12L 7s

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12L 7s
Pattern LLsLLsLLsLsLLsLLsLs
Period 2/1
Generator range 11\19 (694.7¢) to 7\12 (700.0¢)
Parent MOS 7L 5s
Daughter MOSes 19L 12s, 12L 19s
Sister MOS 7L 12s
Equal tunings
Supersoft (L:s = 4:3) 40\69 (695.7¢)
Soft (L:s = 3:2) 29\50 (696.0¢)
Semisoft (L:s = 5:3) 47\81 (696.3¢)
Basic (L:s = 2:1) 18\31 (696.8¢)
Semihard (L:s = 5:2) 43\74 (697.3¢)
Hard (L:s = 3:1) 25\43 (697.7¢)
Superhard (L:s = 4:1) 32\55 (698.2¢)

12L 7s is the MOS pattern of the meantone enharmonic or mega-chromatic scale. This MOS separates its small steps by intervals of 2L-2L-2L-1L-2L-2L-1L like the familiar 12edo diatonic scale. The perfect fifth which generates it measures 11\19 (694.737 cents) to 7\12 (700 cents).

The meantone enharmonic scale with generator between 11\19 (694.737 cents) and 18\31 (696.774 cents) is proper.

Modes

  • 18|0 LLsLLsLLsLsLLsLLsLs
  • 17|1 LLsLLsLsLLsLLsLLsLs
  • 16|2 LLsLLsLsLLsLLsLsLLs
  • 15|3 LLsLsLLsLLsLLsLsLLs
  • 14|4 LLsLsLLsLLsLsLLsLLs
  • 13|5 LsLLsLLsLLsLsLLsLLs
  • 12|6 LsLLsLLsLsLLsLLsLLs
  • 11|7 LsLLsLLsLsLLsLLsLsL
  • 10|8 LsLLsLsLLsLLsLLsLsL
  • 9|9 LsLLsLsLLsLLsLsLLsL
  • 8|10 LsLsLLsLLsLLsLsLLsL
  • 7|11 LsLsLLsLLsLsLLsLLsL
  • 6|12 sLLsLLsLLsLsLLsLLsL
  • 5|13 sLLsLLsLsLLsLLsLLsL
  • 4|14 sLLsLLsLsLLsLLsLsLL
  • 3|15 sLLsLsLLsLLsLLsLsLL
  • 2|16 sLLsLsLLsLLsLsLLsLL
  • 1|17 sLsLLsLLsLLsLsLLsLL
  • 0|18 sLsLLsLLsLsLLsLLsLL

Scale tree

Generator ranges:

  • Chroma-positive generator: 694.7368 cents (11\19) to 700 cents (7\12)
  • Chroma-negative generator: 500 cents (5\12) to 505.2632 cents (8\19)
Generator Cents L s L/s Comments
11\19 694.737 1 1 1.000
62\107 695.327 6 5 1.200
51\88 695.455 5 4 1.250
91\157 695.541 9 7 1.286
40\69 695.652 4 3 1.333
109\188 695.745 11 8 1.375
69\119 695.798 7 5 1.400
98\169 695.858 10 7 1.428
29\50 696.000 3 2 1.500 Meantone / Meanpop
105\181 696.133 11 7 1.571
76\131 696.183 8 5 1.600
123\212 696.226 13 8 1.625 Golden meantone (696.2145¢)
47\81 696.296 5 3 1.667 Meantone / Meanpop
112\193 696.373 12 7 1.714
65\112 696.429 7 4 1.750
83\143 696.503 9 5 1.800
18\31 696.774 2 1 2.000 Basic 12L 7s
(Generators smaller than this are proper)
79\136 697.059 9 4 2.250
61\105 697.143 7 3 2.333 Meantone / Huygens
104\179 697.207 12 5 2.400
43\74 697.297 5 2 2.500 Meantone / Huygens / Grosstone
111\191 697.382 13 5 2.600 Golden grosstone (697.3969¢)
68\117 697.436 8 3 2.667
93\160 697.500 11 4 2.750
25\43 697.674 3 1 3.000 Meantone / Meridetone
82\141 697.872 10 3 3.333
57\98 697.959 7 2 3.500
89\153 698.039 11 3 3.667
32\55 698.182 4 1 4.000
71\122 698.361 9 2 4.500
39\67 698.507 5 1 5.000
46\79 698.734 6 1 6.000
7\12 700.000 1 0 → inf