Septimal ruthenia: Difference between revisions
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''' | The '''septimal ruthenia''' or '''septiruthenia''' ([[monzo]]: {{monzo| -263 88 0 44 }}), known as the '''44-septimal comma''' in earlier materials, is an [[unnoticeable comma|unnoticeable]] [[7-limit [[comma]] of about 0.38 [[cent]]s 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 | 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 == | == Temperaments == | ||
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=== Septimal ruthenian (1848 & 12276 & 14960) === | === Septimal ruthenian (1848 & 12276 & 14960) === | ||
Subgroup: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
Comma list: {{ | [[Comma list]]: {{monzo| -263 88 0 44 }} | ||
Mapping: [{{val|44 | [[Mapping]]: [{{val| 44 0 0 263 }}, {{val| 0 1 0 -2 }}, {{val| 0 0 1 0 }}] | ||
Mapping generators: ~64/63, ~3, ~5 | |||
Vals: {{EDOs|1848, 836, 176, 1012, 352, 484, 528, 308, 1364}}, ... | Vals: {{EDOs|1848, 836, 176, 1012, 352, 484, 528, 308, 1364}}, ... | ||
Revision as of 14:07, 11 October 2022
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