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¢.

Modes

Modes of 3L 7s⟨5/2⟩
UDP Cyclic
order		 Step
pattern
9|0 1 LssLssLsss
8|1 4 LssLsssLss
7|2 7 LsssLssLss
6|3 10 sLssLssLss
5|4 3 sLssLsssLs
4|5 6 sLsssLssLs
3|6 9 ssLssLssLs
2|7 2 ssLssLsssL
1|8 5 ssLsssLssL
0|9 8 sssLssLssL

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¢

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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