3L 11s

From Xenharmonic Wiki
Jump to navigation Jump to search
↖ 2L 10s ↑ 3L 10s 4L 10s ↗
← 2L 11s 3L 11s 4L 11s →
↙ 2L 12s ↓ 3L 12s 4L 12s ↘ 
┌╥┬┬┬╥┬┬┬┬╥┬┬┬┬┐
│║│││║││││║│││││
││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LsssLssssLssss
ssssLssssLsssL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 9\14 to 2\3 (771.4 ¢ to 800.0 ¢)
Dark 1\3 to 5\14 (400.0 ¢ to 428.6 ¢)
TAMNAMS information
Descends from 3L 5s (checkertonic)
Ancestor's step ratio range 3:1 to 1:0 (hard)
Related MOS scales
Parent 3L 8s
Sister 11L 3s
Daughters 14L 3s, 3L 14s
Neutralized 6L 8s
2-Flought 17L 11s, 3L 25s
Equal tunings
Equalized (L:s = 1:1) 9\14 (771.4 ¢)
Supersoft (L:s = 4:3) 29\45 (773.3 ¢)
Soft (L:s = 3:2) 20\31 (774.2 ¢)
Semisoft (L:s = 5:3) 31\48 (775.0 ¢)
Basic (L:s = 2:1) 11\17 (776.5 ¢)
Semihard (L:s = 5:2) 24\37 (778.4 ¢)
Hard (L:s = 3:1) 13\20 (780.0 ¢)
Superhard (L:s = 4:1) 15\23 (782.6 ¢)
Collapsed (L:s = 1:0) 2\3 (800.0 ¢)

3L 11s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 3 large steps and 11 small steps, repeating every octave. 3L 11s is a grandchild scale of 3L 5s, expanding it by 6 tones. Generators that produce this scale range from 771.4 ¢ to 800 ¢, or from 400 ¢ to 428.6 ¢.

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 3L 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 85.7 ¢
Major 1-mosstep M1ms L 85.7 ¢ to 400.0 ¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0 ¢ to 171.4 ¢
Major 2-mosstep M2ms L + s 171.4 ¢ to 400.0 ¢
3-mosstep Minor 3-mosstep m3ms 3s 0.0 ¢ to 257.1 ¢
Major 3-mosstep M3ms L + 2s 257.1 ¢ to 400.0 ¢
4-mosstep Minor 4-mosstep m4ms 4s 0.0 ¢ to 342.9 ¢
Major 4-mosstep M4ms L + 3s 342.9 ¢ to 400.0 ¢
5-mosstep Perfect 5-mosstep P5ms L + 4s 400.0 ¢ to 428.6 ¢
Augmented 5-mosstep A5ms 2L + 3s 428.6 ¢ to 800.0 ¢
6-mosstep Minor 6-mosstep m6ms L + 5s 400.0 ¢ to 514.3 ¢
Major 6-mosstep M6ms 2L + 4s 514.3 ¢ to 800.0 ¢
7-mosstep Minor 7-mosstep m7ms L + 6s 400.0 ¢ to 600.0 ¢
Major 7-mosstep M7ms 2L + 5s 600.0 ¢ to 800.0 ¢
8-mosstep Minor 8-mosstep m8ms L + 7s 400.0 ¢ to 685.7 ¢
Major 8-mosstep M8ms 2L + 6s 685.7 ¢ to 800.0 ¢
9-mosstep Diminished 9-mosstep d9ms L + 8s 400.0 ¢ to 771.4 ¢
Perfect 9-mosstep P9ms 2L + 7s 771.4 ¢ to 800.0 ¢
10-mosstep Minor 10-mosstep m10ms 2L + 8s 800.0 ¢ to 857.1 ¢
Major 10-mosstep M10ms 3L + 7s 857.1 ¢ to 1200.0 ¢
11-mosstep Minor 11-mosstep m11ms 2L + 9s 800.0 ¢ to 942.9 ¢
Major 11-mosstep M11ms 3L + 8s 942.9 ¢ to 1200.0 ¢
12-mosstep Minor 12-mosstep m12ms 2L + 10s 800.0 ¢ to 1028.6 ¢
Major 12-mosstep M12ms 3L + 9s 1028.6 ¢ to 1200.0 ¢
13-mosstep Minor 13-mosstep m13ms 2L + 11s 800.0 ¢ to 1114.3 ¢
Major 13-mosstep M13ms 3L + 10s 1114.3 ¢ to 1200.0 ¢
14-mosstep Perfect 14-mosstep P14ms 3L + 11s 1200.0 ¢

