The Flashmob: Difference between revisions

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'''The Flashmob''' is a collection of temperaments of different ranks that all temper out 12376/12375, the [[flashma]], a 17-limit comma associated with precise systems that model high-limit JI.
'''The Flashmob''' is a collection of temperaments of different ranks that all temper out 12376/12375, the [[flashma]], a 17-limit comma associated with precise systems that model high-limit JI.


Temperaments discussed elsewhere include:
See:
* ''[[Calcium]]'' (+ 9801/9800, 37180/37179, 123201/123200, 903168/903125) → [[20th-octave temperaments#Calcium|20th-octave temperaments]]
* ''[[Bromine]]'' (+ 123201/123200, 194481/194480, 1713660/1713481, 24635975/24634368) → [[35th-octave temperaments#Bromine|35th-octave temperaments]]
* ''17-limit [[minutes]]'' (+ 9801/9800, 28561/28560, 250047/250000, 253755392/253746675) → [[60th-octave temperaments#Minutes|60th-octave temperaments]]
* ''17-limit [[mercury]]'' (+ 9801/9800, 67392/67375, 4230144/4229225, 494534656/494515125) → [[80th-octave temperaments#Mercury|80th-octave temperaments]]
* ''17-limit [[hafnium]]'' (+ 9801/9800, 21879/21875, 194481/194480, 1713660/1713481, 97144749/97140736) → [[72nd-octave temperaments#Hafnium|72nd-octave temperaments]]
* ''[[Iridium]]'' (+ 63792/67375, 194481/194480, 396833125/396829664, 112435984089/112394240000) → [[77th-octave temperaments#Iridium|77th-octave temperaments]]
* ''17-limit [[berkelium-247]]'' (+ 37180/37179, 1990656/1990625, 1146880/1146717, 263299491/263296000) → [[97th-octave temperaments#Berkelium-247|97th-octave temperaments]]
* ''Septendecimal [[jacobin]]'' (+ 6656/6655) → [[The Jacobins#Septendecimal jacobin|The Jacobins]]
* ''17-limit [[iodine]]'' (+ 1701/1700, 6656/6655, 8624/8619, 14875/14872) → [[Mercator family#Iodine|Mercator family]]
* ''17-limit [[noletaland]]'' (+ 2058/2057, 4914/4913, 8624/8619, 250047/250000) → [[Tricot family#Noletaland|Tricot family]]


