¢)
Dark 2\11 to 3\16 (218.2 ¢ to 225.0 ¢)
TAMNAMS information
Related to 5L 1s (machinoid)
With tunings 2:1 to 3:1 (hypohard)
Related MOS scales
Parent 5L 6s
Sister 5L 11s
Daughters 16L 11s, 11L 16s
Neutralized 6L 10s
2-Flought 27L 5s, 11L 21s
Equal tunings
Equalized (L:s = 1:1) 13\16 (975.0 ¢)
Supersoft (L:s = 4:3) 48\59 (976.3 ¢)
Soft (L:s = 3:2) 35\43 (976.7 ¢)
Semisoft (L:s = 5:3) 57\70 (977.1 ¢)
Basic (L:s = 2:1) 22\27 (977.8 ¢)
Semihard (L:s = 5:2) 53\65 (978.5 ¢)
Hard (L:s = 3:1) 31\38 (978.9 ¢)
Superhard (L:s = 4:1) 40\49 (979.6 ¢)
Collapsed (L:s = 1:0) 9\11 (981.8 ¢)

11L 5s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 11 large steps and 5 small steps, repeating every octave. 11L 5s is a grandchild scale of 5L 1s, expanding it by 10 tones. Generators that produce this scale range from 975 ¢ to 981.8 ¢, or from 218.2 ¢ to 225 ¢.

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 interval regions.

Intervals

Intervals of 11L 5s
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 109.1 ¢
2-mosstep Minor 2-mosstep m2ms L + s 109.1 ¢ to 150.0 ¢
Major 2-mosstep M2ms 2L 150.0 ¢ to 218.2 ¢
3-mosstep Perfect 3-mosstep P3ms 2L + s 218.2 ¢ to 225.0 ¢
Augmented 3-mosstep A3ms 3L 225.0 ¢ to 327.3 ¢
4-mosstep Minor 4-mosstep m4ms 2L + 2s 218.2 ¢ to 300.0 ¢
Major 4-mosstep M4ms 3L + s 300.0 ¢ to 327.3 ¢
5-mosstep Minor 5-mosstep m5ms 3L + 2s 327.3 ¢ to 375.0 ¢
Major 5-mosstep M5ms 4L + s 375.0 ¢ to 436.4 ¢
6-mosstep Minor 6-mosstep m6ms 4L + 2s 436.4 ¢ to 450.0 ¢
Major 6-mosstep M6ms 5L + s 450.0 ¢ to 545.5 ¢
7-mosstep Minor 7-mosstep m7ms 4L + 3s 436.4 ¢ to 525.0 ¢
Major 7-mosstep M7ms 5L + 2s 525.0 ¢ to 545.5 ¢
8-mosstep Minor 8-mosstep m8ms 5L + 3s 545.5 ¢ to 600.0 ¢
Major 8-mosstep M8ms 6L + 2s 600.0 ¢ to 654.5 ¢
9-mosstep Minor 9-mosstep m9ms 6L + 3s 654.5 ¢ to 675.0 ¢
Major 9-mosstep M9ms 7L + 2s 675.0 ¢ to 763.6 ¢
10-mosstep Minor 10-mosstep m10ms 6L + 4s 654.5 ¢ to 750.0 ¢
Major 10-mosstep M10ms 7L + 3s 750.0 ¢ to 763.6 ¢
11-mosstep Minor 11-mosstep m11ms 7L + 4s 763.6 ¢ to 825.0 ¢
Major 11-mosstep M11ms 8L + 3s 825.0 ¢ to 872.7 ¢
12-mosstep Minor 12-mosstep m12ms 8L + 4s 872.7 ¢ to 900.0 ¢
Major 12-mosstep M12ms 9L + 3s 900.0 ¢ to 981.8 ¢
13-mosstep Diminished 13-mosstep d13ms 8L + 5s 872.7 ¢ to 975.0 ¢
Perfect 13-mosstep P13ms 9L + 4s 975.0 ¢ to 981.8 ¢
14-mosstep Minor 14-mosstep m14ms 9L + 5s 981.8 ¢ to 1050.0 ¢
Major 14-mosstep M14ms 10L + 4s 1050.0 ¢ to 1090.9 ¢
15-mosstep Minor 15-mosstep m15ms 10L + 5s 1090.9 ¢ to 1125.0 ¢
Major 15-mosstep M15ms 11L + 4s 1125.0 ¢ to 1200.0 ¢
16-mosstep Perfect 16-mosstep P16ms 11L + 5s 1200.0 ¢

