Septimal ruthenia: Difference between revisions
Cleanup; proposing an alternative name; normalize the mapping |
→Temperaments: +OGPV sequence and badness |
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Mapping generators: ~64/63, ~3, ~5 | Mapping generators: ~64/63, ~3, ~5 | ||
{{Val list|legend=1| 176, 308, 352, 484, 528, 836, 1848, 2684, 4532, 7744, 8580, 9592, 10428, 12276, 14960, 27236, 42196, 99352 }}, … | |||
[[Badness]]: 116 × 10<sup>-3</sup> | |||
[[Category:7-limit]] | [[Category:7-limit]] | ||
[[Category:Unnoticeable commas]] | [[Category:Unnoticeable commas]] | ||
Revision as of 14:59, 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
Badness: 116 × 10-3