1012edo: Difference between revisions

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== Theory ==

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 }}. It provides the [[optimal patent val]] for [[quarvish]] temperament in the 7-limit and also in the 11-limit.

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, it 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. Furthermore, it is a [[septiruthenia]]<nowiki/>n system, tempering 64/63 comma to 23 steps, 1/44th of the octave.It provides the [[optimal patent val]] for [[quarvish]] temperament in the 7-limit and also in the 11-limit.

=== Other techniques ===

In addition to containing 22edo and 23edo, it contains a [[22L 1s]] scale produced by generator of 45\1012 associated with [[33/32]], and is associated with the 45 & 1012 temperament, making it [[concoctic]]. A comma basis for the 13-limit is 2401/2400, 6656/6655, 123201/123200, {{monzo| 18 15 -12 -1 0 -3 }}.

In the 2.3.7.11.101, it tempers out [[7777/7776]] and is a tuning for the [[neutron star]] temperament.

=== Prime harmonics ===

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[[2024edo]], which divides the edostep in two, provides a good correction for the 17th harmonic.

~~=== Trivia ===~~

In addition to containing 22edo and 23edo, it contains a [[22L 1s]] scale produced by generator of 45\1012 associated with [[33/32]], and is associated with the 45 & 1012 temperament, making it [[concoctic]]. A comma basis for the 13-limit is 2401/2400, 6656/6655, 123201/123200, {{monzo| 18 15 -12 -1 0 -3 }}.

~~In the 2.3.7.11.101, it tempers out [[7777/7776]] and is a tuning for the [[neutron star]] temperament.~~

== Regular temperament properties ==

@@ Line 2: / Line 2: @@
 {{EDO intro|1012}}
 == Theory ==
-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 }}. It provides the [[optimal patent val]] for [[quarvish]] temperament in the 7-limit and also in the 11-limit.
+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, it 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. Furthermore, it is a [[septiruthenia]]<nowiki/>n system, tempering 64/63 comma to 23 steps, 1/44th of the octave.It provides the [[optimal patent val]] for [[quarvish]] temperament in the 7-limit and also in the 11-limit.
+=== Other techniques ===
+In addition to containing 22edo and 23edo, it contains a [[22L 1s]] scale produced by generator of 45\1012 associated with [[33/32]], and is associated with the 45 & 1012 temperament, making it [[concoctic]]. A comma basis for the 13-limit is 2401/2400, 6656/6655, 123201/123200, {{monzo| 18 15 -12 -1  0 -3 }}.
+In the 2.3.7.11.101, it tempers out [[7777/7776]] and is a tuning for the [[neutron star]] temperament.
 === Prime harmonics ===
@@ Line 11: / Line 18: @@
 [[2024edo]], which divides the edostep in two, provides a good correction for the 17th harmonic.
-=== Trivia ===
-In addition to containing 22edo and 23edo, it contains a [[22L 1s]] scale produced by generator of 45\1012 associated with [[33/32]], and is associated with the 45 & 1012 temperament, making it [[concoctic]]. A comma basis for the 13-limit is 2401/2400, 6656/6655, 123201/123200, {{monzo| 18 15 -12 -1  0 -3 }}.
-In the 2.3.7.11.101, it tempers out [[7777/7776]] and is a tuning for the [[neutron star]] temperament.
 == Regular temperament properties ==