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2L 9s (3/1-equivalent)

Revision as of 23:40, 15 December 2024 by BudjarnLambeth (talk | contribs) (Modes intervals todo)

2L 9s⟨3/1⟩ is a 3/1-equivalent (tritave-equivalent) moment of symmetry scale containing 2 large steps and 9 small steps, repeating every interval of 3/1 (1902.0 ¢). Generators that produce this scale range from 864.5 ¢ to 951 ¢, or from 951 ¢ to 1037.4 ¢.

↖ 1L 8s⟨3/1⟩ ↑ 2L 8s⟨3/1⟩ 3L 8s⟨3/1⟩ ↗
← 1L 9s⟨3/1⟩ 2L 9s (3/1-equivalent) 3L 9s⟨3/1⟩ →
↙ 1L 10s⟨3/1⟩ ↓ 2L 10s⟨3/1⟩ 3L 10s⟨3/1⟩ ↘
Scale structure
Step pattern LssssLsssss
sssssLssssL
Equave 3/1 (1902.0 ¢)
Period 3/1 (1902.0 ¢)
Generator size(edt)
Bright 5\11 to 1\2 (864.5 ¢ to 951.0 ¢)
Dark 1\2 to 6\11 (951.0 ¢ to 1037.4 ¢)
Related MOS scales
Parent 2L 7s⟨3/1⟩
Sister 9L 2s⟨3/1⟩
Daughters 11L 2s⟨3/1⟩, 2L 11s⟨3/1⟩
Neutralized 4L 7s⟨3/1⟩
2-Flought 13L 9s⟨3/1⟩, 2L 20s⟨3/1⟩
Equal tunings(edt)
Equalized (L:s = 1:1) 5\11 (864.5 ¢)
Supersoft (L:s = 4:3) 16\35 (869.5 ¢)
Soft (L:s = 3:2) 11\24 (871.7 ¢)
Semisoft (L:s = 5:3) 17\37 (873.9 ¢)
Basic (L:s = 2:1) 6\13 (877.8 ¢)
Semihard (L:s = 5:2) 13\28 (883.1 ¢)
Hard (L:s = 3:1) 7\15 (887.6 ¢)
Superhard (L:s = 4:1) 8\17 (895.0 ¢)
Collapsed (L:s = 1:0) 1\2 (951.0 ¢)
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The generators of this scale in the hard-of-basic region approximate 5/3. It is a scale of the Arcturus temperament.

Modes

Modes of 2L 9s⟨3/1⟩
UDP Cyclic
order		 Step
pattern
10|0 1 LssssLsssss
9|1 6 LsssssLssss
8|2 11 sLssssLssss
7|3 5 sLsssssLsss
6|4 10 ssLssssLsss
5|5 4 ssLsssssLss
4|6 9 sssLssssLss
3|7 3 sssLsssssLs
2|8 8 ssssLssssLs
1|9 2 ssssLsssssL
0|10 7 sssssLssssL

