3L 7s (5/2-equivalent)

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↖ 2L 6s⟨5/2⟩ ↑ 3L 6s⟨5/2⟩ 4L 6s⟨5/2⟩ ↗
← 2L 7s⟨5/2⟩ 3L 7s (5/2-equivalent) 4L 7s⟨5/2⟩ →
↙ 2L 8s⟨5/2⟩ ↓ 3L 8s⟨5/2⟩ 4L 8s⟨5/2⟩ ↘ 
┌╥┬┬╥┬┬╥┬┬┬┐
│║││║││║││││
││││││││││││
└┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LssLssLsss
sssLssLssL
Equave 5/2 (1586.3 ¢)
Period 5/2 (1586.3 ¢)
Generator size(ed5/2)
Bright 3\10 to 1\3 (475.9 ¢ to 528.8 ¢)
Dark 2\3 to 7\10 (1057.5 ¢ to 1110.4 ¢)
Related MOS scales
Parent 3L 4s⟨5/2⟩
Sister 7L 3s⟨5/2⟩
Daughters 10L 3s⟨5/2⟩, 3L 10s⟨5/2⟩
Neutralized 6L 4s⟨5/2⟩
2-Flought 13L 7s⟨5/2⟩, 3L 17s⟨5/2⟩
Equal tunings(ed5/2)
Equalized (L:s = 1:1) 3\10 (475.9 ¢)
Supersoft (L:s = 4:3) 10\33 (480.7 ¢)
Soft (L:s = 3:2) 7\23 (482.8 ¢)
Semisoft (L:s = 5:3) 11\36 (484.7 ¢)
Basic (L:s = 2:1) 4\13 (488.1 ¢)
Semihard (L:s = 5:2) 9\29 (492.3 ¢)
Hard (L:s = 3:1) 5\16 (495.7 ¢)
Superhard (L:s = 4:1) 6\19 (500.9 ¢)
Collapsed (L:s = 1:0) 1\3 (528.8 ¢)

3L 7s⟨5/2⟩ is a 5/2-equivalent (non-octave) moment of symmetry scale containing 3 large steps and 7 small steps, repeating every interval of 5/2 (1586.3 ¢). Generators that produce this scale range from 475.9 ¢ to 528.8 ¢, or from 1057.5 ¢ to 1110.4 ¢.

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 3L 7s⟨5/2⟩
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 158.6 ¢
Major 1-mosstep M1ms L 158.6 ¢ to 528.8 ¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0 ¢ to 317.3 ¢
Major 2-mosstep M2ms L + s 317.3 ¢ to 528.8 ¢
3-mosstep Diminished 3-mosstep d3ms 3s 0.0 ¢ to 475.9 ¢
Perfect 3-mosstep P3ms L + 2s 475.9 ¢ to 528.8 ¢
4-mosstep Minor 4-mosstep m4ms L + 3s 528.8 ¢ to 634.5 ¢
Major 4-mosstep M4ms 2L + 2s 634.5 ¢ to 1057.5 ¢
5-mosstep Minor 5-mosstep m5ms L + 4s 528.8 ¢ to 793.2 ¢
Major 5-mosstep M5ms 2L + 3s 793.2 ¢ to 1057.5 ¢
6-mosstep Minor 6-mosstep m6ms L + 5s 528.8 ¢ to 951.8 ¢
Major 6-mosstep M6ms 2L + 4s 951.8 ¢ to 1057.5 ¢
7-mosstep Perfect 7-mosstep P7ms 2L + 5s 1057.5 ¢ to 1110.4 ¢
Augmented 7-mosstep A7ms 3L + 4s 1110.4 ¢ to 1586.3 ¢
8-mosstep Minor 8-mosstep m8ms 2L + 6s 1057.5 ¢ to 1269.1 ¢
Major 8-mosstep M8ms 3L + 5s 1269.1 ¢ to 1586.3 ¢
9-mosstep Minor 9-mosstep m9ms 2L + 7s 1057.5 ¢ to 1427.7 ¢
Major 9-mosstep M9ms 3L + 6s 1427.7 ¢ to 1586.3 ¢
10-mosstep Perfect 10-mosstep P10ms 3L + 7s 1586.3 ¢

