5L 12s

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5L 12s
Pattern LssLssLsssLssLsss
Period 2/1
Generator range 10\17 (705.9¢) to 3\5 (720.0¢)
Parent MOS 5L 7s
Daughter MOSes 17L 5s, 5L 17s
Sister MOS 12L 5s
Equal tunings
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¢)

5L 12s is the MOS pattern of the superpyth enharmonic or mega-chromatic scale. In contrast to the schismic enharmonic scale, in which the enharmonic diesis (negative diminished second) is smaller than the chromatic semitone, here the reverse is true: the enharmonic diesis is larger than the chromatic semitone, so the diatonic scale subset is actually improper.

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

  • 16|0 LssLssLsssLssLsss
  • 15|1 LssLsssLssLssLsss
  • 14|2 LssLsssLssLsssLss
  • 13|3 LsssLssLssLsssLss
  • 12|4 LsssLssLsssLssLss
  • 11|5 sLssLssLsssLssLss
  • 10|6 sLssLsssLssLssLss
  • 9|7 sLssLsssLssLsssLs
  • 8|8 sLsssLssLssLsssLs
  • 7|9 sLsssLssLsssLssLs
  • 6|10 ssLssLssLsssLssLs
  • 5|11 ssLssLsssLssLssLs
  • 4|12 ssLssLsssLssLsssL
  • 3|13 ssLsssLssLssLsssL
  • 2|14 ssLsssLssLsssLssL
  • 1|15 sssLssLssLsssLssL
  • 0|16 sssLssLsssLssLssL

Scale tree

Generator ranges:

  • Chroma-positive generator: 705.8824 cents (10\17) to 720 cents (3\5)
  • Chroma-negative generator: 480 cents (2\5) to 494.1176 cents (7\17)
Generator Cents L s L/s Comments
10\17 705.882 1 1 1.000
53\90 706.667 6 5 1.200
43\73 706.849 5 4 1.250
76\129 706.977 9 7 1.286
33\56 707.143 4 3 1.333 Supra
89\151 707.285 11 8 1.375
56\95 707.368 7 5 1.400
79\134 707.463 10 7 1.428
23\39 707.692 3 2 1.500
82\139 707.914 11 7 1.571
59\100 708.000 8 5 1.600
95\161 708.075 13 8 1.625 Golden supra (708.0539¢)
36\61 708.197 5 3 1.667 Quasisuper / quasisupra
85\144 708.333 12 7 1.714
49\83 708.434 7 4 1.750
62\105 708.571 9 5 1.800
13\22 709.091 2 1 2.000 Basic 5L 12s
(Generators smaller than this are proper)
55\93 709.677 9 4 2.250
42\71 709.859 7 3 2.333
71\120 710.000 12 5 2.400
29\49 710.204 5 2 2.500 Superpyth
74\125 710.400 13 5 2.600 Golden superpyth (710.4345¢)
45\76 710.526 8 3 2.667
61\103 710.680 11 4 2.750
16\27 711.111 3 1 3.000
51\86 711.628 10 3 3.333
35\59 711.864 7 2 3.500
54\91 712.088 11 3 3.667
19\32 712.500 4 1 4.000
41\69 713.043 9 2 4.500
22\37 713.514 5 1 5.000 Oceanfront / Ultrapyth
25\42 714.286 6 1 6.000 Hemiseven
3\5 720.000 1 0 → inf