43edo: Difference between revisions

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=<43 tone equal temperament=

=43 tone equal temperament=

~~= =~~

'''43edo''' divides the [[Octave|octave]] into 43 [[Equal|equal]] parts of 27.907 [[cent|cent]]s each. It is strongly associated with 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

'''43edo''' divides the [[Octave|octave]] into 43 [[Equal|equal]] parts of 27.907 [[cent|cent]]s each. It is strongly associated with 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 ~~http://tonalsoft.com/enc/m/meride.aspx]~~

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 <0 1 4 10 18 27|, and grosstone <0 1 4 10 18 -16|; 43 supplies the optimal patent val for meridetone.

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-=<43 tone equal temperament=
+=43 tone equal temperament=
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+'''43edo''' divides the [[Octave|octave]] into 43 [[Equal|equal]] parts of 27.907 [[cent|cent]]s each. It is strongly associated with 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
-'''43edo''' divides the [[Octave|octave]] into 43 [[Equal|equal]] parts of 27.907 [[cent|cent]]s each. It is strongly associated with 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 http://tonalsoft.com/enc/m/meride.aspx]
 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 &lt;0 1 4 10 18 27|, and grosstone &lt;0 1 4 10 18 -16|; 43 supplies the optimal patent val for meridetone.