1407edo: Difference between revisions

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== Theory ==

1407edo is excellent in the 7-limit, in which it supports the 441 & ~~1407~~ [[akjayland]] temperament with period 21. Just like 441edo, it tempers out the akjaysma and the landscape comma. However, unlike 441edo it does not temper out the tritrizo comma, since 1407 is not divisible by 9.

1407edo is excellent in the 7-limit, in which it supports the 441 & 966 [[akjayland]] temperament with period 21. Just like 441edo, it [[tempering out|tempers out]] the [[akjaysma]] and the [[landscape comma]]. However, unlike 441edo it does not temper out the tritrizo comma, since 1407 is not divisible by 9.

It tunes the [[pure bastille]] temperament in the 1407eff val and the [[marvelous bastille]] temperament in the [[patent val]] in the 13-limit.

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=== Subsets and supersets ===

1407~~'s divisors are~~ {{EDOs| 3, 7, 21, 67, 201, 469 }}.

Since 1407 factors into {{factorization|1407}}, 1407edo has subset edos {{EDOs| 3, 7, 21, 67, 201, and 469 }}.

== Regular temperament properties ==

=== 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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|-

| 21

| 686\1407 (16\1407)

| 686\1407 (16\1407)

| 585.074 (13.646)

| 585.074 (13.646)

| 91875/65536 (126/125)

| 91875/65536 (126/125)

| [[Akjayland]]

|}

<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 lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct

[[Category:Akjayland]]

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|1407}}
+{{ED intro}}
 == Theory ==
-edo is excellent in the 7-limit, in which it supports the 441 & 1407 [[akjayland]] temperament with period 21. Just like 441edo, it tempers out the akjaysma and the landscape comma. However, unlike 441edo it does not temper out the tritrizo comma, since 1407 is not divisible by 9.
+edo is excellent in the 7-limit, in which it supports the 441 & 966 [[akjayland]] temperament with period 21. Just like 441edo, it [[tempering out|tempers out]] the [[akjaysma]] and the [[landscape comma]]. However, unlike 441edo it does not temper out the tritrizo comma, since 1407 is not divisible by 9.
 It tunes the [[pure bastille]] temperament in the 1407eff val and the [[marvelous bastille]] temperament in the [[patent val]] in the 13-limit.
@@ Line 11: / Line 11: @@
 === Subsets and supersets ===
-'s divisors are {{EDOs| 3, 7, 21, 67, 201, 469 }}.
+Since 1407 factors into {{factorization|1407}}, 1407edo has subset edos {{EDOs| 3, 7, 21, 67, 201, and 469 }}.
 == Regular temperament properties ==
 === 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 42: / Line 43: @@
 |-
 | 21
-| 686\1407<br>(16\1407)
+| 686\1407<br />(16\1407)
-| 585.074<br>(13.646)
+| 585.074<br />(13.646)
-| 91875/65536<br>(126/125)
+| 91875/65536<br />(126/125)
 | [[Akjayland]]
 |}
-<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 lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
 [[Category:Akjayland]]