7L 5s

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7L 5s
Brightest mode LLsLsLLsLsLs
Period 2/1
Range for bright generator 5\12 (500.0¢) to 3\7 (514.3¢)
Range for dark generator 4\7 (685.7¢) to 7\12 (700.0¢)
Parent MOS 5L 2s
Daughter MOSes 12L 7s, 7L 12s
Sister MOS 5L 7s
TAMNAMS name m-chromatic
Equal tunings
Supersoft (L:s = 4:3) 18\43 (502.3¢)
Soft (L:s = 3:2) 13\31 (503.2¢)
Semisoft (L:s = 5:3) 21\50 (504.0¢)
Basic (L:s = 2:1) 8\19 (505.3¢)
Semihard (L:s = 5:2) 19\45 (506.7¢)
Hard (L:s = 3:1) 11\26 (507.7¢)
Superhard (L:s = 4:1) 14\33 (509.1¢)

7L 5s is the MOS pattern of the meantone chromatic scale, which is the only notable harmonic entropy minimum in this range of possible scales. In meantone, "diatonic" semitones (~16/15), such as appear in the diatonic scale, for example B-C, are larger than "chromatic" semitones (~25/24), the intervals by which flats and sharps alter pitches.

The meantone chromatic scale with generator between 5\12 (500 cents) and 8\19 (505.263 cents) is proper.

Modes

  • 11|0 LLsLsLLsLsLs
  • 10|1 LLsLsLsLLsLs
  • 9|2 LsLLsLsLLsLs
  • 8|3 LsLLsLsLsLLs
  • 7|4 LsLsLLsLsLLs
  • 6|5 LsLsLLsLsLsL
  • 5|6 LsLsLsLLsLsL
  • 4|7 sLLsLsLLsLsL
  • 3|8 sLLsLsLsLLsL
  • 2|9 sLsLLsLsLLsL
  • 1|10 sLsLLsLsLsLL
  • 0|11 sLsLsLLsLsLL

Scales

  • Meaneb471a – an equal beating tuning of meantone
  • Meantone12 – 31edo tuning
  • Ratwolf – 20/13 wolf fifth tuning of meantone
  • Meaneb471 – the other equal beating tuning of meantone
  • Flattone12 – 13-limit POTE tuning of flattone

Scale tree

Generator ranges:

  • Chroma-positive generator: 500 cents (5\12) to 514.2857 cents (3\7)
  • Chroma-negative generator: 685.7143 cents (4\7) to 700 cents (7\12)
Generator Cents L s L/s Comments
5\12 500.000 1 1 1.000
28\67 501.493 6 5 1.200
23\55 501.818 5 4 1.250
41\98 502.041 9 7 1.286
18\43 502.326 4 3 1.333 Meantone / meridetone
49\117 502.564 11 8 1.375
31\74 502.703 7 5 1.400 Meantone / huygens / grosstone
44\105 502.857 10 7 1.428
13\31 503.226 3 2 1.500
47\112 503.571 11 7 1.571
34\81 503.704 8 5 1.600 Meantone
55\131 503.817 13 8 1.625 Golden meantone (503.7855¢)
21\50 504.000 5 3 1.667 Meantone / meanpop
50\119 504.202 12 7 1.714
29\69 504.348 7 4 1.750
37\88 504.545 9 5 1.800
8\19 505.263 2 1 2.000 Basic m-chromatic
(Generators smaller than this are proper)
35\83 506.024 9 4 2.250
27\64 506.250 7 3 2.333
46\109 506.422 12 5 2.400
19\45 506.667 5 2 2.500 Flattone
49\116 506.897 13 5 2.600 Golden flattone (506.9365¢)
30\71 507.042 8 3 2.667
41\97 507.216 11 4 2.750
11\26 507.692 3 1 3.000
36\85 508.235 10 3 3.333
25\59 508.475 7 2 3.500
39\92 508.696 11 3 3.667
14\33 509.091 4 1 4.000
31\73 509.589 9 2 4.500
17\40 510.000 5 1 5.000
20\47 510.638 6 1 6.000
3\7 514.286 1 0 → inf