6561/5120: Difference between revisions

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'''6561/5120''', the '''retroptolemaic major third''', is a [[5-limit]] [[interval]] measuring about 429.32{{cent}}. It is equal to the Pythagorean major third of [[81/64]] ''raised'' by a syntonic comma ([[81/80]]), compared to the just major third [[5/4]] which is the Pythagorean interval ''lowered'' by the syntonic comma. A weird consequence is that this interval is equated to [[5/4]] in [[meantone]] temperament, so it is tuned grossly inaccurately in most "normal" tunings of meantone (if you wanted to for some reason, you could have a meantone tuning with a sharp fifth that would make this interval accurate ~~but~~ 5/4 inaccurate). It differs from [[41/32]], the 41st harmonic, by the unnoticeable comma [[6561/6560]]. It also differs from [[9/7]], the Pythagorean major third, by [[5120/5103]], giving [[hemifamity]] temperaments a more intuitive interpretation of this interval.

'''6561/5120''', the '''retroptolemaic major third''', is a [[5-limit]] [[interval]] measuring about 429.32{{cent}}. It is equal to the Pythagorean major third of [[81/64]] ''raised'' by a syntonic comma ([[81/80]]), compared to the just major third [[5/4]] which is the Pythagorean interval ''lowered'' by the syntonic comma. A weird consequence is that this interval is equated to [[5/4]] in [[meantone]] temperament, so it is tuned grossly inaccurately in most "normal" tunings of meantone (if you wanted to for some reason, you could have a meantone tuning with a sharp fifth that would make this interval the accurate one and 5/4 inaccurate). It differs from [[41/32]], the 41st harmonic, by the unnoticeable comma [[6561/6560]]. It also differs from [[9/7]], the Pythagorean major third, by [[5120/5103]], giving [[hemifamity]] temperaments a more intuitive interpretation of this interval.

[[Category:Major third]]

[[Category:Supermajor third]]

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-'''6561/5120''', the '''retroptolemaic major third''', is a [[5-limit]] [[interval]] measuring about 429.32{{cent}}. It is equal to the Pythagorean major third of [[81/64]] ''raised'' by a syntonic comma ([[81/80]]), compared to the just major third [[5/4]] which is the Pythagorean interval ''lowered'' by the syntonic comma. A weird consequence is that this interval is equated to [[5/4]] in [[meantone]] temperament, so it is tuned grossly inaccurately in most "normal" tunings of meantone (if you wanted to for some reason, you could have a meantone tuning with a sharp fifth that would make this interval accurate but 5/4 inaccurate).  It differs from [[41/32]], the 41st harmonic, by the unnoticeable comma [[6561/6560]]. It also differs from [[9/7]], the Pythagorean major third, by [[5120/5103]], giving [[hemifamity]] temperaments a more intuitive interpretation of this interval.
+'''6561/5120''', the '''retroptolemaic major third''', is a [[5-limit]] [[interval]] measuring about 429.32{{cent}}. It is equal to the Pythagorean major third of [[81/64]] ''raised'' by a syntonic comma ([[81/80]]), compared to the just major third [[5/4]] which is the Pythagorean interval ''lowered'' by the syntonic comma. A weird consequence is that this interval is equated to [[5/4]] in [[meantone]] temperament, so it is tuned grossly inaccurately in most "normal" tunings of meantone (if you wanted to for some reason, you could have a meantone tuning with a sharp fifth that would make this interval the accurate one and 5/4 inaccurate).  It differs from [[41/32]], the 41st harmonic, by the unnoticeable comma [[6561/6560]]. It also differs from [[9/7]], the Pythagorean major third, by [[5120/5103]], giving [[hemifamity]] temperaments a more intuitive interpretation of this interval.
 [[Category:Major third]]
 [[Category:Supermajor third]]