5L 2s (5/3-equivalent)

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↖ 4L 1s⟨5/3⟩ ↑ 5L 1s⟨5/3⟩ 6L 1s⟨5/3⟩ ↗
← 4L 2s⟨5/3⟩ 5L 2s (5/3-equivalent) 6L 2s⟨5/3⟩ →
↙ 4L 3s⟨5/3⟩ ↓ 5L 3s⟨5/3⟩ 6L 3s⟨5/3⟩ ↘ 
┌╥╥╥┬╥╥┬┐
│║║║│║║││
│││││││││
└┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLLsLLs
sLLsLLL
Equave 5/3 (884.4¢)
Period 5/3 (884.4¢)
Generator size(ed5/3)
Bright 4\7 to 3\5 (505.3¢ to 530.6¢)
Dark 2\5 to 3\7 (353.7¢ to 379.0¢)
Related MOS scales
Parent 2L 3s⟨5/3⟩
Sister 2L 5s⟨5/3⟩
Daughters 7L 5s⟨5/3⟩, 5L 7s⟨5/3⟩
Neutralized 3L 4s⟨5/3⟩
2-Flought 12L 2s⟨5/3⟩, 5L 9s⟨5/3⟩
Equal tunings(ed5/3)
Equalized (L:s = 1:1) 4\7 (505.3¢)
Supersoft (L:s = 4:3) 15\26 (510.2¢)
Soft (L:s = 3:2) 11\19 (512.0¢)
Semisoft (L:s = 5:3) 18\31 (513.5¢)
Basic (L:s = 2:1) 7\12 (515.9¢)
Semihard (L:s = 5:2) 17\29 (518.4¢)
Hard (L:s = 3:1) 10\17 (520.2¢)
Superhard (L:s = 4:1) 13\22 (522.6¢)
Collapsed (L:s = 1:0) 3\5 (530.6¢)

5L 2s⟨5/3⟩ is a 5/3-equivalent (non-octave) moment of symmetry scale containing 5 large steps and 2 small steps, repeating every interval of 5/3 (884.4¢). Generators that produce this scale range from 505.3¢ to 530.6¢, or from 353.7¢ to 379¢.

Modes

Modes of 5L 2s⟨5/3⟩
UDP Cyclic
order		 Step
pattern
6|0 1 LLLsLLs
5|1 5 LLsLLLs
4|2 2 LLsLLsL
3|3 6 LsLLLsL
2|4 3 LsLLsLL
1|5 7 sLLLsLL
0|6 4 sLLsLLL

Intervals

Intervals of 5L 2s⟨5/3⟩
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 126.3¢
Major 1-mosstep M1ms L 126.3¢ to 176.9¢
2-mosstep Minor 2-mosstep m2ms L + s 176.9¢ to 252.7¢
Major 2-mosstep M2ms 2L 252.7¢ to 353.7¢
3-mosstep Perfect 3-mosstep P3ms 2L + s 353.7¢ to 379.0¢
Augmented 3-mosstep A3ms 3L 379.0¢ to 530.6¢
4-mosstep Diminished 4-mosstep d4ms 2L + 2s 353.7¢ to 505.3¢
Perfect 4-mosstep P4ms 3L + s 505.3¢ to 530.6¢
5-mosstep Minor 5-mosstep m5ms 3L + 2s 530.6¢ to 631.7¢
Major 5-mosstep M5ms 4L + s 631.7¢ to 707.5¢
6-mosstep Minor 6-mosstep m6ms 4L + 2s 707.5¢ to 758.0¢
Major 6-mosstep M6ms 5L + s 758.0¢ to 884.4¢
7-mosstep Perfect 7-mosstep P7ms 5L + 2s 884.4¢

Scale tree

Scale Tree and Tuning Spectrum of 5L 2s⟨5/3⟩
Generator(ed5/3) Cents Step ratio Comments
Bright Dark L:s Hardness
4\7 505.348 379.011 1:1 1.000 Equalized 5L 2s⟨5/3⟩
23\40 508.506 375.852 6:5 1.200
19\33 509.176 375.182 5:4 1.250
34\59 509.630 374.728 9:7 1.286
15\26 510.207 374.152 4:3 1.333 Supersoft 5L 2s⟨5/3⟩
41\71 510.686 373.673 11:8 1.375
26\45 510.963 373.396 7:5 1.400
37\64 511.270 373.089 10:7 1.429
11\19 511.997 372.362 3:2 1.500 Soft 5L 2s⟨5/3⟩
40\69 512.672 371.687 11:7 1.571
29\50 512.928 371.431 8:5 1.600
47\81 513.146 371.212 13:8 1.625
18\31 513.499 370.860 5:3 1.667 Semisoft 5L 2s⟨5/3⟩
43\74 513.884 370.475 12:7 1.714
25\43 514.162 370.197 7:4 1.750
32\55 514.536 369.823 9:5 1.800
7\12 515.876 368.483 2:1 2.000 Basic 5L 2s⟨5/3⟩
Scales with tunings softer than this are proper
31\53 517.266 367.092 9:4 2.250
24\41 517.673 366.685 7:3 2.333
41\70 517.982 366.377 12:5 2.400
17\29 518.417 365.942 5:2 2.500 Semihard 5L 2s⟨5/3⟩
44\75 518.824 365.535 13:5 2.600
27\46 519.080 365.279 8:3 2.667
37\63 519.385 364.973 11:4 2.750
10\17 520.211 364.148 3:1 3.000 Hard 5L 2s⟨5/3⟩
33\56 521.140 363.219 10:3 3.333
23\39 521.545 362.814 7:2 3.500
36\61 521.917 362.442 11:3 3.667
13\22 522.576 361.783 4:1 4.000 Superhard 5L 2s⟨5/3⟩
29\49 523.396 360.963 9:2 4.500
16\27 524.064 360.294 5:1 5.000
19\32 525.088 359.271 6:1 6.000
3\5 530.615 353.743 1:0 → ∞ Collapsed 5L 2s⟨5/3⟩


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