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7L 11s

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7L 11s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 7 large steps and 11 small steps, repeating every octave. 7L 11s is a grandchild scale of 4L 3s, expanding it by 11 tones. Generators that produce this scale range from 333.3 ¢ to 342.9 ¢, or from 857.1 ¢ to 866.7 ¢.

↖ 6L 10s ↑ 7L 10s 8L 10s ↗
← 6L 11s 7L 11s 8L 11s →
↙ 6L 12s ↓ 7L 12s 8L 12s ↘
Scale structure
Step pattern LsLssLsLssLsLssLss
ssLssLsLssLsLssLsL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 5\18 to 2\7 (333.3 ¢ to 342.9 ¢)
Dark 5\7 to 13\18 (857.1 ¢ to 866.7 ¢)
TAMNAMS information
Related to 4L 3s (smitonic)
With tunings 1:1 to 3:2 (soft)
Related MOS scales
Parent 7L 4s
Sister 11L 7s
Daughters 18L 7s, 7L 18s
Neutralized 14L 4s
2-Flought 25L 11s, 7L 29s
Equal tunings
Equalized (L:s = 1:1) 5\18 (333.3 ¢)
Supersoft (L:s = 4:3) 17\61 (334.4 ¢)
Soft (L:s = 3:2) 12\43 (334.9 ¢)
Semisoft (L:s = 5:3) 19\68 (335.3 ¢)
Basic (L:s = 2:1) 7\25 (336.0 ¢)
Semihard (L:s = 5:2) 16\57 (336.8 ¢)
Hard (L:s = 3:1) 9\32 (337.5 ¢)
Superhard (L:s = 4:1) 11\39 (338.5 ¢)
Collapsed (L:s = 1:0) 2\7 (342.9 ¢)
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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 7L 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 66.7 ¢
Major 1-mosstep M1ms L 66.7 ¢ to 171.4 ¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0 ¢ to 133.3 ¢
Major 2-mosstep M2ms L + s 133.3 ¢ to 171.4 ¢
3-mosstep Minor 3-mosstep m3ms L + 2s 171.4 ¢ to 200.0 ¢
Major 3-mosstep M3ms 2L + s 200.0 ¢ to 342.9 ¢
4-mosstep Minor 4-mosstep m4ms L + 3s 171.4 ¢ to 266.7 ¢
Major 4-mosstep M4ms 2L + 2s 266.7 ¢ to 342.9 ¢
5-mosstep Diminished 5-mosstep d5ms L + 4s 171.4 ¢ to 333.3 ¢
Perfect 5-mosstep P5ms 2L + 3s 333.3 ¢ to 342.9 ¢
6-mosstep Minor 6-mosstep m6ms 2L + 4s 342.9 ¢ to 400.0 ¢
Major 6-mosstep M6ms 3L + 3s 400.0 ¢ to 514.3 ¢
7-mosstep Minor 7-mosstep m7ms 2L + 5s 342.9 ¢ to 466.7 ¢
Major 7-mosstep M7ms 3L + 4s 466.7 ¢ to 514.3 ¢
8-mosstep Minor 8-mosstep m8ms 3L + 5s 514.3 ¢ to 533.3 ¢
Major 8-mosstep M8ms 4L + 4s 533.3 ¢ to 685.7 ¢
9-mosstep Minor 9-mosstep m9ms 3L + 6s 514.3 ¢ to 600.0 ¢
Major 9-mosstep M9ms 4L + 5s 600.0 ¢ to 685.7 ¢
10-mosstep Minor 10-mosstep m10ms 3L + 7s 514.3 ¢ to 666.7 ¢
Major 10-mosstep M10ms 4L + 6s 666.7 ¢ to 685.7 ¢
11-mosstep Minor 11-mosstep m11ms 4L + 7s 685.7 ¢ to 733.3 ¢
Major 11-mosstep M11ms 5L + 6s 733.3 ¢ to 857.1 ¢
12-mosstep Minor 12-mosstep m12ms 4L + 8s 685.7 ¢ to 800.0 ¢
Major 12-mosstep M12ms 5L + 7s 800.0 ¢ to 857.1 ¢
13-mosstep Perfect 13-mosstep P13ms 5L + 8s 857.1 ¢ to 866.7 ¢
Augmented 13-mosstep A13ms 6L + 7s 866.7 ¢ to 1028.6 ¢
14-mosstep Minor 14-mosstep m14ms 5L + 9s 857.1 ¢ to 933.3 ¢
Major 14-mosstep M14ms 6L + 8s 933.3 ¢ to 1028.6 ¢
15-mosstep Minor 15-mosstep m15ms 5L + 10s 857.1 ¢ to 1000.0 ¢
Major 15-mosstep M15ms 6L + 9s 1000.0 ¢ to 1028.6 ¢
16-mosstep Minor 16-mosstep m16ms 6L + 10s 1028.6 ¢ to 1066.7 ¢
Major 16-mosstep M16ms 7L + 9s 1066.7 ¢ to 1200.0 ¢
17-mosstep Minor 17-mosstep m17ms 6L + 11s 1028.6 ¢ to 1133.3 ¢
Major 17-mosstep M17ms 7L + 10s 1133.3 ¢ to 1200.0 ¢
18-mosstep Perfect 18-mosstep P18ms 7L + 11s 1200.0 ¢

