894edo: Difference between revisions

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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]].

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]]. It provides the [[optimal patent val]] for the 13-limit [[trivish]] temperament.

=== Prime harmonics ===

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| 25/24

| [[Vishnu]] (5-limit)

|-

| 6

| 53\894

| 71.14

| 25/24

| [[Trivish]]

|}

<nowiki/>* [[~~Normal~~ forms #~~Equave-reduced~~-generator form|~~Octave~~-~~reduced~~ form]]~~, reduced to the first half-octave, and~~ [[~~normal forms #Minimal-generator form|minimal form~~]] ~~in parentheses if distinct~~

<nowiki/>* In [[normal forms #Minimal-generator form|minimal-generator form]]

[[Category:Trivish]]

@@ Line 5: / Line 5: @@
 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]].
+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]]. It provides the [[optimal patent val]] for the 13-limit [[trivish]] temperament.
 === Prime harmonics ===
@@ Line 98: / Line 98: @@
 | 25/24
 | [[Vishnu]] (5-limit)
+|-
+| 6
+| 53\894
+| 71.14
+| 25/24
+| [[Trivish]]
 |}
-<nowiki/>* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct
+<nowiki/>* In [[normal forms #Minimal-generator form|minimal-generator form]]
+[[Category:Trivish]]