783edo: Difference between revisions

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 {{Infobox ET}}
-{{EDO intro|783}}
+{{ED intro}}
-It provides solid approximations of the 5-limit, the 7-limit and the 11-limit, and is consistent up to the 11-limit, making it a flexible and versatile tuning. It is a tuning for the [[counterschismic]], [[dodifo]], [[ennealimmal]], [[raider]], [[vavoom]], and [[Very high accuracy temperaments#Francium|francium]]
+== Theory ==
+edo 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]].
-It supports the rank-3 temperaments: [[Breed]], [[Landscape]], [[Ragismic]].
 === Prime harmonics ===
-{{harmonics in equal|783}}
+{{Harmonics in equal|783}}
-[[Category:783edo]]
+=== Subsets and supersets ===
-[[Category:Equal divisions of the octave]]
+Since 783 factors into {{factorization|783}}, 783edo has subset edos {{EDOs| 3, 9, 27, 29, 87, and 261 }}.
-[[Category:Breed]]
-[[Category:Ennealimmal]]
+== Regular temperament properties ==
-[[Category:Ragismic]]
+=== Rank-2 temperaments ===
+{| 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
+| 73\783
+| 111.877
+| 16/15
+| [[Vavoom]]
+|-
+| 1
+| 224\783
+| 343.295
+| 8000/6561
+| [[Raider]]
+|-
+| 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]]
+|-
+| 29
+| 325\783<br />(1\723)
+| 498.084<br />(1.533)
+| 4/3<br />(32805/32768)
+| [[Copper]]
+|-
+| 87
+| 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