Septimal ruthenia

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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.

Temperaments

Since ruthenium is a name that would be allocated to a rank-2 temprament following the fractional-octave convention, the rank-3 temperament corresponding to this comma will be called septimal ruthenian.

Septimal ruthenian (1848 & 12276 & 14960)

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

Vals: 1848, 836, 176, 1012, 352, 484, 528, 308, 1364, ...