Septimal ruthenia: Difference between revisions
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== Temperaments == | == Temperaments == | ||
In the full 7-limit, tempering out this comma leads to the rank-3 '''septiruthenian temperament''' (cf. ruthenium, the rank-2 2.3.7 temperament). You may find a list of good equal temperament supporting it below. | 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 === | === Septiruthenian === | ||
Revision as of 23:17, 24 October 2022
The septimal ruthenia or septiruthenia (monzo: [-263 88 0 44⟩), known as the 44-septimal comma in earlier materials[citation needed], 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