3L 7s (3/1-equivalent)

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↖ 2L 6s⟨3/1⟩ ↑ 3L 6s⟨3/1⟩ 4L 6s⟨3/1⟩ ↗
← 2L 7s⟨3/1⟩ 3L 7s (3/1-equivalent) 4L 7s⟨3/1⟩ →
↙ 2L 8s⟨3/1⟩ ↓ 3L 8s⟨3/1⟩ 4L 8s⟨3/1⟩ ↘ 
┌╥┬┬╥┬┬╥┬┬┬┐
│║││║││║││││
││││││││││││
└┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LssLssLsss
sssLssLssL
Equave 3/1 (1902.0¢)
Period 3/1 (1902.0¢)
Generator size(edt)
Bright 3\10 to 1\3 (570.6¢ to 634.0¢)
Dark 2\3 to 7\10 (1268.0¢ to 1331.4¢)
Related MOS scales
Parent 3L 4s⟨3/1⟩
Sister 7L 3s⟨3/1⟩
Daughters 10L 3s⟨3/1⟩, 3L 10s⟨3/1⟩
Neutralized 6L 4s⟨3/1⟩
2-Flought 13L 7s⟨3/1⟩, 3L 17s⟨3/1⟩
Equal tunings(edt)
Equalized (L:s = 1:1) 3\10 (570.6¢)
Supersoft (L:s = 4:3) 10\33 (576.4¢)
Soft (L:s = 3:2) 7\23 (578.9¢)
Semisoft (L:s = 5:3) 11\36 (581.2¢)
Basic (L:s = 2:1) 4\13 (585.2¢)
Semihard (L:s = 5:2) 9\29 (590.3¢)
Hard (L:s = 3:1) 5\16 (594.4¢)
Superhard (L:s = 4:1) 6\19 (600.6¢)
Collapsed (L:s = 1:0) 1\3 (634.0¢)

3L 7s⟨3/1⟩ is a 3/1-equivalent (tritave-equivalent) moment of symmetry scale containing 3 large steps and 7 small steps, repeating every interval of 3/1 (1902.0¢). Generators that produce this scale range from 570.6¢ to 634¢, or from 1268¢ to 1331.4¢.

It is the decatonic scale of the 7/5-generated Canopus temperament, one of the most notable no-twos temperaments after Bohlen-Pierce-Stearns. Basic 3L 7s〈3/1〉 is in 13edt (Bohlen-Pierce).

Modes

Modes of 3L 7s⟨3/1⟩
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⟨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 634.0¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0¢ to 380.4¢
Major 2-mosstep M2ms L + s 380.4¢ to 634.0¢
3-mosstep Diminished 3-mosstep d3ms 3s 0.0¢ to 570.6¢
Perfect 3-mosstep P3ms L + 2s 570.6¢ to 634.0¢
4-mosstep Minor 4-mosstep m4ms L + 3s 634.0¢ to 760.8¢
Major 4-mosstep M4ms 2L + 2s 760.8¢ to 1268.0¢
5-mosstep Minor 5-mosstep m5ms L + 4s 634.0¢ to 951.0¢
Major 5-mosstep M5ms 2L + 3s 951.0¢ to 1268.0¢
6-mosstep Minor 6-mosstep m6ms L + 5s 634.0¢ to 1141.2¢
Major 6-mosstep M6ms 2L + 4s 1141.2¢ to 1268.0¢
7-mosstep Perfect 7-mosstep P7ms 2L + 5s 1268.0¢ to 1331.4¢
Augmented 7-mosstep A7ms 3L + 4s 1331.4¢ to 1902.0¢
8-mosstep Minor 8-mosstep m8ms 2L + 6s 1268.0¢ to 1521.6¢
Major 8-mosstep M8ms 3L + 5s 1521.6¢ to 1902.0¢
9-mosstep Minor 9-mosstep m9ms 2L + 7s 1268.0¢ to 1711.8¢
Major 9-mosstep M9ms 3L + 6s 1711.8¢ to 1902.0¢
10-mosstep Perfect 10-mosstep P10ms 3L + 7s 1902.0¢

Scale tree

Scale Tree and Tuning Spectrum of 3L 7s⟨3/1⟩
Generator(edt) Cents Step ratio Comments
Bright Dark L:s Hardness
3\10 570.587 1331.369 1:1 1.000 Equalized 3L 7s⟨3/1⟩
16\53 574.175 1327.780 6:5 1.200
13\43 575.010 1326.945 5:4 1.250
23\76 575.592 1326.363 9:7 1.286
10\33 576.350 1325.605 4:3 1.333 Supersoft 3L 7s⟨3/1⟩
27\89 576.998 1324.957 11:8 1.375
17\56 577.379 1324.576 7:5 1.400
24\79 577.809 1324.146 10:7 1.429
7\23 578.856 1323.099 3:2 1.500 Soft 3L 7s⟨3/1⟩
25\82 579.864 1322.091 11:7 1.571
18\59 580.257 1321.698 8:5 1.600
29\95 580.597 1321.358 13:8 1.625
11\36 581.153 1320.802 5:3 1.667 Semisoft 3L 7s⟨3/1⟩
26\85 581.774 1320.181 12:7 1.714
15\49 582.231 1319.724 7:4 1.750
19\62 582.857 1319.098 9:5 1.800
4\13 585.217 1316.738 2:1 2.000 Basic 3L 7s⟨3/1⟩
Scales with tunings softer than this are proper
Canopus is around here
17\55 587.877 1314.078 9:4 2.250
13\42 588.700 1313.255 7:3 2.333
22\71 589.338 1312.617 12:5 2.400
9\29 590.262 1311.693 5:2 2.500 Semihard 3L 7s⟨3/1⟩
23\74 591.148 1310.807 13:5 2.600
14\45 591.719 1310.236 8:3 2.667
19\61 592.412 1309.543 11:4 2.750
5\16 594.361 1307.594 3:1 3.000 Hard 3L 7s⟨3/1⟩
16\51 596.692 1305.263 10:3 3.333
11\35 597.757 1304.198 7:2 3.500
17\54 598.764 1303.191 11:3 3.667
6\19 600.617 1301.338 4:1 4.000 Superhard 3L 7s⟨3/1⟩
13\41 603.059 1298.896 9:2 4.500
7\22 605.168 1296.788 5:1 5.000
8\25 608.626 1293.329 6:1 6.000
1\3 633.985 1267.970 1:0 → ∞ Collapsed 3L 7s⟨3/1⟩
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