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 ¢.

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 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 ¢

Generator chain

Generator chain of 5L 2s⟨5/3⟩
Bright gens Scale degree Abbrev.
11 Augmented 2-mosdegree A2md
10 Augmented 5-mosdegree A5md
9 Augmented 1-mosdegree A1md
8 Augmented 4-mosdegree A4md
7 Augmented 0-mosdegree A0md
6 Augmented 3-mosdegree A3md
5 Major 6-mosdegree M6md
4 Major 2-mosdegree M2md
3 Major 5-mosdegree M5md
2 Major 1-mosdegree M1md
1 Perfect 4-mosdegree P4md
0 Perfect 0-mosdegree
Perfect 7-mosdegree		 P0md
P7md
−1 Perfect 3-mosdegree P3md
−2 Minor 6-mosdegree m6md
−3 Minor 2-mosdegree m2md
−4 Minor 5-mosdegree m5md
−5 Minor 1-mosdegree m1md
−6 Diminished 4-mosdegree d4md
−7 Diminished 7-mosdegree d7md
−8 Diminished 3-mosdegree d3md
−9 Diminished 6-mosdegree d6md
−10 Diminished 2-mosdegree d2md
−11 Diminished 5-mosdegree d5md

Modes

Scale degrees of the modes of 5L 2s⟨5/3⟩
UDP Cyclic
order		 Step
pattern		 Scale degree (mosdegree)
0 1 2 3 4 5 6 7
6|0 1 LLLsLLs Perf. Maj. Maj. Aug. Perf. Maj. Maj. Perf.
5|1 5 LLsLLLs Perf. Maj. Maj. Perf. Perf. Maj. Maj. Perf.
4|2 2 LLsLLsL Perf. Maj. Maj. Perf. Perf. Maj. Min. Perf.
3|3 6 LsLLLsL Perf. Maj. Min. Perf. Perf. Maj. Min. Perf.
2|4 3 LsLLsLL Perf. Maj. Min. Perf. Perf. Min. Min. Perf.
1|5 7 sLLLsLL Perf. Min. Min. Perf. Perf. Min. Min. Perf.
0|6 4 sLLsLLL Perf. Min. Min. Perf. Dim. Min. Min. Perf.

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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