7L 5s: Difference between revisions
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'''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 [[5L 2s|diatonic scale]], for example B-C, are larger than "chromatic" semitones (~25/24), the intervals by which flats and sharps alter pitches. | '''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 [[5L 2s|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 [[Rothenberg propriety|proper]]. | The meantone chromatic scale with generator between 5\12 (500 cents) and 8\19 (505.263 cents) is [[Rothenberg propriety|proper]]. | ||
== Modes == | == Modes == | ||
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| || || || || || 41\98 || 502.041 || 9 || 7 || 1.286 || | | || || || || || 41\98 || 502.041 || 9 || 7 || 1.286 || | ||
|- | |- | ||
| || || || 18\43 || || || 502.326 || 4 || 3 || 1.333 || Meantone/meridetone | | || || || 18\43 || || || 502.326 || 4 || 3 || 1.333 || [[Meantone]] / [[meridetone]] | ||
|- | |- | ||
| || || || || || 49\117 || 502.564 || 11 || 8 || 1.375 || | | || || || || || 49\117 || 502.564 || 11 || 8 || 1.375 || | ||
|- | |- | ||
| || || || || 31\74 || || 502.703 || 7 || 5 || 1.400 || Meantone/huygens | | || || || || 31\74 || || 502.703 || 7 || 5 || 1.400 || [[Meantone]] / [[huygens]] / [[grosstone]] | ||
|- | |- | ||
| || || || || || 44\105 || 502.857 || 10 || 7 || 1.428 || | | || || || || || 44\105 || 502.857 || 10 || 7 || 1.428 || | ||
|- | |- | ||
| || || 13\31 || || || || 503.226 || 3 || 2 || 1.500 || | | || || 13\31 || || || || 503.226 || 3 || 2 || 1.500 || | ||
|- | |- | ||
| || || || || || 47\112 || 503.571 || 11 || 7 || 1.571 || | | || || || || || 47\112 || 503.571 || 11 || 7 || 1.571 || | ||
|- | |- | ||
| || || || || 34\81 || || 503.704 || 8 || 5 || 1.600 || Meantone | | || || || || 34\81 || || 503.704 || 8 || 5 || 1.600 || [[Meantone]] | ||
|- | |- | ||
| || || || || || 55\131 || 503.817 || 13 || 8 || 1.625 || Golden meantone | | || || || || || 55\131 || 503.817 || 13 || 8 || 1.625 || [[Golden meantone]] (Generator: 503.7855 cents) | ||
|- | |- | ||
| || || || 21\50 || || || 504.000 || 5 || 3 || 1.667 || Meantone/meanpop | | || || || 21\50 || || || 504.000 || 5 || 3 || 1.667 || [[Meantone]] / [[meanpop]] | ||
|- | |- | ||
| || || || || || 50\119 || 504.202 || 12 || 7 || 1.714 || | | || || || || || 50\119 || 504.202 || 12 || 7 || 1.714 || | ||
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| || || || || || 37\88 || 504.545 || 9 || 5 || 1.800 || | | || || || || || 37\88 || 504.545 || 9 || 5 || 1.800 || | ||
|- | |- | ||
| || 8\19 || || || || || 505.263 || 2 || 1 || 2.000 || Basic m-chromatic<br>(Generators smaller than this are proper) | | || 8\19 || || || || || 505.263 || 2 || 1 || 2.000 || Basic m-chromatic <br>(Generators smaller than this are proper) | ||
|- | |- | ||
| || || || || || 35\83 || 506.024 || 9 || 4 || 2.250 || | | || || || || || 35\83 || 506.024 || 9 || 4 || 2.250 || | ||
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| || || || || || 46\109 || 506.422 || 12 || 5 || 2.400 || | | || || || || || 46\109 || 506.422 || 12 || 5 || 2.400 || | ||
|- | |- | ||
| || || || 19\45 || || || 506.667 || 5 || 2 || 2.500 || Flattone | | || || || 19\45 || || || 506.667 || 5 || 2 || 2.500 || [[Flattone]] | ||
|- | |- | ||
| || || || || || 49\116 || 506.897 || 13 || 5 || 2.600 || Golden flattone | | || || || || || 49\116 || 506.897 || 13 || 5 || 2.600 || Golden flattone (Generator: 506.9365 cents) | ||
|- | |- | ||
| || || || || 30\71 || || 507.042 || 8 || 3 || 2.667 || | | || || || || 30\71 || || 507.042 || 8 || 3 || 2.667 || | ||
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| || || || || || 41\97 || 507.216 || 11 || 4 || 2.750 || | | || || || || || 41\97 || 507.216 || 11 || 4 || 2.750 || | ||
|- | |- | ||
| || || 11\26 || || || || 507.692 || 3 || 1 || 3.000 || | | || || 11\26 || || || || 507.692 || 3 || 1 || 3.000 || | ||
|- | |- | ||
| || || || || || 36\85 || 508.235 || 10 || 3 || 3.333 || | | || || || || || 36\85 || 508.235 || 10 || 3 || 3.333 || | ||
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[[Category:Abstract MOS patterns]] | [[Category:Abstract MOS patterns]] | ||
[[Category:M-chromatic| ]] <!-- main article --> | [[Category:M-chromatic| ]] <!-- main article --> | ||
[[Category:Chromatic scales]] | |||