Uniwiz comma: Difference between revisions
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{{Infobox Interval|Name=uniwiz comma | {{Infobox Interval | ||
| Name = uniwiz comma, uniwizma | |||
| Color name = quadzoyo 2nd, z^4y^42 | |||
| Comma = true | |||
}} | |||
The '''uniwiz comma''' ({{monzo|legend=1| -11 -6 4 4 }}, [[ratio]]: 1500625/1492992), is the small interval that separates a stack of four [[35/24]] subfifths with the just major ninth [[9/2]]. It also is the difference between [[9/8]] and a stack of four [[36/35]] quartertones. This has the effect of splitting the whole tone in 4 equal parts, and the octave to be split in half. | |||
== Approximations == | == Approximations == | ||
It is very well approximated by | It is very well approximated by [[145edo|1\145]] and [[270edo|2\270]], and consistently represented in edos such as [[171edo|171]], [[224edo|224]], and [[441edo|441]]. | ||
== Temperaments == | == Temperaments == | ||
When tempered alone, it leads to the rank-3 [[uniwiz]] temperament, which has ~36/35 (or ~35/24) and ~5/4 as generators, and [[ | When tempered out alone, it leads to the rank-3 [[uniwiz]] temperament, which has ~36/35 (or ~35/24) and ~5/4 as generators, and [[sqrt(2/1)|semioctave]] period. Because it has 2 periods per octave, odd edos cannot be tempering out this comma. When the [[schisma]] is added, it leads to the rank-2 [[kleischismic]], for which [[94edo|94]] and [[118edo|118]] are great edos. | ||
Despite the name "kleischismic", it does not temper the [[15625/15552|kleisma]]. It finds ~3/2 at 2 generators plus a semioctave. By tempering [[1225/1224]], it also finds ~[[17/16]] at two generators. | Despite the name "kleischismic", it does not temper out the [[15625/15552|kleisma]]. It finds ~3/2 at 2 generators plus a semioctave. By tempering out [[1225/1224]], it also finds ~[[17/16]] at two generators. | ||
[[Category:Uniwiz]] | |||
Revision as of 15:35, 15 September 2025
| Interval information |
uniwizma
The uniwiz comma (monzo: [-11 -6 4 4⟩, ratio: 1500625/1492992), is the small interval that separates a stack of four 35/24 subfifths with the just major ninth 9/2. It also is the difference between 9/8 and a stack of four 36/35 quartertones. This has the effect of splitting the whole tone in 4 equal parts, and the octave to be split in half.
Approximations
It is very well approximated by 1\145 and 2\270, and consistently represented in edos such as 171, 224, and 441.
Temperaments
When tempered out alone, it leads to the rank-3 uniwiz temperament, which has ~36/35 (or ~35/24) and ~5/4 as generators, and semioctave period. Because it has 2 periods per octave, odd edos cannot be tempering out this comma. When the schisma is added, it leads to the rank-2 kleischismic, for which 94 and 118 are great edos.
Despite the name "kleischismic", it does not temper out the kleisma. It finds ~3/2 at 2 generators plus a semioctave. By tempering out 1225/1224, it also finds ~17/16 at two generators.