512/315

Interval information

Ratio	512/315
Factorization	29 × 3-2 × 5-1 × 7-1
Monzo	[9 -2 -1 -1⟩
Size in cents	840.9504¢
Names	minismic tridecimal otonal sixth, septimal pseudotridecimal otonal sixth
Color name	srg6, sarugu 6th
FJS name	[math]\displaystyle{ \text{m6}_{5,7} }[/math]
Special properties	reduced, reduced subharmonic
Tenney norm (log2 nd)	17.2992
Weil norm (log2 max(n, d))	18
Wilson norm (sopfr(nd))	36
Open this interval in xen-calc

512/315 is the sum of the tridecimal otonal sixth 13/8, and 4096/4095. Most Sagittal systems conflate both it and 13/8, via fudging in 13-limit JI, or tempering, leading to minismic temperaments. As is the case of minismic temperaments, tempering these two intervals together results in a lower-rank approximation of prime 13, with negligible error.

In Sagittal, it (and likely also 13/8) is (are) represented with as a pyth major sixth minus the 35 large diesis accidental. From C, the interval would be C - A.