175edo: Difference between revisions

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~~The ''175 equal division'' divides the octave into 175 equal parts of 6.857 cents each. It~~ tempers out 1029/1024 ~~and 225/224~~, so that it [[support]]s 7-limit [[~~Miracle|~~miracle ~~temperament~~]], and in fact provides an excellent alternative to [[~~72edo|~~72edo]] for 7-limit miracle. In the 11-limit, it tempers out 243/242, 385/384, 441/440 and 540/~~439~~, and supports 11-limit miracle. In the 13-limit, 175f tempers out 351/350 just as 72 does, and provides a tuning for benediction temperament very close to the POTE tuning.

== Theory ==

175et [[tempering out|tempers out]] [[225/224]] and [[1029/1024]], so that it [[support]]s 7-limit [[miracle]], and in fact provides an excellent alternative to [[72edo]] for 7-limit miracle with improved [[5/1|5]] and [[7/1|7]] at the cost of a slightly flatter [[3/1|3]]. In the 11-limit, it tempers out [[243/242]], [[385/384]], [[441/440]] and [[540/539]], and supports 11-limit miracle. In the 13-limit, the 175f val, {{val| 175 277 406 491 605 '''647''' }} tempers out [[351/350]] just as 72 does, and provides a tuning for [[benediction]] temperament very close to the POTE tuning.

=== Odd harmonics ===

=== Subsets and supersets ===

Since 175 factors into {{factorization|175}}, 175edo has subset edos {{EDOs| 5, 7, 25, and 35 }}.

== Music ==

* [http://www.archive.org/details/RachmaninoffPlaysBlackjack ~~http://www.archive.org/details/RachmaninoffPlaysBlackjack~~]

; [[Gene Ward Smith]]

* [http://www.archive.org/download/RachmaninoffPlaysBlackjack/rachman.mp3 play]

* ''Rachmaninoff Plays Blackjack'' (archived 2010) – [http://www.archive.org/details/RachmaninoffPlaysBlackjack detail] | [http://www.archive.org/download/RachmaninoffPlaysBlackjack/rachman.mp3 play] – [[Blackjack]] in 175edo tuning

[[~~Category:Equal divisions of the octave|###~~]] ~~~~

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-The ''175 equal division'' divides the octave into 175 equal parts of 6.857 cents each. It tempers out 1029/1024 and 225/224, so that it [[support]]s 7-limit [[Miracle|miracle temperament]], and in fact provides an excellent alternative to [[72edo|72edo]] for 7-limit miracle. In the 11-limit, it tempers out 243/242, 385/384, 441/440 and 540/439, and supports 11-limit miracle. In the 13-limit, 175f tempers out 351/350 just as 72 does, and provides a tuning for benediction temperament very close to the POTE tuning.
+{{Infobox ET}}
+{{ED intro}}
+== Theory ==
+et [[tempering out|tempers out]] [[225/224]] and [[1029/1024]], so that it [[support]]s 7-limit [[miracle]], and in fact provides an excellent alternative to [[72edo]] for 7-limit miracle with improved [[5/1|5]] and [[7/1|7]] at the cost of a slightly flatter [[3/1|3]]. In the 11-limit, it tempers out [[243/242]], [[385/384]], [[441/440]] and [[540/539]], and supports 11-limit miracle. In the 13-limit, the 175f val, {{val| 175 277 406 491 605 '''647''' }} tempers out [[351/350]] just as 72 does, and provides a tuning for [[benediction]] temperament very close to the POTE tuning.
+=== Odd harmonics ===
+{{Harmonics in equal|175}}
+=== Subsets and supersets ===
+Since 175 factors into {{factorization|175}}, 175edo has subset edos {{EDOs| 5, 7, 25, and 35 }}.
 == Music ==
-* [http://www.archive.org/details/RachmaninoffPlaysBlackjack http://www.archive.org/details/RachmaninoffPlaysBlackjack]
+; [[Gene Ward Smith]]
-* [http://www.archive.org/download/RachmaninoffPlaysBlackjack/rachman.mp3 play]
+* ''Rachmaninoff Plays Blackjack'' (archived 2010) – [http://www.archive.org/details/RachmaninoffPlaysBlackjack detail] | [http://www.archive.org/download/RachmaninoffPlaysBlackjack/rachman.mp3 play] – [[Blackjack]] in 175edo tuning
-[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->