Generator chain

Generator chain of 3L 11s
Bright gens Scale degree Abbrev.
16 Augmented 4-mosdegree A4md
15 Augmented 9-mosdegree A9md
14 Augmented 0-mosdegree A0md
13 Augmented 5-mosdegree A5md
12 Major 10-mosdegree M10md
11 Major 1-mosdegree M1md
10 Major 6-mosdegree M6md
9 Major 11-mosdegree M11md
8 Major 2-mosdegree M2md
7 Major 7-mosdegree M7md
6 Major 12-mosdegree M12md
5 Major 3-mosdegree M3md
4 Major 8-mosdegree M8md
3 Major 13-mosdegree M13md
2 Major 4-mosdegree M4md
1 Perfect 9-mosdegree P9md
0 Perfect 0-mosdegree
Perfect 14-mosdegree		 P0md
P14md
−1 Perfect 5-mosdegree P5md
−2 Minor 10-mosdegree m10md
−3 Minor 1-mosdegree m1md
−4 Minor 6-mosdegree m6md
−5 Minor 11-mosdegree m11md
−6 Minor 2-mosdegree m2md
−7 Minor 7-mosdegree m7md
−8 Minor 12-mosdegree m12md
−9 Minor 3-mosdegree m3md
−10 Minor 8-mosdegree m8md
−11 Minor 13-mosdegree m13md
−12 Minor 4-mosdegree m4md
−13 Diminished 9-mosdegree d9md
−14 Diminished 14-mosdegree d14md
−15 Diminished 5-mosdegree d5md
−16 Diminished 10-mosdegree d10md

Modes

Scale degrees of the modes of 3L 11s
UDP Cyclic
order		 Step
pattern		 Scale degree (mosdegree)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
13|0 1 LsssLssssLssss Perf. Maj. Maj. Maj. Maj. Aug. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Perf.
12|1 10 LssssLsssLssss Perf. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Perf.
11|2 5 LssssLssssLsss Perf. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Perf. Min. Maj. Maj. Maj. Perf.
10|3 14 sLsssLssssLsss Perf. Min. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Perf. Min. Maj. Maj. Maj. Perf.
9|4 9 sLssssLsssLsss Perf. Min. Maj. Maj. Maj. Perf. Min. Maj. Maj. Perf. Min. Maj. Maj. Maj. Perf.
8|5 4 sLssssLssssLss Perf. Min. Maj. Maj. Maj. Perf. Min. Maj. Maj. Perf. Min. Min. Maj. Maj. Perf.
7|6 13 ssLsssLssssLss Perf. Min. Min. Maj. Maj. Perf. Min. Maj. Maj. Perf. Min. Min. Maj. Maj. Perf.
6|7 8 ssLssssLsssLss Perf. Min. Min. Maj. Maj. Perf. Min. Min. Maj. Perf. Min. Min. Maj. Maj. Perf.
5|8 3 ssLssssLssssLs Perf. Min. Min. Maj. Maj. Perf. Min. Min. Maj. Perf. Min. Min. Min. Maj. Perf.
4|9 12 sssLsssLssssLs Perf. Min. Min. Min. Maj. Perf. Min. Min. Maj. Perf. Min. Min. Min. Maj. Perf.
3|10 7 sssLssssLsssLs Perf. Min. Min. Min. Maj. Perf. Min. Min. Min. Perf. Min. Min. Min. Maj. Perf.
2|11 2 sssLssssLssssL Perf. Min. Min. Min. Maj. Perf. Min. Min. Min. Perf. Min. Min. Min. Min. Perf.
1|12 11 ssssLsssLssssL Perf. Min. Min. Min. Min. Perf. Min. Min. Min. Perf. Min. Min. Min. Min. Perf.
0|13 6 ssssLssssLsssL Perf. Min. Min. Min. Min. Perf. Min. Min. Min. Dim. Min. Min. Min. Min. Perf.

Scale tree

Scale tree and tuning spectrum of 3L 11s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
9\14 771.429 428.571 1:1 1.000 Equalized 3L 11s
47\73 772.603 427.397 6:5 1.200
38\59 772.881 427.119 5:4 1.250
67\104 773.077 426.923 9:7 1.286
29\45 773.333 426.667 4:3 1.333 Supersoft 3L 11s
78\121 773.554 426.446 11:8 1.375
49\76 773.684 426.316 7:5 1.400
69\107 773.832 426.168 10:7 1.429
20\31 774.194 425.806 3:2 1.500 Soft 3L 11s
Squares and Sentinel are around here
71\110 774.545 425.455 11:7 1.571
51\79 774.684 425.316 8:5 1.600
82\127 774.803 425.197 13:8 1.625
31\48 775.000 425.000 5:3 1.667 Semisoft 3L 11s
73\113 775.221 424.779 12:7 1.714
42\65 775.385 424.615 7:4 1.750
53\82 775.610 424.390 9:5 1.800
11\17 776.471 423.529 2:1 2.000 Basic 3L 11s
Scales with tunings softer than this are proper
46\71 777.465 422.535 9:4 2.250
35\54 777.778 422.222 7:3 2.333
59\91 778.022 421.978 12:5 2.400
24\37 778.378 421.622 5:2 2.500 Semihard 3L 11s
61\94 778.723 421.277 13:5 2.600
37\57 778.947 421.053 8:3 2.667
50\77 779.221 420.779 11:4 2.750 Symbolic is around here
13\20 780.000 420.000 3:1 3.000 Hard 3L 11s
41\63 780.952 419.048 10:3 3.333
28\43 781.395 418.605 7:2 3.500
43\66 781.818 418.182 11:3 3.667
15\23 782.609 417.391 4:1 4.000 Superhard 3L 11s
32\49 783.673 416.327 9:2 4.500
17\26 784.615 415.385 5:1 5.000
19\29 786.207 413.793 6:1 6.000
2\3 800.000 400.000 1:0 → ∞ Collapsed 3L 11s
Icon-Stub.png This page is a stub. You can help the Xenharmonic Wiki by expanding it.
Retrieved from "https://en.xen.wiki/index.php?title=3L_11s&oldid=184102"