The Flashmob: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older editNewer edit →
VisualWikitext
Cmloegcmluin (talk | contribs)
autopatrolled, emailconfirmed
5,160 edits
"optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence
Eliora (talk | contribs)
autopatrolled, emailconfirmed
3,352 edits
→Hafnium: move Hafnium to 72nd-octave temperaments as tempering of 12376/12375 is not the most interesting thing about it
Line 56: Line 56:


{{Optimal ET sequence|legend=1|282, 759def, 1041, 1323, 2082de}}
{{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 ==

Revision as of 23:53, 8 July 2023

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:

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: [⟨3 6 19 30 35 36 29], ⟨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: [⟨3 6 19 30 35 36 29 18], ⟨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: [⟨3 6 19 30 35 36 29 18 31], ⟨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: [⟨3 6 19 30 35 36 29 18 31 19], ⟨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: 282, 759def, 1041, 1323, 2082de

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: [⟨77 1 203 313 339 527 460], ⟨0 5 -1 -4 -3 -10 -6]]

Mapping generators: ~429/425 = 1\77, 975/784 = 377.269

Optimal ET sequence: 385, 1848, 7777

Retrieved from "https://en.xen.wiki/index.php?title=The_Flashmob&oldid=119207"