12L 5s

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12L 5s
Pattern LLLsLLsLLLsLLsLLs
Period 2/1
Generator range 7\17 (494.1¢) to 5\12 (500.0¢)
Parent MOS 5L 7s
Daughter MOSes 17L 12s, 12L 17s
Sister MOS 5L 12s
Equal tunings
Supersoft (L:s = 4:3) 26\63 (495.2¢)
Soft (L:s = 3:2) 19\46 (495.7¢)
Semisoft (L:s = 5:3) 31\75 (496.0¢)
Basic (L:s = 2:1) 12\29 (496.6¢)
Semihard (L:s = 5:2) 29\70 (497.1¢)
Hard (L:s = 3:1) 17\41 (497.6¢)
Superhard (L:s = 4:1) 22\53 (498.1¢)

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

This MOS separates its small steps by intervals of 3L-2L-3L-2L-2L. Its major third of -4 generators approximates an interval between 24/19 and 32/25, thus its generator is a perfect fourth between 7\17 (494.118 cents) and 5\12 (500 cents).

The leapday/leapweek version is proper, but the Pythagorean/schismic version is improper (it does not become proper until you add 12 more notes to form the schismic 29-note scale).

Modes

  • 16|0 LLLsLLsLLLsLLsLLs
  • 15|1 LLLsLLsLLsLLLsLLs
  • 14|2 LLsLLLsLLsLLLsLLs
  • 13|3 LLsLLLsLLsLLsLLLs
  • 12|4 LLsLLsLLLsLLsLLLs
  • 11|5 LLsLLsLLLsLLsLLsL
  • 10|6 LLsLLsLLsLLLsLLsL
  • 9|7 LsLLLsLLsLLLsLLsL
  • 8|8 LsLLLsLLsLLsLLLsL
  • 7|9 LsLLsLLLsLLsLLLsL
  • 6|10 LsLLsLLLsLLsLLsLL
  • 5|11 LsLLsLLsLLLsLLsLL
  • 4|12 sLLLsLLsLLLsLLsLL
  • 3|13 sLLLsLLsLLsLLLsLL
  • 2|14 sLLsLLLsLLsLLLsLL
  • 1|15 sLLsLLLsLLsLLsLLL
  • 0|16 sLLsLLsLLLsLLsLLL

Scales

Scale tree

Generator ranges:

  • Chroma-positive generator: 494.1176 cents (7\17) to 500 cents (5\12)
  • Chroma-negative generator: 700 cents (7\12) to 705.8824 cents (10\17)
Generator Cents L s L/s Comments
7\17 494.118 1 1 1.000
40\97 494.845 6 5 1.200
33\80 495.000 5 4 1.250
59\143 495.105 9 7 1.286
26\63 495.238 4 3 1.333 Leapfrog
71\172 495.349 11 8 1.375
45\109 495.413 7 5 1.400 Leapweek
64\155 495.484 10 7 1.428
19\46 495.652 3 2 1.500
69\167 495.808 11 7 1.571 Leapday / polypyth
50\121 495.868 8 5 1.600
81\196 495.918 13 8 1.625 Golden neogothic (495.9044¢)
31\75 496.000 5 3 1.667
74\179 496.089 12 7 1.714
43\104 496.154 7 4 1.750
55\133 496.241 9 5 1.800
12\29 496.552 2 1 2.000 Basic 12L 5s
(Generators smaller than this are proper)
53\128 496.875 9 4 2.250
41\99 496.970 7 3 2.333 Undecental
70\169 497.041 12 5 2.400 Argent tuning (497.0563¢)
29\70 497.143 5 2 2.500
75\181 497.238 13 5 2.600 Unnamed golden tuning (497.2540¢)
46\111 497.297 8 3 2.667
63\152 497.368 11 4 2.750 Kwai
17\41 497.561 3 1 3.000 Garibaldi / andromeda
56\135 497.778 10 3 3.333
39\94 497.872 7 2 3.500 Garibaldi / cassandra
61\147 497.959 11 3 3.667
22\53 498.113 4 1 4.000 Garibaldi / helenus, Pythagorean tuning (498.0450¢)
49\118 498.305 9 2 4.500 Pontiac
27\65 498.462 5 1 5.000 Photia
32\77 498.701 6 1 6.000 Grackle
5\12 500.000 1 0 → inf