5L 12s

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↖ 4L 11s ↑ 5L 11s 6L 11s ↗
← 4L 12s 5L 12s 6L 12s →
↙ 4L 13s ↓ 5L 13s 6L 13s ↘ 
┌╥┬┬╥┬┬╥┬┬┬╥┬┬╥┬┬┬┐
│║││║││║│││║││║││││
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└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LssLssLsssLssLsss
sssLssLsssLssLssL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 10\17 to 3\5 (705.9 ¢ to 720.0 ¢)
Dark 2\5 to 7\17 (480.0 ¢ to 494.1 ¢)
TAMNAMS information
Related to 5L 2s (diatonic)
With tunings 3:1 to 1:0 (hard)
Related MOS scales
Parent 5L 7s
Sister 12L 5s
Daughters 17L 5s, 5L 17s
Neutralized 10L 7s
2-Flought 22L 12s, 5L 29s
Equal tunings
Equalized (L:s = 1:1) 10\17 (705.9 ¢)
Supersoft (L:s = 4:3) 33\56 (707.1 ¢)
Soft (L:s = 3:2) 23\39 (707.7 ¢)
Semisoft (L:s = 5:3) 36\61 (708.2 ¢)
Basic (L:s = 2:1) 13\22 (709.1 ¢)
Semihard (L:s = 5:2) 29\49 (710.2 ¢)
Hard (L:s = 3:1) 16\27 (711.1 ¢)
Superhard (L:s = 4:1) 19\32 (712.5 ¢)
Collapsed (L:s = 1:0) 3\5 (720.0 ¢)

5L 12s, also called s-enharmonic, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 5 large steps and 12 small steps, repeating every octave. 5L 12s is a grandchild scale of 5L 2s, expanding it by 10 tones. Generators that produce this scale range from 705.9 ¢ to 720 ¢, or from 480 ¢ to 494.1 ¢.

This scale is characterized by having a diesis (the difference between a large step and two small steps) that is larger than the chroma.

The supra/quasisuper version is proper, but the superpyth/ultrapyth version is improper (it does not become proper until you add 5 more notes to form the superpyth 22-note scale).

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 interval regions.

Intervals

Intervals of 5L 12s
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 70.6 ¢
Major 1-mosstep M1ms L 70.6 ¢ to 240.0 ¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0 ¢ to 141.2 ¢
Major 2-mosstep M2ms L + s 141.2 ¢ to 240.0 ¢
3-mosstep Minor 3-mosstep m3ms 3s 0.0 ¢ to 211.8 ¢
Major 3-mosstep M3ms L + 2s 211.8 ¢ to 240.0 ¢
4-mosstep Minor 4-mosstep m4ms L + 3s 240.0 ¢ to 282.4 ¢
Major 4-mosstep M4ms 2L + 2s 282.4 ¢ to 480.0 ¢
5-mosstep Minor 5-mosstep m5ms L + 4s 240.0 ¢ to 352.9 ¢
Major 5-mosstep M5ms 2L + 3s 352.9 ¢ to 480.0 ¢
6-mosstep Minor 6-mosstep m6ms L + 5s 240.0 ¢ to 423.5 ¢
Major 6-mosstep M6ms 2L + 4s 423.5 ¢ to 480.0 ¢
7-mosstep Perfect 7-mosstep P7ms 2L + 5s 480.0 ¢ to 494.1 ¢
Augmented 7-mosstep A7ms 3L + 4s 494.1 ¢ to 720.0 ¢
8-mosstep Minor 8-mosstep m8ms 2L + 6s 480.0 ¢ to 564.7 ¢
Major 8-mosstep M8ms 3L + 5s 564.7 ¢ to 720.0 ¢
9-mosstep Minor 9-mosstep m9ms 2L + 7s 480.0 ¢ to 635.3 ¢
Major 9-mosstep M9ms 3L + 6s 635.3 ¢ to 720.0 ¢
10-mosstep Diminished 10-mosstep d10ms 2L + 8s 480.0 ¢ to 705.9 ¢
Perfect 10-mosstep P10ms 3L + 7s 705.9 ¢ to 720.0 ¢
11-mosstep Minor 11-mosstep m11ms 3L + 8s 720.0 ¢ to 776.5 ¢
Major 11-mosstep M11ms 4L + 7s 776.5 ¢ to 960.0 ¢
12-mosstep Minor 12-mosstep m12ms 3L + 9s 720.0 ¢ to 847.1 ¢
Major 12-mosstep M12ms 4L + 8s 847.1 ¢ to 960.0 ¢
13-mosstep Minor 13-mosstep m13ms 3L + 10s 720.0 ¢ to 917.6 ¢
Major 13-mosstep M13ms 4L + 9s 917.6 ¢ to 960.0 ¢
14-mosstep Minor 14-mosstep m14ms 4L + 10s 960.0 ¢ to 988.2 ¢
Major 14-mosstep M14ms 5L + 9s 988.2 ¢ to 1200.0 ¢
15-mosstep Minor 15-mosstep m15ms 4L + 11s 960.0 ¢ to 1058.8 ¢
Major 15-mosstep M15ms 5L + 10s 1058.8 ¢ to 1200.0 ¢
16-mosstep Minor 16-mosstep m16ms 4L + 12s 960.0 ¢ to 1129.4 ¢
Major 16-mosstep M16ms 5L + 11s 1129.4 ¢ to 1200.0 ¢
17-mosstep Perfect 17-mosstep P17ms 5L + 12s 1200.0 ¢

