145edo: Difference between revisions
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| Fifth = 85\145 (703.45¢) (→ [[29edo|17\29]]) | | Fifth = 85\145 (703.45¢) (→ [[29edo|17\29]]) | ||
| Major 2nd = 25\145 (206.90¢) | | Major 2nd = 25\145 (206.90¢) | ||
| | | Semitones = 15:10 (124.14¢ : 82.76¢) | ||
| | | Consistency = 11 | ||
}} | }} | ||
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. | |||
The '''145 equal divisions of the octave''' ( | |||
== Theory == | == 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 | It is the [[optimal patent val]] for the 11-limit [[mystery]] temperament and the 11-limit rank-3 [[pele]] temperament. 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. | ||
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]]. | ||
=== Prime harmonics === | === Prime harmonics === | ||