145edo: Difference between revisions
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{{Nowrap| 145 {{=}} 5 × 29 }}, and 145edo shares the same perfect fifth with [[29edo]]. It is generally a sharp-tending system, with [[prime harmonic]]s 3 to 23 all tuned sharp except for [[7/1|7]], which is slightly flat. It is [[consistent]] to the [[11-odd-limit]], or the no-13 no-15 [[23-odd-limit]], with [[13/7]], [[15/14]], [[15/8]] and their [[octave complement]]s being the only intervals going over the line. | {{Nowrap| 145 {{=}} 5 × 29 }}, and 145edo shares the same perfect fifth with [[29edo]]. It is generally a sharp-tending system, with [[prime harmonic]]s 3 to 23 all tuned sharp except for [[7/1|7]], which is slightly flat. It is [[consistent]] to the [[11-odd-limit]], or the no-13 no-15 [[23-odd-limit]], with [[13/7]], [[15/14]], [[15/8]] and their [[octave complement]]s being the only intervals going over the line. | ||
As an equal temperament, 145et [[tempering out|tempers out]] | As an equal temperament, 145et [[tempering out|tempers out]] 1600000/1594323 ([[amity comma]]) and {{monzo| 28 -3 -10 }} ([[mabila comma]]) in the [[5-limit]]; 4375/4374 ([[ragisma]]), 5120/5103 ([[aberschisma]]), and 50421/50000 ([[trimyna comma]]) in the [[7-limit]]; [[441/440]] and [[896/891]] in the [[11-limit]]; [[196/195]], [[352/351]], [[364/363]], [[676/675]], [[847/845]], and [[1001/1000]] in the [[13-limit]]; [[595/594]] in the [[17-limit]]; [[343/342]] and [[476/475]] in the [[19-limit]]. | ||
It | It provides an excellent [[optimal patent val]] for the 5-limit [[mabila]] temperament, the 11-limit [[mystery]] temperament and the 11-limit rank-3 [[pele]] temperament. It also [[support]]s and provides a good tuning for 13-limit mystery. 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 [[major minthmic chords]], because it tempers out 364/363 it allows [[minor minthmic chords]], and because it tempers out 847/845 it allows the [[cuthbert chords]], making it a very flexible harmonic system. The same is true of [[232edo]], the optimal patent val for 13-limit mystery. | ||
The 145c val provides a tuning for [[magic]] which is nearly identical to the [[POTE tuning]]. | The 145c val provides a tuning for [[magic]] which is nearly identical to the [[POTE tuning]]. | ||
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== Music == | == Music == | ||
; [[Chris Vaisvil]] ([http://www.chrisvaisvil.com/ site]) | ; [[Chris Vaisvil]] ([http://www.chrisvaisvil.com/ site]) | ||
* [http://micro.soonlabel.com/magic/daily20120113-piano-magic16-.mp3 ''Chromatic piece in magic 16''] – | * [http://micro.soonlabel.com/magic/daily20120113-piano-magic16-.mp3 ''Chromatic piece in magic 16''] – Magic[16] in 145edo tuning | ||
[[Category:Mabila]] | |||
[[Category:Mystery]] | [[Category:Mystery]] | ||
[[Category:Pele]] | [[Category:Pele]] | ||
[[Category:Magic]] | [[Category:Magic]] | ||
[[Category:Listen]] | [[Category:Listen]] | ||