1012edo: Difference between revisions

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1012edo is a strong 13-limit system, distinctly [[consistent]] through the 15-odd-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 {{monzo| 2 6 -1 2 0 4 }}.

In the 5-limit, 1012edo is enfactored, with the same mapping as [[506edo]], providing a tuning for [[vishnu]], [[monzismic]], and [[lafa]]. In the 7-limit, it tempers out the [[breedsma]], 2401/2400, and tunes [[osiris]] temperament. Furthermore, noting its exceptional strength in the 2.3.7 subgroup, it is a [[septiruthenia]]~~<nowiki/>~~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.

In the 5-limit, 1012edo is enfactored, with the same mapping as [[506edo]], providing a tuning for [[vishnu]], [[monzismic]], and [[lafa]]. In the 7-limit, it tempers out the [[breedsma]], 2401/2400, and tunes [[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.

=== Other techniques ===

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1012 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 ==

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 edo is a strong 13-limit system, distinctly [[consistent]] through the 15-odd-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 {{monzo| 2 6 -1 2 0 4 }}.
-In the 5-limit, 1012edo is enfactored, with the same mapping as [[506edo]], providing a tuning for [[vishnu]], [[monzismic]], and [[lafa]]. In the 7-limit, it tempers out the [[breedsma]], 2401/2400, and tunes [[osiris]] temperament. Furthermore, noting its exceptional strength in the 2.3.7 subgroup, it is a [[septiruthenia]]<nowiki/>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.
+In the 5-limit, 1012edo is enfactored, with the same mapping as [[506edo]], providing a tuning for [[vishnu]], [[monzismic]], and [[lafa]]. In the 7-limit, it tempers out the [[breedsma]], 2401/2400, and tunes [[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.
 === Other techniques ===
@@ Line 17: / Line 17: @@
 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 ==