783edo: Difference between revisions
Clarify the title row of the rank-2 temp table |
m Adopt template: Factorization; misc. cleanup |
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== Theory == | == Theory == | ||
783edo provides solid approximations of the 5-limit, the 7-limit and to some extent the 11-limit, and is [[consistent]] up to the 11-limit, making it a flexible and versatile tuning. | 783edo provides solid approximations of the 5-limit, the 7-limit and to some extent the 11-limit, and is [[consistent]] up to the [[11-odd-limit]], making it a flexible and versatile tuning. The equal temperament [[tempering out|tempers out]] the [[ennealimma]] and the [[counterschisma]] in the 5-limit; [[2401/2400]], and [[4375/4374]] in the 7-limit. It [[support]]s [[counterschismic]], [[dodifo]], [[ennealimmal]], [[raider]], [[vavoom]], and [[Very high accuracy temperaments #Francium|francium]]. | ||
=== Prime harmonics === | === Prime harmonics === | ||
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=== Subsets and supersets === | === Subsets and supersets === | ||
Since 783 factors into | Since 783 factors into {{factorization|783}}, 783edo has subset edos {{EDOs| 3, 9, 27, 29, 87, and 261 }}. | ||
== Regular temperament properties == | == Regular temperament properties == | ||
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! Generator* | ! Generator* | ||
! Cents* | ! Cents* | ||
! Associated<br>Ratio | ! Associated<br>Ratio* | ||
! Temperaments | ! Temperaments | ||
|- | |- | ||
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| 472.031<br>(3.065) | | 472.031<br>(3.065) | ||
| {{monzo| 35 1 -6 -3 -4 }}<br>(?) | | {{monzo| 35 1 -6 -3 -4 }}<br>(?) | ||
| [[87th-octave temperaments#Francium|Francium]] | | [[87th-octave temperaments #Francium|Francium]] | ||
|} | |} | ||
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct | <nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct | ||