6561/5120

Interval information

Ratio	6561/5120
Factorization	2-10 × 38 × 5-1
Monzo	[-10 8 -1⟩
Size in cents	429.3263¢
Name	retroptolemaic major third
Color name	lagu 3rd, Lg3
FJS name	[math]\displaystyle{ \text{M3}_{5} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	25.0016
Weil norm (log2 max(n, d))	25.3594
Wilson norm (sopfr(nd))	49
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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 aberschismic temperaments a more intuitive interpretation of this interval.