4L 9s

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↖ 3L 8s ↑4L 8s 5L 8s ↗
← 3L 9s4L 9s 5L 9s →
↙ 3L 10s ↓4L 10s 5L 10s ↘
┌╥┬┬╥┬┬╥┬┬╥┬┬┬┐
│║││║││║││║││││
│││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LssLssLssLsss
sssLssLssLssL
Equave 2/1 (1200.0¢)
Period 2/1 (1200.0¢)
Generator size
Bright 3\13 to 1\4 (276.9¢ to 300.0¢)
Dark 3\4 to 10\13 (900.0¢ to 923.1¢)
TAMNAMS information
Descends from 4L 5s (gramitonic)
Required step ratio range 2:1 to 1:0 (hard-of-basic)
Related MOS scales
Parent 4L 5s
Sister 9L 4s
Daughters 13L 4s, 4L 13s
Neutralized 8L 5s
2-Flought 17L 9s, 4L 22s
Equal tunings
Equalized (L:s = 1:1) 3\13 (276.9¢)
Supersoft (L:s = 4:3) 10\43 (279.1¢)
Soft (L:s = 3:2) 7\30 (280.0¢)
Semisoft (L:s = 5:3) 11\47 (280.9¢)
Basic (L:s = 2:1) 4\17 (282.4¢)
Semihard (L:s = 5:2) 9\38 (284.2¢)
Hard (L:s = 3:1) 5\21 (285.7¢)
Superhard (L:s = 4:1) 6\25 (288.0¢)
Collapsed (L:s = 1:0) 1\4 (300.0¢)

4L 9s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 4 large steps and 9 small steps, repeating every octave. 4L 9s is a child scale of 4L 5s, expanding it by 4 tones. Generators that produce this scale range from 276.9¢ to 300¢, or from 900¢ to 923.1¢.

4L 9s represents chromatic scales of Huxley, Lovecraft and gariberttet temperaments. The harmonic entropy minimum for this pattern maps +2, +3, and +5 bright generators to 7/5, 5/3 and 7/3, respectively.

Modes

Modes of 4L 9s
UDP Rotational order Step pattern
12 | 0 1 LssLssLssLsss
11 | 1 4 LssLssLsssLss
10 | 2 7 LssLsssLssLss
9 | 3 10 LsssLssLssLss
8 | 4 13 sLssLssLssLss
7 | 5 3 sLssLssLsssLs
6 | 6 6 sLssLsssLssLs
5 | 7 9 sLsssLssLssLs
4 | 8 12 ssLssLssLssLs
3 | 9 2 ssLssLssLsssL
2 | 10 5 ssLssLsssLssL
1 | 11 8 ssLsssLssLssL
0 | 12 11 sssLssLssLssL

Scale tree

Scale Tree and Tuning Spectrum of 4L 9s
Generator(edo) Cents Step Ratio Comments
Bright Dark L:s Hardness
3\13 276.923 923.077 1:1 1.000 Equalized 4L 9s
16\69 278.261 921.739 6:5 1.200
13\56 278.571 921.429 5:4 1.250
23\99 278.788 921.212 9:7 1.286
10\43 279.070 920.930 4:3 1.333 Supersoft 4L 9s
27\116 279.310 920.690 11:8 1.375
17\73 279.452 920.548 7:5 1.400
24\103 279.612 920.388 10:7 1.429
7\30 280.000 920.000 3:2 1.500 Soft 4L 9s
25\107 280.374 919.626 11:7 1.571
18\77 280.519 919.481 8:5 1.600
29\124 280.645 919.355 13:8 1.625
11\47 280.851 919.149 5:3 1.667 Semisoft 4L 9s
26\111 281.081 918.919 12:7 1.714
15\64 281.250 918.750 7:4 1.750
19\81 281.481 918.519 9:5 1.800
4\17 282.353 917.647 2:1 2.000 Basic 4L 9s
Scales with tunings softer than this are proper
17\72 283.333 916.667 9:4 2.250
13\55 283.636 916.364 7:3 2.333
22\93 283.871 916.129 12:5 2.400
9\38 284.211 915.789 5:2 2.500 Semihard 4L 9s
23\97 284.536 915.464 13:5 2.600
14\59 284.746 915.254 8:3 2.667
19\80 285.000 915.000 11:4 2.750
5\21 285.714 914.286 3:1 3.000 Hard 4L 9s
16\67 286.567 913.433 10:3 3.333
11\46 286.957 913.043 7:2 3.500
17\71 287.324 912.676 11:3 3.667
6\25 288.000 912.000 4:1 4.000 Superhard 4L 9s
13\54 288.889 911.111 9:2 4.500
7\29 289.655 910.345 5:1 5.000
8\33 290.909 909.091 6:1 6.000
1\4 300.000 900.000 1:0 → ∞ Collapsed 4L 9s