392edo: Difference between revisions

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== Theory ==

392et is [[consistent]] to the [[7-odd-limit]] with a flat tendency in the [[prime harmonic]]s. ~~The~~ equal temperament [[tempering out|tempers out]] the [[parakleisma]] in the 5-limit; 321489/320000 (varunisma), 420175/419904 (wizma), 703125/702464 ([[meter]]), and 823543/819200 (quince comma) in the 7-limit; and [[441/440]], [[8019/8000]], [[9801/9800]], and [[41503/41472]] in the 11-limit. It [[support]]s [[qak]] and [[octowerck]].

392et is [[consistent]] to the [[7-odd-limit]] with a flat tendency in the [[prime harmonic]]s. As an equal temperament, it [[tempering out|tempers out]] the [[parakleisma]] in the 5-limit; 321489/320000 ([[varunisma]]), 420175/419904 ([[wizma]]), 703125/702464 ([[meter]]), and 823543/819200 ([[quince comma]]) in the 7-limit; and [[441/440]], [[8019/8000]], [[9801/9800]], and [[41503/41472]] in the 11-limit. It [[support]]s [[qak]] and [[octowerck]].

=== Odd harmonics ===

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=== Subsets and supersets ===

392 factors into 23 × 72, with subset edos {{EDOs|2, 4, 7, 8, 14, 28, 49, 56, 98, and 196}}.

392 factors into 23 × 72, with subset edos {{EDOs| 2, 4, 7, 8, 14, 28, 49, 56, 98, and 196 }}.

== Regular temperament properties ==

{~~{comma basis begin}}~~

{| class="wikitable center-4 center-5 center-6"

|-

! rowspan="2" | [[Subgroup]]

! rowspan="2" | [[Comma list]]

! rowspan="2" | [[Mapping]]

! rowspan="2" | Optimal 8ve stretch (¢)

! colspan="2" | Tuning error

|-

! [[TE error|Absolute]] (¢)

! [[TE simple badness|Relative]] (%)

|-

| 2.3

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| 0.2335

| 7.63

~~{{comma basis end}~~}

|}

=== Rank-2 temperaments ===

{{rank-2 ~~begin}}~~

{| class="wikitable center-all left-5"

|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator

|-

! Periods per 8ve

! Generator*

! Cents*

! Associated ratio*

! Temperaments

|-

| 1

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| 4/3 (105/104)

| [[Oquatonic]] (5-limit)

~~{{rank-2 end}~~}

|}

~~{{orf}}~~

<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

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|392}}
+{{ED intro}}
 == Theory ==
-et is [[consistent]] to the [[7-odd-limit]] with a flat tendency in the [[prime harmonic]]s. The equal temperament [[tempering out|tempers out]] the [[parakleisma]] in the 5-limit; 321489/320000 (varunisma), 420175/419904 (wizma), 703125/702464 ([[meter]]), and 823543/819200 (quince comma) in the 7-limit; and [[441/440]], [[8019/8000]], [[9801/9800]], and [[41503/41472]] in the 11-limit. It [[support]]s [[qak]] and [[octowerck]].
+et is [[consistent]] to the [[7-odd-limit]] with a flat tendency in the [[prime harmonic]]s. As an equal temperament, it [[tempering out|tempers out]] the [[parakleisma]] in the 5-limit; 321489/320000 ([[varunisma]]), 420175/419904 ([[wizma]]), 703125/702464 ([[meter]]), and 823543/819200 ([[quince comma]]) in the 7-limit; and [[441/440]], [[8019/8000]], [[9801/9800]], and [[41503/41472]] in the 11-limit. It [[support]]s [[qak]] and [[octowerck]].
 === Odd harmonics ===
@@ Line 9: / Line 9: @@
 === Subsets and supersets ===
-factors into 2<sup>3</sup> × 7<sup>2</sup>, with subset edos {{EDOs|2, 4, 7, 8, 14, 28, 49, 56, 98, and 196}}.
+factors into 2<sup>3</sup> × 7<sup>2</sup>, with subset edos {{EDOs| 2, 4, 7, 8, 14, 28, 49, 56, 98, and 196 }}.
 == Regular temperament properties ==
-{{comma basis begin}}
+{| class="wikitable center-4 center-5 center-6"
+|-
+! rowspan="2" | [[Subgroup]]
+! rowspan="2" | [[Comma list]]
+! rowspan="2" | [[Mapping]]
+! rowspan="2" | Optimal<br />8ve stretch (¢)
+! colspan="2" | Tuning error
+|-
+! [[TE error|Absolute]] (¢)
+! [[TE simple badness|Relative]] (%)
 |-
 | 2.3
@@ Line 41: / Line 50: @@
 | 0.2335
 | 7.63
-{{comma basis end}}
+|}
 === Rank-2 temperaments ===
-{{rank-2 begin}}
+{| class="wikitable center-all left-5"
+|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
+|-
+! Periods<br />per 8ve
+! Generator*
+! Cents*
+! Associated<br />ratio*
+! Temperaments
 |-
 | 1
@@ Line 75: / Line 91: @@
 | 4/3<br />(105/104)
 | [[Oquatonic]] (5-limit)
-{{rank-2 end}}
+|}
-{{orf}}
+<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