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~~{{Citation needed}}~~, 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.

{{Infobox Interval

| Monzo = -263 88 0 44

| Name = septimal ruthenia, septiruthenia

| Color name = L19z448, 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.

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.

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]].

=== ~~Septiruthenian~~ ===

=== Septiruthenic ===

[[Subgroup]]: 2.3.5.7

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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 }}, …

{{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 × 10-3

[[Category:~~7-limit~~]]

==== Septiruthenian ====

[[Category:~~Unnoticeable commas~~]]

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 ==

[[Category:Commas named after elements]]

[[Category:Commas named after their color name]]

@@ Line 1: / Line 1: @@
-The '''septimal ruthenia''' or '''septiruthenia''' ([[monzo]]: {{monzo| -263 88 0 44 }}), known as the '''44-septimal comma''' in earlier materials{{Citation needed}}, 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.
+{{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.
 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.
+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]].
-=== Septiruthenian ===
+=== Septiruthenic ===
 [[Subgroup]]: 2.3.5.7
@@ Line 15: / Line 22: @@
 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 }}, …
+{{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>
-[[Category:7-limit]]
+==== Septiruthenian ====
-[[Category:Unnoticeable commas]]
+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 ==
+<references/>
+[[Category:Commas named after elements]]
+[[Category:Commas named after their color name]]