43edo: Difference between revisions

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43edo is strongly associated with [[Meantone|meantone temperament]], particularly [[1/5-comma meantone]], being a good tuning system in the 5, 7, 11, and 13-limit. The version of 11-limit meantone is the one tempering out [[99/98]], [[176/175]] and [[441/440]] sometimes called Huygens. 43-equal has the first good 13-limit meantone available as an equal division of the octave. The baroque, French, ironically hearing and speech impaired acoustician [http://en.wikipedia.org/wiki/Joseph_Sauveur Joseph Sauveur] based his system on 43 equal tones to the octave, calling them "merides". Further information: http://tonalsoft.com/enc/m/meride.aspx

The composer [[http://juhanpuhmmusic.ca Juhan Puhm]] uses 43edo in some of his meantone suites for fortepiano and prefers it to [[31edo]].

The composer [http://juhanpuhmmusic.ca Juhan Puhm] uses 43edo in some of his meantone suites for fortepiano and prefers it to [[31edo]].

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.

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 edo is strongly associated with [[Meantone|meantone temperament]], particularly [[1/5-comma meantone]], being a good tuning system in the 5, 7, 11, and 13-limit. The version of 11-limit meantone is the one tempering out [[99/98]], [[176/175]] and [[441/440]] sometimes called Huygens. 43-equal has the first good 13-limit meantone available as an equal division of the octave. The baroque, French, ironically hearing and speech impaired acoustician [http://en.wikipedia.org/wiki/Joseph_Sauveur Joseph Sauveur] based his system on 43 equal tones to the octave, calling them "merides". Further information: http://tonalsoft.com/enc/m/meride.aspx
-The composer [[http://juhanpuhmmusic.ca Juhan Puhm]] uses 43edo in some of his meantone suites for fortepiano and prefers it to [[31edo]].
+The composer [http://juhanpuhmmusic.ca Juhan Puhm] uses 43edo in some of his meantone suites for fortepiano and prefers it to [[31edo]].
 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.