43edo: Difference between revisions

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== Theory ==

43edo tempers out [[81/80]] in the 5-limit, and as such it is strongly associated with [[meantone]]. It tunes the major third sharp of [[5/4]] and perfect fifth flat of [[3/2]] by slightly more than four cents on both of them. Other 5-limit commas tempered out include the [[hypovishnuzma]] and the [[escapade comma]], so that ~~in 43edo~~ six chromatic semitones make a perfect fourth and eight minor seconds make a major sixth.

43edo tempers out [[81/80]] in the 5-limit, and as such it is strongly associated with [[meantone]]. Specifically, it is (for all practical purposes) equivalent to [[1/5-comma meantone]], as it tunes the major third sharp of [[5/4]] and perfect fifth flat of [[3/2]] by slightly more than four cents on both of them. Other 5-limit commas tempered out include the [[hypovishnuzma]] and the [[escapade comma]], so that six chromatic semitones make a perfect fourth and eight minor seconds make a major sixth.

Except for 9/7, 14/9, 11/9, and 18/11, all [[15-odd-limit]] intervals have consistent approximations in 43edo, making it an excellent tuning in the 7-, 11-, and 13-limit. In the 7-limit, it supports septimal meantone, as it tempers out 126/125, 225/224, and 3136/3125. The version of 11-limit meantone is the one tempering out [[99/98]], [[176/175]], and [[441/440]], sometimes called [[Huygens temperament|Huygens]]. In the 13-limit it supports [[Meantone family #Meridetone|meridetone]], which tempers out [[78/77]], and [[Meantone family #Grosstone|grosstone]], which tempers out [[144/143]]. Meridetone has generator map {{val| 0 1 4 10 18 27 }}, for which 43 supplies the [[optimal patent val]] for, and grosstone {{val| 0 1 4 10 18 -16 }}.

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 == Theory ==
-edo tempers out [[81/80]] in the 5-limit, and as such it is strongly associated with [[meantone]]. It tunes the major third sharp of [[5/4]] and perfect fifth flat of [[3/2]] by slightly more than four cents on both of them. Other 5-limit commas tempered out include the [[hypovishnuzma]] and the [[escapade comma]], so that in 43edo six chromatic semitones make a perfect fourth and eight minor seconds make a major sixth.
+edo tempers out [[81/80]] in the 5-limit, and as such it is strongly associated with [[meantone]]. Specifically, it is (for all practical purposes) equivalent to [[1/5-comma meantone]], as it tunes the major third sharp of [[5/4]] and perfect fifth flat of [[3/2]] by slightly more than four cents on both of them. Other 5-limit commas tempered out include the [[hypovishnuzma]] and the [[escapade comma]], so that six chromatic semitones make a perfect fourth and eight minor seconds make a major sixth.
 Except for 9/7, 14/9, 11/9, and 18/11, all [[15-odd-limit]] intervals have consistent approximations in 43edo, making it an excellent tuning in the 7-, 11-, and 13-limit. In the 7-limit, it supports septimal meantone, as it tempers out 126/125, 225/224, and 3136/3125. The version of 11-limit meantone is the one tempering out [[99/98]], [[176/175]], and [[441/440]], sometimes called [[Huygens temperament|Huygens]]. In the 13-limit it supports [[Meantone family #Meridetone|meridetone]], which tempers out [[78/77]], and [[Meantone family #Grosstone|grosstone]], which tempers out [[144/143]]. Meridetone has generator map {{val| 0 1 4 10 18 27 }}, for which 43 supplies the [[optimal patent val]] for, and grosstone {{val| 0 1 4 10 18 -16 }}.