Uniwiz comma: Difference between revisions

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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~~.

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 ==

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== 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 [[~~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~~.

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 edos cannot be tempering out this comma.

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.

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]]

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-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.
+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 ==
@@ Line 11: / Line 11: @@
 == 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 [[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.
+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 edos cannot be tempering out this comma.
-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.
+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]]