5L 5s (3/1-equivalent)

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↖ 4L 4s⟨3/1⟩ ↑ 5L 4s⟨3/1⟩ 6L 4s⟨3/1⟩ ↗
← 4L 5s⟨3/1⟩ 5L 5s (3/1-equivalent) 6L 5s⟨3/1⟩ →
↙ 4L 6s⟨3/1⟩ ↓ 5L 6s⟨3/1⟩ 6L 6s⟨3/1⟩ ↘ 
┌╥┬╥┬╥┬╥┬╥┬┐
│║│║│║│║│║││
││││││││││││
└┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LsLsLsLsLs
sLsLsLsLsL
Equave 3/1 (1902.0¢)
Period 1\5edt (380.4¢)
Generator size(edt)
Bright 1\10 to 1\5 (190.2¢ to 380.4¢)
Dark 0\5 to 1\10 (0.0¢ to 190.2¢)
Related MOS scales
Parent 5L 0s⟨3/1⟩
Sister 5L 5s⟨3/1⟩
Daughters 10L 5s⟨3/1⟩, 5L 10s⟨3/1⟩
Neutralized 10L 0s⟨3/1⟩
2-Flought 15L 5s⟨3/1⟩, 5L 15s⟨3/1⟩
Equal tunings(edt)
Equalized (L:s = 1:1) 1\10 (190.2¢)
Supersoft (L:s = 4:3) 4\35 (217.4¢)
Soft (L:s = 3:2) 3\25 (228.2¢)
Semisoft (L:s = 5:3) 5\40 (237.7¢)
Basic (L:s = 2:1) 2\15 (253.6¢)
Semihard (L:s = 5:2) 5\35 (271.7¢)
Hard (L:s = 3:1) 3\20 (285.3¢)
Superhard (L:s = 4:1) 4\25 (304.3¢)
Collapsed (L:s = 1:0) 1\5 (380.4¢)

5L 5s⟨3/1⟩ is a 3/1-equivalent (tritave-equivalent) moment of symmetry scale containing 5 large steps and 5 small steps, with a period of 1 large step and 1 small step that repeats every 380.4¢, or 5 times every interval of 3/1 (1902.0¢). Generators that produce this scale range from 190.2¢ to 380.4¢, or from 0¢ to 190.2¢. Scales of the true MOS form, where every period is the same, are proper because there is only one small step per period. Its period can be interpreted as a 5/4 (~386¢) flattened by about 6¢.

Modes

Modes of 5L 5s⟨3/1⟩
UDP Cyclic
order		 Step
pattern
5|0(5) 1 LsLsLsLsLs
0|5(5) 2 sLsLsLsLsL

Intervals

Intervals of 5L 5s⟨3/1⟩
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 190.2¢
Major 1-mosstep M1ms L 190.2¢ to 380.4¢
2-mosstep Perfect 2-mosstep P2ms L + s 380.4¢
3-mosstep Minor 3-mosstep m3ms L + 2s 380.4¢ to 570.6¢
Major 3-mosstep M3ms 2L + s 570.6¢ to 760.8¢
4-mosstep Perfect 4-mosstep P4ms 2L + 2s 760.8¢
5-mosstep Minor 5-mosstep m5ms 2L + 3s 760.8¢ to 951.0¢
Major 5-mosstep M5ms 3L + 2s 951.0¢ to 1141.2¢
6-mosstep Perfect 6-mosstep P6ms 3L + 3s 1141.2¢
7-mosstep Minor 7-mosstep m7ms 3L + 4s 1141.2¢ to 1331.4¢
Major 7-mosstep M7ms 4L + 3s 1331.4¢ to 1521.6¢
8-mosstep Perfect 8-mosstep P8ms 4L + 4s 1521.6¢
9-mosstep Minor 9-mosstep m9ms 4L + 5s 1521.6¢ to 1711.8¢
Major 9-mosstep M9ms 5L + 4s 1711.8¢ to 1902.0¢
10-mosstep Perfect 10-mosstep P10ms 5L + 5s 1902.0¢

Scale tree

Scale Tree and Tuning Spectrum of 5L 5s⟨3/1⟩
Generator(edt) Cents Step ratio Comments(always proper)
Bright Dark L:s Hardness
1\10 190.196 190.196 1:1 1.000 Equalized 5L 5s⟨3/1⟩
6\55 207.486 172.905 6:5 1.200
5\45 211.328 169.063 5:4 1.250
9\80 213.970 166.421 9:7 1.286
4\35 217.366 163.025 4:3 1.333 Supersoft 5L 5s⟨3/1⟩
11\95 220.226 160.165 11:8 1.375
7\60 221.895 158.496 7:5 1.400
10\85 223.759 156.632 10:7 1.429
3\25 228.235 152.156 3:2 1.500 Soft 5L 5s⟨3/1⟩
11\90 232.461 147.930 11:7 1.571
8\65 234.087 146.304 8:5 1.600
13\105 235.480 144.911 13:8 1.625
5\40 237.744 142.647 5:3 1.667 Semisoft 5L 5s⟨3/1⟩
12\95 240.247 140.144 12:7 1.714
7\55 242.067 138.324 7:4 1.750
9\70 244.537 135.854 9:5 1.800
2\15 253.594 126.797 2:1 2.000 Basic 5L 5s⟨3/1⟩
9\65 263.348 117.043 9:4 2.250
7\50 266.274 114.117 7:3 2.333
12\85 268.511 111.880 12:5 2.400
5\35 271.708 108.683 5:2 2.500 Semihard 5L 5s⟨3/1⟩
13\90 274.727 105.664 13:5 2.600
8\55 276.648 103.743 8:3 2.667
11\75 278.953 101.438 11:4 2.750
3\20 285.293 95.098 3:1 3.000 Hard 5L 5s⟨3/1⟩
10\65 292.608 87.783 10:3 3.333
7\45 295.860 84.531 7:2 3.500
11\70 298.879 81.512 11:3 3.667
4\25 304.313 76.078 4:1 4.000 Superhard 5L 5s⟨3/1⟩
9\55 311.229 69.162 9:2 4.500
5\30 316.993 63.399 5:1 5.000
6\35 326.049 54.342 6:1 6.000
1\5 380.391 0.000 1:0 → ∞ Collapsed 5L 5s⟨3/1⟩


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