415edo: Difference between revisions

Expand on theory; adopt template: Factorization
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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|415}}
{{ED intro}}


If [[5/1|harmonic 5]] is used, 415edo tends very sharp. In the 5-limit the equal temperament [[tempering out|tempers out]] the [[parakleisma]], {{monzo| 8 14 -13 }}; in the 7-limit [[3136/3125]] and [[4375/4374]], so that it [[support]]s [[parakleismic]], the 99 & 316 temperament, and provides the [[optimal patent val]]. In the 11-limit it tempers out 12005/11979, [[16384/16335]], and [[41503/41472]]; and in the 13-limit, [[676/675]], [[1001/1000]], [[2080/2079]], 3584/3575, and [[10648/10647]].  
If [[5/1|harmonic 5]] is used, 415edo tends very sharp. In the 5-limit the equal temperament [[tempering out|tempers out]] the [[parakleisma]], {{monzo| 8 14 -13 }}; in the 7-limit [[3136/3125]] and [[4375/4374]], so that it [[support]]s [[parakleismic]], the 99 & 316 temperament, and provides the [[optimal patent val]]. In the 11-limit it tempers out 12005/11979, [[16384/16335]], and [[41503/41472]]; and in the 13-limit, [[676/675]], [[1001/1000]], [[2080/2079]], 3584/3575, and [[10648/10647]].