Septimal ruthenia: Difference between revisions
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{{Infobox Interval | |||
| Monzo = -263 88 0 44 | |||
| Name = septimal ruthenia, septiruthenia | |||
| Color name = L<sup>19</sup>z<sup>44</sup>8, nela-lequadzo octave | |||
| Comma = yes | |||
| FJS name = - | |||
}} | |||
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. | 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. | ||
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== Temperaments == | == Temperaments == | ||
In the full 7-limit, tempering out this comma leads to the rank-3 '''septiruthenian | In the full 7-limit, tempering out this comma leads to the rank-3 '''septiruthenic temperament''', and in the 2.3.7 subgroup, rank-2 '''septiruthenian''' temperament (cf. ruthenium, the rank-2 2.3.5.7 temperament). You may find a list of good equal temperament supporting it below. See also [[44th-octave temperaments]]. | ||
=== | === Septiruthenic === | ||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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Mapping generators: ~64/63, ~3, ~5 | Mapping generators: ~64/63, ~3, ~5 | ||
{{ | {{Optimal ET sequence|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> | [[Badness]]: 116 × 10<sup>-3</sup> | ||
==== Septiruthenian ==== | |||
Subgroup: 2.3.7 | |||
Comma list: {{monzo| -263 88 44 }} | |||
[[Mapping]]: [{{val| 44 0 263 }}, {{val| 0 1 -2 }}] | |||
Mapping generators: ~64/63, ~3 | |||
Another notable system tempering out the septiruthenia is [[1012edo]], which is a [[zeta peak edo]]. | |||
== Trivia == | |||
Quite coincidentally, the color name for 64/63 is "Ru unison", and the 44th chemical element ruthenium, the namesake of this comma, has the symbol Ru. | |||
== Notes == | == Notes == | ||
<references/> | <references/> | ||
[[Category: | [[Category:Commas named after elements]] | ||
[[Category: | [[Category:Commas named after their color name]] | ||
Latest revision as of 23:36, 3 November 2024
| Interval information |
septiruthenia
reduced harmonic
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 septiruthenic temperament, and in the 2.3.7 subgroup, rank-2 septiruthenian temperament (cf. ruthenium, the rank-2 2.3.5.7 temperament). You may find a list of good equal temperament supporting it below. See also 44th-octave temperaments.
Septiruthenic
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
Optimal ET sequence: 176, 308, 352, 484, 528, 836, 1848, 2684, 4532, 7744, 8580, 9592, 10428, 12276, 14960, 27236, 42196, 99352, …
Badness: 116 × 10-3
Septiruthenian
Subgroup: 2.3.7
Comma list: [-263 88 44⟩
Mapping: [⟨44 0 263], ⟨0 1 -2]]
Mapping generators: ~64/63, ~3
Another notable system tempering out the septiruthenia is 1012edo, which is a zeta peak edo.
Trivia
Quite coincidentally, the color name for 64/63 is "Ru unison", and the 44th chemical element ruthenium, the namesake of this comma, has the symbol Ru.
Notes
- ↑ The first occurrence of the name seems to be in the page of unnoticeable comma, archived on October 26, 2016.