Septimal ruthenia: Difference between revisions

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'''~~Septimal~~ ruthenia''', {{~~Monzo~~|-263 88 0 44}}, is an unnoticeable comma of about 0.38 ~~cents~~ 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, 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 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.

~~It's full expression as a number is 14824640687984246187061099152503501809016771517414462285446734604193473168610561/14821387422376473014217086081112052205218558037201992197050570753012880593911808~~.

== Temperaments ==

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=== Septimal ruthenian (1848 & 12276 & 14960) ===

Subgroup: 2.3.5.7

[[Subgroup]]: 2.3.5.7

Comma list: {{~~Monzo~~|-263 88 0 44}}

[[Comma list]]: {{monzo| -263 88 0 44 }}

Mapping: [{{val|44 ~~44 88 175~~}}, {{val|0 1 0 -2}}, {{val|0 0 1 0}}]

[[Mapping]]: [{{val| 44 0 0 263 }}, {{val| 0 1 0 -2 }}, {{val| 0 0 1 0 }}]

~~Optimal tuning (CTE)~~: ~64/63, ~3/2, ~5/4

Mapping generators: ~64/63, ~3, ~5

Vals: {{EDOs|1848, 836, 176, 1012, 352, 484, 528, 308, 1364}}, ...

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-'''Septimal ruthenia''', {{Monzo|-263 88 0 44}}, is an unnoticeable comma of about 0.38 cents 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, 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 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.
-It's full expression as a number is 14824640687984246187061099152503501809016771517414462285446734604193473168610561/14821387422376473014217086081112052205218558037201992197050570753012880593911808.
 == Temperaments ==
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 === Septimal ruthenian (1848 & 12276 & 14960) ===
-Subgroup: 2.3.5.7
+[[Subgroup]]: 2.3.5.7
-Comma list: {{Monzo|-263 88 0 44}}
+[[Comma list]]: {{monzo| -263 88 0 44 }}
-Mapping: [{{val|44 44 88 175}}, {{val|0 1 0 -2}}, {{val|0 0 1 0}}]
+[[Mapping]]: [{{val| 44 0 0 263 }}, {{val| 0 1 0 -2 }}, {{val| 0 0 1 0 }}]
-Optimal tuning (CTE): ~64/63, ~3/2, ~5/4
+Mapping generators: ~64/63, ~3, ~5
 Vals: {{EDOs|1848, 836, 176, 1012, 352, 484, 528, 308, 1364}}, ...