8L 11s

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↖ 7L 10s ↑ 8L 10s 9L 10s ↗
← 7L 11s 8L 11s 9L 11s →
↙ 7L 12s ↓ 8L 12s 9L 12s ↘ 
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Scale structure
Step pattern LsLsLssLsLsLssLsLss
ssLsLssLsLsLssLsLsL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 7\19 to 3\8 (442.1 ¢ to 450.0 ¢)
Dark 5\8 to 12\19 (750.0 ¢ to 757.9 ¢)
TAMNAMS information
Descends from 3L 5s (checkertonic)
Ancestor's step ratio range 1:1 to 3:2 (soft)
Related MOS scales
Parent 8L 3s
Sister 11L 8s
Daughters 19L 8s, 8L 19s
Neutralized 16L 3s
2-Flought 27L 11s, 8L 30s
Equal tunings
Equalized (L:s = 1:1) 7\19 (442.1 ¢)
Supersoft (L:s = 4:3) 24\65 (443.1 ¢)
Soft (L:s = 3:2) 17\46 (443.5 ¢)
Semisoft (L:s = 5:3) 27\73 (443.8 ¢)
Basic (L:s = 2:1) 10\27 (444.4 ¢)
Semihard (L:s = 5:2) 23\62 (445.2 ¢)
Hard (L:s = 3:1) 13\35 (445.7 ¢)
Superhard (L:s = 4:1) 16\43 (446.5 ¢)
Collapsed (L:s = 1:0) 3\8 (450.0 ¢)

8L 11s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 8 large steps and 11 small steps, repeating every octave. 8L 11s is a grandchild scale of 3L 5s, expanding it by 11 tones. Generators that produce this scale range from 442.1 ¢ to 450 ¢, or from 750 ¢ to 757.9 ¢.

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

The intervals of 8L 11s are named after the number of mossteps (L and s) they subtend. Each interval, apart from the root and octave (perfect 0-mosstep and perfect 19-mosstep), has two varieties, or sizes, each. Interval varieties are named major and minor for the large and small sizes, respectively, and augmented, perfect, and diminished for the scale's generators.

Intervals of 8L 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 63.2 ¢
Major 1-mosstep M1ms L 63.2 ¢ to 150.0 ¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0 ¢ to 126.3 ¢
Major 2-mosstep M2ms L + s 126.3 ¢ to 150.0 ¢
3-mosstep Minor 3-mosstep m3ms L + 2s 150.0 ¢ to 189.5 ¢
Major 3-mosstep M3ms 2L + s 189.5 ¢ to 300.0 ¢
4-mosstep Minor 4-mosstep m4ms L + 3s 150.0 ¢ to 252.6 ¢
Major 4-mosstep M4ms 2L + 2s 252.6 ¢ to 300.0 ¢
5-mosstep Minor 5-mosstep m5ms 2L + 3s 300.0 ¢ to 315.8 ¢
Major 5-mosstep M5ms 3L + 2s 315.8 ¢ to 450.0 ¢
6-mosstep Minor 6-mosstep m6ms 2L + 4s 300.0 ¢ to 378.9 ¢
Major 6-mosstep M6ms 3L + 3s 378.9 ¢ to 450.0 ¢
7-mosstep Diminished 7-mosstep d7ms 2L + 5s 300.0 ¢ to 442.1 ¢
Perfect 7-mosstep P7ms 3L + 4s 442.1 ¢ to 450.0 ¢
8-mosstep Minor 8-mosstep m8ms 3L + 5s 450.0 ¢ to 505.3 ¢
Major 8-mosstep M8ms 4L + 4s 505.3 ¢ to 600.0 ¢
9-mosstep Minor 9-mosstep m9ms 3L + 6s 450.0 ¢ to 568.4 ¢
Major 9-mosstep M9ms 4L + 5s 568.4 ¢ to 600.0 ¢
10-mosstep Minor 10-mosstep m10ms 4L + 6s 600.0 ¢ to 631.6 ¢
Major 10-mosstep M10ms 5L + 5s 631.6 ¢ to 750.0 ¢
11-mosstep Minor 11-mosstep m11ms 4L + 7s 600.0 ¢ to 694.7 ¢
Major 11-mosstep M11ms 5L + 6s 694.7 ¢ to 750.0 ¢
12-mosstep Perfect 12-mosstep P12ms 5L + 7s 750.0 ¢ to 757.9 ¢
Augmented 12-mosstep A12ms 6L + 6s 757.9 ¢ to 900.0 ¢
13-mosstep Minor 13-mosstep m13ms 5L + 8s 750.0 ¢ to 821.1 ¢
Major 13-mosstep M13ms 6L + 7s 821.1 ¢ to 900.0 ¢
14-mosstep Minor 14-mosstep m14ms 5L + 9s 750.0 ¢ to 884.2 ¢
Major 14-mosstep M14ms 6L + 8s 884.2 ¢ to 900.0 ¢
15-mosstep Minor 15-mosstep m15ms 6L + 9s 900.0 ¢ to 947.4 ¢
Major 15-mosstep M15ms 7L + 8s 947.4 ¢ to 1050.0 ¢
16-mosstep Minor 16-mosstep m16ms 6L + 10s 900.0 ¢ to 1010.5 ¢
Major 16-mosstep M16ms 7L + 9s 1010.5 ¢ to 1050.0 ¢
17-mosstep Minor 17-mosstep m17ms 7L + 10s 1050.0 ¢ to 1073.7 ¢
Major 17-mosstep M17ms 8L + 9s 1073.7 ¢ to 1200.0 ¢
18-mosstep Minor 18-mosstep m18ms 7L + 11s 1050.0 ¢ to 1136.8 ¢
Major 18-mosstep M18ms 8L + 10s 1136.8 ¢ to 1200.0 ¢
19-mosstep Perfect 19-mosstep P19ms 8L + 11s 1200.0 ¢