* ''Minutes'' → [[60th-octave temperaments#Minutes]]
* ''Mercury'' → [[80th-octave temperaments#Mercury]]
== Noletaland ==
Noletaland is described as 282 & 1323, and it combines the smallest consistent edo in the 29-odd-limit with the smallest uniquely consistent. It reaches 4/3 in nine generators ([[noleta]]-...) and tempers out the landscape comma (...-land). Noletaland reaches [[13/11]] in 2 generators, and [[29/19]] in 5. Then there's [[44/25]] in 4, and [[152/115]] in also 4.
Subgroup: 2.3.5.7.11.13.17
Comma list: 2058/2057, 12376/12375, 14875/14872, 43904/43875, 250047/250000
Mapping: [{{val|3 6 19 30 35 36 29}}, {{val|0 -9 -87 -156 -178 -180 -121}}]
Mapping generators: ~63/50 = 1\3, ~4725/4576 = 55.330
Optimal tuning (CTE): ~351/340 = 55.329
=== 19-limit ===
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 2926/2925, 3136/3135, 5985/5984, 12376/12375, 14875/14872, 256000/255879
Mapping: [{{val|3 6 19 30 35 36 29 18}}, {{val|0 -9 -87 -156 -178 -180 -121 -38}}]
Mapping generators: ~63/50 = 1\3, ~4725/4576 = 55.330
Optimal tuning (CTE): ~351/340 = 55.329
=== 23-limit ===
Subgroup: 2.3.5.7.11.13.17.19.23
Comma list: 2926/2925, 3136/3135, 5985/5984, 10626/10625, 12376/12375, 21736/21735, 256000/255879
Mapping: [{{val|3 6 19 30 35 36 29 18 31}}, {{val|0 -9 -87 -156 -178 -180 -121 -38 -126}}]
Mapping generators: ~63/50 = 1\3, ~4725/4576 = 55.330
Optimal tuning (CTE): ~4725/4576 = 55.330
=== 29-limit ===
Subgroup: 2.3.5.7.11.13.17.19.23.29
Comma list: 2926/2925, 3136/3135, 5104/5103, 5985/5984, 12376/12375, 21736/21735, 10626/10625, 256000/255879
Mapping: [{{val|3 6 19 30 35 36 29 18 31 19}}, {{val|0 -9 -87 -156 -178 -180 -121 -38 -126 -32}}]
Mapping generators: ~63/50 = 1\3, ~4725/4576 = 55.330
Optimal tuning (CTE): ~4725/4576 = 55.330
{{Optimal ET sequence|legend=1|282, 759def, 1041, 1323, 2082de}}
== Hafnium ==
Hafnium is a period-72 temperament created by temperament-merging 4320edo and 5544edo, equal temperaments notable for their high divisibility. Named after the 72nd element.
Subgroup: 2.3.5.7.11.13
Comma list: 9801/9800, 250047/250000, 184549376/184528125, 463373664/463203125
Mapping: [{{val|72 72 462 876 1302 1193}}, {{val|0 1 -7 -16 -25 -22}}]
Mapping generators: ~105/104 = 1\72, ~3/2 = 701.948
Optimal tuning (CTE): ~3/2 = 701.948
{{Optimal ET sequence|legend=1|1224, 1872def, 4320, 5544}}
===17-limit===
Subgroup: 2.3.5.7.11.13.17
Comma list: 9801/9800, 12376/12375, 21879/21875, 194481/194480, 1713660/1713481, 97144749/97140736
Mapping: [{{val|72 72 462 876 1302 1193 547}}, {{val|0 1 -7 -16 -25 -22 -6}}]
Mapping generators: ~105/104 = 1\72, ~3/2 = 701.948
Optimal tuning (CTE): ~3/2 = 701.948
{{Optimal ET sequence|legend=1|1224, 1872def, 4320, 5544}}
===2.3.5.7.11.13.17.31 subgroup===
Since 4320edo and 5544edo have good 31st and 37th harmonics, addition of these subgroups is prescribed.
Subgroup: 2.3.5.7.11.13.17.31
Comma list: 9801/9800, 10881/10880, 12376/12375, 57629/57624, 179712/179707, 61456384/61448625
Sval mapping: [{{val|72 72 462 876 1302 1193 547 356}}, {{val|0 1 -7 -16 -25 -22 -6 6}}]
Mapping generators: ~105/104 = 1\72, ~3/2 = 701.948
Optimal tuning (CTE): ~3/2 = 701.948
===2.3.5.7.11.13.17.31.37 subgroup===
[[37/22]] is mapped to exact three-quarters of the octave.
Subgroup: 2.3.5.7.11.13.17.31
Comma list: 10881/10880, 12376/12375, 16576/16575, 93093/93092, 954304/954261, 2737889/2737800, 126607131/126605120
Sval mapping: [{{val|72 72 462 876 1302 1193 547 356 378}}, {{val|0 1 -7 -16 -25 -22 -6 6 -25}}]
Mapping generators: ~105/104 = 1\72, ~3/2 = 701.948
Optimal tuning (CTE): ~3/2 = 701.948
== Iridium ==
Iridium is named after 77th element, being period-77.
Subgroup: 2.3.5.7.11.13.17
Comma list: 12376/12375, 63792/67375, 194481/194480, 396833125/396829664, 112435984089/112394240000
Mapping: [{{Val|77 1 203 313 339 527 460}}, {{Val|0 5 -1 -4 -3 -10 -6}}]
Mapping generators: ~429/425 = 1\77, 975/784 = 377.269
{{Optimal ET sequence|legend=1|385, 1848, 7777}}
[[Category:Commatic realms]]
[[Category:Commatic realms]]
[[Category:Flashmic]]
[[Category:Flashmic]]

Latest revision as of 05:53, 24 February 2024

The Flashmob is a collection of temperaments of different ranks that all temper out 12376/12375, the flashma, a 17-limit comma associated with precise systems that model high-limit JI.

See:

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