5L 9s
↖ 4L 8s | ↑ 5L 8s | 6L 8s ↗ |
← 4L 9s | 5L 9s | 6L 9s → |
↙ 4L 10s | ↓ 5L 10s | 6L 10s ↘ |
┌╥┬╥┬┬╥┬┬╥┬┬╥┬┬┐ │║│║││║││║││║│││ ││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
ssLssLssLssLsL
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.
Scale tree
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 |