3L 4s (3/1-equivalent)

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↖ 2L 3s⟨3/1⟩ ↑ 3L 3s⟨3/1⟩ 4L 3s⟨3/1⟩ ↗
← 2L 4s⟨3/1⟩ 3L 4s (3/1-equivalent) 4L 4s⟨3/1⟩ →
↙ 2L 5s⟨3/1⟩ ↓ 3L 5s⟨3/1⟩ 4L 5s⟨3/1⟩ ↘ 
┌╥┬╥┬╥┬┬┐
│║│║│║│││
│││││││││
└┴┴┴┴┴┴┴┘
Scale structure
Step pattern LsLsLss
ssLsLsL
Equave 3/1 (1902.0 ¢)
Period 3/1 (1902.0 ¢)
Generator size(edt)
Bright 2\7 to 1\3 (543.4 ¢ to 634.0 ¢)
Dark 2\3 to 5\7 (1268.0 ¢ to 1358.5 ¢)
Related MOS scales
Parent 3L 1s⟨3/1⟩
Sister 4L 3s⟨3/1⟩
Daughters 7L 3s⟨3/1⟩, 3L 7s⟨3/1⟩
Neutralized 6L 1s⟨3/1⟩
2-Flought 10L 4s⟨3/1⟩, 3L 11s⟨3/1⟩
Equal tunings(edt)
Equalized (L:s = 1:1) 2\7 (543.4 ¢)
Supersoft (L:s = 4:3) 7\24 (554.7 ¢)
Soft (L:s = 3:2) 5\17 (559.4 ¢)
Semisoft (L:s = 5:3) 8\27 (563.5 ¢)
Basic (L:s = 2:1) 3\10 (570.6 ¢)
Semihard (L:s = 5:2) 7\23 (578.9 ¢)
Hard (L:s = 3:1) 4\13 (585.2 ¢)
Superhard (L:s = 4:1) 5\16 (594.4 ¢)
Collapsed (L:s = 1:0) 1\3 (634.0 ¢)

3L 4s⟨3/1⟩ is a 3/1-equivalent (tritave-equivalent) moment of symmetry scale containing 3 large steps and 4 small steps, repeating every interval of 3/1 (1902.0 ¢). Generators that produce this scale range from 543.4 ¢ to 634 ¢, or from 1268 ¢ to 1358.5 ¢.

Theory

Modes

Modes of 3L 4s⟨3/1⟩
UDP Cyclic
order		 Step
pattern
6|0 1 LsLsLss
5|1 3 LsLssLs
4|2 5 LssLsLs
3|3 7 sLsLsLs
2|4 2 sLsLssL
1|5 4 sLssLsL
0|6 6 ssLsLsL

Temperament interpretations

Icon-Todo.png Todo: expand

Intervals

Intervals of 3L 4s⟨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 271.7 ¢
Major 1-mosstep M1ms L 271.7 ¢ to 634.0 ¢
2-mosstep Diminished 2-mosstep d2ms 2s 0.0 ¢ to 543.4 ¢
Perfect 2-mosstep P2ms L + s 543.4 ¢ to 634.0 ¢
3-mosstep Minor 3-mosstep m3ms L + 2s 634.0 ¢ to 815.1 ¢
Major 3-mosstep M3ms 2L + s 815.1 ¢ to 1268.0 ¢
4-mosstep Minor 4-mosstep m4ms L + 3s 634.0 ¢ to 1086.8 ¢
Major 4-mosstep M4ms 2L + 2s 1086.8 ¢ to 1268.0 ¢
5-mosstep Perfect 5-mosstep P5ms 2L + 3s 1268.0 ¢ to 1358.5 ¢
Augmented 5-mosstep A5ms 3L + 2s 1358.5 ¢ to 1902.0 ¢
6-mosstep Minor 6-mosstep m6ms 2L + 4s 1268.0 ¢ to 1630.2 ¢
Major 6-mosstep M6ms 3L + 3s 1630.2 ¢ to 1902.0 ¢
7-mosstep Perfect 7-mosstep P7ms 3L + 4s 1902.0 ¢

