The septimal ruthenia or septiruthenia (monzo: [-263 88 0 44⟩), known as the 44-septimal comma in earlier materials, is an unnoticeable 7-limit comma of about 0.38 cents which is defined as the difference between a stack of fourty-four 64/63's and the octave.
It's called "ruthenia" because of the 44th element, ruthenium, following the convention of naming certain fractional-octave temperaments after chemical elements. For edos N up to ~16000, it is tempered out if and only if 44 divides N. The relationship between 64/63 and one step of 44edo is highly precise, even up many thousands of edos.
In the full 7-limit, tempering out this comma leads to the rank-3 septiruthenic temperament, and in the 2.3.7 subgroup, rank-2 septiruthenian temperament (cf. ruthenium, the rank-2 18.104.22.168 temperament). You may find a list of good equal temperament supporting it below. See also 44th-octave temperaments.
Comma list: [-263 88 0 44⟩
Mapping: [⟨44 0 0 263], ⟨0 1 0 -2], ⟨0 0 1 0]]
Mapping generators: ~64/63, ~3, ~5
Badness: 116 × 10-3
- The first occurrence of the name seems to be in the page of unnoticeable comma, archived on October 26, 2016.