Uniwiz comma: Difference between revisions

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{{Infobox Interval
{{Infobox interval
| Ratio = 1500625/1492992
| Monzo = -11 -6 4 4
| Monzo = -11 -6 4 4
| Name = uniwiz comma, uniwizma
| Name = uniwiz comma, uniwizma
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== Temperaments ==
== 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 edos cannot be tempering out this comma.  
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 [[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.
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]]
[[Category:Uniwiz]]

Latest revision as of 03:34, 20 May 2026

Interval information
Ratio 1500625/1492992
Factorization 2-11 × 3-6 × 54 × 74
Monzo [-11 -6 4 4
Size in cents 8.828476¢
Names uniwiz comma,
uniwizma
Color name quadzoyo 2nd, z^4y^42
FJS name [math]\displaystyle{ \text{M2}^{5,5,5,5,7,7,7,7} }[/math]
Special properties reduced
Tenney norm (log2 nd) 41.0269
Weil norm (log2 max(n, d)) 41.0343
Wilson norm (sopfr(nd)) 88
Comma size small
Open this interval in xen-calc

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.