692edo: Difference between revisions

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== Theory ==

692edo is [[consistent]] to the [[19-odd-limit]], and has a sharp tendency, with odd [[harmonic]]s 3 through 19 all tuned sharp.

692edo is [[consistent]] to the [[19-odd-limit]] and almost the [[21-odd-limit]]; the only inconsistently mapped intervals in the 21-odd-limit are [[21/16]] and its [[octave complement]]. It has a sharp tendency, with odd [[harmonic]]s 3 through 19 all tuned sharp.

As an equal temperament, it [[tempering out|tempers out]] {{monzo| 23 6 -14 }} ([[vishnuzma]]) in the [[5-limit]]; 4375/4374 ([[ragisma]]) and 29360128/29296875 ([[quasiorwellisma]]) in the [[7-limit]]; [[3025/3024]], [[5632/5625]], [[9801/9800]], and [[19712/19683]] in the [[11-limit]]; [[1716/1715]], [[2080/2079]], and [[6656/6655]] in the [[13-limit]]; [[2431/2430]], [[2500/2499]], and [[4914/4913]] in the [[17-limit]]; [[1216/1215]], [[1331/1330]], [[1540/1539]], [[2432/2431]], [[2926/2925]], [[3136/3135]], and [[3250/3249]] in the [[19-limit]]. It [[support]]s and provides a good tuning for [[vishnu]] and its 13-limit extension [[acyuta]].

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=== Subsets and supersets ===

Since 692 factors into primes as {{~~factorization~~| 22 × 173 }}, 692edo has subset edos {{EDOs| 2, 4, 173, and 346 }}.

Since 692 factors into primes as {{nowrap| 22 × 173 }}, 692edo has subset edos {{EDOs| 2, 4, 173, and 346 }}.

== Regular temperament properties ==

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! Associated ratio*

! Temperaments

|-

| 1

| 259\692

| 449.13

| 35/27

| [[Semidimi]]

|-

| 2

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| [[Vishnu]] / [[acyuta]]

|}

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

<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

[[Category:Vishnu]]

@@ Line 3: / Line 3: @@
 == Theory ==
-edo is [[consistent]] to the [[19-odd-limit]], and has a sharp tendency, with odd [[harmonic]]s 3 through 19 all tuned sharp.
+edo is [[consistent]] to the [[19-odd-limit]] and almost the [[21-odd-limit]]; the only inconsistently mapped intervals in the 21-odd-limit are [[21/16]] and its [[octave complement]]. It has a sharp tendency, with odd [[harmonic]]s 3 through 19 all tuned sharp.
 As an equal temperament, it [[tempering out|tempers out]] {{monzo| 23 6 -14 }} ([[vishnuzma]]) in the [[5-limit]]; 4375/4374 ([[ragisma]]) and 29360128/29296875 ([[quasiorwellisma]]) in the [[7-limit]]; [[3025/3024]], [[5632/5625]], [[9801/9800]], and [[19712/19683]] in the [[11-limit]]; [[1716/1715]], [[2080/2079]], and [[6656/6655]] in the [[13-limit]]; [[2431/2430]], [[2500/2499]], and [[4914/4913]] in the [[17-limit]]; [[1216/1215]], [[1331/1330]], [[1540/1539]], [[2432/2431]], [[2926/2925]], [[3136/3135]], and [[3250/3249]] in the [[19-limit]]. It [[support]]s and provides a good tuning for [[vishnu]] and its 13-limit extension [[acyuta]].
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 === Subsets and supersets ===
-Since 692 factors into primes as {{factorization| 2<sup>2</sup> × 173 }}, 692edo has subset edos {{EDOs| 2, 4, 173, and 346 }}.
+Since 692 factors into primes as {{nowrap| 2<sup>2</sup> × 173 }}, 692edo has subset edos {{EDOs| 2, 4, 173, and 346 }}.
 == Regular temperament properties ==
@@ Line 84: / Line 84: @@
 ! Associated<br>ratio*
 ! Temperaments
+|-
+| 1
+| 259\692
+| 449.13
+| 35/27
+| [[Semidimi]]
 |-
 | 2
@@ Line 91: / Line 97: @@
 | [[Vishnu]] / [[acyuta]]
 |}
-<nowiki/>* [[Normal forms|Octave-reduced form]], reduced to the first half-octave, and [[normal forms|minimal form]] in parentheses if distinct
+<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
 [[Category:Vishnu]]