Generator chain

Generator chain of 5L 12s
Bright gens Scale degree Abbrev.
21 Augmented 6-mosdegree A6md
20 Augmented 13-mosdegree A13md
19 Augmented 3-mosdegree A3md
18 Augmented 10-mosdegree A10md
17 Augmented 0-mosdegree A0md
16 Augmented 7-mosdegree A7md
15 Major 14-mosdegree M14md
14 Major 4-mosdegree M4md
13 Major 11-mosdegree M11md
12 Major 1-mosdegree M1md
11 Major 8-mosdegree M8md
10 Major 15-mosdegree M15md
9 Major 5-mosdegree M5md
8 Major 12-mosdegree M12md
7 Major 2-mosdegree M2md
6 Major 9-mosdegree M9md
5 Major 16-mosdegree M16md
4 Major 6-mosdegree M6md
3 Major 13-mosdegree M13md
2 Major 3-mosdegree M3md
1 Perfect 10-mosdegree P10md
0 Perfect 0-mosdegree
Perfect 17-mosdegree		 P0md
P17md
−1 Perfect 7-mosdegree P7md
−2 Minor 14-mosdegree m14md
−3 Minor 4-mosdegree m4md
−4 Minor 11-mosdegree m11md
−5 Minor 1-mosdegree m1md
−6 Minor 8-mosdegree m8md
−7 Minor 15-mosdegree m15md
−8 Minor 5-mosdegree m5md
−9 Minor 12-mosdegree m12md
−10 Minor 2-mosdegree m2md
−11 Minor 9-mosdegree m9md
−12 Minor 16-mosdegree m16md
−13 Minor 6-mosdegree m6md
−14 Minor 13-mosdegree m13md
−15 Minor 3-mosdegree m3md
−16 Diminished 10-mosdegree d10md
−17 Diminished 17-mosdegree d17md
−18 Diminished 7-mosdegree d7md
−19 Diminished 14-mosdegree d14md
−20 Diminished 4-mosdegree d4md
−21 Diminished 11-mosdegree d11md

Modes

Scale degrees of the modes of 5L 12s
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

Scale tree and tuning spectrum of 5L 12s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
10\17 705.882 494.118 1:1 1.000 Equalized 5L 12s
53\90 706.667 493.333 6:5 1.200
43\73 706.849 493.151 5:4 1.250
76\129 706.977 493.023 9:7 1.286
33\56 707.143 492.857 4:3 1.333 Supersoft 5L 12s
Supra
89\151 707.285 492.715 11:8 1.375
56\95 707.368 492.632 7:5 1.400
79\134 707.463 492.537 10:7 1.429
23\39 707.692 492.308 3:2 1.500 Soft 5L 12s
82\139 707.914 492.086 11:7 1.571
59\100 708.000 492.000 8:5 1.600
95\161 708.075 491.925 13:8 1.625 Golden supra (708.0539 ¢)
36\61 708.197 491.803 5:3 1.667 Semisoft 5L 12s
Quasisuper/quasisupra
85\144 708.333 491.667 12:7 1.714
49\83 708.434 491.566 7:4 1.750
62\105 708.571 491.429 9:5 1.800
13\22 709.091 490.909 2:1 2.000 Basic 5L 12s
Scales with tunings softer than this are proper
55\93 709.677 490.323 9:4 2.250
42\71 709.859 490.141 7:3 2.333
71\120 710.000 490.000 12:5 2.400
29\49 710.204 489.796 5:2 2.500 Semihard 5L 12s
Superpyth
74\125 710.400 489.600 13:5 2.600 Golden superpyth (710.4345 ¢)
45\76 710.526 489.474 8:3 2.667
61\103 710.680 489.320 11:4 2.750
16\27 711.111 488.889 3:1 3.000 Hard 5L 12s
51\86 711.628 488.372 10:3 3.333
35\59 711.864 488.136 7:2 3.500 Quasiultra
54\91 712.088 487.912 11:3 3.667
19\32 712.500 487.500 4:1 4.000 Superhard 5L 12s
41\69 713.043 486.957 9:2 4.500
22\37 713.514 486.486 5:1 5.000 Oceanfront/ultrapyth
25\42 714.286 485.714 6:1 6.000 Hemiseven ↓
3\5 720.000 480.000 1:0 → ∞ Collapsed 5L 12s
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