525edo: Difference between revisions

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525edo is distinctly [[consistent]] through the [[25-odd-limit]]. It tempers out the [[schisma]], 32805/32768, and {{monzo| 8 77 -56 }} in the 5-limit; [[250047/250000]], [[703125/702464]] and {{monzo| 21 3 1 -10 }} in the 7-limit; [[3025/3024]], 24057/24010, 102487/102400 and 180224/180075 in the 11-limit; [[729/728]], [[1716/1715]], [[2200/2197]], [[4096/4095]] and 14641/14625 in the 13-limit.

~~It supports the 140 &~~ 525 ~~temperament~~, ~~with period 35 which sets 7/~~5 ~~and 10/~~7 ~~to two "legs" of 35edo (17\~~35 ~~and 18\35) opposing the tonic and tempers out {{monzo| 34 0 70 -70~~ }}~~, setting a circle of thirty-five [[50/49]]'s equal with the octave. In addition, it supports 21st-octave period called [[akjayland]]~~.

525's divisors are {{EDOs| 1, 3, 5, 7, 15, 21, 25, 35, 75, 105, 175}}.

525~~'s divisors are~~ {{~~EDOs~~| 1, 3, 5, 7, 15, 21, ~~25, 35, 75, 105, 175}}~~.

=== Fractional-octave temperaments. ===

It supports the 140 & 525 temperament, with period 35 which sets 7/5 and 10/7 to two "legs" of 35edo (17\35 and 18\35) opposing the tonic and tempers out {{monzo| 34 0 70 -70 }}, setting a circle of thirty-five [[50/49]]'s equal with the octave.

525edo supports 21st-octave period called [[akjayland]], and the 23-limit extension of akjayland called [[21st-octave temperaments|vasca]], defined as 357 & 525. It is more suitable to view this temperament as vasca in 525edo as opposed to simply akjayland, since 525edo is consistent in the 23-limit, while other EDOs which support akjayland are not. In addition to splitting octave into 21 parts, 525edo also supports the relationship that sets 11\21 to [[23/16]].

=== Prime harmonics ===

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| 585.14<br>(13.71)

| 91875/65536<br>(126/125)

| [[Akjayland]]

| [[Akjayland]] / [[vasca]]

|}

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

[[Category:Akjayland]]

@@ Line 5: / Line 5: @@
 edo is distinctly [[consistent]] through the [[25-odd-limit]]. It tempers out the [[schisma]], 32805/32768, and {{monzo| 8 77 -56 }} in the 5-limit; [[250047/250000]], [[703125/702464]] and {{monzo| 21 3 1 -10 }} in the 7-limit; [[3025/3024]], 24057/24010, 102487/102400 and 180224/180075 in the 11-limit; [[729/728]], [[1716/1715]], [[2200/2197]], [[4096/4095]] and 14641/14625 in the 13-limit.
-It supports the 140 & 525 temperament, with period 35 which sets 7/5 and 10/7 to two "legs" of 35edo (17\35 and 18\35) opposing the tonic and tempers out {{monzo| 34 0 70 -70 }}, setting a circle of thirty-five [[50/49]]'s equal with the octave. In addition, it supports 21st-octave period called [[akjayland]].
+'s divisors are {{EDOs| 1, 3, 5, 7, 15, 21, 25, 35, 75, 105, 175}}.
-'s divisors are {{EDOs| 1, 3, 5, 7, 15, 21, 25, 35, 75, 105, 175}}.
+=== Fractional-octave temperaments. ===
+It supports the 140 & 525 temperament, with period 35 which sets 7/5 and 10/7 to two "legs" of 35edo (17\35 and 18\35) opposing the tonic and tempers out {{monzo| 34 0 70 -70 }}, setting a circle of thirty-five [[50/49]]'s equal with the octave.
+edo supports 21st-octave period called [[akjayland]], and the 23-limit extension of akjayland called [[21st-octave temperaments|vasca]], defined as 357 & 525. It is more suitable to view this temperament as vasca in 525edo as opposed to simply akjayland, since 525edo is consistent in the 23-limit, while other EDOs which support akjayland are not. In addition to splitting octave into 21 parts, 525edo also supports the relationship that sets 11\21 to [[23/16]].
 === Prime harmonics ===
@@ Line 110: / Line 113: @@
 | 585.14<br>(13.71)
 | 91875/65536<br>(126/125)
-| [[Akjayland]]
+| [[Akjayland]] / [[vasca]]
 |}
 [[Category:Equal divisions of the octave|###]]
 [[Category:Akjayland]]