145edo: Difference between revisions

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== Theory ==

145et [[tempering out|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.

145 = 5 × 29, and 145edo shares the same perfect fifth with [[29edo]]. It is generally a sharp-tending system, with prime harmonics 3 to 23 all tuned sharp except for 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]], [[15/8]] and their [[octave complement]]s being the only intervals going over the line.

As an equal temperament, 145et [[tempering out|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.

It is the [[optimal patent val]] for 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, 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 chords]], making it a very flexible harmonic system. The same is true of [[232edo]], the optimal patent val for 13-limit mystery.

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=== Prime harmonics ===

=== Subsets and supersets ===

~~145 = 5 × 29,~~ and ~~145edo shares the same excellent fifth with~~ [[29edo]].

145edo contains [[5edo]] and [[29edo]] as subset edos.

== Regular temperament properties ==

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 == Theory ==
-et [[tempering out|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.
+= 5 × 29, and 145edo shares the same perfect fifth with [[29edo]]. It is generally a sharp-tending system, with prime harmonics 3 to 23 all tuned sharp except for 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]], [[15/8]] and their [[octave complement]]s being the only intervals going over the line.
+As an equal temperament, 145et [[tempering out|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.
 It is the [[optimal patent val]] for 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, 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 chords]], making it a very flexible harmonic system. The same is true of [[232edo]], the optimal patent val for 13-limit mystery.
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 === Prime harmonics ===
-{{Harmonics in equal|145|columns=11}}
+{{Harmonics in equal|145|intervals=prime}}
 === Subsets and supersets ===
-= 5 × 29, and 145edo shares the same excellent fifth with [[29edo]].
+edo contains [[5edo]] and [[29edo]] as subset edos.
 == Regular temperament properties ==