7L 5s
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Pattern | LLsLsLLsLsLs | |
Period | 2/1 | |
Generator range | 5\12 (500.0¢) to 3\7 (514.3¢) | |
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
- Meantone12 – 31edo tuning
- Meaneb471a – 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 |