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
Related to 5L 4s (semiquartal)
With tunings 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 and [math]\displaystyle{ \sqrt{\frac{4}{3}} }[/math] where it is ideal for barbados subgroup harmonies.

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 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 ¢

Generator chain

Generator chain of 5L 9s
Bright gens Scale degree Abbrev.
18 Augmented 2-mosdegree A2md
17 Augmented 5-mosdegree A5md
16 Augmented 8-mosdegree A8md
15 Augmented 11-mosdegree A11md
14 Augmented 0-mosdegree A0md
13 Augmented 3-mosdegree A3md
12 Major 6-mosdegree M6md
11 Major 9-mosdegree M9md
10 Major 12-mosdegree M12md
9 Major 1-mosdegree M1md
8 Major 4-mosdegree M4md
7 Major 7-mosdegree M7md
6 Major 10-mosdegree M10md
5 Major 13-mosdegree M13md
4 Major 2-mosdegree M2md
3 Major 5-mosdegree M5md
2 Major 8-mosdegree M8md
1 Perfect 11-mosdegree P11md
0 Perfect 0-mosdegree
Perfect 14-mosdegree		 P0md
P14md
−1 Perfect 3-mosdegree P3md
−2 Minor 6-mosdegree m6md
−3 Minor 9-mosdegree m9md
−4 Minor 12-mosdegree m12md
−5 Minor 1-mosdegree m1md
−6 Minor 4-mosdegree m4md
−7 Minor 7-mosdegree m7md
−8 Minor 10-mosdegree m10md
−9 Minor 13-mosdegree m13md
−10 Minor 2-mosdegree m2md
−11 Minor 5-mosdegree m5md
−12 Minor 8-mosdegree m8md
−13 Diminished 11-mosdegree d11md
−14 Diminished 14-mosdegree d14md
−15 Diminished 3-mosdegree d3md
−16 Diminished 6-mosdegree d6md
−17 Diminished 9-mosdegree d9md
−18 Diminished 12-mosdegree d12md

Modes

Scale degrees of the modes of 5L 9s
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 LsLssLssLssLss Perf. Maj. Maj. Aug. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Perf.
12|1 12 LssLsLssLssLss Perf. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Perf.
11|2 9 LssLssLsLssLss Perf. Maj. Maj. Perf. Maj. Maj. Min. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Perf.
10|3 6 LssLssLssLsLss Perf. Maj. Maj. Perf. Maj. Maj. Min. Maj. Maj. Min. Maj. Perf. Maj. Maj. Perf.
9|4 3 LssLssLssLssLs Perf. Maj. Maj. Perf. Maj. Maj. Min. Maj. Maj. Min. Maj. Perf. Min. Maj. Perf.
8|5 14 sLsLssLssLssLs Perf. Min. Maj. Perf. Maj. Maj. Min. Maj. Maj. Min. Maj. Perf. Min. Maj. Perf.
7|6 11 sLssLsLssLssLs Perf. Min. Maj. Perf. Min. Maj. Min. Maj. Maj. Min. Maj. Perf. Min. Maj. Perf.
6|7 8 sLssLssLsLssLs Perf. Min. Maj. Perf. Min. Maj. Min. Min. Maj. Min. Maj. Perf. Min. Maj. Perf.
5|8 5 sLssLssLssLsLs Perf. Min. Maj. Perf. Min. Maj. Min. Min. Maj. Min. Min. Perf. Min. Maj. Perf.
4|9 2 sLssLssLssLssL Perf. Min. Maj. Perf. Min. Maj. Min. Min. Maj. Min. Min. Perf. Min. Min. Perf.
3|10 13 ssLsLssLssLssL Perf. Min. Min. Perf. Min. Maj. Min. Min. Maj. Min. Min. Perf. Min. Min. Perf.
2|11 10 ssLssLsLssLssL Perf. Min. Min. Perf. Min. Min. Min. Min. Maj. Min. Min. Perf. Min. Min. Perf.
1|12 7 ssLssLssLsLssL Perf. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Perf.
0|13 4 ssLssLssLssLsL Perf. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Dim. Min. Min. Perf.

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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