The Jacobins: Difference between revisions
"Gene's jacobin" -> "genojacobin" per talk. Cleanup and mark todo |
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The main focus here will be on the 2.5.11.13 [[subgroup]], the subgorup of the comma. Besides, in the full 13-limit the jacobin comma often functions as a part of a basis of other temperaments of other families and groups, like [[vidar]]. | The main focus here will be on the 2.5.11.13 [[subgroup]], the subgorup of the comma. Besides, in the full 13-limit the jacobin comma often functions as a part of a basis of other temperaments of other families and groups, like [[vidar]]. | ||
Quite coincidentally, [[1789edo]] supports an enormous amount of these temperaments. Since 1789edo has a bad approximation to the 3rd harmonic, 2.5.7.11.13 is also the main subgroup for many temperaments, and 7-limit extensions to 2.5.11.13 temperaments are named "septimal | Quite coincidentally, [[1789edo]] supports an enormous amount of these temperaments. Since 1789edo has a bad approximation to the 3rd harmonic, 2.5.7.11.13 is also the main subgroup for many temperaments, and 7-limit extensions to 2.5.11.13 temperaments are named "septimal …" after the original temperament. | ||
== Jacobin == | == Jacobin == | ||
[[Subgroup]]: 2.3.5.7.11.13 | [[Subgroup]]: 2.3.5.7.11.13 | ||
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Optimal tuning (CTE): ~16/11 = 648.608 | Optimal tuning (CTE): ~16/11 = 648.608 | ||
== | == Genojacobin == | ||
Described as the 1789 & 3395 temperament, and named in honor of [[Gene Ward Smith]], who named the jacobin comma, and the fact that 3395edo provides the optimal patent val for the comma. 7 generators are equal to [[55/32]]. | Described as the 1789 & 3395 temperament, and named in honor of [[Gene Ward Smith]], who named the jacobin comma, and the fact that 3395edo provides the optimal patent val for the comma. 7 generators are equal to [[55/32]]. | ||
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{{Optimal ET sequence|legend=1|229, 1789}}, ... | {{Optimal ET sequence|legend=1|229, 1789}}, ... | ||
== Pure | == Pure bastille == | ||
Subgroup: 2.5.11.13 | Subgroup: 2.5.11.13 | ||
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{{Optimal ET sequence|legend=1|1407eff, 1789, 4985eff}} | {{Optimal ET sequence|legend=1|1407eff, 1789, 4985eff}} | ||
== Double | == Double bastille == | ||
Described as the 1789 & 2814 temperament, and named because 2814 divided in two is 1407. | Described as the 1789 & 2814 temperament, and named because 2814 divided in two is 1407. | ||
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{{Optimal ET sequence|legend=1|159, 1460, 1619, 1778}}, .. | {{Optimal ET sequence|legend=1|159, 1460, 1619, 1778}}, .. | ||
== Declaration of | == Declaration of rights == | ||
Defined as the 1789 & 1793 temperament, and called so because that's what both these years have in common. | Defined as the 1789 & 1793 temperament, and called so because that's what both these years have in common. | ||
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{{Optimal ET sequence|legend=1|353, 357, 361, 710, 718, 1789, 1793}}, ... | {{Optimal ET sequence|legend=1|353, 357, 361, 710, 718, 1789, 1793}}, ... | ||
== Eternal | == Eternal revolutionary == | ||
Described as the 1789 & 1880 temperament, and is named after a [[Wikipedia:ua:Вічний революціонер|poem by Ivan Franko]] <sup>[UA, no EN]</sup> which was written in the year 1880, hence the name. | Described as the 1789 & 1880 temperament, and is named after a [[Wikipedia:ua:Вічний революціонер|poem by Ivan Franko]] <sup>[UA, no EN]</sup> which was written in the year 1880, hence the name. | ||
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{{Optimal ET sequence|legend=1|91, 1698, 1789, 1880, 3669}}, ... | {{Optimal ET sequence|legend=1|91, 1698, 1789, 1880, 3669}}, ... | ||
=== Septimal | |||
=== Septimal eternal revolutionary=== | |||
Subgroup: 2.5.7.11.13 | Subgroup: 2.5.7.11.13 | ||
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{{Optimal ET sequence|legend=1|31f, 91d, 1789, 3669}}, ... | {{Optimal ET sequence|legend=1|31f, 91d, 1789, 3669}}, ... | ||
[[Category:Commatic realms]] | [[Category:Commatic realms]] | ||
[[Category:Jacobin]] | [[Category:Jacobin]] | ||
{{Todo| review }} | |||