Generator chain

Generator chain of 11L 5s
Bright gens Scale degree Abbrev.
26 Augmented 2-mosdegree A2md
25 Augmented 5-mosdegree A5md
24 Augmented 8-mosdegree A8md
23 Augmented 11-mosdegree A11md
22 Augmented 14-mosdegree A14md
21 Augmented 1-mosdegree A1md
20 Augmented 4-mosdegree A4md
19 Augmented 7-mosdegree A7md
18 Augmented 10-mosdegree A10md
17 Augmented 13-mosdegree A13md
16 Augmented 0-mosdegree A0md
15 Augmented 3-mosdegree A3md
14 Major 6-mosdegree M6md
13 Major 9-mosdegree M9md
12 Major 12-mosdegree M12md
11 Major 15-mosdegree M15md
10 Major 2-mosdegree M2md
9 Major 5-mosdegree M5md
8 Major 8-mosdegree M8md
7 Major 11-mosdegree M11md
6 Major 14-mosdegree M14md
5 Major 1-mosdegree M1md
4 Major 4-mosdegree M4md
3 Major 7-mosdegree M7md
2 Major 10-mosdegree M10md
1 Perfect 13-mosdegree P13md
0 Perfect 0-mosdegree
Perfect 16-mosdegree		 P0md
P16md
−1 Perfect 3-mosdegree P3md
−2 Minor 6-mosdegree m6md
−3 Minor 9-mosdegree m9md
−4 Minor 12-mosdegree m12md
−5 Minor 15-mosdegree m15md
−6 Minor 2-mosdegree m2md
−7 Minor 5-mosdegree m5md
−8 Minor 8-mosdegree m8md
−9 Minor 11-mosdegree m11md
−10 Minor 14-mosdegree m14md
−11 Minor 1-mosdegree m1md
−12 Minor 4-mosdegree m4md
−13 Minor 7-mosdegree m7md
−14 Minor 10-mosdegree m10md
−15 Diminished 13-mosdegree d13md
−16 Diminished 16-mosdegree d16md
−17 Diminished 3-mosdegree d3md
−18 Diminished 6-mosdegree d6md
−19 Diminished 9-mosdegree d9md
−20 Diminished 12-mosdegree d12md
−21 Diminished 15-mosdegree d15md
−22 Diminished 2-mosdegree d2md
−23 Diminished 5-mosdegree d5md
−24 Diminished 8-mosdegree d8md
−25 Diminished 11-mosdegree d11md
−26 Diminished 14-mosdegree d14md