Generator chain

A chain of bright generators, each a perfect 7-mosstep, produces the following scale degrees. A chain of 19 bright generators contains the scale degrees of one of the modes of 8L 11s. Expanding the chain to 27 scale degrees produces the modes of either 19L 8s (for soft-of-basic tunings) or 8L 19s (for hard-of-basic tunings).

Generator chain of 8L 11s
Bright gens Scale degree Abbrev.
26 Augmented 11-mosdegree A11md
25 Augmented 4-mosdegree A4md
24 Augmented 16-mosdegree A16md
23 Augmented 9-mosdegree A9md
22 Augmented 2-mosdegree A2md
21 Augmented 14-mosdegree A14md
20 Augmented 7-mosdegree A7md
19 Augmented 0-mosdegree A0md
18 Augmented 12-mosdegree A12md
17 Major 5-mosdegree M5md
16 Major 17-mosdegree M17md
15 Major 10-mosdegree M10md
14 Major 3-mosdegree M3md
13 Major 15-mosdegree M15md
12 Major 8-mosdegree M8md
11 Major 1-mosdegree M1md
10 Major 13-mosdegree M13md
9 Major 6-mosdegree M6md
8 Major 18-mosdegree M18md
7 Major 11-mosdegree M11md
6 Major 4-mosdegree M4md
5 Major 16-mosdegree M16md
4 Major 9-mosdegree M9md
3 Major 2-mosdegree M2md
2 Major 14-mosdegree M14md
1 Perfect 7-mosdegree P7md
0 Perfect 0-mosdegree
Perfect 19-mosdegree		 P0md
P19md
−1 Perfect 12-mosdegree P12md
−2 Minor 5-mosdegree m5md
−3 Minor 17-mosdegree m17md
−4 Minor 10-mosdegree m10md
−5 Minor 3-mosdegree m3md
−6 Minor 15-mosdegree m15md
−7 Minor 8-mosdegree m8md
−8 Minor 1-mosdegree m1md
−9 Minor 13-mosdegree m13md
−10 Minor 6-mosdegree m6md
−11 Minor 18-mosdegree m18md
−12 Minor 11-mosdegree m11md
−13 Minor 4-mosdegree m4md
−14 Minor 16-mosdegree m16md
−15 Minor 9-mosdegree m9md
−16 Minor 2-mosdegree m2md
−17 Minor 14-mosdegree m14md
−18 Diminished 7-mosdegree d7md
−19 Diminished 19-mosdegree d19md
−20 Diminished 12-mosdegree d12md
−21 Diminished 5-mosdegree d5md
−22 Diminished 17-mosdegree d17md
−23 Diminished 10-mosdegree d10md
−24 Diminished 3-mosdegree d3md
−25 Diminished 15-mosdegree d15md
−26 Diminished 8-mosdegree d8md

