Uniwiz comma: Difference between revisions

Line 1:

{{Infobox Interval|Name=uniwiz comma

{{Infobox Interval

~~uniwizma~~|Color name=quadzoyo 2nd, z^4y^42|~~Sound~~=|~~Comma~~=1}}1500625/1492992~~, the uniwiz comma~~, 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.

| 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 ==

== 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 [[~~Sqrt~~(2/1)|semioctave]] period. Because it has 2 periods per octave, odd edos cannot be tempering 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 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]]

@@ Line 1: / Line 1: @@
-{{Infobox Interval|Name=uniwiz comma
+{{Infobox Interval
-uniwizma|Color name=quadzoyo 2nd, z^4y^42|Sound=|Comma=1}}1500625/1492992, the uniwiz comma, 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.
+| 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 ==
-It is very well approximated by 1\[[145edo|145]] and 2\[[270edo|270]], and consistently represented in edos such as [[171edo|171]], [[224edo|224]], and [[441edo|441]].
+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 ==
-When tempered 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 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 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]]