Septimal ruthenia
| Interval information |
septiruthenia
reduced harmonic
(Shannon, [math]\sqrt{nd}[/math])
The septimal ruthenia or septiruthenia (monzo: [-263 88 0 44⟩), known as the 44-septimal comma in earlier materials[1], 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.
Temperaments
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 2.3.5.7 temperament). You may find a list of good equal temperament supporting it below. See also 44th-octave temperaments.
Septiruthenic
Subgroup: 2.3.5.7
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
Optimal ET sequence: 176, 308, 352, 484, 528, 836, 1848, 2684, 4532, 7744, 8580, 9592, 10428, 12276, 14960, 27236, 42196, 99352, …
Badness: 116 × 10-3
Septiruthenian
Subgroup: 2.3.7
Comma list: [-263 88 44⟩
Mapping: [⟨44 0 263], ⟨0 1 -2]]
Mapping generators: ~64/63, ~3
Another notable system tempering out the septiruthenia is 1012edo, which is a zeta peak edo.
Trivia
Quite coincidentally, the color name for 64/63 is "Ru unison", and the 44th chemical element ruthenium, the namesake of this comma, has the symbol Ru.
Notes
- ↑ The first occurrence of the name seems to be in the page of unnoticeable comma, archived on October 26, 2016.