Praveensma

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Interval information
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

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