# Parimo

 Ratio 1771561/1771470 Factorization 2-1 × 3-11 × 5-1 × 116 Monzo [-1 -11 -1 0 6⟩ Size in cents 0.088930804¢ Name parimo Color name satribilo-agu comma FJS name $\text{ddd1}^{11,11,11,11,11,11}_{5}$ Special properties reduced Tenney height (log2 nd) 41.5131 Weil height (log2 max(n, d)) 41.5132 Wilson height (sopfr (nd)) 106 Harmonic entropy(Shannon, $\sqrt{nd}$) ~1.19989 bits Comma size unnoticeable open this interval in xen-calc

The parimo (ratio: 1771561/1771470, monzo[-1 -11 -1 0 6) is an unnoticeable 11-limit comma with a value of approximately 0.09 ¢. It is the amount by which an octave-reduced stack of six 11/9 neutral thirds exceeds 5/3, 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

Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 701.9581, ~18/11 = 852.6073

### 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

Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 701.9581, ~18/11 = 852.6073