9L 4s

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↖ 8L 3s ↑ 9L 3s 10L 3s ↗
← 8L 4s 9L 4s 10L 4s →
↙ 8L 5s ↓ 9L 5s 10L 5s ↘ 
┌╥╥╥┬╥╥┬╥╥┬╥╥┬┐
│║║║│║║│║║│║║││
│││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLLsLLsLLsLLs
sLLsLLsLLsLLL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 10\13 to 7\9 (923.1 ¢ to 933.3 ¢)
Dark 2\9 to 3\13 (266.7 ¢ to 276.9 ¢)
TAMNAMS information
Descends from 4L 5s (gramitonic)
Ancestor's step ratio range 1:1 to 2:1 (soft-of-basic)
Related MOS scales
Parent 4L 5s
Sister 4L 9s
Daughters 13L 9s, 9L 13s
Neutralized 5L 8s
2-Flought 22L 4s, 9L 17s
Equal tunings
Equalized (L:s = 1:1) 10\13 (923.1 ¢)
Supersoft (L:s = 4:3) 37\48 (925.0 ¢)
Soft (L:s = 3:2) 27\35 (925.7 ¢)
Semisoft (L:s = 5:3) 44\57 (926.3 ¢)
Basic (L:s = 2:1) 17\22 (927.3 ¢)
Semihard (L:s = 5:2) 41\53 (928.3 ¢)
Hard (L:s = 3:1) 24\31 (929.0 ¢)
Superhard (L:s = 4:1) 31\40 (930.0 ¢)
Collapsed (L:s = 1:0) 7\9 (933.3 ¢)

9L 4s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 9 large steps and 4 small steps, repeating every octave. 9L 4s is a child scale of 4L 5s, expanding it by 4 tones. Generators that produce this scale range from 923.1 ¢ to 933.3 ¢, or from 266.7 ¢ to 276.9 ¢.

It is the chromatic scale of Orwell temperament. The harmonic entropy minimum for this scale has three dark generators map to 8/5 (~813.6 ¢), where the generator is ~271.2 ¢.

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

Intervals of 9L 4s
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 133.3 ¢
2-mosstep Minor 2-mosstep m2ms L + s 133.3 ¢ to 184.6 ¢
Major 2-mosstep M2ms 2L 184.6 ¢ to 266.7 ¢
3-mosstep Perfect 3-mosstep P3ms 2L + s 266.7 ¢ to 276.9 ¢
Augmented 3-mosstep A3ms 3L 276.9 ¢ to 400.0 ¢
4-mosstep Minor 4-mosstep m4ms 2L + 2s 266.7 ¢ to 369.2 ¢
Major 4-mosstep M4ms 3L + s 369.2 ¢ to 400.0 ¢
5-mosstep Minor 5-mosstep m5ms 3L + 2s 400.0 ¢ to 461.5 ¢
Major 5-mosstep M5ms 4L + s 461.5 ¢ to 533.3 ¢
6-mosstep Minor 6-mosstep m6ms 4L + 2s 533.3 ¢ to 553.8 ¢
Major 6-mosstep M6ms 5L + s 553.8 ¢ to 666.7 ¢
7-mosstep Minor 7-mosstep m7ms 4L + 3s 533.3 ¢ to 646.2 ¢
Major 7-mosstep M7ms 5L + 2s 646.2 ¢ to 666.7 ¢
8-mosstep Minor 8-mosstep m8ms 5L + 3s 666.7 ¢ to 738.5 ¢
Major 8-mosstep M8ms 6L + 2s 738.5 ¢ to 800.0 ¢
9-mosstep Minor 9-mosstep m9ms 6L + 3s 800.0 ¢ to 830.8 ¢
Major 9-mosstep M9ms 7L + 2s 830.8 ¢ to 933.3 ¢
10-mosstep Diminished 10-mosstep d10ms 6L + 4s 800.0 ¢ to 923.1 ¢
Perfect 10-mosstep P10ms 7L + 3s 923.1 ¢ to 933.3 ¢
11-mosstep Minor 11-mosstep m11ms 7L + 4s 933.3 ¢ to 1015.4 ¢
Major 11-mosstep M11ms 8L + 3s 1015.4 ¢ to 1066.7 ¢
12-mosstep Minor 12-mosstep m12ms 8L + 4s 1066.7 ¢ to 1107.7 ¢
Major 12-mosstep M12ms 9L + 3s 1107.7 ¢ to 1200.0 ¢
13-mosstep Perfect 13-mosstep P13ms 9L + 4s 1200.0 ¢

