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 ==

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

|-

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

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

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

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

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

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

! colspan="2" | Tuning ~~Error~~

! colspan="2" | Tuning error

|-

! [[TE error|Absolute]] (¢)

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

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=== Rank-2 temperaments ===

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

|+Table of rank-2 temperaments by generator

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

! Periods per 8ve

|-

! Periods per 8ve

! Generator*

! Cents*

! Associated ~~Ratio~~*

! Associated ratio*

! Temperaments

|-

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|-

| 8

| 185\392 (11\392)

| 185\392 (11\392)

| 566.33 (33.67)

| 566.33 (33.67)

| 104/75 (55/54)

| 104/75 (55/54)

| [[Octowerck]] (392f)

|-

| 28

| 163\392 (5\392)

| 163\392 (5\392)

| 498.98 (15.31)

| 498.98 (15.31)

| 4/3 (105/104)

| 4/3 (105/104)

| [[Oquatonic]] (5-limit)

|}

<nowiki>*~~</nowiki>~~ [[Normal ~~lists~~|~~octave~~-reduced form]], reduced to the first half-octave, and [[~~Normal lists~~|minimal form]] in parentheses if ~~it is~~ 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

@@ 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 ==
 {| class="wikitable center-4 center-5 center-6"
+|-
 ! rowspan="2" | [[Subgroup]]
-! rowspan="2" | [[Comma list|Comma List]]
+! rowspan="2" | [[Comma list]]
 ! rowspan="2" | [[Mapping]]
-! rowspan="2" | Optimal<br>8ve Stretch (¢)
+! rowspan="2" | Optimal<br />8ve stretch (¢)
-! colspan="2" | Tuning Error
+! colspan="2" | Tuning error
 |-
 ! [[TE error|Absolute]] (¢)
 ! [[TE simple badness|Relative]] (%)
@@ Line 53: / Line 54: @@
 === Rank-2 temperaments ===
 {| class="wikitable center-all left-5"
-|+Table of rank-2 temperaments by generator
+|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
-! Periods<br>per 8ve
+|-
+! Periods<br />per 8ve
 ! Generator*
 ! Cents*
-! Associated<br>Ratio*
+! Associated<br />ratio*
 ! Temperaments
 |-
@@ Line 79: / Line 81: @@
 |-
 | 8
-| 185\392<br>(11\392)
+| 185\392<br />(11\392)
-| 566.33<br>(33.67)
+| 566.33<br />(33.67)
-| 104/75<br>(55/54)
+| 104/75<br />(55/54)
 | [[Octowerck]] (392f)
 |-
 | 28
-| 163\392<br>(5\392)
+| 163\392<br />(5\392)
-| 498.98<br>(15.31)
+| 498.98<br />(15.31)
-| 4/3<br>(105/104)
+| 4/3<br />(105/104)
 | [[Oquatonic]] (5-limit)
 |}
-<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is 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