Scale degrees

Scale degrees of the modes of 3L 4s⟨3/1⟩
UDP Cyclic
order		 Step
pattern		 Scale degree (mosdegree)
0 1 2 3 4 5 6 7
6|0 1 LsLsLss Perf. Maj. Perf. Maj. Maj. Aug. Maj. Perf.
5|1 3 LsLssLs Perf. Maj. Perf. Maj. Maj. Perf. Maj. Perf.
4|2 5 LssLsLs Perf. Maj. Perf. Min. Maj. Perf. Maj. Perf.
3|3 7 sLsLsLs Perf. Min. Perf. Min. Maj. Perf. Maj. Perf.
2|4 2 sLsLssL Perf. Min. Perf. Min. Maj. Perf. Min. Perf.
1|5 4 sLssLsL Perf. Min. Perf. Min. Min. Perf. Min. Perf.
0|6 6 ssLsLsL Perf. Min. Dim. Min. Min. Perf. Min. Perf.

Scale tree

Icon-Deprecated.png Scale tree is deprecated. Please use Template: MOS tuning spectrum instead.
Use of a single Comments parameter has become unmaintainable. Existing scale trees should be migrated to the new template, where comments are entered using a step ratio p/q as a parameter: 
{{MOS tuning spectrum
| 3/2 = Example comment
| 4/3 = Another example comment
}}


The parameters tuning and depth have been replaced with Scale Signature and Depth, respectively.


Scale tree and tuning spectrum of 3L 4s⟨3/1⟩
Generator(edt) Cents Step ratio Comments
Bright Dark L:s Hardness
2\7 543.416 1358.539 1:1 1.000 Equalized 3L 4s⟨3/1⟩
11\38 550.566 1351.389 6:5 1.200
9\31 552.180 1349.775 5:4 1.250
16\55 553.296 1348.659 9:7 1.286
7\24 554.737 1347.218 4:3 1.333 Supersoft 3L 4s⟨3/1⟩
19\65 555.956 1345.999 11:8 1.375
12\41 556.670 1345.285 7:5 1.400
17\58 557.470 1344.485 10:7 1.429
5\17 559.399 1342.556 3:2 1.500 Soft 3L 4s⟨3/1⟩
18\61 561.233 1340.722 11:7 1.571
13\44 561.941 1340.014 8:5 1.600
21\71 562.550 1339.405 13:8 1.625
8\27 563.542 1338.413 5:3 1.667 Semisoft 3L 4s⟨3/1⟩
19\64 564.643 1337.312 12:7 1.714
11\37 565.446 1336.509 7:4 1.750
14\47 566.540 1335.415 9:5 1.800
3\10 570.587 1331.369 2:1 2.000 Basic 3L 4s⟨3/1⟩
Scales with tunings softer than this are proper
13\43 575.010 1326.945 9:4 2.250
10\33 576.350 1325.605 7:3 2.333
17\56 577.379 1324.576 12:5 2.400
7\23 578.856 1323.099 5:2 2.500 Semihard 3L 4s⟨3/1⟩
18\59 580.257 1321.698 13:5 2.600
11\36 581.153 1320.802 8:3 2.667
15\49 582.231 1319.724 11:4 2.750
4\13 585.217 1316.738 3:1 3.000 Hard 3L 4s⟨3/1⟩
13\42 588.700 1313.255 10:3 3.333
9\29 590.262 1311.693 7:2 3.500
14\45 591.719 1310.236 11:3 3.667
5\16 594.361 1307.594 4:1 4.000 Superhard 3L 4s⟨3/1⟩
11\35 597.757 1304.198 9:2 4.500
6\19 600.617 1301.338 5:1 5.000
7\22 605.168 1296.788 6:1 6.000
1\3 633.985 1267.970 1:0 → ∞ Collapsed 3L 4s⟨3/1⟩
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