Generator chain

Generator chain of 9L 4s
Bright gens Scale degree Abbrev.
21 Augmented 2-mosdegree A2md
20 Augmented 5-mosdegree A5md
19 Augmented 8-mosdegree A8md
18 Augmented 11-mosdegree A11md
17 Augmented 1-mosdegree A1md
16 Augmented 4-mosdegree A4md
15 Augmented 7-mosdegree A7md
14 Augmented 10-mosdegree A10md
13 Augmented 0-mosdegree A0md
12 Augmented 3-mosdegree A3md
11 Major 6-mosdegree M6md
10 Major 9-mosdegree M9md
9 Major 12-mosdegree M12md
8 Major 2-mosdegree M2md
7 Major 5-mosdegree M5md
6 Major 8-mosdegree M8md
5 Major 11-mosdegree M11md
4 Major 1-mosdegree M1md
3 Major 4-mosdegree M4md
2 Major 7-mosdegree M7md
1 Perfect 10-mosdegree P10md
0 Perfect 0-mosdegree
Perfect 13-mosdegree		 P0md
P13md
−1 Perfect 3-mosdegree P3md
−2 Minor 6-mosdegree m6md
−3 Minor 9-mosdegree m9md
−4 Minor 12-mosdegree m12md
−5 Minor 2-mosdegree m2md
−6 Minor 5-mosdegree m5md
−7 Minor 8-mosdegree m8md
−8 Minor 11-mosdegree m11md
−9 Minor 1-mosdegree m1md
−10 Minor 4-mosdegree m4md
−11 Minor 7-mosdegree m7md
−12 Diminished 10-mosdegree d10md
−13 Diminished 13-mosdegree d13md
−14 Diminished 3-mosdegree d3md
−15 Diminished 6-mosdegree d6md
−16 Diminished 9-mosdegree d9md
−17 Diminished 12-mosdegree d12md
−18 Diminished 2-mosdegree d2md
−19 Diminished 5-mosdegree d5md
−20 Diminished 8-mosdegree d8md
−21 Diminished 11-mosdegree d11md

Modes

Scale degrees of the modes of 9L 4s
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 LLLsLLsLLsLLs Perf. Maj. Maj. Aug. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Perf.
11|1 11 LLsLLLsLLsLLs Perf. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Perf.
10|2 8 LLsLLsLLLsLLs Perf. Maj. Maj. Perf. Maj. Maj. Min. Maj. Maj. Maj. Perf. Maj. Maj. Perf.
9|3 5 LLsLLsLLsLLLs Perf. Maj. Maj. Perf. Maj. Maj. Min. Maj. Maj. Min. Perf. Maj. Maj. Perf.
8|4 2 LLsLLsLLsLLsL Perf. Maj. Maj. Perf. Maj. Maj. Min. Maj. Maj. Min. Perf. Maj. Min. Perf.
7|5 12 LsLLLsLLsLLsL Perf. Maj. Min. Perf. Maj. Maj. Min. Maj. Maj. Min. Perf. Maj. Min. Perf.
6|6 9 LsLLsLLLsLLsL Perf. Maj. Min. Perf. Maj. Min. Min. Maj. Maj. Min. Perf. Maj. Min. Perf.
5|7 6 LsLLsLLsLLLsL Perf. Maj. Min. Perf. Maj. Min. Min. Maj. Min. Min. Perf. Maj. Min. Perf.
4|8 3 LsLLsLLsLLsLL Perf. Maj. Min. Perf. Maj. Min. Min. Maj. Min. Min. Perf. Min. Min. Perf.
3|9 13 sLLLsLLsLLsLL Perf. Min. Min. Perf. Maj. Min. Min. Maj. Min. Min. Perf. Min. Min. Perf.
2|10 10 sLLsLLLsLLsLL Perf. Min. Min. Perf. Min. Min. Min. Maj. Min. Min. Perf. Min. Min. Perf.
1|11 7 sLLsLLsLLLsLL Perf. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Perf.
0|12 4 sLLsLLsLLsLLL Perf. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Dim. Min. Min. Perf.

Scale tree

Scale tree and tuning spectrum of 9L 4s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
10\13 923.077 276.923 1:1 1.000 Equalized 9L 4s
57\74 924.324 275.676 6:5 1.200
47\61 924.590 275.410 5:4 1.250
84\109 924.771 275.229 9:7 1.286
37\48 925.000 275.000 4:3 1.333 Supersoft 9L 4s
101\131 925.191 274.809 11:8 1.375
64\83 925.301 274.699 7:5 1.400
91\118 925.424 274.576 10:7 1.429
27\35 925.714 274.286 3:2 1.500 Soft 9L 4s
98\127 925.984 274.016 11:7 1.571
71\92 926.087 273.913 8:5 1.600
115\149 926.174 273.826 13:8 1.625
44\57 926.316 273.684 5:3 1.667 Semisoft 9L 4s
105\136 926.471 273.529 12:7 1.714
61\79 926.582 273.418 7:4 1.750
78\101 926.733 273.267 9:5 1.800
17\22 927.273 272.727 2:1 2.000 Basic 9L 4s
Scales with tunings softer than this are proper
75\97 927.835 272.165 9:4 2.250
58\75 928.000 272.000 7:3 2.333
99\128 928.125 271.875 12:5 2.400
41\53 928.302 271.698 5:2 2.500 Semihard 9L 4s
106\137 928.467 271.533 13:5 2.600
65\84 928.571 271.429 8:3 2.667
89\115 928.696 271.304 11:4 2.750
24\31 929.032 270.968 3:1 3.000 Hard 9L 4s
79\102 929.412 270.588 10:3 3.333
55\71 929.577 270.423 7:2 3.500
86\111 929.730 270.270 11:3 3.667
31\40 930.000 270.000 4:1 4.000 Superhard 9L 4s
69\89 930.337 269.663 9:2 4.500
38\49 930.612 269.388 5:1 5.000
45\58 931.034 268.966 6:1 6.000
7\9 933.333 266.667 1:0 → ∞ Collapsed 9L 4s
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