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]\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
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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