Uniwiz comma: Difference between revisions
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{{Infobox | {{Infobox interval | ||
| Ratio = 1500625/1492992 | |||
| Monzo = -11 -6 4 4 | |||
| 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. | |||
== 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 7-limit version of the rank-3 [[uniwiz]] temperament, which has ~36/35 (or ~35/24) and ~5/4 as generators, and a [[semi-octave]] period. This has the effect of splitting the whole tone in four equal parts. Because it has 2 periods per octave, odd-numbered edos cannot be tempering out this comma. | ||
Despite the name | 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 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]] | |||
Latest revision as of 03:34, 20 May 2026
| 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.
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 7-limit version of the rank-3 uniwiz temperament, which has ~36/35 (or ~35/24) and ~5/4 as generators, and a semi-octave period. This has the effect of splitting the whole tone in four equal parts. Because it has 2 periods per octave, odd-numbered 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.