17th-octave temperaments: Difference between revisions

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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..."
 
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"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


Vals: {{EDOs|323, 1700, 2023}}
{{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

Optimal ET sequence323, 1700, 2023