407edo: Difference between revisions

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== Theory ==

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=== Subsets and supersets ===

407 factors into 11 × 37, with [[11edo]] and [[37edo]] as its subset edos. [[814edo]], which doubles it, gives a good correction to harmonics 7 and 17, and is a notable full 23-limit temperament.

407 factors into {{nowrap|11 × 37}}, with [[11edo]] and [[37edo]] as its subset edos. [[814edo]], which doubles it, gives a good correction to harmonics 7 and 17, and is a notable full 23-limit temperament.

== 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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| 498.28

| 4/3

| [[Helmholtz]]

| [[Helmholtz (temperament)|Helmholtz]]

|}

<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

[[Category:Subsemifourth]]

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|407}}
+{{ED intro}}
 == Theory ==
@@ Line 9: / Line 9: @@
 === Subsets and supersets ===
-factors into 11 × 37, with [[11edo]] and [[37edo]] as its subset edos. [[814edo]], which doubles it, gives a good correction to harmonics 7 and 17, and is a notable full 23-limit temperament.
+factors into {{nowrap|11 × 37}}, with [[11edo]] and [[37edo]] as its subset edos. [[814edo]], which doubles it, gives a good correction to harmonics 7 and 17, and is a notable full 23-limit temperament.
 == 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 39: / Line 40: @@
 === 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 62: / Line 64: @@
 | 498.28
 | 4/3
-| [[Helmholtz]]
+| [[Helmholtz (temperament)|Helmholtz]]
 |}
-<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
 [[Category:Subsemifourth]]