Modes

Scale degrees of the modes of 8L 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 19
18|0 1 LsLsLssLsLsLssLsLss Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Aug. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
17|1 8 LsLsLssLsLssLsLsLss Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
16|2 15 LsLssLsLsLssLsLsLss Perf. Maj. Maj. Maj. Maj. Min. Maj. Perf. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
15|3 3 LsLssLsLsLssLsLssLs Perf. Maj. Maj. Maj. Maj. Min. Maj. Perf. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Min. Maj. Perf.
14|4 10 LsLssLsLssLsLsLssLs Perf. Maj. Maj. Maj. Maj. Min. Maj. Perf. Maj. Maj. Min. Maj. Perf. Maj. Maj. Maj. Maj. Min. Maj. Perf.
13|5 17 LssLsLsLssLsLsLssLs Perf. Maj. Maj. Min. Maj. Min. Maj. Perf. Maj. Maj. Min. Maj. Perf. Maj. Maj. Maj. Maj. Min. Maj. Perf.
12|6 5 LssLsLsLssLsLssLsLs Perf. Maj. Maj. Min. Maj. Min. Maj. Perf. Maj. Maj. Min. Maj. Perf. Maj. Maj. Min. Maj. Min. Maj. Perf.
11|7 12 LssLsLssLsLsLssLsLs Perf. Maj. Maj. Min. Maj. Min. Maj. Perf. Min. Maj. Min. Maj. Perf. Maj. Maj. Min. Maj. Min. Maj. Perf.
10|8 19 sLsLsLssLsLsLssLsLs Perf. Min. Maj. Min. Maj. Min. Maj. Perf. Min. Maj. Min. Maj. Perf. Maj. Maj. Min. Maj. Min. Maj. Perf.
9|9 7 sLsLsLssLsLssLsLsLs Perf. Min. Maj. Min. Maj. Min. Maj. Perf. Min. Maj. Min. Maj. Perf. Min. Maj. Min. Maj. Min. Maj. Perf.
8|10 14 sLsLssLsLsLssLsLsLs Perf. Min. Maj. Min. Maj. Min. Min. Perf. Min. Maj. Min. Maj. Perf. Min. Maj. Min. Maj. Min. Maj. Perf.
7|11 2 sLsLssLsLsLssLsLssL Perf. Min. Maj. Min. Maj. Min. Min. Perf. Min. Maj. Min. Maj. Perf. Min. Maj. Min. Maj. Min. Min. Perf.
6|12 9 sLsLssLsLssLsLsLssL Perf. Min. Maj. Min. Maj. Min. Min. Perf. Min. Maj. Min. Min. Perf. Min. Maj. Min. Maj. Min. Min. Perf.
5|13 16 sLssLsLsLssLsLsLssL Perf. Min. Maj. Min. Min. Min. Min. Perf. Min. Maj. Min. Min. Perf. Min. Maj. Min. Maj. Min. Min. Perf.
4|14 4 sLssLsLsLssLsLssLsL Perf. Min. Maj. Min. Min. Min. Min. Perf. Min. Maj. Min. Min. Perf. Min. Maj. Min. Min. Min. Min. Perf.
3|15 11 sLssLsLssLsLsLssLsL Perf. Min. Maj. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Perf. Min. Maj. Min. Min. Min. Min. Perf.
2|16 18 ssLsLsLssLsLsLssLsL Perf. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Perf. Min. Maj. Min. Min. Min. Min. Perf.
1|17 6 ssLsLsLssLsLssLsLsL Perf. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Perf.
0|18 13 ssLsLssLsLsLssLsLsL Perf. Min. Min. Min. Min. Min. Min. Dim. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Perf.

Scale tree

Scale tree and tuning spectrum of 8L 11s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
7\19 442.105 757.895 1:1 1.000 Equalized 8L 11s
38\103 442.718 757.282 6:5 1.200
31\84 442.857 757.143 5:4 1.250
55\149 442.953 757.047 9:7 1.286
24\65 443.077 756.923 4:3 1.333 Supersoft 8L 11s
65\176 443.182 756.818 11:8 1.375
41\111 443.243 756.757 7:5 1.400
58\157 443.312 756.688 10:7 1.429
17\46 443.478 756.522 3:2 1.500 Soft 8L 11s
61\165 443.636 756.364 11:7 1.571
44\119 443.697 756.303 8:5 1.600
71\192 443.750 756.250 13:8 1.625
27\73 443.836 756.164 5:3 1.667 Semisoft 8L 11s
64\173 443.931 756.069 12:7 1.714
37\100 444.000 756.000 7:4 1.750
47\127 444.094 755.906 9:5 1.800
10\27 444.444 755.556 2:1 2.000 Basic 8L 11s
Scales with tunings softer than this are proper
43\116 444.828 755.172 9:4 2.250
33\89 444.944 755.056 7:3 2.333
56\151 445.033 754.967 12:5 2.400
23\62 445.161 754.839 5:2 2.500 Semihard 8L 11s
59\159 445.283 754.717 13:5 2.600
36\97 445.361 754.639 8:3 2.667
49\132 445.455 754.545 11:4 2.750
13\35 445.714 754.286 3:1 3.000 Hard 8L 11s
42\113 446.018 753.982 10:3 3.333
29\78 446.154 753.846 7:2 3.500
45\121 446.281 753.719 11:3 3.667
16\43 446.512 753.488 4:1 4.000 Superhard 8L 11s
35\94 446.809 753.191 9:2 4.500
19\51 447.059 752.941 5:1 5.000
22\59 447.458 752.542 6:1 6.000
3\8 450.000 750.000 1:0 → ∞ Collapsed 8L 11s
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