4L 9s

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← 3L 9s 4L 9s 5L 9s →
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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)
Ancestor's 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, gariberttet, and subklei temperaments. The harmonic entropy minimum for this pattern maps +2, +3, and +5 bright generators to 7/5, 5/3, and 7/3, respectively.

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 4L 9s 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 13-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 4L 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 92.3 ¢
Major 1-mosstep M1ms L 92.3 ¢ to 300.0 ¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0 ¢ to 184.6 ¢
Major 2-mosstep M2ms L + s 184.6 ¢ to 300.0 ¢
3-mosstep Diminished 3-mosstep d3ms 3s 0.0 ¢ to 276.9 ¢
Perfect 3-mosstep P3ms L + 2s 276.9 ¢ to 300.0 ¢
4-mosstep Minor 4-mosstep m4ms L + 3s 300.0 ¢ to 369.2 ¢
Major 4-mosstep M4ms 2L + 2s 369.2 ¢ to 600.0 ¢
5-mosstep Minor 5-mosstep m5ms L + 4s 300.0 ¢ to 461.5 ¢
Major 5-mosstep M5ms 2L + 3s 461.5 ¢ to 600.0 ¢
6-mosstep Minor 6-mosstep m6ms L + 5s 300.0 ¢ to 553.8 ¢
Major 6-mosstep M6ms 2L + 4s 553.8 ¢ to 600.0 ¢
7-mosstep Minor 7-mosstep m7ms 2L + 5s 600.0 ¢ to 646.2 ¢
Major 7-mosstep M7ms 3L + 4s 646.2 ¢ to 900.0 ¢
8-mosstep Minor 8-mosstep m8ms 2L + 6s 600.0 ¢ to 738.5 ¢
Major 8-mosstep M8ms 3L + 5s 738.5 ¢ to 900.0 ¢
9-mosstep Minor 9-mosstep m9ms 2L + 7s 600.0 ¢ to 830.8 ¢
Major 9-mosstep M9ms 3L + 6s 830.8 ¢ to 900.0 ¢
10-mosstep Perfect 10-mosstep P10ms 3L + 7s 900.0 ¢ to 923.1 ¢
Augmented 10-mosstep A10ms 4L + 6s 923.1 ¢ to 1200.0 ¢
11-mosstep Minor 11-mosstep m11ms 3L + 8s 900.0 ¢ to 1015.4 ¢
Major 11-mosstep M11ms 4L + 7s 1015.4 ¢ to 1200.0 ¢
12-mosstep Minor 12-mosstep m12ms 3L + 9s 900.0 ¢ to 1107.7 ¢
Major 12-mosstep M12ms 4L + 8s 1107.7 ¢ to 1200.0 ¢
13-mosstep Perfect 13-mosstep P13ms 4L + 9s 1200.0 ¢

Generator chain

A chain of bright generators, each a perfect 3-mosstep, produces the following scale degrees. A chain of 13 bright generators contains the scale degrees of one of the modes of 4L 9s. Expanding the chain to 17 scale degrees produces the modes of either 13L 4s (for soft-of-basic tunings) or 4L 13s (for hard-of-basic tunings).

Generator chain of 4L 9s
Bright gens Scale degree Abbrev.
16 Augmented 9-mosdegree A9md
15 Augmented 6-mosdegree A6md
14 Augmented 3-mosdegree A3md
13 Augmented 0-mosdegree A0md
12 Augmented 10-mosdegree A10md
11 Major 7-mosdegree M7md
10 Major 4-mosdegree M4md
9 Major 1-mosdegree M1md
8 Major 11-mosdegree M11md
7 Major 8-mosdegree M8md
6 Major 5-mosdegree M5md
5 Major 2-mosdegree M2md
4 Major 12-mosdegree M12md
3 Major 9-mosdegree M9md
2 Major 6-mosdegree M6md
1 Perfect 3-mosdegree P3md
0 Perfect 0-mosdegree
Perfect 13-mosdegree		 P0md
P13md
−1 Perfect 10-mosdegree P10md
−2 Minor 7-mosdegree m7md
−3 Minor 4-mosdegree m4md
−4 Minor 1-mosdegree m1md
−5 Minor 11-mosdegree m11md
−6 Minor 8-mosdegree m8md
−7 Minor 5-mosdegree m5md
−8 Minor 2-mosdegree m2md
−9 Minor 12-mosdegree m12md
−10 Minor 9-mosdegree m9md
−11 Minor 6-mosdegree m6md
−12 Diminished 3-mosdegree d3md
−13 Diminished 13-mosdegree d13md
−14 Diminished 10-mosdegree d10md
−15 Diminished 7-mosdegree d7md
−16 Diminished 4-mosdegree d4md

Modes

Scale degrees of the modes of 4L 9s 
UDP Cyclic
order		 Step
pattern		 Scale degree (mosdegree)
0 1 2 3 4 5 6 7 8 9 10 11 12 13
12|0 1 LssLssLssLsss Perf. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Aug. Maj. Maj. Perf.
11|1 4 LssLssLsssLss Perf. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Perf.
10|2 7 LssLsssLssLss Perf. Maj. Maj. Perf. Maj. Maj. Maj. Min. Maj. Maj. Perf. Maj. Maj. Perf.
9|3 10 LsssLssLssLss Perf. Maj. Maj. Perf. Min. Maj. Maj. Min. Maj. Maj. Perf. Maj. Maj. Perf.
8|4 13 sLssLssLssLss Perf. Min. Maj. Perf. Min. Maj. Maj. Min. Maj. Maj. Perf. Maj. Maj. Perf.
7|5 3 sLssLssLsssLs Perf. Min. Maj. Perf. Min. Maj. Maj. Min. Maj. Maj. Perf. Min. Maj. Perf.
6|6 6 sLssLsssLssLs Perf. Min. Maj. Perf. Min. Maj. Maj. Min. Min. Maj. Perf. Min. Maj. Perf.
5|7 9 sLsssLssLssLs Perf. Min. Maj. Perf. Min. Min. Maj. Min. Min. Maj. Perf. Min. Maj. Perf.
4|8 12 ssLssLssLssLs Perf. Min. Min. Perf. Min. Min. Maj. Min. Min. Maj. Perf. Min. Maj. Perf.
3|9 2 ssLssLssLsssL Perf. Min. Min. Perf. Min. Min. Maj. Min. Min. Maj. Perf. Min. Min. Perf.
2|10 5 ssLssLsssLssL Perf. Min. Min. Perf. Min. Min. Maj. Min. Min. Min. Perf. Min. Min. Perf.
1|11 8 ssLsssLssLssL Perf. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Perf.
0|12 11 sssLssLssLssL Perf. Min. Min. Dim. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Perf.

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
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