Septimal ruthenia: Difference between revisions
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→Temperaments: ruthenium isn't formally agreed upon yet, although I propose 1848 & 2684 with mapping ~64/63, ~3/2. |
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== Temperaments == | == Temperaments == | ||
Since ruthenium is a name that | 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) === | === Septimal ruthenian (1848 & 12276 & 14960) === | ||
Revision as of 11:56, 11 October 2022
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 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 44 88 175], ⟨0 1 0 -2], ⟨0 0 1 0]]
Optimal tuning (CTE): ~64/63, ~3/2, ~5/4