Praveensma
(Redirected from 31213/31104)
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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 | |
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