Praveensma: Difference between revisions
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The '''praveensma''', '''31213/31104''' is a 13 limit comma which is the difference between | The '''praveensma''', '''31213/31104''', is a [[small comma|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]]). | ||
A chain of 7/6's tempering out the praveensma gives | |||
== 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 12:13:14:16 | ||
| Line 15: | Line 23: | ||
* inversions of these chords | * inversions of these chords | ||
* eight copies of 12:14:18:21 | * eight copies of 12:14:18:21 | ||
[[Category:Praveensmic]] | |||
[[Category:Commas named after composers]] | |||
[[Category:Commas named after music theorists]] | |||
{{todo|add etymology|research|comment=is it named after Praveen Venkataramana?}} | |||
Latest revision as of 02:38, 4 November 2024
| Interval information |
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