45edo: Difference between revisions

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== Theory ==

45edo effectively has two approximate [[5/4|major thirds]], each almost equally far from just, but the flat one is slightly closer. Combined with a [[3/2|perfect fifth]] 8.6 cents flat of just, it can be used as a [[meantone]] tuning, forming a good approximation to [[2/5-comma meantone]] (in fact falling into the [[flattone]] range). It is a flat-tending system in the [[7-limit]], with [[3/1|3]], [[5/1|5]], and [[7/1|7]] all flat, ~~but~~ the [[11/1|11]] is sharp.

45edo effectively has two approximate [[5/4|major thirds]], each almost equally far from just, but the flat one is slightly closer. Combined with a [[3/2|perfect fifth]] 8.6 cents flat of just, it can be used as a [[meantone]] tuning, forming a good approximation to [[2/5-comma meantone]] (in fact falling into the [[flattone]] range). It is a flat-tending system in the [[7-limit]], with [[3/1|3]], [[5/1|5]], and [[7/1|7]] all flat. However, the [[11/1|11]] and [[13/1|13]] is sharp, but this can be fixed with the 45ef val.

=== Odd harmonics ===

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=== Subsets and supersets ===

Since 45 factors into primes as {{nowrap| 3<sup>2</sup> × 5 }}, 45edo has subset edos {{EDOs| 3, 5, 9, and 15 }}. [[135edo]], which triples it, corrects its primes 3, 7, and 11 to near-just qualities, and 270edo offers even more.

== Intervals ==

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 == Theory ==
-edo effectively has two approximate [[5/4|major thirds]], each almost equally far from just, but the flat one is slightly closer. Combined with a [[3/2|perfect fifth]] 8.6 cents flat of just, it can be used as a [[meantone]] tuning, forming a good approximation to [[2/5-comma meantone]] (in fact falling into the [[flattone]] range). It is a flat-tending system in the [[7-limit]], with [[3/1|3]], [[5/1|5]], and [[7/1|7]] all flat, but the [[11/1|11]] is sharp.
+edo effectively has two approximate [[5/4|major thirds]], each almost equally far from just, but the flat one is slightly closer. Combined with a [[3/2|perfect fifth]] 8.6 cents flat of just, it can be used as a [[meantone]] tuning, forming a good approximation to [[2/5-comma meantone]] (in fact falling into the [[flattone]] range). It is a flat-tending system in the [[7-limit]], with [[3/1|3]], [[5/1|5]], and [[7/1|7]] all flat. However, the [[11/1|11]] and [[13/1|13]] is sharp, but this can be fixed with the 45ef val.
 === Odd harmonics ===
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 === Subsets and supersets ===
 Since 45 factors into primes as {{nowrap| 3<sup>2</sup> × 5 }}, 45edo has subset edos {{EDOs| 3, 5, 9, and 15 }}. [[135edo]], which triples it, corrects its primes 3, 7, and 11 to near-just qualities, and 270edo offers even more.
 == Intervals ==