User:Overthink/Draft edits: Difference between revisions

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=== Miscellaneous properties ===

One step of 56edo is the closest to the syntonic comma, [[81/80]], of any integer edo's step size by [[direct approximation]], 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 has a step size very close to the syntonic comma, 56edo contains very accurate approximations of both the classic major third [[5/4]] at 18\56, and the Pythagorean major third [[81/64]] at 19\56. Unfortunately, the major third ~~reached by stacking four fifths and [[Octave reduction|octave-reducing]] in 56edo is not~~ 19\56, but ~~rather~~ 20\56, a supermajor third of 428.6{{c}}. However, the Pythagorean major third is ~~represented as~~ 19\56 consistently in [[224edo]], which is the quadruple of 56edo.

One step of 56edo is the closest to the syntonic comma, [[81/80]], of any integer edo's step size by [[direct approximation]], 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 has a step size very close to the syntonic comma, 56edo contains very accurate approximations of both the classic major third [[5/4]] at 18\56, and the Pythagorean major third [[81/64]] at 19\56. Unfortunately, 56edo does not map the Pythagorean major third 19\56, but instead inconsistently to 20\56, a supermajor third of 428.6{{c}}. However, the Pythagorean major third is mapped to 19\56 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]].

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 === Miscellaneous properties ===
-One step of 56edo is the closest to the syntonic comma, [[81/80]], of any integer edo's step size by [[direct approximation]], 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 has a step size very close to the syntonic comma, 56edo contains very accurate approximations of both the classic major third [[5/4]] at 18\56, and the Pythagorean major third [[81/64]] at 19\56. Unfortunately, the major third reached by stacking four fifths and [[Octave reduction|octave-reducing]] in 56edo is not 19\56, but rather 20\56, a supermajor third of 428.6{{c}}. However, the Pythagorean major third is represented as 19\56 consistently in [[224edo]], which is the quadruple of 56edo.
+One step of 56edo is the closest to the syntonic comma, [[81/80]], of any integer edo's step size by [[direct approximation]], 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 has a step size very close to the syntonic comma, 56edo contains very accurate approximations of both the classic major third [[5/4]] at 18\56, and the Pythagorean major third [[81/64]] at 19\56. Unfortunately, 56edo does not map the Pythagorean major third 19\56, but instead inconsistently to 20\56, a supermajor third of 428.6{{c}}. However, the Pythagorean major third is mapped to 19\56 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]].