Orwell: Difference between revisions

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Compatible [[equal temperaments]] include [[22edo]], [[31edo]], [[53edo]], and [[84edo]]. Orwell is in better tune in lower limits than higher ones; the [[optimal patent val]] is [[296edo]] in the 5-limit, [[137edo]] in the 7-limit, and [[53edo]] in the 11-limit.

See [[Semicomma family #Orwell]] for technical details.

See [[Semicomma family #Orwell]] for technical details. See [[Orwell extensions]] for details about 13-limit extensions.

== Theory ==

~~=== Tempering information ===~~

It tempers out the [[semicomma]] (2109375/2097152) in the 5-limit, and so belongs to the [[semicomma family]]. In the 7-limit it tempers out 225/224, 1728/1715, [[2430/2401]] and [[6144/6125]], and in the 11-limit, 99/98, 121/120, [[176/175]], [[385/384]] and [[540/539]]. By adding [[275/273]] to the list of commas it can be extended to the [[13-limit]] as [[Semicomma family #Orwell|tridecimal orwell]], and by adding instead [[66/65]], [[Semicomma family #Winston|winston temperament]]. See [[Orwell extensions]] for details about 13-limit extensions.

=== Interval chain ===

Odd harmonics 1–21 and their inverses are in '''bold'''.

@@ Line 28: / Line 28: @@
 Compatible [[equal temperaments]] include [[22edo]], [[31edo]], [[53edo]], and [[84edo]]. Orwell is in better tune in lower limits than higher ones; the [[optimal patent val]] is [[296edo]] in the 5-limit, [[137edo]] in the 7-limit, and [[53edo]] in the 11-limit.
-See [[Semicomma family #Orwell]] for technical details.
+See [[Semicomma family #Orwell]] for technical details. See [[Orwell extensions]] for details about 13-limit extensions.
 == Theory ==
-=== Tempering information ===
-It tempers out the [[semicomma]] (2109375/2097152) in the 5-limit, and so belongs to the [[semicomma family]]. In the 7-limit it tempers out 225/224, 1728/1715, [[2430/2401]] and [[6144/6125]], and in the 11-limit, 99/98, 121/120, [[176/175]], [[385/384]] and [[540/539]]. By adding [[275/273]] to the list of commas it can be extended to the [[13-limit]] as [[Semicomma family #Orwell|tridecimal orwell]], and by adding instead [[66/65]], [[Semicomma family #Winston|winston temperament]]. See [[Orwell extensions]] for details about 13-limit extensions.
 === Interval chain ===
 Odd harmonics 1–21 and their inverses are in '''bold'''.