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\5 (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 none
Sister 5L 5s⟨3/1⟩ (self)
Daughters 10L 5s⟨3/1⟩, 5L 10s⟨3/1⟩
Neutralized 10edt
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 ¢.

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 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 ¢

Generator chain

Generator chain of 5L 5s⟨3/1⟩
Bright gens Scale degree Abbrev. Scale degree Abbrev. Scale degree Abbrev. Scale degree Abbrev. Scale degree Abbrev.
2 Augmented 0-mosdegree A0md Augmented 2-mosdegree A2md Augmented 4-mosdegree A4md Augmented 6-mosdegree A6md Augmented 8-mosdegree A8md
1 Major 1-mosdegree M1md Major 3-mosdegree M3md Major 5-mosdegree M5md Major 7-mosdegree M7md Major 9-mosdegree M9md
0 Perfect 0-mosdegree
Perfect 2-mosdegree		 P0md
P2md		 Perfect 2-mosdegree
Perfect 4-mosdegree		 P2md
P4md		 Perfect 4-mosdegree
Perfect 6-mosdegree		 P4md
P6md		 Perfect 6-mosdegree
Perfect 8-mosdegree		 P6md
P8md		 Perfect 8-mosdegree
Perfect 10-mosdegree		 P8md
P10md
−1 Minor 1-mosdegree m1md Minor 3-mosdegree m3md Minor 5-mosdegree m5md Minor 7-mosdegree m7md Minor 9-mosdegree m9md
−2 Diminished 2-mosdegree d2md Diminished 4-mosdegree d4md Diminished 6-mosdegree d6md Diminished 8-mosdegree d8md Diminished 10-mosdegree d10md

Modes

Scale degrees of the modes of 5L 5s⟨3/1⟩
UDP Cyclic
order		 Step
pattern		 Scale degree (mosdegree)
0 1 2 3 4 5 6 7 8 9 10
5|0(5) 1 LsLsLsLsLs Perf. Maj. Perf. Maj. Perf. Maj. Perf. Maj. Perf. Maj. Perf.
0|5(5) 2 sLsLsLsLsL Perf. Min. Perf. Min. Perf. Min. Perf. Min. Perf. Min. Perf.

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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