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. This has the effect of splitting the whole tone in 4 equal parts, and the octave to be split in half.

Interval information

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 rank-3 uniwiz temperament, which has ~36/35 (or ~35/24) and ~5/4 as generators, and 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 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.