145edo: Difference between revisions

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~~The~~ ''~~145 equal division~~'' divides the octave into 145 equal parts of 8.276 cents each. It is the [[Optimal_patent_val|optimal patent val]] for 11-limit [[Hemifamity_temperaments|mystery temperament]] and 11-limit rank three temperament [[Hemifamity_family|pele temperament]]. It tempers out 1600000/1594323 in the 5-limit; 4375/4374 and 5120/5103 in the 7-limit; 441/440 and 896/891 in the 11-limit; 196/195, 352/351 and 364/363 in the 13-limit; 595/594 in the 17-limit; 343/342 and 476/475 in the 19-limit. The 145c val provides a tuning for [[Magic|magic]] which is nearly identical to the POTE tuning. It also supports and provides a good tuning for 13-limit mystery, and because it tempers out 441/440 it allows [[werckismic_chords|werckismic chords]], because it tempers out 196/195 it allows [[mynucumic_chords|mynucumic chords]], because it tempers out 352/351 it allows [[minthmic_chords|minthmic chords]], because it tempers out 364/363 it allows [[gentle_chords|gentle chords]], and because it tempers out 847/845 it allows the [[cuthbert_triad|cuthbert triad]], making it a very flexible harmonic system. The same is true of [[232edo|232edo]], the optimal patent val for 13-limit mystery.

'''145edo''' divides the octave into 145 equal parts of 8.276 cents each.

=Music=

145et is the [[optimal patent val]] for 11-limit [[Hemifamity temperaments #Mystery|mystery temperament]] and 11-limit rank-3 temperament [[Hemifamity family #Pele|pele temperament]].

[http://micro.soonlabel.com/magic/daily20120113-piano-magic16-.mp3 Chromatic piece in magic 16] [http://www.chrisvaisvil.com/ Chris Vaisvil]

It tempers out [[1600000/1594323]] in the [[5-limit]]; [[4375/4374]] and [[5120/5103]] in the [[7-limit]]; [[441/440]] and [[896/891]] in the 11-limit; [[196/195]], [[352/351]] and [[364/363]] in the 13-limit; [[595/594]] in the 17-limit; [[343/342]] and [[476/475]] in the 19-limit.

The 145c val provides a tuning for [[magic]] which is nearly identical to the [[POTE tuning]].

It also supports and provides a good tuning for 13-limit mystery, and because it tempers out 441/440 it allows [[werckismic chords]], because it tempers out 196/195 it allows [[mynucumic chords]], because it tempers out 352/351 it allows [[minthmic chords]], because it tempers out 364/363 it allows [[gentle chords]], and because it tempers out 847/845 it allows the [[cuthbert triad]], making it a very flexible harmonic system. The same is true of [[232edo]], the optimal patent val for 13-limit mystery.

== Music ==

* [http://micro.soonlabel.com/magic/daily20120113-piano-magic16-.mp3 Chromatic piece in magic 16] [http://www.chrisvaisvil.com/ Chris Vaisvil]

[[Category:145edo]]

[[Category:Equal divisions of the octave]]

[[Category:Mystery]]

[[Category:Pele]]

[[Category:Magic]]

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-The ''145 equal division'' divides the octave into 145 equal parts of 8.276 cents each. It is the [[Optimal_patent_val|optimal patent val]] for 11-limit [[Hemifamity_temperaments|mystery temperament]] and 11-limit rank three temperament [[Hemifamity_family|pele temperament]]. It tempers out 1600000/1594323 in the 5-limit; 4375/4374 and 5120/5103 in the 7-limit; 441/440 and 896/891 in the 11-limit; 196/195, 352/351 and 364/363 in the 13-limit; 595/594 in the 17-limit; 343/342 and 476/475 in the 19-limit. The 145c val provides a tuning for [[Magic|magic]] which is nearly identical to the POTE tuning. It also supports and provides a good tuning for 13-limit mystery, and because it tempers out 441/440 it allows [[werckismic_chords|werckismic chords]], because it tempers out 196/195 it allows [[mynucumic_chords|mynucumic chords]], because it tempers out 352/351 it allows [[minthmic_chords|minthmic chords]], because it tempers out 364/363 it allows [[gentle_chords|gentle chords]], and because it tempers out 847/845 it allows the [[cuthbert_triad|cuthbert triad]], making it a very flexible harmonic system. The same is true of [[232edo|232edo]], the optimal patent val for 13-limit mystery.
+'''145edo''' divides the octave into 145 equal parts of 8.276 cents each.
-=Music=
+et is the [[optimal patent val]] for 11-limit [[Hemifamity temperaments #Mystery|mystery temperament]] and 11-limit rank-3 temperament [[Hemifamity family #Pele|pele temperament]].
-[http://micro.soonlabel.com/magic/daily20120113-piano-magic16-.mp3 Chromatic piece in magic 16] [http://www.chrisvaisvil.com/ Chris Vaisvil]
+It tempers out [[1600000/1594323]] in the [[5-limit]]; [[4375/4374]] and [[5120/5103]] in the [[7-limit]]; [[441/440]] and [[896/891]] in the 11-limit; [[196/195]], [[352/351]] and [[364/363]] in the 13-limit; [[595/594]] in the 17-limit; [[343/342]] and [[476/475]] in the 19-limit.
+The 145c val provides a tuning for [[magic]] which is nearly identical to the [[POTE tuning]].
+It also supports and provides a good tuning for 13-limit mystery, and because it tempers out 441/440 it allows [[werckismic chords]], because it tempers out 196/195 it allows [[mynucumic chords]], because it tempers out 352/351 it allows [[minthmic chords]], because it tempers out 364/363 it allows [[gentle chords]], and because it tempers out 847/845 it allows the [[cuthbert triad]], making it a very flexible harmonic system. The same is true of [[232edo]], the optimal patent val for 13-limit mystery.
+== Music ==
+* [http://micro.soonlabel.com/magic/daily20120113-piano-magic16-.mp3 Chromatic piece in magic 16] [http://www.chrisvaisvil.com/ Chris Vaisvil]
+[[Category:145edo]]
+[[Category:Equal divisions of the octave]]
+[[Category:Mystery]]
+[[Category:Pele]]
+[[Category:Magic]]