17th-octave temperaments: Difference between revisions
Created page with "17edo is a "wheel" for some fractional-octave temperaments. The most notable relationship is the tempering out of septendecima, the amount by which seventeen 25/24 chr..." |
Cmloegcmluin (talk | contribs) "optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence |
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Optimal tuning (CTE): ~765/728 = 85.421 | Optimal tuning (CTE): ~765/728 = 85.421 | ||
{{Optimal ET sequence|legend=1|323, 1700, 2023}} | |||
[[Category:17edo]] | [[Category:17edo]] | ||
[[Category:Temperament collections]] | [[Category:Temperament collections]] | ||
[[Category:Rank 2]] | [[Category:Rank 2]] | ||
Revision as of 20:06, 7 May 2023
17edo is a "wheel" for some fractional-octave temperaments. The most notable relationship is the tempering out of septendecima, the amount by which seventeen 25/24 chromatic semitones exceed an octave.
Chlorine
See Ragismic microtemperaments#Chlorine
Leaves
Defined as the 323 & 2023 temperament. 2 generators reach 17/13, 7 generators reach 5/4, 10 generators produce 13/11.
Subgroup: 2.3.5.7.11.13
Comma list: 160083/160000, 928125/927472, 1990656/1990625, 20726199/20706224
Mapping: [⟨17 10 31 9 106 98], ⟨0 14 7 32 -39 -29]]
Mapping generators: ~25/24, ~1024/975
Optimal tuning (CTE): ~1024/975 = 85.421
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 57375/57344, 111537/111475, 140800/140777, 111537/111475, 1026675/1026256
Mapping: [⟨17 10 31 9 106 98 107], ⟨0 14 7 32 -39 -29 -31]]
Mapping generators: ~25/24, ~765/728
Optimal tuning (CTE): ~765/728 = 85.421