Uniwiz comma

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.

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
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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.