1407edo: Difference between revisions

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~~{{novelty}}{{stub}}~~{{Infobox ET}}

== Theory ==

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.

=== Prime harmonics ===

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.

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

=== Subsets and supersets ===

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

1407~~'s divisors are~~ {{EDOs|1, 3, 7, 21, 67, 201, 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

|-

! Generator~~ (Reduced)~~

! Periods per 8ve

! Cents~~ (Reduced)~~

! Generator*

! Associated ~~Ratio~~

! Cents*

! Associated ratio*

! Temperaments

|-

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| 814\1407

| 694.243

| {{~~Monzo~~|381 0 -159 -4}}

| {{monzo| 381 0 -159 -4 }}

| [[Bastille]] (2.5.7) / [[pure bastille]] (1407eff) / [[marvelous bastille]] (1407)

|-

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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]]

|}

[[~~Category:Equal divisions of~~ the octave|~~####~~]] ~~~~

<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: @@
-{{novelty}}{{stub}}{{Infobox ET}}
+{{Infobox ET}}
-{{EDO intro|1407}}
+{{ED intro}}
 == Theory ==
+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.
+=== Prime harmonics ===
 {{Harmonics in equal|1407}}
-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.
-It tunes the [[pure bastille]] temperament in the 1407eff val and the [[marvelous bastille]] temperament in the patent val in the 13-limit.
+=== Subsets and supersets ===
+Since 1407 factors into {{factorization|1407}}, 1407edo has subset edos {{EDOs| 3, 7, 21, 67, 201, and 469 }}.
-'s divisors are {{EDOs|1, 3, 7, 21, 67, 201, 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
+|-
-! Generator<br>(Reduced)
+! Periods<br />per 8ve
-! Cents<br>(Reduced)
+! Generator*
-! Associated<br>Ratio
+! Cents*
+! Associated<br />ratio*
 ! Temperaments
 |-
@@ Line 23: / Line 27: @@
 | 814\1407
 | 694.243
-| {{Monzo|381 0 -159 -4}}
+| {{monzo| 381 0 -159 -4 }}
 | [[Bastille]] (2.5.7) / [[pure bastille]] (1407eff) / [[marvelous bastille]] (1407)
 |-
@@ Line 39: / 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]]
 |}
-[[Category:Equal divisions of the octave|####]] <!-- 4-digit number -->
+<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
 [[Category:Akjayland]]