429edo: Difference between revisions

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== Theory ==

429et is [[consistent]] to the [[11-odd-limit]]. The equal temperament [[tempering out|tempers out]] [[65625/65536]], [[250047/250000]], and 823543/820125 in the 7-limit; [[3025/3024]], 12005/11979, [[19712/19683]], 42875/42768, and 102487/102400 in the 11-limit. It [[support]]s [[vavoom]], [[turkey]], [[counterhanson]] and [[aluminium]].

429et is [[consistent]] to the [[11-odd-limit]]. The equal temperament [[tempering out|tempers out]] [[65625/65536]], [[250047/250000]], and 823543/820125 in the 7-limit; [[3025/3024]], 12005/11979, [[19712/19683]], 42875/42768, and 102487/102400 in the 11-limit. It [[support]]s [[vavoom]], [[turkey]], [[counterhanson]], and [[aluminium]].

=== Prime harmonics ===

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=== Subsets and supersets ===

429 factors into ~~3 × 11 × 13~~, with subset edos {{EDOs|3, 11, 13, 33, 39, and 143}}.

429 factors into {{factorisation|429}}, with subset edos {{EDOs|3, 11, 13, 33, 39, and 143}}.

== 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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| {{monzo| 680 -429 }}

| {{mapping| 429 680 }}

| -0.0451

| −0.0451

| 0.0451

| 1.61

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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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|-

| 3

| 138\429 (5\429)

| 138\429 (5\429)

| 386.01 (13.99)

| 386.01 (13.99)

| 5/4 (126/125)

| 5/4 (126/125)

| [[Mutt]]

|}

<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|429}}
+{{ED intro}}
 == Theory ==
-et is [[consistent]] to the [[11-odd-limit]]. The equal temperament [[tempering out|tempers out]] [[65625/65536]], [[250047/250000]], and 823543/820125 in the 7-limit; [[3025/3024]], 12005/11979, [[19712/19683]], 42875/42768, and 102487/102400 in the 11-limit. It [[support]]s [[vavoom]], [[turkey]], [[counterhanson]] and [[aluminium]].
+et is [[consistent]] to the [[11-odd-limit]]. The equal temperament [[tempering out|tempers out]] [[65625/65536]], [[250047/250000]], and 823543/820125 in the 7-limit; [[3025/3024]], 12005/11979, [[19712/19683]], 42875/42768, and 102487/102400 in the 11-limit. It [[support]]s [[vavoom]], [[turkey]], [[counterhanson]], and [[aluminium]].
 === Prime harmonics ===
@@ Line 9: / Line 9: @@
 === Subsets and supersets ===
-factors into 3 × 11 × 13, with subset edos {{EDOs|3, 11, 13, 33, 39, and 143}}.
+factors into {{factorisation|429}}, with subset edos {{EDOs|3, 11, 13, 33, 39, and 143}}.
 == 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 25: / Line 26: @@
 | {{monzo| 680 -429 }}
 | {{mapping| 429 680 }}
-| -0.0451
+| −0.0451
 | 0.0451
 | 1.61
@@ Line 60: / Line 61: @@
 === 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 86: / Line 88: @@
 |-
 | 3
-| 138\429<br>(5\429)
+| 138\429<br />(5\429)
-| 386.01<br>(13.99)
+| 386.01<br />(13.99)
-| 5/4<br>(126/125)
+| 5/4<br />(126/125)
 | [[Mutt]]
 |}
-<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