Parimo

Interval information

Ratio	1771561/1771470
Factorization	2-1 × 3-11 × 5-1 × 116
Monzo	[-1 -11 -1 0 6⟩
Size in cents	0.0889308¢
Name	parimo
FJS name	[math]\displaystyle{ \text{ddd1}^{11,11,11,11,11,11}_{5} }[/math]
Special properties	reduced
Tenney height (log2 nd)	41.5131
Weil height (log2 max(n, d))	41.5132
Wilson height (sopfr(nd))	106
Open this interval in xen-calc

The parimo is an 11-limit unnoticeable comma with a ratio of 1771561/1771470 = [-1 -11 -1 0 6⟩ and a value of approximately 0.09 cents. It is the amount by which an octave-reduced stack of five 11/9 neutral thirds exceeds 15/11, as well as the amount by which a stack of three rastmas falls short of a syntonic comma.

Temperaments

Tempering it out leads to a form of parimic temperament, which can be said to be the undecimal counterpart of the metric temperament in that the syntonic comma is split into three equal parts in both systems. However, in parimic temperament, the parts represent different intervals – one part represents the rastma, and two represent the biyatisma. The corresponding 2.3.5.11 subgroup temperament is tritomere.

Parimic

Subgroup: 2.3.5.7.11

Comma list: 1771561/1771470

Mapping: [⟨1 0 5 0 1], ⟨0 1 1 0 2], ⟨0 0 -6 0 -1], ⟨0 0 0 1 0]]

Mapping generators: ~2, ~3, ~18/11, ~7

POTE generators: ~3/2 = 701.9581, ~18/11 = 852.6073

Badness: 0.0279 × 10^-6

Tritomere

Subgroup: 2.3.5.11

Comma list: 1771561/1771470

Sval mapping: [⟨1 0 5 1], ⟨0 1 1 2], ⟨0 0 -6 -1]]

Sval mapping generators: ~2, ~3, ~18/11

POTE generators: ~3/2 = 701.9581, ~18/11 = 852.6073

Badness: 0.00712 × 10^-3

See also

• Unnoticeable comma