5L 9s

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↖ 4L 8s ↑ 5L 8s 6L 8s ↗
← 4L 9s 5L 9s 6L 9s →
↙ 4L 10s ↓ 5L 10s 6L 10s ↘ 
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Scale structure
Step pattern LsLssLssLssLss
ssLssLssLssLsL
Equave 2/1 (1200.0¢)
Period 2/1 (1200.0¢)
Generator size
Bright 11\14 to 4\5 (942.9¢ to 960.0¢)
Dark 1\5 to 3\14 (240.0¢ to 257.1¢)
TAMNAMS information
Descends from 5L 4s
Ancestor's step ratio range 2:1 to 1:0 (hard-of-basic)
Related MOS scales
Parent 5L 4s
Sister 9L 5s
Daughters 14L 5s, 5L 14s
Neutralized 10L 4s
2-Flought 19L 9s, 5L 23s
Equal tunings
Equalized (L:s = 1:1) 11\14 (942.9¢)
Supersoft (L:s = 4:3) 37\47 (944.7¢)
Soft (L:s = 3:2) 26\33 (945.5¢)
Semisoft (L:s = 5:3) 41\52 (946.2¢)
Basic (L:s = 2:1) 15\19 (947.4¢)
Semihard (L:s = 5:2) 34\43 (948.8¢)
Hard (L:s = 3:1) 19\24 (950.0¢)
Superhard (L:s = 4:1) 23\29 (951.7¢)
Collapsed (L:s = 1:0) 4\5 (960.0¢)

5L 9s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 5 large steps and 9 small steps, repeating every octave. 5L 9s is a child scale of 5L 4s, expanding it by 5 tones. Generators that produce this scale range from 942.9 ¢ to 960 ¢, or from 240 ¢ to 257.1 ¢.

The associated fifth ranges from 8\14 to 3\5, thus guaranteeing a diatonic fifth.

4/3 being approximated by +2 generators, the generator is called a semi-fourth. The most salient feature of the semi-fourth interval is that it is an ambiguous 8/7~7/6, or an approximate 15/13 if the scale is viewed as involving factors of 13.

This MOS can be viewed as two parallel diatonic scales separated by a semi-fourth, and has analogous points of low harmonic entropy where two generators would approximate a meantone or superpyth 5th, plus an additional one between 15/13 & sqrt(4/3) where it is ideal for barbados subgroup harmonies.

Modes

Modes of 5L 9s
UDP Cyclic
order		 Step
pattern
13|0 1 LsLssLssLssLss
12|1 12 LssLsLssLssLss
11|2 9 LssLssLsLssLss
10|3 6 LssLssLssLsLss
9|4 3 LssLssLssLssLs
8|5 14 sLsLssLssLssLs
7|6 11 sLssLsLssLssLs
6|7 8 sLssLssLsLssLs
5|8 5 sLssLssLssLsLs
4|9 2 sLssLssLssLssL
3|10 13 ssLsLssLssLssL
2|11 10 ssLssLsLssLssL
1|12 7 ssLssLssLsLssL
0|13 4 ssLssLssLssLsL

