Praveensma

Interval information

Ratio	31213/31104
Factorization	2-7 × 3-5 × 74 × 13
Monzo	[-7 -5 0 4 0 1⟩
Size in cents	6.056283¢
Name	praveensma
Color name	thoquadzo comma
FJS name	[math]\displaystyle{ \text{dd3}^{7,7,7,7,13} }[/math]
Special properties	reduced
Tenney height (log2 nd)	29.8547
Weil height (log2 max(n, d))	29.8597
Wilson height (sopfr(nd))	70
Comma size	small
Open this interval in xen-calc

The praveensma, 31213/31104 is a 13 limit comma which is the difference between four 7/6's and a 24/13. Notable edos tempering it out are 41edo, 63edo, 104edo, and 167edo, all magic temperaments, and 50edo, a meantone temperament.

The 9 note praveensmic MOS

A chain of 7/6's tempering out the praveensma gives an MOS with four 12:13:14 and four 1/(14:13:12) chords, which makes it suitable for secundal harmony. Furthermore, two instances of this MOS separated by a 3/2 gives a 3-MOS with lots of consonant 13-limit chords:

• four copies of 12:13:14:16
• four copies of 12:13:14:18:21
• inversions of these chords
• eight copies of 12:14:18:21