894edo: Difference between revisions

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== Theory ==

894edo is [[consistent]] to the [[17-odd-limit]], and except for [[19/13]], [[19/17]] and their [[octave complement]]s, it is consistent to the [[31-odd-limit]], thus making it a ~~good~~ [[31-limit]] system. Its [[prime interval|primes]] [[5/1|5]], [[17/1|17]], [[19/1|19]], and [[23/1|23]] come from [[149edo]], its [[11/1|11]] from [[298edo]], and its [[7/1|7]] and [[13/1|13]] from [[447edo]].

894edo is [[consistent]] to the [[17-odd-limit]], and except for [[19/13]], [[19/17]], [[25/13]], [[25/17]] and their [[octave complement]]s, it is consistent to the [[31-odd-limit]], thus making it a reasonable [[31-limit]] system. Its [[prime interval|primes]] [[5/1|5]], [[17/1|17]], [[19/1|19]], and [[23/1|23]] come from [[149edo]], its [[11/1|11]] from [[298edo]], and its [[7/1|7]] and [[13/1|13]] from [[447edo]].

As an equal temperament, it [[tempering out|tempers out]] {{monzo| 23 6 -14 }} ([[vishnu comma]]) in the [[5-limit]]; 250047/250000 ([[landscape comma]]) in the [[7-limit]]; [[9801/9800]], [[131072/130977]], [[151263/151250]] in the [[11-limit]]; [[1716/1715]], [[2080/2079]], [[4096/4095]], [[4225/4224]], 34398/34375 in the [[13-limit]]; [[1156/1155]], [[2431/2430]], [[2601/2600]], [[11016/11011]] in the [[17-limit]]; [[1521/1520]], [[2376/2375]], [[3250/3249]] in the [[19-limit]]; and [[1863/1862]], [[2300/2299]] among others in the [[23-limit]].

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 == Theory ==
-edo is [[consistent]] to the [[17-odd-limit]], and except for [[19/13]], [[19/17]] and their [[octave complement]]s, it is consistent to the [[31-odd-limit]], thus making it a good [[31-limit]] system. Its [[prime interval|primes]] [[5/1|5]], [[17/1|17]], [[19/1|19]], and [[23/1|23]] come from [[149edo]], its [[11/1|11]] from [[298edo]], and its [[7/1|7]] and [[13/1|13]] from [[447edo]].
+edo is [[consistent]] to the [[17-odd-limit]], and except for [[19/13]], [[19/17]], [[25/13]], [[25/17]] and their [[octave complement]]s, it is consistent to the [[31-odd-limit]], thus making it a reasonable [[31-limit]] system. Its [[prime interval|primes]] [[5/1|5]], [[17/1|17]], [[19/1|19]], and [[23/1|23]] come from [[149edo]], its [[11/1|11]] from [[298edo]], and its [[7/1|7]] and [[13/1|13]] from [[447edo]].
 As an equal temperament, it [[tempering out|tempers out]] {{monzo| 23 6 -14 }} ([[vishnu comma]]) in the [[5-limit]]; 250047/250000 ([[landscape comma]]) in the [[7-limit]]; [[9801/9800]], [[131072/130977]], [[151263/151250]] in the [[11-limit]]; [[1716/1715]], [[2080/2079]], [[4096/4095]], [[4225/4224]], 34398/34375 in the [[13-limit]]; [[1156/1155]], [[2431/2430]], [[2601/2600]], [[11016/11011]] in the [[17-limit]]; [[1521/1520]], [[2376/2375]], [[3250/3249]] in the [[19-limit]]; and [[1863/1862]], [[2300/2299]] among others in the [[23-limit]].