Septimal ruthenia: Difference between revisions
→Temperaments: ruthenium isn't formally agreed upon yet, although I propose 1848 & 2684 with mapping ~64/63, ~3/2. |
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'''Septimal ruthenia''', {{Monzo|-263 88 0 44}}, is | '''Septimal ruthenia''', {{Monzo|-263 88 0 44}}, is an unnoticeable 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. | 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. | ||
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. | It's full expression as a number is 14824640687984246187061099152503501809016771517414462285446734604193473168610561/14821387422376473014217086081112052205218558037201992197050570753012880593911808. | ||
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[[Category:7-limit]] | [[Category:7-limit]] | ||
[[Category:Unnoticeable commas]] | |||
Revision as of 12:01, 11 October 2022
Septimal ruthenia, [-263 88 0 44⟩, is an unnoticeable 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 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