783edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== 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-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 === | ||
{{ | {{Harmonics in equal|783}} | ||
=== Subsets and supersets === | |||
Since 783 factors into {{factorization|783}}, 783edo has subset edos {{EDOs| 3, 9, 27, 29, 87, and 261 }}. | |||
== Regular temperament properties == | == Regular temperament properties == | ||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{| class="wikitable center-all left-5" | {| class="wikitable center-all left-5" | ||
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | |||
|- | |- | ||
! Periods<br />per 8ve | |||
! Generator* | |||
! Cents* | |||
! Associated<br />ratio* | |||
! Temperaments | |||
|- | |- | ||
|1 | | 1 | ||
| | | 73\783 | ||
| | | 111.877 | ||
| | | 16/15 | ||
| | | [[Vavoom]] | ||
|- | |- | ||
|1 | | 1 | ||
| | | 224\783 | ||
| | | 343.295 | ||
| | | 8000/6561 | ||
| | | [[Raider]] | ||
|- | |- | ||
|1 | | 1 | ||
| | | 233\783 | ||
| | | 357.088 | ||
| | | 768/625 | ||
| | | [[Dodifo]] (5-limit) | ||
|- | |- | ||
| | | 1 | ||
| | | 325\783 | ||
| 498.084 | |||
| | | 4/3 | ||
| | | [[Counterschismic]] | ||
| | |||
|- | |- | ||
| | | 9 | ||
| | | 206\783<br />(32\783) | ||
( | | 315.709<br />(49.042) | ||
| | | 6/5<br />(36/35) | ||
| | | [[Ennealimmal]] | ||
( | |||
| | |||
|- | |- | ||
|87 | | 29 | ||
|308\783 | | 325\783<br />(1\723) | ||
(2\783) | | 498.084<br />(1.533) | ||
| | | 4/3<br />(32805/32768) | ||
| | | [[Copper]] | ||
|- | |||
(?) | | 87 | ||
|Francium | | 308\783<br />(2\783) | ||
|}< | | 472.031<br />(3.065) | ||
[[ | | {{monzo| 35 1 -6 -3 -4 }}<br />(?) | ||
[[ | | [[87th-octave temperaments #Francium|Francium]] | ||
|} | |||
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct | |||