7L 5s
This 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 is proper.
| Generator | in cents | Comments | |||||
|---|---|---|---|---|---|---|---|
| 3\7 | 514.286 | ||||||
| 20\47 | 510.638 | ||||||
| 17\40 | 510 | ||||||
| 31\73 | 509.589 | ||||||
| 14\33 | 509.091 | ||||||
| 39\92 | 508.696 | ||||||
| 25\59 | 508.475 | ||||||
| 36\85 | 508.235 | ||||||
| 507.934 | L/s = pi | ||||||
| 11\26 | 507.692 | Flattone | |||||
| 41\97 | 507.216 | Flattone | |||||
| 507.151 | L/s = e | ||||||
| 30\71 | 507.042 | Flattone | |||||
| 506.9365 | L/s = phi+1 | ||||||
| 49\116 | 506.897 | Flattone | |||||
| 19\45 | 506.667 | Flattone | |||||
| 46\109 | 506.422 | Flattone | |||||
| 27\64 | 506.25 | Flattone | |||||
| 35\83 | 506.024 | ||||||
| 8\19 | 505.263 | Boundary of propriety: generators smaller than this are proper.
Meanenneadecal; L/s = 2 | |||||
| 37\88 | 504.5455 | ||||||
| 504.507 | Lucy Tuning | ||||||
| 29\69 | 504.348 | ||||||
| 504.275 | L/s = sqrt(3) | ||||||
| 50\119 | 504.202 | ||||||
| 21\50 | 504 | Meantone / Meanpop | |||||
| 55\131 | 503.817 | Golden meantone | |||||
| 503.7855 | L/s = phi | ||||||
| 34\81 | 503.704 | Optimal meantone is around here | |||||
| 47\112 | 503.571 | Meantone / Meanpop | |||||
| 503.5685 | L/s = pi/2 | ||||||
| 13\31 | 503.226 | Optimal rank range (L/s = 3/2) | |||||
| 44\105 | 502.857 | Meantone / Huygens | |||||
| 31\74 | 502.703 | Meantone / Huygens | |||||
| 49\117 | 502.564 | ||||||
| 18\43 | 502.326 | Meantone / Meridetone | |||||
| 41\98 | 502.041 | ||||||
| 23\55 | 501.818 | ||||||
| 28\67 | 501.493 | ||||||
| 5\12 | 500 | ||||||