512/315: Difference between revisions

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{{Infobox Interval|Name=schisminic tridecimal otonal sixth
{{Infobox Interval
septimal pseudotridecimal otonal sixth|Color name=srg6, sarugu 6th|Sound=}}512/315 is the sum of the tridecimal otonal sixth 13/8, and the [[4096/4095|schismina]]. Most Sagittal systems conflate both it and [[13/8]], via fudging in 13+ -limit JI, or tempering, leading to schisminic temperaments. As is the case of schisminic temperaments, tempering these two intervals together results in a lower rank approximation of prime 13, with negligible error.
| Name = minismic tridecimal otonal sixth, septimal pseudotridecimal otonal sixth
| Color name = srg6, sarugu 6th
| Sound =  
}}
'''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 [[8505/8192|35 large diesis]] accidental. From C, the interval would be C - A{{sagittal|\!)}}.
In Sagittal, it (and likely also 13/8) is (are) represented with as a pyth major sixth minus the [[8505/8192|35 large diesis]] accidental. From C, the interval would be C - A{{sagittal|\!)}}.

Latest revision as of 09:59, 3 March 2026

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.