1789edo: Difference between revisions

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== Theory ==

1789edo ~~can be adapted for use with~~ the 2.5~~.11.13.29.31.47.59.61~~ [[~~subgroup~~]]. ~~Perhaps the most notable fact about 1789edo~~, is ~~the fact that it tempers out the jacobin comma (~~[[~~6656~~/~~6655~~]]), and it ~~is also consistent on the subgroup~~ 2.5.11.13 of the comma, which is quite appropriate for edo's number. Although there are temperaments which are better suited for tempering this comma, 1789edo is unique in that its number is the hallmark year of the French Revolution, thus making the tempering of the jacobin comma on topic.

1789edo is in[[consistent]] to the [[5-odd-limit]] and [[harmonic]] [[3/1|3]] is about halfway between its steps. Otherwise, it is excellent in approximating harmonics [[5/1|5]], [[9/1|9]], [[11/1|11]], [[13/1|13]] and [[21/1|21]], making it suitable for a 2.9.5.21.11.13 [[subgroup]] interpretation.

1789edo ~~is consistent in~~ the ~~no-threes~~ 13~~-odd-limit~~. ~~Since its double,~~ [[~~3578edo~~]]~~, is consistent in~~ the ~~21-odd-limit, it can be thought of as a~~ [[~~K*N subgroups|2*1789~~]] 2.9.5.7.11.13.~~225.289.361.21 subgroup temperament~~, on ~~which it shares mapping with 3578edo and tempers out the same commas~~.

For higher harmonics, 1789edo can be adapted for use with the 2.9.5.21.11.13.29.31.47.59.61 subgroup. Perhaps the most notable fact about 1789edo is that it [[tempering out|tempers out]] the jacobin comma ([[6656/6655]]), and it is also consistent on the subgroup 2.5.11.13 of the comma, which is quite appropriate for edo's number. Although there are temperaments which are better suited for tempering this comma, 1789edo is unique in that its number is the hallmark year of the French Revolution, thus making the tempering of the jacobin comma on topic.

=== Odd harmonics ===

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=== Jacobin temperaments ===

Since 1789edo tempers out the jacobin comma and it is defined by stacking three 11/8s to reach 13/10, one can use that as a generator. The resulting temperament is 37 & 1789, called onzonic. Name "onzonic" comes from the French word for eleven, ''onze''.

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=== Subsets and supersets ===

1789edo is the 278th [[prime edo]].

1789edo is the 278th [[prime edo]]. [[3578edo]], which doubles it, is consistent in the [[21-odd-limit]].

== Table of selected intervals ==

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=== Rank-2 temperaments ===

{| class="wikitable center-all left-4"

|+Table of rank-2 temperaments by generator

|-

! Generator*

! Cents*

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 == Theory ==
-edo can be adapted for use with the 2.5.11.13.29.31.47.59.61 [[subgroup]]. Perhaps the most notable fact about 1789edo, is the fact that it tempers out the jacobin comma ([[6656/6655]]), and it is also consistent on the subgroup 2.5.11.13 of the comma, which is quite appropriate for edo's number. Although there are temperaments which are better suited for tempering this comma, 1789edo is unique in that its number is the hallmark year of the French Revolution, thus making the tempering of the jacobin comma on topic.
+edo is in[[consistent]] to the [[5-odd-limit]] and [[harmonic]] [[3/1|3]] is about halfway between its steps. Otherwise, it is excellent in approximating harmonics [[5/1|5]], [[9/1|9]], [[11/1|11]], [[13/1|13]] and [[21/1|21]], making it suitable for a 2.9.5.21.11.13 [[subgroup]] interpretation.
-edo is consistent in the no-threes 13-odd-limit. Since its double, [[3578edo]], is consistent in the 21-odd-limit, it can be thought of as a [[K*N subgroups|2*1789]] 2.9.5.7.11.13.225.289.361.21 subgroup temperament, on which it shares mapping with 3578edo and tempers out the same commas.
+For higher harmonics, 1789edo can be adapted for use with the 2.9.5.21.11.13.29.31.47.59.61 subgroup. Perhaps the most notable fact about 1789edo is that it [[tempering out|tempers out]] the jacobin comma ([[6656/6655]]), and it is also consistent on the subgroup 2.5.11.13 of the comma, which is quite appropriate for edo's number. Although there are temperaments which are better suited for tempering this comma, 1789edo is unique in that its number is the hallmark year of the French Revolution, thus making the tempering of the jacobin comma on topic.
 === Odd harmonics ===
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 === Jacobin temperaments ===
-{{Main | The Jacobins }}
+{{Main| The Jacobins }}
 Since 1789edo tempers out the jacobin comma and it is defined by stacking three 11/8s to reach 13/10, one can use that as a generator. The resulting temperament is 37 & 1789, called onzonic. Name "onzonic" comes from the French word for eleven, ''onze''.
@@ Line 29: / Line 29: @@
 === Subsets and supersets ===
-edo is the 278th [[prime edo]].
+edo is the 278th [[prime edo]]. [[3578edo]], which doubles it, is consistent in the [[21-odd-limit]].
 == Table of selected intervals ==
@@ Line 218: / Line 218: @@
 === Rank-2 temperaments ===
 {| class="wikitable center-all left-4"
+|+Table of rank-2 temperaments by generator
+|-
 ! Generator*
 ! Cents*