Generator chain

Generator chain of 3L 7s⟨5/2⟩
Bright gens Scale degree Abbrev.
12 Augmented 6-mosdegree A6md
11 Augmented 3-mosdegree A3md
10 Augmented 0-mosdegree A0md
9 Augmented 7-mosdegree A7md
8 Major 4-mosdegree M4md
7 Major 1-mosdegree M1md
6 Major 8-mosdegree M8md
5 Major 5-mosdegree M5md
4 Major 2-mosdegree M2md
3 Major 9-mosdegree M9md
2 Major 6-mosdegree M6md
1 Perfect 3-mosdegree P3md
0 Perfect 0-mosdegree
Perfect 10-mosdegree		 P0md
P10md
−1 Perfect 7-mosdegree P7md
−2 Minor 4-mosdegree m4md
−3 Minor 1-mosdegree m1md
−4 Minor 8-mosdegree m8md
−5 Minor 5-mosdegree m5md
−6 Minor 2-mosdegree m2md
−7 Minor 9-mosdegree m9md
−8 Minor 6-mosdegree m6md
−9 Diminished 3-mosdegree d3md
−10 Diminished 10-mosdegree d10md
−11 Diminished 7-mosdegree d7md
−12 Diminished 4-mosdegree d4md

Modes

Scale degrees of the modes of 3L 7s⟨5/2⟩
UDP Cyclic
order		 Step
pattern		 Scale degree (mosdegree)
0 1 2 3 4 5 6 7 8 9 10
9|0 1 LssLssLsss Perf. Maj. Maj. Perf. Maj. Maj. Maj. Aug. Maj. Maj. Perf.
8|1 4 LssLsssLss Perf. Maj. Maj. Perf. Maj. Maj. Maj. Perf. Maj. Maj. Perf.
7|2 7 LsssLssLss Perf. Maj. Maj. Perf. Min. Maj. Maj. Perf. Maj. Maj. Perf.
6|3 10 sLssLssLss Perf. Min. Maj. Perf. Min. Maj. Maj. Perf. Maj. Maj. Perf.
5|4 3 sLssLsssLs Perf. Min. Maj. Perf. Min. Maj. Maj. Perf. Min. Maj. Perf.
4|5 6 sLsssLssLs Perf. Min. Maj. Perf. Min. Min. Maj. Perf. Min. Maj. Perf.
3|6 9 ssLssLssLs Perf. Min. Min. Perf. Min. Min. Maj. Perf. Min. Maj. Perf.
2|7 2 ssLssLsssL Perf. Min. Min. Perf. Min. Min. Maj. Perf. Min. Min. Perf.
1|8 5 ssLsssLssL Perf. Min. Min. Perf. Min. Min. Min. Perf. Min. Min. Perf.
0|9 8 sssLssLssL Perf. Min. Min. Dim. Min. Min. Min. Perf. Min. Min. Perf.

Scale tree

Scale tree and tuning spectrum of 3L 7s⟨5/2⟩
Generator(ed5/2) Cents Step ratio Comments
Bright Dark L:s Hardness
3\10 475.894 1110.420 1:1 1.000 Equalized 3L 7s⟨5/2⟩
16\53 478.887 1107.427 6:5 1.200
13\43 479.583 1106.730 5:4 1.250
23\76 480.069 1106.245 9:7 1.286
10\33 480.701 1105.613 4:3 1.333 Supersoft 3L 7s⟨5/2⟩
27\89 481.241 1105.072 11:8 1.375
17\56 481.560 1104.754 7:5 1.400
24\79 481.918 1104.396 10:7 1.429
7\23 482.791 1103.523 3:2 1.500 Soft 3L 7s⟨5/2⟩
25\82 483.632 1102.681 11:7 1.571
18\59 483.960 1102.354 8:5 1.600
29\95 484.243 1102.071 13:8 1.625
11\36 484.707 1101.607 5:3 1.667 Semisoft 3L 7s⟨5/2⟩
26\85 485.225 1101.088 12:7 1.714
15\49 485.606 1100.707 7:4 1.750
19\62 486.128 1100.185 9:5 1.800
4\13 488.097 1098.217 2:1 2.000 Basic 3L 7s⟨5/2⟩
Scales with tunings softer than this are proper
17\55 490.315 1095.999 9:4 2.250
13\42 491.002 1095.312 7:3 2.333
22\71 491.534 1094.780 12:5 2.400
9\29 492.304 1094.009 5:2 2.500 Semihard 3L 7s⟨5/2⟩
23\74 493.043 1093.270 13:5 2.600
14\45 493.520 1092.794 8:3 2.667
19\61 494.098 1092.216 11:4 2.750
5\16 495.723 1090.591 3:1 3.000 Hard 3L 7s⟨5/2⟩
16\51 497.667 1088.647 10:3 3.333
11\35 498.556 1087.758 7:2 3.500
17\54 499.395 1086.919 11:3 3.667
6\19 500.941 1085.373 4:1 4.000 Superhard 3L 7s⟨5/2⟩
13\41 502.978 1083.336 9:2 4.500
7\22 504.736 1081.578 5:1 5.000
8\25 507.620 1078.693 6:1 6.000
1\3 528.771 1057.542 1:0 → ∞ Collapsed 3L 7s⟨5/2⟩
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