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.

Modes

Modes of 4L 1s⟨5/3⟩
UDP Cyclic
order		 Step
pattern
4|0 1 LLLLs
3|1 2 LLLsL
2|2 3 LLsLL
1|3 4 LsLLL
0|4 5 sLLLL

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¢

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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