User:Overthink/Draft edits: Difference between revisions

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One step of 56edo is the closest direct approximation to the syntonic comma, [[81/80]], with the number of directly approximated syntonic commas per octave being 55.7976. [[Barium]] temperament realizes this proximity through regular temperament theory, and is supported by notable edos like [[224edo]], [[1848edo]], and [[2520edo]], which is a [[highly composite edo]]. Because it contains 28edo's major third and also has a step size very close to the syntonic comma, 56edo contains very accurate approximations of both the classic major third [[5/4]] and the Pythagorean major third [[81/64]]. Unfortunately, this "Pythagorean major third" is not the major third as is stacked by fifths in 56edo, which is in fact a supermajor third of 428.6 [[cent]]s. However, the Pythagorean major third is represented as such consistently in [[224edo]], which is the quadruple of 56edo.

The perfect fifth generates a [[5L 2s|diatonic]] scale with a [[step ratio]] that is a convergent towards the [[Metallic harmonic series|bronze metallic mean]], following [[17edo]] and preceding [[185edo]].

=== Prime harmonics ===

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 One step of 56edo is the closest direct approximation to the syntonic comma, [[81/80]], with the number of directly approximated syntonic commas per octave being 55.7976. [[Barium]] temperament realizes this proximity through regular temperament theory, and is supported by notable edos like [[224edo]], [[1848edo]], and [[2520edo]], which is a [[highly composite edo]]. Because it contains 28edo's major third and also has a step size very close to the syntonic comma, 56edo contains very accurate approximations of both the classic major third [[5/4]] and the Pythagorean major third [[81/64]]. Unfortunately, this "Pythagorean major third" is not the major third as is stacked by fifths in 56edo, which is in fact a supermajor third of 428.6 [[cent]]s. However, the Pythagorean major third is represented as such consistently in [[224edo]], which is the quadruple of 56edo.
+The perfect fifth generates a [[5L 2s|diatonic]] scale with a [[step ratio]] that is a convergent towards the [[Metallic harmonic series|bronze metallic mean]], following [[17edo]] and preceding [[185edo]].
 === Prime harmonics ===