Intervals

Intervals of 2L 9s⟨3/1⟩
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 172.9 ¢
Major 1-mosstep M1ms L 172.9 ¢ to 951.0 ¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0 ¢ to 345.8 ¢
Major 2-mosstep M2ms L + s 345.8 ¢ to 951.0 ¢
3-mosstep Minor 3-mosstep m3ms 3s 0.0 ¢ to 518.7 ¢
Major 3-mosstep M3ms L + 2s 518.7 ¢ to 951.0 ¢
4-mosstep Minor 4-mosstep m4ms 4s 0.0 ¢ to 691.6 ¢
Major 4-mosstep M4ms L + 3s 691.6 ¢ to 951.0 ¢
5-mosstep Diminished 5-mosstep d5ms 5s 0.0 ¢ to 864.5 ¢
Perfect 5-mosstep P5ms L + 4s 864.5 ¢ to 951.0 ¢
6-mosstep Perfect 6-mosstep P6ms L + 5s 951.0 ¢ to 1037.4 ¢
Augmented 6-mosstep A6ms 2L + 4s 1037.4 ¢ to 1902.0 ¢
7-mosstep Minor 7-mosstep m7ms L + 6s 951.0 ¢ to 1210.3 ¢
Major 7-mosstep M7ms 2L + 5s 1210.3 ¢ to 1902.0 ¢
8-mosstep Minor 8-mosstep m8ms L + 7s 951.0 ¢ to 1383.2 ¢
Major 8-mosstep M8ms 2L + 6s 1383.2 ¢ to 1902.0 ¢
9-mosstep Minor 9-mosstep m9ms L + 8s 951.0 ¢ to 1556.1 ¢
Major 9-mosstep M9ms 2L + 7s 1556.1 ¢ to 1902.0 ¢
10-mosstep Minor 10-mosstep m10ms L + 9s 951.0 ¢ to 1729.1 ¢
Major 10-mosstep M10ms 2L + 8s 1729.1 ¢ to 1902.0 ¢
11-mosstep Perfect 11-mosstep P11ms 2L + 9s 1902.0 ¢

Scale tree

  Template: Scale tree is deprecated. Please use Template: MOS tuning spectrum instead. Details:
Use of a single Comments parameter has become unmaintainable. Existing scale trees should be migrated to the new template, where comments are entered using a step ratio p/q as a parameter: 
{{MOS tuning spectrum
| 3/2 = Example comment
| 4/3 = Another example comment
}}


The parameters tuning and depth have been replaced with Scale Signature and Depth, respectively.


Scale tree and tuning spectrum of 2L 9s⟨3/1⟩
Generator(edt) Cents Step ratio Comments
Bright Dark L:s Hardness
5\11 864.525 1037.430 1:1 1.000 Equalized 2L 9s⟨3/1⟩
26\57 867.558 1034.397 6:5 1.200
21\46 868.284 1033.671 5:4 1.250
37\81 868.794 1033.161 9:7 1.286
16\35 869.465 1032.490 4:3 1.333 Supersoft 2L 9s⟨3/1⟩
43\94 870.043 1031.912 11:8 1.375
27\59 870.386 1031.569 7:5 1.400
38\83 870.775 1031.180 10:7 1.429
11\24 871.729 1030.226 3:2 1.500 Soft 2L 9s⟨3/1⟩
39\85 872.662 1029.293 11:7 1.571
28\61 873.029 1028.926 8:5 1.600
45\98 873.347 1028.608 13:8 1.625
17\37 873.871 1028.084 5:3 1.667 Semisoft 2L 9s⟨3/1⟩
40\87 874.462 1027.493 12:7 1.714
23\50 874.899 1027.056 7:4 1.750
29\63 875.503 1026.452 9:5 1.800
6\13 877.825 1024.130 2:1 2.000 Basic 2L 9s⟨3/1⟩
Scales with tunings softer than this are proper
25\54 880.535 1021.420 9:4 2.250
19\41 881.394 1020.561 7:3 2.333
32\69 882.066 1019.889 12:5 2.400
13\28 883.051 1018.904 5:2 2.500 Semihard 2L 9s⟨3/1⟩
33\71 884.007 1017.948 13:5 2.600
20\43 884.630 1017.325 8:3 2.667
27\58 885.393 1016.562 11:4 2.750
7\15 887.579 1014.376 3:1 3.000 Hard 2L 9s⟨3/1⟩
22\47 890.277 1011.678 10:3 3.333
15\32 891.541 1010.414 7:2 3.500
23\49 892.754 1009.201 11:3 3.667
8\17 895.038 1006.917 4:1 4.000 Superhard 2L 9s⟨3/1⟩
17\36 898.145 1003.810 9:2 4.500
9\19 900.926 1001.029 5:1 5.000
10\21 905.693 996.262 6:1 6.000
1\2 950.978 950.978 1:0 → ∞ Collapsed 2L 9s⟨3/1⟩
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