Generator chain

Generator chain of 7L 11s
Bright gens Scale degree Abbrev.
24 Augmented 12-mosdegree A12md
23 Augmented 7-mosdegree A7md
22 Augmented 2-mosdegree A2md
21 Augmented 15-mosdegree A15md
20 Augmented 10-mosdegree A10md
19 Augmented 5-mosdegree A5md
18 Augmented 0-mosdegree A0md
17 Augmented 13-mosdegree A13md
16 Major 8-mosdegree M8md
15 Major 3-mosdegree M3md
14 Major 16-mosdegree M16md
13 Major 11-mosdegree M11md
12 Major 6-mosdegree M6md
11 Major 1-mosdegree M1md
10 Major 14-mosdegree M14md
9 Major 9-mosdegree M9md
8 Major 4-mosdegree M4md
7 Major 17-mosdegree M17md
6 Major 12-mosdegree M12md
5 Major 7-mosdegree M7md
4 Major 2-mosdegree M2md
3 Major 15-mosdegree M15md
2 Major 10-mosdegree M10md
1 Perfect 5-mosdegree P5md
0 Perfect 0-mosdegree
Perfect 18-mosdegree		 P0md
P18md
−1 Perfect 13-mosdegree P13md
−2 Minor 8-mosdegree m8md
−3 Minor 3-mosdegree m3md
−4 Minor 16-mosdegree m16md
−5 Minor 11-mosdegree m11md
−6 Minor 6-mosdegree m6md
−7 Minor 1-mosdegree m1md
−8 Minor 14-mosdegree m14md
−9 Minor 9-mosdegree m9md
−10 Minor 4-mosdegree m4md
−11 Minor 17-mosdegree m17md
−12 Minor 12-mosdegree m12md
−13 Minor 7-mosdegree m7md
−14 Minor 2-mosdegree m2md
−15 Minor 15-mosdegree m15md
−16 Minor 10-mosdegree m10md
−17 Diminished 5-mosdegree d5md
−18 Diminished 18-mosdegree d18md
−19 Diminished 13-mosdegree d13md
−20 Diminished 8-mosdegree d8md
−21 Diminished 3-mosdegree d3md
−22 Diminished 16-mosdegree d16md
−23 Diminished 11-mosdegree d11md
−24 Diminished 6-mosdegree d6md

