7L 2s (5/2-equivalent)

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↖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
Brightest mode LLLLsLLLs
Equave (cents) 5/2 (1586.3¢)
Period (cents) 5/2 (1586.3¢)
Generator ranges
Bright 5\9ed5/2 (881.3¢) to 4\7ed5/2 (906.5¢)
Dark 3\7ed5/2 (679.8¢) to 4\9ed5/2 (705.0¢)
Related scales
Parent 2L 5s⟨5/2⟩
Sister 2L 7s⟨5/2⟩
Daughters 9L 7s⟨5/2⟩, 7L 9s⟨5/2⟩
Equal tunings
Equalized (L:s = 1:1) 5\9ed5/2 (881.3¢)
Supersoft (L:s = 4:3) 19\34ed5/2 (886.5¢)
Soft (L:s = 3:2) 14\25ed5/2 (888.3¢)
Semisoft (L:s = 5:3) 23\41ed5/2 (889.9¢)
Basic (L:s = 2:1) 9\16ed5/2 (892.3¢)
Semihard (L:s = 5:2) 22\39ed5/2 (894.8¢)
Hard (L:s = 3:1) 13\23ed5/2 (896.6¢)
Superhard (L:s = 4:1) 17\30ed5/2 (898.9¢)
Collapsed (L:s = 1:0) 4\7ed5/2 (906.5¢)

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).

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 Rotational 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

Tuning spectrum

Scale tree and tuning spectrum of 7L 2s⟨5/2⟩
Generator (in steps of 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⟩