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No-threes subgroup temperaments: Difference between revisions

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Move "estates general" here and various cleanup
Eliora (talk | contribs)
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→Estates general: Temperament makes sense in all subgroups except the raw 2.5.11.13, so *That* one should get a different name, instead of estates general. Besides, maximum evenness scale of 1789 notes in 3125edo uses this 522-cent generaor as well, which translates to 778\1789 and 1359\3125.
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== Estates general ==
== Estates general ==
Named so because it is defined as the 1789 & 3125 temperament due to 3125 providing optimal patent val for the jacobin comma, 3125 is 5 to the 5th power, and Estates General were called by Louis XVI on 5th May 1789 (05/05). Defined for the 2.5.11.13.19 subgroup.
Named so because it is defined as the 1789 & 3125 temperament due to 3125 providing optimal patent val for the jacobin comma, 3125 is 5 to the 5th power, and Estates General were called by Louis XVI on 5th May 1789 (05/05). Defined starting with the 2.5.11.13.19 subgroup, upwards to the 2.5.11.13.19.23.29.31 subgroup.


[[Subgroup]]: 2.5.11.13
Subgroup: 2.5.11.13.19
 
Comma list: 6656/6655, 40960000000/40943078891, {{monzo| -133 50 -7 18 -6 }}
 
Mapping: [{{val| 1 118 -107 -212 450 }}, {{val| 0 -266 254 496 -1025 }}]
 
Optimal tuning (CTE): ~2588443885831192576/1914932769775390625 = 521.856
 
=== 2.5.11.13.19.23 subgroup ===
Subgroup: 2.5.11.13.19.23
 
Comma list: 6656/6655, 62500/62491, 190676992/190653125, {{Monzo|-92 23 -2 14 -10  8}}
 
Mapping: [{{val| 1 118 -107 -212 450 579}}, {{val| 0 -266 254 496 -1025 -1321}}]


[[Comma list]]: 6656/6655, {{monzo| 314 -78 14 -49 }}
Optimal tuning (CTE): ~2592407900127232/1918105439453125 = 521.856


[[Mapping]]: [{{val| 1 118 -107 -212 }}, {{val| 0 -133 127 248 }}]
=== 2.5.11.13.19.23.29 subgroup ===
Subgroup: 2.5.11.13.19.23.29


[[Optimal tuning]] ([[POTE]]): ~995765040283203125/544935554911830016 = 1043.712
Comma list: 6656/6655, 62500/62491, 190676992/190653125, 7592198144/7591796875, 897740062375/897648164864


=== 2.5.11.13.19 subgroup ===
Mapping: [{{val| 1 118 -107 -212 450 579 251}}, {{val| 0 -266 254 496 -1025 -1321 -566}}]
{{Todo|inline=1|comment=Weak extension, must use a different name. }}


Subgroup: 2.5.11.13.19
Optimal tuning (CTE): ~184000/136097 = 521.856


Comma list: 6656/6655, 40960000000/40943078891, {{monzo| -133 50 -7 18 -6 }}
=== 2.5.11.13.19.23.29.31 subgroup ===
Subgroup: 2.5.11.13.19.23.29.31


Mapping: [{{val| 1 118 -107 -212 450 }}, {{val| 0 -266 254 496 -1025 }}]
Comma list: 6656/6655, 62500/62491, 9425/9424, 190676992/190653125, 507528125/507510784, 519411073024/519363934375


Optimal tuning (POTE): ~2588443885831192576/1914932769775390625 = 521.856
Mapping: [{{val| 1 118 -107 -212 450 579 251 -179}}, {{val| 0 -266 254 496 -1025 -1321 -566 423}}]


Optimal tuning (CTE): ~80275/59392 = 521.856
[[Category:Temperament collections]]
[[Category:Temperament collections]]
[[Category:Subgroup temperaments]]
[[Category:Subgroup temperaments]]
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