Modes

Scale degrees of the modes of 7L 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 17 18
17|0 1 LsLssLsLssLsLssLss Perf. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Aug. Maj. Maj. Maj. Maj. Perf.
16|1 6 LsLssLsLssLssLsLss Perf. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Perf.
15|2 11 LsLssLssLsLssLsLss Perf. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Min. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Perf.
14|3 16 LssLsLssLsLssLsLss Perf. Maj. Maj. Min. Maj. Perf. Maj. Maj. Min. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Perf.
13|4 3 LssLsLssLsLssLssLs Perf. Maj. Maj. Min. Maj. Perf. Maj. Maj. Min. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Min. Maj. Perf.
12|5 8 LssLsLssLssLsLssLs Perf. Maj. Maj. Min. Maj. Perf. Maj. Maj. Min. Maj. Maj. Min. Maj. Perf. Maj. Maj. Min. Maj. Perf.
11|6 13 LssLssLsLssLsLssLs Perf. Maj. Maj. Min. Maj. Perf. Min. Maj. Min. Maj. Maj. Min. Maj. Perf. Maj. Maj. Min. Maj. Perf.
10|7 18 sLsLssLsLssLsLssLs Perf. Min. Maj. Min. Maj. Perf. Min. Maj. Min. Maj. Maj. Min. Maj. Perf. Maj. Maj. Min. Maj. Perf.
9|8 5 sLsLssLsLssLssLsLs Perf. Min. Maj. Min. Maj. Perf. Min. Maj. Min. Maj. Maj. Min. Maj. Perf. Min. Maj. Min. Maj. Perf.
8|9 10 sLsLssLssLsLssLsLs Perf. Min. Maj. Min. Maj. Perf. Min. Maj. Min. Min. Maj. Min. Maj. Perf. Min. Maj. Min. Maj. Perf.
7|10 15 sLssLsLssLsLssLsLs Perf. Min. Maj. Min. Min. Perf. Min. Maj. Min. Min. Maj. Min. Maj. Perf. Min. Maj. Min. Maj. Perf.
6|11 2 sLssLsLssLsLssLssL Perf. Min. Maj. Min. Min. Perf. Min. Maj. Min. Min. Maj. Min. Maj. Perf. Min. Maj. Min. Min. Perf.
5|12 7 sLssLsLssLssLsLssL Perf. Min. Maj. Min. Min. Perf. Min. Maj. Min. Min. Maj. Min. Min. Perf. Min. Maj. Min. Min. Perf.
4|13 12 sLssLssLsLssLsLssL Perf. Min. Maj. Min. Min. Perf. Min. Min. Min. Min. Maj. Min. Min. Perf. Min. Maj. Min. Min. Perf.
3|14 17 ssLsLssLsLssLsLssL Perf. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Maj. Min. Min. Perf. Min. Maj. Min. Min. Perf.
2|15 4 ssLsLssLsLssLssLsL Perf. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Maj. Min. Min. Perf. Min. Min. Min. Min. Perf.
1|16 9 ssLsLssLssLsLssLsL Perf. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Perf.
0|17 14 ssLssLsLssLsLssLsL Perf. Min. Min. Min. Min. Dim. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Perf.

Scale tree

Scale tree and tuning spectrum of 7L 11s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
5\18 333.333 866.667 1:1 1.000 Equalized 7L 11s
27\97 334.021 865.979 6:5 1.200
22\79 334.177 865.823 5:4 1.250
39\140 334.286 865.714 9:7 1.286
17\61 334.426 865.574 4:3 1.333 Supersoft 7L 11s
46\165 334.545 865.455 11:8 1.375
29\104 334.615 865.385 7:5 1.400
41\147 334.694 865.306 10:7 1.429
12\43 334.884 865.116 3:2 1.500 Soft 7L 11s
43\154 335.065 864.935 11:7 1.571
31\111 335.135 864.865 8:5 1.600
50\179 335.196 864.804 13:8 1.625
19\68 335.294 864.706 5:3 1.667 Semisoft 7L 11s
45\161 335.404 864.596 12:7 1.714
26\93 335.484 864.516 7:4 1.750
33\118 335.593 864.407 9:5 1.800
7\25 336.000 864.000 2:1 2.000 Basic 7L 11s
Scales with tunings softer than this are proper
30\107 336.449 863.551 9:4 2.250
23\82 336.585 863.415 7:3 2.333
39\139 336.691 863.309 12:5 2.400
16\57 336.842 863.158 5:2 2.500 Semihard 7L 11s
41\146 336.986 863.014 13:5 2.600
25\89 337.079 862.921 8:3 2.667
34\121 337.190 862.810 11:4 2.750
9\32 337.500 862.500 3:1 3.000 Hard 7L 11s
29\103 337.864 862.136 10:3 3.333
20\71 338.028 861.972 7:2 3.500
31\110 338.182 861.818 11:3 3.667
11\39 338.462 861.538 4:1 4.000 Superhard 7L 11s
24\85 338.824 861.176 9:2 4.500
13\46 339.130 860.870 5:1 5.000
15\53 339.623 860.377 6:1 6.000
2\7 342.857 857.143 1:0 → ∞ Collapsed 7L 11s
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