5L 12s (3/1-equivalent)

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↖ 4L 11s⟨3/1⟩ ↑ 5L 11s⟨3/1⟩ 6L 11s⟨3/1⟩ ↗
← 4L 12s⟨3/1⟩ 5L 12s (3/1-equivalent) 6L 12s⟨3/1⟩ →
↙ 4L 13s⟨3/1⟩ ↓ 5L 13s⟨3/1⟩ 6L 13s⟨3/1⟩ ↘
Scale structure
Step pattern LssLssLsssLssLsss
sssLssLsssLssLssL
Equave 3/1 (1902.0 ¢)
Period 3/1 (1902.0 ¢)
Generator size(edt)
Bright 10\17 to 3\5 (1118.8 ¢ to 1141.2 ¢)
Dark 2\5 to 7\17 (760.8 ¢ to 783.2 ¢)
Related MOS scales
Parent 5L 7s⟨3/1⟩
Sister 12L 5s⟨3/1⟩
Daughters 17L 5s⟨3/1⟩, 5L 17s⟨3/1⟩
Neutralized 10L 7s⟨3/1⟩
2-Flought 22L 12s⟨3/1⟩, 5L 29s⟨3/1⟩
Equal tunings(edt)
Equalized (L:s = 1:1) 10\17 (1118.8 ¢)
Supersoft (L:s = 4:3) 33\56 (1120.8 ¢)
Soft (L:s = 3:2) 23\39 (1121.7 ¢)
Semisoft (L:s = 5:3) 36\61 (1122.5 ¢)
Basic (L:s = 2:1) 13\22 (1123.9 ¢)
Semihard (L:s = 5:2) 29\49 (1125.6 ¢)
Hard (L:s = 3:1) 16\27 (1127.1 ¢)
Superhard (L:s = 4:1) 19\32 (1129.3 ¢)
Collapsed (L:s = 1:0) 3\5 (1141.2 ¢)
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5L 12s⟨3/1⟩ is a 3/1-equivalent (tritave-equivalent) moment of symmetry scale containing 5 large steps and 12 small steps, repeating every interval of 3/1 (1902.0 ¢). Generators that produce this scale range from 1118.8 ¢ to 1141.2 ¢, or from 760.8 ¢ to 783.2 ¢.

Theory

Modes

Modes of 5L 12s⟨3/1⟩
UDP Cyclic
order		 Step
pattern
16|0 1 LssLssLsssLssLsss
15|1 11 LssLsssLssLssLsss
14|2 4 LssLsssLssLsssLss
13|3 14 LsssLssLssLsssLss
12|4 7 LsssLssLsssLssLss
11|5 17 sLssLssLsssLssLss
10|6 10 sLssLsssLssLssLss
9|7 3 sLssLsssLssLsssLs
8|8 13 sLsssLssLssLsssLs
7|9 6 sLsssLssLsssLssLs
6|10 16 ssLssLssLsssLssLs
5|11 9 ssLssLsssLssLssLs
4|12 2 ssLssLsssLssLsssL
3|13 12 ssLsssLssLssLsssL
2|14 5 ssLsssLssLsssLssL
1|15 15 sssLssLssLsssLssL
0|16 8 sssLssLsssLssLssL

