1152edo: Difference between revisions

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1152edo is [[consistent]] in the [[9-odd-limit]], where it corrects the [[576edo]]'s mapping for 5.

1152edo is [[consistent]] in the [[9-odd-limit]], where it corrects the [[576edo]]'s mapping for 5. The equal temperament tempers out the ennealimma, {{Monzo|1 -27 18}}, as well as {{monzo|99 2 -44}}, in the 5-limit, 2401/2400, 4375/4374, 250047/250000, 420175/419904, [[40353607/40310784]] (tritrizo), [[78125000/78121827]] (euzenius), as well as {{Monzo|94 -33 -24 5}} in the 7-limit. It supports the [[hemiennealimmal]] temperament and [[germanium]] temperament in the 11-limit despite not being consistent.

It is a strong 2.3.5.7.13.17.23 subgroup tuning, or alternatively a no-11, no-17, no-19 23-limit tuning. More so, if intervals containing 11, 17, and 19 are removed, 1152edo consistently represents the intervals of the [[23-odd-limit]] ~~and not just~~ [[~~23-limit|23-prime-limit~~]].

It is a strong 2.3.5.7.13.17.23 subgroup tuning, or alternatively a no-11, no-17, no-19 23-limit tuning. More so, if intervals containing 11, 17, and 19 are removed, 1152edo consistently represents the remaining intervals of the [[25-odd-limit]]. A comma basis for the 2.3.5.7.13.17.23 subgroup is {3381/3380, 4375/4374, 4761/4760, 4914/4913, 8281/8280, 19136/19125}. It also tempers out the comma associating [[70/69]] to 1 step of [[48edo]].

The 1152deef val provides a tuning close to the POTE tuning of the [[stockhausenic]] temperament.

=== Prime harmonics ===

=== Subsets and supersets ===

Since 1152 factors as {{Factorization|1152}}, 1152edo has subset edos {{EDOs|1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 128, 144, 192, 288, 384, 576}}.

1152edo is a [[highly factorable edo]].

1152edo is a [[highly factorable edo]]. Its [[abundancy index]] is around 1.87.

[[Category:Ennealimmal]]

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 {{Infobox ET}}
-{{EDO intro|1152}}
+{{ED intro}}
-edo is [[consistent]] in the [[9-odd-limit]], where it corrects the [[576edo]]'s mapping for 5.
+edo is [[consistent]] in the [[9-odd-limit]], where it corrects the [[576edo]]'s mapping for 5. The equal temperament tempers out the ennealimma, {{Monzo|1 -27 18}}, as well as {{monzo|99 2 -44}}, in the 5-limit, 2401/2400, 4375/4374, 250047/250000, 420175/419904, [[40353607/40310784]] (tritrizo), [[78125000/78121827]] (euzenius), as well as {{Monzo|94 -33 -24 5}} in the 7-limit. It supports the [[hemiennealimmal]] temperament and [[germanium]] temperament in the 11-limit despite not being consistent.
-It is a strong 2.3.5.7.13.17.23 subgroup tuning, or alternatively a no-11, no-17, no-19 23-limit tuning. More so, if intervals containing 11, 17, and 19 are removed, 1152edo consistently represents the intervals of the [[23-odd-limit]] and not just [[23-limit|23-prime-limit]].
+It is a strong 2.3.5.7.13.17.23 subgroup tuning, or alternatively a no-11, no-17, no-19 23-limit tuning. More so, if intervals containing 11, 17, and 19 are removed, 1152edo consistently represents the remaining intervals of the [[25-odd-limit]]. A comma basis for the 2.3.5.7.13.17.23 subgroup is {3381/3380, 4375/4374, 4761/4760, 4914/4913, 8281/8280, 19136/19125}. It also tempers out the comma associating [[70/69]] to 1 step of [[48edo]].
+The 1152deef val provides a tuning close to the POTE tuning of the [[stockhausenic]] temperament.
+=== Prime harmonics ===
 {{harmonics in equal|1152}}
 === Subsets and supersets ===
+Since 1152 factors as {{Factorization|1152}}, 1152edo has subset edos {{EDOs|1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 128, 144, 192, 288, 384, 576}}.
-edo is a [[highly factorable edo]].
+edo is a [[highly factorable edo]]. Its [[abundancy index]] is around 1.87.
+[[Category:Ennealimmal]]