43edo: Difference between revisions

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In the 13-limit, we get two versions of meantone equivalent in 43et, one, [[Meantone_family#Septimal meantone-Unidecimal meantone aka Huygens-Meridetone|meridetone]], tempering out [[78/77]], the other, [[Meantone_family#Septimal meantone-Unidecimal meantone aka Huygens-Grosstone|grosstone]], [[144/143]]. Meridetone has generator mapping {{val|0 1 4 10 18 27}}, and grosstone {{val|0 1 4 10 18 -16}}; 43 supplies the [[optimal patent val]] for meridetone.

The 43 patent val {{val|43 68 100 121 149 159}} maps 5 to 100 steps, allowing the divison of 5 into 20 equal parts, leading to [[Meantone_family#Jerome|jerome temperament]], an interesting higher-limit system for which 43 supplies the optimal patent val in the 7, 11, 13, 17, 19 and 23 limits. It also provides the optimal patent val for 11- and 13-limit [[Marvel_temperaments#Amavil|amavil temperament]], which is not a meantone temperament. [[Thuja|Thuja temperament]] is also a possibility, in which five generators, (~11/8)^5 = ~5/1, with [[MOS]] of 15 and 28.

The 43 patent val {{val|43 68 100 121 149 159}} maps 5 to 100 steps, allowing the divison of 5 into 20 equal parts, leading to [[Meantone_family#Jerome|jerome temperament]], an interesting higher-limit system for which 43 supplies the optimal patent val in the 7, 11, 13, 17, 19 and 23 limits. It also provides the optimal patent val for 11- and 13-limit [[Marvel_temperaments#Amavil|amavil temperament]], which is not a meantone temperament. [[Starling_temperaments#Thuja|Thuja temperament]] is also a possibility, in which five generators, (~11/8)^5 = ~5/1, with [[MOS]] of 15 and 28.

43edo is the 14th [[prime_numbers|prime]] edo, following [[41edo]] and coming before [[47edo]].

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 In the 13-limit, we get two versions of meantone equivalent in 43et, one, [[Meantone_family#Septimal meantone-Unidecimal meantone aka Huygens-Meridetone|meridetone]], tempering out [[78/77]], the other, [[Meantone_family#Septimal meantone-Unidecimal meantone aka Huygens-Grosstone|grosstone]], [[144/143]]. Meridetone has generator mapping {{val|0 1 4 10 18 27}}, and grosstone {{val|0 1 4 10 18 -16}}; 43 supplies the [[optimal patent val]] for meridetone.
-The 43 patent val {{val|43 68 100 121 149 159}} maps 5 to 100 steps, allowing the divison of 5 into 20 equal parts, leading to [[Meantone_family#Jerome|jerome temperament]], an interesting higher-limit system for which 43 supplies the optimal patent val in the 7, 11, 13, 17, 19 and 23 limits. It also provides the optimal patent val for 11- and 13-limit [[Marvel_temperaments#Amavil|amavil temperament]], which is not a meantone temperament. [[Thuja|Thuja temperament]] is also a possibility, in which five generators, (~11/8)^5 = ~5/1, with [[MOS]] of 15 and 28.
+The 43 patent val {{val|43 68 100 121 149 159}} maps 5 to 100 steps, allowing the divison of 5 into 20 equal parts, leading to [[Meantone_family#Jerome|jerome temperament]], an interesting higher-limit system for which 43 supplies the optimal patent val in the 7, 11, 13, 17, 19 and 23 limits. It also provides the optimal patent val for 11- and 13-limit [[Marvel_temperaments#Amavil|amavil temperament]], which is not a meantone temperament. [[Starling_temperaments#Thuja|Thuja temperament]] is also a possibility, in which five generators, (~11/8)^5 = ~5/1, with [[MOS]] of 15 and 28.
 edo is the 14th [[prime_numbers|prime]] edo, following [[41edo]] and coming before [[47edo]].