Praveensma
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Ratio
31213/31104
Factorization
2-7 × 3-5 × 74 × 13
Monzo
[-7 -5 0 4 0 1⟩
Size in cents
6.0562833¢
Name
praveensma
Color name
thoquadzo comma
FJS name
[math]\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
Harmonic entropy
(Shannon, [math]\sqrt{nd}[/math])
~1.53557 bits
Comma size
small
open this interval in xen-calc
Interval information |
(Shannon, [math]\sqrt{nd}[/math])
The praveensma, 31213/31104, is a small 13-limit comma which is the difference between 24/13 and a stack of four 7/6's.
It factors into simpler commas as (325/324)(2401/2400) or (385/384)(4459/4455).
Temperaments
Tempering out this comma in the 13-limit results in the praveensmic temperament. Notable edos tempering it out are 41edo, 50edo, 63edo, 104edo, and 167edo.
It is also tempered out in 13-limit superpyth temperament, which maps 13/8 to the doubly-augmented fourth.
Scales
9-note praveensmic mos
A chain of 7/6's tempering out the praveensma gives a 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