Intervals

Intervals of 5L 9s
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 240.0 ¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0 ¢ to 171.4 ¢
Major 2-mosstep M2ms L + s 171.4 ¢ to 240.0 ¢
3-mosstep Perfect 3-mosstep P3ms L + 2s 240.0 ¢ to 257.1 ¢
Augmented 3-mosstep A3ms 2L + s 257.1 ¢ to 480.0 ¢
4-mosstep Minor 4-mosstep m4ms L + 3s 240.0 ¢ to 342.9 ¢
Major 4-mosstep M4ms 2L + 2s 342.9 ¢ to 480.0 ¢
5-mosstep Minor 5-mosstep m5ms L + 4s 240.0 ¢ to 428.6 ¢
Major 5-mosstep M5ms 2L + 3s 428.6 ¢ to 480.0 ¢
6-mosstep Minor 6-mosstep m6ms 2L + 4s 480.0 ¢ to 514.3 ¢
Major 6-mosstep M6ms 3L + 3s 514.3 ¢ to 720.0 ¢
7-mosstep Minor 7-mosstep m7ms 2L + 5s 480.0 ¢ to 600.0 ¢
Major 7-mosstep M7ms 3L + 4s 600.0 ¢ to 720.0 ¢
8-mosstep Minor 8-mosstep m8ms 2L + 6s 480.0 ¢ to 685.7 ¢
Major 8-mosstep M8ms 3L + 5s 685.7 ¢ to 720.0 ¢
9-mosstep Minor 9-mosstep m9ms 3L + 6s 720.0 ¢ to 771.4 ¢
Major 9-mosstep M9ms 4L + 5s 771.4 ¢ to 960.0 ¢
10-mosstep Minor 10-mosstep m10ms 3L + 7s 720.0 ¢ to 857.1 ¢
Major 10-mosstep M10ms 4L + 6s 857.1 ¢ to 960.0 ¢
11-mosstep Diminished 11-mosstep d11ms 3L + 8s 720.0 ¢ to 942.9 ¢
Perfect 11-mosstep P11ms 4L + 7s 942.9 ¢ to 960.0 ¢
12-mosstep Minor 12-mosstep m12ms 4L + 8s 960.0 ¢ to 1028.6 ¢
Major 12-mosstep M12ms 5L + 7s 1028.6 ¢ to 1200.0 ¢
13-mosstep Minor 13-mosstep m13ms 4L + 9s 960.0 ¢ to 1114.3 ¢
Major 13-mosstep M13ms 5L + 8s 1114.3 ¢ to 1200.0 ¢
14-mosstep Perfect 14-mosstep P14ms 5L + 9s 1200.0¢

Scale tree

Scale tree and tuning spectrum of 5L 9s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
11\14 942.857 257.143 1:1 1.000 Equalized 5L 9s
59\75 944.000 256.000 6:5 1.200
48\61 944.262 255.738 5:4 1.250
85\108 944.444 255.556 9:7 1.286
37\47 944.681 255.319 4:3 1.333 Supersoft 5L 9s
100\127 944.882 255.118 11:8 1.375
63\80 945.000 255.000 7:5 1.400
89\113 945.133 254.867 10:7 1.429
26\33 945.455 254.545 3:2 1.500 Soft 5L 9s
93\118 945.763 254.237 11:7 1.571
67\85 945.882 254.118 8:5 1.600
108\137 945.985 254.015 13:8 1.625
41\52 946.154 253.846 5:3 1.667 Semisoft 5L 9s
97\123 946.341 253.659 12:7 1.714
56\71 946.479 253.521 7:4 1.750
71\90 946.667 253.333 9:5 1.800
15\19 947.368 252.632 2:1 2.000 Basic 5L 9s
Scales with tunings softer than this are proper
64\81 948.148 251.852 9:4 2.250
49\62 948.387 251.613 7:3 2.333
83\105 948.571 251.429 12:5 2.400
34\43 948.837 251.163 5:2 2.500 Semihard 5L 9s
87\110 949.091 250.909 13:5 2.600
53\67 949.254 250.746 8:3 2.667
72\91 949.451 250.549 11:4 2.750
19\24 950.000 250.000 3:1 3.000 Hard 5L 9s
61\77 950.649 249.351 10:3 3.333
42\53 950.943 249.057 7:2 3.500
65\82 951.220 248.780 11:3 3.667
23\29 951.724 248.276 4:1 4.000 Superhard 5L 9s
50\63 952.381 247.619 9:2 4.500
27\34 952.941 247.059 5:1 5.000
31\39 953.846 246.154 6:1 6.000
4\5 960.000 240.000 1:0 → ∞ Collapsed 5L 9s
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