Temperament interpretations

Todo: expand

Intervals

Intervals of 5L 12s⟨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 111.9 ¢
Major 1-mosstep M1ms L 111.9 ¢ to 380.4 ¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0 ¢ to 223.8 ¢
Major 2-mosstep M2ms L + s 223.8 ¢ to 380.4 ¢
3-mosstep Minor 3-mosstep m3ms 3s 0.0 ¢ to 335.6 ¢
Major 3-mosstep M3ms L + 2s 335.6 ¢ to 380.4 ¢
4-mosstep Minor 4-mosstep m4ms L + 3s 380.4 ¢ to 447.5 ¢
Major 4-mosstep M4ms 2L + 2s 447.5 ¢ to 760.8 ¢
5-mosstep Minor 5-mosstep m5ms L + 4s 380.4 ¢ to 559.4 ¢
Major 5-mosstep M5ms 2L + 3s 559.4 ¢ to 760.8 ¢
6-mosstep Minor 6-mosstep m6ms L + 5s 380.4 ¢ to 671.3 ¢
Major 6-mosstep M6ms 2L + 4s 671.3 ¢ to 760.8 ¢
7-mosstep Perfect 7-mosstep P7ms 2L + 5s 760.8 ¢ to 783.2 ¢
Augmented 7-mosstep A7ms 3L + 4s 783.2 ¢ to 1141.2 ¢
8-mosstep Minor 8-mosstep m8ms 2L + 6s 760.8 ¢ to 895.0 ¢
Major 8-mosstep M8ms 3L + 5s 895.0 ¢ to 1141.2 ¢
9-mosstep Minor 9-mosstep m9ms 2L + 7s 760.8 ¢ to 1006.9 ¢
Major 9-mosstep M9ms 3L + 6s 1006.9 ¢ to 1141.2 ¢
10-mosstep Diminished 10-mosstep d10ms 2L + 8s 760.8 ¢ to 1118.8 ¢
Perfect 10-mosstep P10ms 3L + 7s 1118.8 ¢ to 1141.2 ¢
11-mosstep Minor 11-mosstep m11ms 3L + 8s 1141.2 ¢ to 1230.7 ¢
Major 11-mosstep M11ms 4L + 7s 1230.7 ¢ to 1521.6 ¢
12-mosstep Minor 12-mosstep m12ms 3L + 9s 1141.2 ¢ to 1342.6 ¢
Major 12-mosstep M12ms 4L + 8s 1342.6 ¢ to 1521.6 ¢
13-mosstep Minor 13-mosstep m13ms 3L + 10s 1141.2 ¢ to 1454.4 ¢
Major 13-mosstep M13ms 4L + 9s 1454.4 ¢ to 1521.6 ¢
14-mosstep Minor 14-mosstep m14ms 4L + 10s 1521.6 ¢ to 1566.3 ¢
Major 14-mosstep M14ms 5L + 9s 1566.3 ¢ to 1902.0 ¢
15-mosstep Minor 15-mosstep m15ms 4L + 11s 1521.6 ¢ to 1678.2 ¢
Major 15-mosstep M15ms 5L + 10s 1678.2 ¢ to 1902.0 ¢
16-mosstep Minor 16-mosstep m16ms 4L + 12s 1521.6 ¢ to 1790.1 ¢
Major 16-mosstep M16ms 5L + 11s 1790.1 ¢ to 1902.0 ¢
17-mosstep Perfect 17-mosstep P17ms 5L + 12s 1902.0 ¢