Modes

Scale degrees of the modes of 11L 5s
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 LLLsLLsLLsLLsLLs Perf. Maj. Maj. Aug. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Perf.
14|1 14 LLsLLLsLLsLLsLLs Perf. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Perf.
13|2 11 LLsLLsLLLsLLsLLs Perf. Maj. Maj. Perf. Maj. Maj. Min. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Perf.
12|3 8 LLsLLsLLsLLLsLLs Perf. Maj. Maj. Perf. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Maj. Perf. Maj. Maj. Perf.
11|4 5 LLsLLsLLsLLsLLLs Perf. Maj. Maj. Perf. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Min. Perf. Maj. Maj. Perf.
10|5 2 LLsLLsLLsLLsLLsL Perf. Maj. Maj. Perf. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Min. Perf. Maj. Min. Perf.
9|6 15 LsLLLsLLsLLsLLsL Perf. Maj. Min. Perf. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Min. Perf. Maj. Min. Perf.
8|7 12 LsLLsLLLsLLsLLsL Perf. Maj. Min. Perf. Maj. Min. Min. Maj. Maj. Min. Maj. Maj. Min. Perf. Maj. Min. Perf.
7|8 9 LsLLsLLsLLLsLLsL Perf. Maj. Min. Perf. Maj. Min. Min. Maj. Min. Min. Maj. Maj. Min. Perf. Maj. Min. Perf.
6|9 6 LsLLsLLsLLsLLLsL Perf. Maj. Min. Perf. Maj. Min. Min. Maj. Min. Min. Maj. Min. Min. Perf. Maj. Min. Perf.
5|10 3 LsLLsLLsLLsLLsLL Perf. Maj. Min. Perf. Maj. Min. Min. Maj. Min. Min. Maj. Min. Min. Perf. Min. Min. Perf.
4|11 16 sLLLsLLsLLsLLsLL Perf. Min. Min. Perf. Maj. Min. Min. Maj. Min. Min. Maj. Min. Min. Perf. Min. Min. Perf.
3|12 13 sLLsLLLsLLsLLsLL Perf. Min. Min. Perf. Min. Min. Min. Maj. Min. Min. Maj. Min. Min. Perf. Min. Min. Perf.
2|13 10 sLLsLLsLLLsLLsLL Perf. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Maj. Min. Min. Perf. Min. Min. Perf.
1|14 7 sLLsLLsLLsLLLsLL Perf. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Perf.
0|15 4 sLLsLLsLLsLLsLLL Perf. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Dim. Min. Min. Perf.

Scale tree

Scale tree and tuning spectrum of 11L 5s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
13\16 975.000 225.000 1:1 1.000 Equalized 11L 5s
74\91 975.824 224.176 6:5 1.200
61\75 976.000 224.000 5:4 1.250
109\134 976.119 223.881 9:7 1.286
48\59 976.271 223.729 4:3 1.333 Supersoft 11L 5s
131\161 976.398 223.602 11:8 1.375
83\102 976.471 223.529 7:5 1.400
118\145 976.552 223.448 10:7 1.429
35\43 976.744 223.256 3:2 1.500 Soft 11L 5s
Kumonga
127\156 976.923 223.077 11:7 1.571
92\113 976.991 223.009 8:5 1.600
149\183 977.049 222.951 13:8 1.625
57\70 977.143 222.857 5:3 1.667 Semisoft 11L 5s
136\167 977.246 222.754 12:7 1.714
79\97 977.320 222.680 7:4 1.750
101\124 977.419 222.581 9:5 1.800
22\27 977.778 222.222 2:1 2.000 Basic 11L 5s
Scales with tunings softer than this are proper
97\119 978.151 221.849 9:4 2.250
75\92 978.261 221.739 7:3 2.333
128\157 978.344 221.656 12:5 2.400
53\65 978.462 221.538 5:2 2.500 Semihard 11L 5s
Fortune
137\168 978.571 221.429 13:5 2.600
84\103 978.641 221.359 8:3 2.667
115\141 978.723 221.277 11:4 2.750
31\38 978.947 221.053 3:1 3.000 Hard 11L 5s
102\125 979.200 220.800 10:3 3.333
71\87 979.310 220.690 7:2 3.500
111\136 979.412 220.588 11:3 3.667
40\49 979.592 220.408 4:1 4.000 Superhard 11L 5s
89\109 979.817 220.183 9:2 4.500
49\60 980.000 220.000 5:1 5.000
58\71 980.282 219.718 6:1 6.000
9\11 981.818 218.182 1:0 → ∞ Collapsed 11L 5s
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