5L 12s

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↖ 4L 11s ↑ 5L 11s 6L 11s ↗
← 4L 12s 5L 12s 6L 12s →
↙ 4L 13s ↓ 5L 13s 6L 13s ↘ 
┌╥┬┬╥┬┬╥┬┬┬╥┬┬╥┬┬┬┐
│║││║││║│││║││║││││
│││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
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
Descends from 5L 2s
Ancestor's step ratio range 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).

Modes

Modes of 5L 12s
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

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¢

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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