Septimal ruthenia

Septimal ruthenia, [-263 88 0 44⟩, is a comma 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 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.

It's full expression as a number is 14824640687984246187061099152503501809016771517414462285446734604193473168610561/14821387422376473014217086081112052205218558037201992197050570753012880593911808.

Temperaments

Since ruthenium is a name that is taken by a rank two temperament (namely, 1848 & 2684), the rank three 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 44 88 175, 0 1 0 -2, 0 0 1 0

Optimal tuning (CTE): ~64/63, ~3/2, ~5/4

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