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 | '''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:Major third]] | ||
[[Category:Supermajor third]] | [[Category:Supermajor third]] | ||
Latest revision as of 08:06, 2 May 2026
| Interval information |
6561/5120, the retroptolemaic major third, is a 5-limit interval measuring about 429.32 ¢. 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.