4L 1s (5/3-equivalent)

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← 3L 1s⟨5/3⟩ 4L 1s (5/3-equivalent) 5L 1s⟨5/3⟩ →
↙ 3L 2s⟨5/3⟩ ↓ 4L 2s⟨5/3⟩ 5L 2s⟨5/3⟩ ↘ 
┌╥╥╥╥┬┐
│║║║║││
│││││││
└┴┴┴┴┴┘
Scale structure
Step pattern LLLLs
sLLLL
Equave 5/3 (884.4 ¢)
Period 5/3 (884.4 ¢)
Generator size(ed5/3)
Bright 1\5 to 1\4 (176.9 ¢ to 221.1 ¢)
Dark 3\4 to 4\5 (663.3 ¢ to 707.5 ¢)
Related MOS scales
Parent 1L 3s⟨5/3⟩
Sister 1L 4s⟨5/3⟩
Daughters 5L 4s⟨5/3⟩, 4L 5s⟨5/3⟩
Neutralized 3L 2s⟨5/3⟩
2-Flought 9L 1s⟨5/3⟩, 4L 6s⟨5/3⟩
Equal tunings(ed5/3)
Equalized (L:s = 1:1) 1\5 (176.9 ¢)
Supersoft (L:s = 4:3) 4\19 (186.2 ¢)
Soft (L:s = 3:2) 3\14 (189.5 ¢)
Semisoft (L:s = 5:3) 5\23 (192.3 ¢)
Basic (L:s = 2:1) 2\9 (196.5 ¢)
Semihard (L:s = 5:2) 5\22 (201.0 ¢)
Hard (L:s = 3:1) 3\13 (204.1 ¢)
Superhard (L:s = 4:1) 4\17 (208.1 ¢)
Collapsed (L:s = 1:0) 1\4 (221.1 ¢)

4L 1s⟨5/3⟩ is a 5/3-equivalent (non-octave) moment of symmetry scale containing 4 large steps and 1 small step, repeating every interval of 5/3 (884.4 ¢). Generators that produce this scale range from 176.9 ¢ to 221.1 ¢, or from 663.3 ¢ to 707.5 ¢. Scales of this form are always proper because there is only one small step.

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 4L 1s⟨5/3⟩
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-mosstep Perfect 0-mosstep P0ms 0 0.0 ¢
1-mosstep Diminished 1-mosstep d1ms s 0.0 ¢ to 176.9 ¢
Perfect 1-mosstep P1ms L 176.9 ¢ to 221.1 ¢
2-mosstep Minor 2-mosstep m2ms L + s 221.1 ¢ to 353.7 ¢
Major 2-mosstep M2ms 2L 353.7 ¢ to 442.2 ¢
3-mosstep Minor 3-mosstep m3ms 2L + s 442.2 ¢ to 530.6 ¢
Major 3-mosstep M3ms 3L 530.6 ¢ to 663.3 ¢
4-mosstep Perfect 4-mosstep P4ms 3L + s 663.3 ¢ to 707.5 ¢
Augmented 4-mosstep A4ms 4L 707.5 ¢ to 884.4 ¢
5-mosstep Perfect 5-mosstep P5ms 4L + s 884.4 ¢

Generator chain

Generator chain of 4L 1s⟨5/3⟩
Bright gens Scale degree Abbrev.
8 Augmented 3-mosdegree A3md
7 Augmented 2-mosdegree A2md
6 Augmented 1-mosdegree A1md
5 Augmented 0-mosdegree A0md
4 Augmented 4-mosdegree A4md
3 Major 3-mosdegree M3md
2 Major 2-mosdegree M2md
1 Perfect 1-mosdegree P1md
0 Perfect 0-mosdegree
Perfect 5-mosdegree		 P0md
P5md
−1 Perfect 4-mosdegree P4md
−2 Minor 3-mosdegree m3md
−3 Minor 2-mosdegree m2md
−4 Diminished 1-mosdegree d1md
−5 Diminished 5-mosdegree d5md
−6 Diminished 4-mosdegree d4md
−7 Diminished 3-mosdegree d3md
−8 Diminished 2-mosdegree d2md

Modes

Scale degrees of the modes of 4L 1s⟨5/3⟩
UDP Cyclic
order		 Step
pattern		 Scale degree (mosdegree)
0 1 2 3 4 5
4|0 1 LLLLs Perf. Perf. Maj. Maj. Aug. Perf.
3|1 2 LLLsL Perf. Perf. Maj. Maj. Perf. Perf.
2|2 3 LLsLL Perf. Perf. Maj. Min. Perf. Perf.
1|3 4 LsLLL Perf. Perf. Min. Min. Perf. Perf.
0|4 5 sLLLL Perf. Dim. Min. Min. Perf. Perf.

Scale tree

Scale tree and tuning spectrum of 4L 1s⟨5/3⟩
Generator(ed5/3) Cents Step ratio Comments(always proper)
Bright Dark L:s Hardness
1\5 176.872 707.487 1:1 1.000 Equalized 4L 1s⟨5/3⟩
6\29 182.971 701.388 6:5 1.200
5\24 184.241 700.117 5:4 1.250
9\43 185.098 699.260 9:7 1.286
4\19 186.181 698.178 4:3 1.333 Supersoft 4L 1s⟨5/3⟩
11\52 187.076 697.283 11:8 1.375
7\33 187.591 696.767 7:5 1.400
10\47 188.161 696.197 10:7 1.429
3\14 189.505 694.853 3:2 1.500 Soft 4L 1s⟨5/3⟩
11\51 190.744 693.615 11:7 1.571
8\37 191.213 693.146 8:5 1.600
13\60 191.611 692.748 13:8 1.625
5\23 192.252 692.107 5:3 1.667 Semisoft 4L 1s⟨5/3⟩
12\55 192.951 691.408 12:7 1.714
7\32 193.453 690.905 7:4 1.750
9\41 194.128 690.231 9:5 1.800
2\9 196.524 687.835 2:1 2.000 Basic 4L 1s⟨5/3⟩
9\40 198.981 685.378 9:4 2.250
7\31 199.694 684.665 7:3 2.333
12\53 200.232 684.127 12:5 2.400
5\22 200.991 683.368 5:2 2.500 Semihard 4L 1s⟨5/3⟩
13\57 201.696 682.663 13:5 2.600
8\35 202.139 682.220 8:3 2.667
11\48 202.666 681.693 11:4 2.750
3\13 204.083 680.276 3:1 3.000 Hard 4L 1s⟨5/3⟩
10\43 205.665 678.694 10:3 3.333
7\30 206.350 678.008 7:2 3.500
11\47 206.978 677.381 11:3 3.667
4\17 208.084 676.274 4:1 4.000 Superhard 4L 1s⟨5/3⟩
9\38 209.453 674.905 9:2 4.500
5\21 210.562 673.797 5:1 5.000
6\25 212.246 672.113 6:1 6.000
1\4 221.090 663.269 1:0 → ∞ Collapsed 4L 1s⟨5/3⟩
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