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 | The '''septimal ruthenia''' or '''septiruthenia''' ([[monzo]]: {{monzo| -263 88 0 44 }}), known as the '''44-septimal comma''' in earlier materials<ref>The first occurrence of the name seems to be in the page of [https://en.xen.wiki/index.php?title=Unnoticeable_comma&oldid=28693 ''unnoticeable comma'', archived on October 26, 2016]. </ref>, 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 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. | 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. | ||
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[[Badness]]: 116 × 10<sup>-3</sup> | [[Badness]]: 116 × 10<sup>-3</sup> | ||
== Notes == | |||
<references/> | |||
[[Category:7-limit]] | [[Category:7-limit]] | ||
[[Category:Unnoticeable commas]] | [[Category:Unnoticeable commas]] | ||
Revision as of 06:35, 25 October 2022
The septimal ruthenia or septiruthenia (monzo: [-263 88 0 44⟩), known as the 44-septimal comma in earlier materials[1], 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
In the full 7-limit, tempering out this comma leads to the rank-3 septiruthenian temperament (cf. ruthenium, the rank-2 2.3.5.7 temperament). You may find a list of good equal temperament supporting it below.
Septiruthenian
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
Badness: 116 × 10-3
Notes
- ↑ The first occurrence of the name seems to be in the page of unnoticeable comma, archived on October 26, 2016.