Scale degrees

Scale degrees of the modes of 5L 12s⟨3/1⟩
UDP Cyclic
order 		Step
pattern 		Scale degree (mosdegree)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
16|0 1 LssLssLsssLssLsss Perf. Maj. Maj. Maj. Maj. Maj. Maj. Aug. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
15|1 11 LssLsssLssLssLsss Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
14|2 4 LssLsssLssLsssLss Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Perf. Maj. Maj. Maj. Min. Maj. Maj. Perf.
13|3 14 LsssLssLssLsssLss Perf. Maj. Maj. Maj. Min. Maj. Maj. Perf. Maj. Maj. Perf. Maj. Maj. Maj. Min. Maj. Maj. Perf.
12|4 7 LsssLssLsssLssLss Perf. Maj. Maj. Maj. Min. Maj. Maj. Perf. Maj. Maj. Perf. Min. Maj. Maj. Min. Maj. Maj. Perf.
11|5 17 sLssLssLsssLssLss Perf. Min. Maj. Maj. Min. Maj. Maj. Perf. Maj. Maj. Perf. Min. Maj. Maj. Min. Maj. Maj. Perf.
10|6 10 sLssLsssLssLssLss Perf. Min. Maj. Maj. Min. Maj. Maj. Perf. Min. Maj. Perf. Min. Maj. Maj. Min. Maj. Maj. Perf.
9|7 3 sLssLsssLssLsssLs Perf. Min. Maj. Maj. Min. Maj. Maj. Perf. Min. Maj. Perf. Min. Maj. Maj. Min. Min. Maj. Perf.
8|8 13 sLsssLssLssLsssLs Perf. Min. Maj. Maj. Min. Min. Maj. Perf. Min. Maj. Perf. Min. Maj. Maj. Min. Min. Maj. Perf.
7|9 6 sLsssLssLsssLssLs Perf. Min. Maj. Maj. Min. Min. Maj. Perf. Min. Maj. Perf. Min. Min. Maj. Min. Min. Maj. Perf.
6|10 16 ssLssLssLsssLssLs Perf. Min. Min. Maj. Min. Min. Maj. Perf. Min. Maj. Perf. Min. Min. Maj. Min. Min. Maj. Perf.
5|11 9 ssLssLsssLssLssLs Perf. Min. Min. Maj. Min. Min. Maj. Perf. Min. Min. Perf. Min. Min. Maj. Min. Min. Maj. Perf.
4|12 2 ssLssLsssLssLsssL Perf. Min. Min. Maj. Min. Min. Maj. Perf. Min. Min. Perf. Min. Min. Maj. Min. Min. Min. Perf.
3|13 12 ssLsssLssLssLsssL Perf. Min. Min. Maj. Min. Min. Min. Perf. Min. Min. Perf. Min. Min. Maj. Min. Min. Min. Perf.
2|14 5 ssLsssLssLsssLssL Perf. Min. Min. Maj. Min. Min. Min. Perf. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Perf.
1|15 15 sssLssLssLsssLssL Perf. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Perf.
0|16 8 sssLssLsssLssLssL Perf. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Dim. Min. Min. Min. Min. Min. Min. Perf.

Scale tree

Template: Scale tree is deprecated. Please use Template: MOS tuning spectrum instead. Details:
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 5L 12s⟨3/1⟩
Generator(edt) Cents Step ratio Comments
Bright Dark L:s Hardness
10\17 1118.797 783.158 1:1 1.000 Equalized 5L 12s⟨3/1⟩
53\90 1120.040 781.915 6:5 1.200
43\73 1120.330 781.625 5:4 1.250
76\129 1120.532 781.423 9:7 1.286
33\56 1120.795 781.160 4:3 1.333 Supersoft 5L 12s⟨3/1⟩
89\151 1121.020 780.935 11:8 1.375
56\95 1121.152 780.803 7:5 1.400
79\134 1121.302 780.653 10:7 1.429
23\39 1121.666 780.289 3:2 1.500 Soft 5L 12s⟨3/1⟩
82\139 1122.017 779.938 11:7 1.571
59\100 1122.153 779.802 8:5 1.600
95\161 1122.272 779.683 13:8 1.625
36\61 1122.465 779.490 5:3 1.667 Semisoft 5L 12s⟨3/1⟩
85\144 1122.682 779.273 12:7 1.714
49\83 1122.841 779.114 7:4 1.750
62\105 1123.059 778.896 9:5 1.800
13\22 1123.883 778.073 2:1 2.000 Basic 5L 12s⟨3/1⟩
Scales with tunings softer than this are proper
55\93 1124.812 777.143 9:4 2.250
42\71 1125.100 776.855 7:3 2.333
71\120 1125.323 776.632 12:5 2.400
29\49 1125.647 776.308 5:2 2.500 Semihard 5L 12s⟨3/1⟩
74\125 1125.957 775.998 13:5 2.600
45\76 1126.158 775.797 8:3 2.667
61\103 1126.401 775.554 11:4 2.750
16\27 1127.084 774.871 3:1 3.000 Hard 5L 12s⟨3/1⟩
51\86 1127.904 774.051 10:3 3.333
35\59 1128.278 773.677 7:2 3.500
54\91 1128.633 773.322 11:3 3.667
19\32 1129.286 772.669 4:1 4.000 Superhard 5L 12s⟨3/1⟩
41\69 1130.147 771.808 9:2 4.500
22\37 1130.892 771.063 5:1 5.000
25\42 1132.116 769.839 6:1 6.000
3\5 1141.173 760.782 1:0 → ∞ Collapsed 5L 12s⟨3/1⟩
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