1012edo: Difference between revisions

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 {{Infobox ET}}
-{{EDO intro|1012}}
+{{ED intro}}
 == Theory ==
-It is a strong 13-limit system, distinctly consistent through the 15 limit. It is a [[The_Riemann_Zeta_Function_and_Tuning#Zeta EDO lists|zeta peak edo]], though not zeta integral nor zeta gap. A basis for the 13-limit commas is 2401/2400, 4096/4095, 6656/6655, 9801/9800 and | 2 6 -1 2 0 4 &gt;.
+edo is a strong 13-limit system, [[consistency|distinctly consistent]] through the [[15-odd-limit]]. It is a [[zeta peak edo]], though not [[zeta integral edo|zeta integral]] nor [[zeta gap edo|zeta gap]]. A basis for the 13-limit [[comma]]s consists of [[2401/2400]], [[4096/4095]], [[6656/6655]], [[9801/9800]] and {{monzo| 2 6 -1 2 0 4 }}.
-edo conta
+In the 5-limit, 1012edo is [[enfactoring|enfactored]], with the same tuning as [[506edo]], [[support]]ing [[vishnu]], [[monzismic]], and [[lafa]]. In the 7-limit, it [[tempering out|tempers out]] the [[breedsma]], 2401/2400, and tunes the [[osiris]] temperament. Furthermore, noting its exceptional strength in the 2.3.7 [[subgroup]], it is a [[septiruthenia]]n system, tempering 64/63 comma to 1/44th of the octave, that is 23 steps. It provides the [[optimal patent val]] for [[quarvish]] temperament in the 7-limit and also in the 11-limit.
-[[Category:Equal divisions of the octave|####]] <!-- 4-digit number -->
+=== Prime harmonics ===
+{{Harmonics in equal|1012}}
+=== Subsets and supersets ===
+Since 1012 factors into {{nowrap| 2<sup>2</sup> × 11 × 23 }}, 1012edo has subset edos {{EDOs| 2, 4, 11, 22, 23, 44, 46, 92, 253, 506 }}. [[2024edo]], which divides the edostep in two, provides a good correction for the 17th harmonic.
+== Regular temperament properties ==
+=== 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
+| 361\1012
+| 428.06
+| 2800/2187
+| [[Osiris]]
+|-
+| 2
+| 145\1012
+| 171.94
+| 243/220
+| [[Semiosiris]]
+|-
+| 2
+| 420\1012
+| 498.02
+| 7/5
+| [[Quarvish]]
+|-
+| 44
+| 420\1012<br>(6\1012)
+| 498.02<br>(7.11)
+| 4/3<br>(18375/18304)
+| [[Ruthenium]]
+|}
+<nowiki/>* In [[normal forms #Minimal-generator form|minimal-generator form]]