94edo: Difference between revisions

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| Augmented 1sn = 9\94 = 115¢

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The '''94 equal ~~temperament~~''', ~~often abbreviated~~ '''94-~~tET~~''', '''~~94-[[EDO]]~~''', or '''~~94-ET~~''', results from dividing the [[octave]] into 94 ~~equally~~-sized steps, where each step is 12.766 [[cent~~|cents~~]].

The '''94 equal divisions of the octave''' ('''94edo'''), or the '''94(-tone) equal temperament''' ('''94tet''', '''94et''') when viewed from a [[regular temperament]] perspective, results from dividing the [[octave]] into 94 [[equal]]ly-sized steps, where each step is 12.766 [[cent]]s.

== Theory ==

94edo is a remarkable all-around utility ~~temperament~~, good from low [[prime limit]] to very high prime limit situations. It is the first ~~equal temperament~~ to be [[consistent]] through the [[23-limit]], and no other ~~equal temperament~~ is so consistent until [[282edo|282]] and [[311edo|311]] make their appearance.

94edo is a remarkable all-around utility tuning system, good from low [[prime limit]] to very high prime limit situations. It is the first edo to be [[consistent]] through the [[23-odd-limit]], and no other edo is so consistent until [[282edo|282]] and [[311edo|311]] make their appearance.

The list of 23-limit commas it tempers out is huge, but it's worth noting that it tempers out [[32805/32768]] and is thus a [[schismatic]] system, that it tempers out [[225/224]] and [[385/384]] and so is a [[marvel]] system, and that it also tempers out [[3125/3087]], [[4000/3969]], [[5120/5103]] and [[540/539]]. It provides the [[optimal patent val]] for the rank ~~five~~ temperament tempering out [[275/273]], and for a number of other temperaments, such as [[isis]].

The list of 23-limit commas it tempers out is huge, but it is worth noting that it tempers out [[32805/32768]] and is thus a [[schismatic]] system, that it tempers out [[225/224]] and [[385/384]] and so is a [[marvel]] system, and that it also tempers out [[3125/3087]], [[4000/3969]], [[5120/5103]] and [[540/539]]. It provides the [[optimal patent val]] for the rank-5 temperament tempering out [[275/273]], and for a number of other temperaments, such as [[isis]].

=== Prime harmonics ===

@@ Line 7: / Line 7: @@
 | Augmented 1sn = 9\94 = 115¢
 }}
-The '''94 equal temperament''', often abbreviated '''94-tET''', '''94-[[EDO]]''', or '''94-ET''', results from dividing the [[octave]] into 94 equally-sized steps, where each step is 12.766 [[cent|cents]].
+The '''94 equal divisions of the octave''' ('''94edo'''), or the '''94(-tone) equal temperament''' ('''94tet''', '''94et''') when viewed from a [[regular temperament]] perspective, results from dividing the [[octave]] into 94 [[equal]]ly-sized steps, where each step is 12.766 [[cent]]s.
 == Theory ==
-edo is a remarkable all-around utility temperament, good from low [[prime limit]] to very high prime limit situations. It is the first equal temperament to be [[consistent]] through the [[23-limit]], and no other equal temperament is so consistent until [[282edo|282]] and [[311edo|311]] make their appearance.
+edo is a remarkable all-around utility tuning system, good from low [[prime limit]] to very high prime limit situations. It is the first edo to be [[consistent]] through the [[23-odd-limit]], and no other edo is so consistent until [[282edo|282]] and [[311edo|311]] make their appearance.
-The list of 23-limit commas it tempers out is huge, but it's worth noting that it tempers out [[32805/32768]] and is thus a [[schismatic]] system, that it tempers out [[225/224]] and [[385/384]] and so is a [[marvel]] system, and that it also tempers out [[3125/3087]], [[4000/3969]], [[5120/5103]] and [[540/539]]. It provides the [[optimal patent val]] for the rank five temperament tempering out [[275/273]], and for a number of other temperaments, such as [[isis]].
+The list of 23-limit commas it tempers out is huge, but it is worth noting that it tempers out [[32805/32768]] and is thus a [[schismatic]] system, that it tempers out [[225/224]] and [[385/384]] and so is a [[marvel]] system, and that it also tempers out [[3125/3087]], [[4000/3969]], [[5120/5103]] and [[540/539]]. It provides the [[optimal patent val]] for the rank-5 temperament tempering out [[275/273]], and for a number of other temperaments, such as [[isis]].
 === Prime harmonics ===