145edo: Difference between revisions

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~~The '''~~145 equal divisions of the octave''' ('''145edo''') or '''145(-tone) equal temperament''' ('''145tet''', '''145et''') when viewed from a [[regular temperament]] perspective, is the tuning system derived by dividing the [[octave]] into 145 [[equal]] parts of 8.28 [[cent]]s each.

== Theory ==

145et 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 ~~triad~~]], making it a very flexible harmonic system. The same is true of [[232edo]], the optimal patent val for 13-limit mystery.

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.

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

=== Prime harmonics ===

=== Subsets and supersets ===

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

== Regular temperament properties ==

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 {{Infobox ET}}
-The '''145 equal divisions of the octave''' ('''145edo''') or '''145(-tone) equal temperament''' ('''145tet''', '''145et''') when viewed from a [[regular temperament]] perspective, is the tuning system derived by dividing the [[octave]] into 145 [[equal]] parts of 8.28 [[cent]]s each.
+{{EDO intro|145}}
 == Theory ==
 et 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 triad]], making it a very flexible harmonic system. The same is true of [[232edo]], the optimal patent val for 13-limit mystery.
+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.
 The 145c val provides a tuning for [[magic]] which is nearly identical to the [[POTE tuning]].
 === Prime harmonics ===
-{{Harmonics in equal|145|intervals=prime|columns=11}}
+{{Harmonics in equal|145|columns=11}}
+=== Subsets and supersets ===
+= 5 × 29, and 145edo shares the same excellent fifth with [[29edo]].
 == Regular temperament properties ==