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→Eternal revolutionary: rework completely - there is a simpler mapping
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== Eternal revolutionary ==
== 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 91 & 1880 temperament, or 1789bd & 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.


Subgroup: 2.5.11.13
Subgroup: 2.5.11.13
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Optimal tuning (CTE): ~2.5.11.13 {{monzo|294 -46 7 -57}} = 580.212
Optimal tuning (CTE): ~2.5.11.13 {{monzo|294 -46 7 -57}} = 580.212


{{Optimal ET sequence|legend=1|91, 1698, 1789, 1880, 3669}}, ...
[[Support]]ing [[ET]]s: {{EDOs|91, 1698, 1789, 1880, 3487, 3669, 5458, 7247}}, ...
 
=== Septimal eternal revolutionary===
Subgroup: 2.5.7.11.13
 
Comma list: 6656/6655, {{Monzo|-26 5 1 -2 5}}, {{Monzo|-43 35 35 -17 -21}}
 
Sval mapping: [{{Val|1 261 -472 -159 -225}}, {{Val|0 -535 982 336 473}}]
 
Optima tuning (CTE): ~482745786865234375/344859973188583424 = 580.213
 
{{Optimal ET sequence|legend=1|91d, 1698d, 1789, 1880, 1971cd, 3669}}
 
=== 13-limit (1789bd) ===
Described as the 1789bd & 1880 temperament, as 1880edo contains the 94edo fifth and 1789bd val is better tuned than the patent val.


=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


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[[Optimal tuning]] ([[CTE]]): ~6875/4914 = 580.213
[[Optimal tuning]] ([[CTE]]): ~6875/4914 = 580.213


[[Support]]ing [[ET]]s: {{EDOs|91, 1789bd, 1880}}, ...
[[Support]]ing [[ET]]s: {{EDOs|91, 1698bdd, 1789bd, 1880, 1971c}}, ...


=== Hymn (rank-3) ===
=== Hymn (rank-3) ===
An expansion of Eternal Revolutionary resulting from the 31 & 91 maximal evenness scale. Described as the 31f & 91d & 1789 temperament.
An expansion of eternal revolutionary resulting from the 31 & 91 maximal evenness scale. Described as the 31f & 91 & 1880 temperament. It contains as a subset a rank-2 extension of the [[tritoni]] temperament into the 13-limit.


Subgroup: 2.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 6656/6655, 2.5.7.11.13{{monzo| -677 206 124 -71 26 }}
Comma list: 6656/6655, {{monzo|-17 -12 6 4 1 2}}, {{monzo|-12 2 17 -11 -1 1}}


Sval mapping: [{{Val|1 0 3 77 222}}, {{Val|0 1 4 -104 -311}}, {{Val| 0 0 7 -124 -372}}]
{{Mapping|legend=2| 1 4 14 19 -15 40 | 0 -5 -6 -10 4 6 | 0 0 -17 22 32 79 }}


Sval mapping generators: ~2 = 1\1, ~5 = 2786.260, ~{{monzo|-291 0 89 53 -30 11}} = 1625.181
Sval mapping generators: ~2 = 1\1, ~3773/2700 = 579.594, ~290304/203125 = 619.783


{{Optimal ET sequence|legend=1|31f, 91d, 1789, 3669}}, ...
[[Support]]ing [[ET]]s: {{EDOs|31f, 60f, 91, 122, 1789bd, 1880, 1911f, 2002c}}, ...


[[Category:Commatic realms]]
[[Category:Commatic realms]]
[[Category:Jacobin]]
[[Category:Jacobin]]
{{Todo| review }}
{{Todo| review }}
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