43edo: Difference between revisions

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The French Baroque acoustician [[wikipedia: Joseph Sauveur|Joseph Sauveur]], who was ironically hearing and speech impaired, based his tuning system on 43 equal tones to the octave, calling them "mérides". Sauveur favoured 43-tone equal temperament because the small intervals are well represented in it. <ref>[http://www.huygens-fokker.org/docs/measures.html Stichting Huygens-Fokker: Logarithmic Interval Measures]</ref>

The composer [[Juhan Puhm]] uses 43edo in some of his ~~meantone~~ suites ~~for fortepiano~~ and prefers it to [[31edo]].

The composer [[Juhan Puhm]] uses 43edo in some of his fortepiano suites and prefers it to [[31edo]].

43edo's 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 the [[jerome]] temperament, an interesting higher-limit system for which 43 supplies the optimal patent val in the 7-, 11-, 13-, 17-, 19-, and even 23-limit. It also provides the optimal patent val for the 11- and 13-limit [[amavil]] temperament, which is not a meantone ~~temperament~~. ~~The~~ [[~~thuja~~]] ~~temperament~~ is also a possibility, ~~in which~~ five ~~generators,~~ (~11/8)<sup>5</sup> ~~= ~~~5/1, with [[mos]] of 15 and 28.

43edo's 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 the [[jerome]] temperament, an interesting higher-limit system for which 43 supplies the optimal patent val in the 7-, 11-, 13-, 17-, 19-, and even 23-limit. It also provides the optimal patent val for the 11- and 13-limit [[amavil]] temperament, which is not meantone. [[Thuja]] is also a possibility, whose 11-limit extension makes five 11/8s stack to a major third (i.e. {{nowrap|(11/8)<sup>5</sup> → 5/1}}), with [[mos]]es of 15 and 28.

=== Prime harmonics ===

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 The French Baroque acoustician [[wikipedia: Joseph Sauveur|Joseph Sauveur]], who was ironically hearing and speech impaired, based his tuning system on 43 equal tones to the octave, calling them "mérides". Sauveur favoured 43-tone equal temperament because the small intervals are well represented in it. <ref>[http://www.huygens-fokker.org/docs/measures.html Stichting Huygens&#45;Fokker&#58; Logarithmic Interval Measures]</ref>
-The composer [[Juhan Puhm]] uses 43edo in some of his meantone suites for fortepiano and prefers it to [[31edo]].
+The composer [[Juhan Puhm]] uses 43edo in some of his fortepiano suites and prefers it to [[31edo]].
-edo's 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 the [[jerome]] temperament, an interesting higher-limit system for which 43 supplies the optimal patent val in the 7-, 11-, 13-, 17-, 19-, and even 23-limit. It also provides the optimal patent val for the 11- and 13-limit [[amavil]] temperament, which is not a meantone temperament. The [[thuja]] temperament is also a possibility, in which five generators, (~11/8)<sup>5</sup> = ~5/1, with [[mos]] of 15 and 28.
+edo's 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 the [[jerome]] temperament, an interesting higher-limit system for which 43 supplies the optimal patent val in the 7-, 11-, 13-, 17-, 19-, and even 23-limit. It also provides the optimal patent val for the 11- and 13-limit [[amavil]] temperament, which is not meantone. [[Thuja]] is also a possibility, whose 11-limit extension makes five 11/8s stack to a major third (i.e. {{nowrap|(11/8)<sup>5</sup> &rarr; 5/1}}), with [[mos]]es of 15 and 28.
 === Prime harmonics ===