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7L 2s (5/2-equivalent)

Revision as of 00:41, 16 December 2024 by BudjarnLambeth (talk | contribs) (== Intervals == {{MOS intervals}})

This page is about a MOS scale with a period of 5/2 and 7 large steps and 2 small steps arranged LLLsLLLLs (or any rotation of that, such as LLsLLLsLL).

↖ 6L 1s⟨5/2⟩ ↑ 7L 1s⟨5/2⟩ 8L 1s⟨5/2⟩ ↗
← 6L 2s⟨5/2⟩ 7L 2s (5/2-equivalent) 8L 2s⟨5/2⟩ →
↙ 6L 3s⟨5/2⟩ ↓ 7L 3s⟨5/2⟩ 8L 3s⟨5/2⟩ ↘
Scale structure
Step pattern LLLLsLLLs
sLLLsLLLL
Equave 5/2 (1586.3 ¢)
Period 5/2 (1586.3 ¢)
Generator size(ed5/2)
Bright 5\9 to 4\7 (881.3 ¢ to 906.5 ¢)
Dark 3\7 to 4\9 (679.8 ¢ to 705.0 ¢)
Related MOS scales
Parent 2L 5s⟨5/2⟩
Sister 2L 7s⟨5/2⟩
Daughters 9L 7s⟨5/2⟩, 7L 9s⟨5/2⟩
Neutralized 5L 4s⟨5/2⟩
2-Flought 16L 2s⟨5/2⟩, 7L 11s⟨5/2⟩
Equal tunings(ed5/2)
Equalized (L:s = 1:1) 5\9 (881.3 ¢)
Supersoft (L:s = 4:3) 19\34 (886.5 ¢)
Soft (L:s = 3:2) 14\25 (888.3 ¢)
Semisoft (L:s = 5:3) 23\41 (889.9 ¢)
Basic (L:s = 2:1) 9\16 (892.3 ¢)
Semihard (L:s = 5:2) 22\39 (894.8 ¢)
Hard (L:s = 3:1) 13\23 (896.6 ¢)
Superhard (L:s = 4:1) 17\30 (898.9 ¢)
Collapsed (L:s = 1:0) 4\7 (906.5 ¢)
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7L 2s⟨5/2⟩ is a 5/2-equivalent (non-octave) moment of symmetry scale containing 7 large steps and 2 small steps, repeating every interval of 5/2 (1586.3 ¢). Generators that produce this scale range from 881.3 ¢ to 906.5 ¢, or from 679.8 ¢ to 705 ¢.

Modes

Modes of 7L 2s⟨5/2⟩
UDP Cyclic
order		 Step
pattern
8|0 1 LLLLsLLLs
7|1 6 LLLsLLLLs
6|2 2 LLLsLLLsL
5|3 7 LLsLLLLsL
4|4 3 LLsLLLsLL
3|5 8 LsLLLLsLL
2|6 4 LsLLLsLLL
1|7 9 sLLLLsLLL
0|8 5 sLLLsLLLL

Intervals

Intervals of 7L 2s⟨5/2⟩
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 176.3 ¢
Major 1-mosstep M1ms L 176.3 ¢ to 226.6 ¢
2-mosstep Minor 2-mosstep m2ms L + s 226.6 ¢ to 352.5 ¢
Major 2-mosstep M2ms 2L 352.5 ¢ to 453.2 ¢
3-mosstep Minor 3-mosstep m3ms 2L + s 453.2 ¢ to 528.8 ¢
Major 3-mosstep M3ms 3L 528.8 ¢ to 679.8 ¢
4-mosstep Perfect 4-mosstep P4ms 3L + s 679.8 ¢ to 705.0 ¢
Augmented 4-mosstep A4ms 4L 705.0 ¢ to 906.5 ¢
5-mosstep Diminished 5-mosstep d5ms 3L + 2s 679.8 ¢ to 881.3 ¢
Perfect 5-mosstep P5ms 4L + s 881.3 ¢ to 906.5 ¢
6-mosstep Minor 6-mosstep m6ms 4L + 2s 906.5 ¢ to 1057.5 ¢
Major 6-mosstep M6ms 5L + s 1057.5 ¢ to 1133.1 ¢
7-mosstep Minor 7-mosstep m7ms 5L + 2s 1133.1 ¢ to 1233.8 ¢
Major 7-mosstep M7ms 6L + s 1233.8 ¢ to 1359.7 ¢
8-mosstep Minor 8-mosstep m8ms 6L + 2s 1359.7 ¢ to 1410.1 ¢
Major 8-mosstep M8ms 7L + s 1410.1 ¢ to 1586.3 ¢
9-mosstep Perfect 9-mosstep P9ms 7L + 2s 1586.3 ¢

Tuning spectrum

  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 7L 2s⟨5/2⟩
Generator(ed5/2) Cents Step ratio Comments
Bright Dark L:s Hardness
5\9 881.285 705.028 1:1 1.000 Equalized 7L 2s⟨5/2⟩
29\52 884.675 701.639 6:5 1.200
24\43 885.384 700.929 5:4 1.250
43\77 885.864 700.450 9:7 1.286
19\34 886.469 699.844 4:3 1.333 Supersoft 7L 2s⟨5/2⟩
52\93 886.971 699.343 11:8 1.375
33\59 887.260 699.054 7:5 1.400
47\84 887.580 698.733 10:7 1.429
14\25 888.336 697.978 3:2 1.500 Soft 7L 2s⟨5/2⟩
51\91 889.033 697.281 11:7 1.571
37\66 889.297 697.017 8:5 1.600
60\107 889.522 696.792 13:8 1.625
23\41 889.883 696.430 5:3 1.667 Semisoft 7L 2s⟨5/2⟩
55\98 890.278 696.036 12:7 1.714
32\57 890.562 695.752 7:4 1.750
41\73 890.943 695.370 9:5 1.800
9\16 892.301 694.012 2:1 2.000 Basic 7L 2s⟨5/2⟩
Scales with tunings softer than this are proper
40\71 893.698 692.616 9:4 2.250
31\55 894.104 692.210 7:3 2.333
53\94 894.411 691.903 12:5 2.400
22\39 894.844 691.470 5:2 2.500 Semihard 7L 2s⟨5/2⟩
57\101 895.246 691.067 13:5 2.600
35\62 895.500 690.814 8:3 2.667
48\85 895.801 690.513 11:4 2.750
13\23 896.612 689.702 3:1 3.000 Hard 7L 2s⟨5/2⟩
43\76 897.520 688.794 10:3 3.333
30\53 897.913 688.400 7:2 3.500
47\83 898.274 688.040 11:3 3.667
17\30 898.911 687.403 4:1 4.000 Superhard 7L 2s⟨5/2⟩
38\67 899.700 686.613 9:2 4.500
21\37 900.340 685.973 5:1 5.000
25\44 901.315 684.999 6:1 6.000
4\7 906.465 679.849 1:0 → ∞ Collapsed 7L 2s⟨5/2⟩


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