525edo: Difference between revisions

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{{Infobox ET

| Prime factorization = 3 × 5<sup>2</sup> × 7

| Step size = 2.28571¢

| Fifth = 307\525 (701.71¢)

| Semitones = 49:40 (112.00¢ : 91.43¢)

| Consistency = 25

}}

== Theory ==

It is consistent ~~and uniquely consistent~~ through the 25-limit. It tempers out the schisma, 32805/32768 and |8 77 -~~56>~~ in the 5-limit; 250047/250000, 703125/702464 and ~~283115520/282475249~~ 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.

525edo is distinctly [[consistent]] through the [[25-odd-limit]]. It tempers out the [[schisma]], 32805/32768, and {{monzo| 8 77 -5 }} 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 a 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 35 50/~~49s~~ equal with the octave. In addition, it ~~suppors~~ 21st-octave period called [[akjayland]].

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}}.

=== Prime harmonics ===

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

~~{{Harmonics in equal|525}}~~

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

[[Category:Akjayland]]

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+{{Infobox ET
+| Prime factorization = 3 × 5<sup>2</sup> × 7
+| Step size = 2.28571¢
+| Fifth = 307\525 (701.71¢)
+| Semitones = 49:40 (112.00¢ : 91.43¢)
+| Consistency = 25
+}}
 {{EDO intro|525}}
 == Theory ==
-It is consistent and uniquely consistent through the 25-limit. It tempers out the schisma, 32805/32768 and |8 77 -56&gt; in the 5-limit; 250047/250000, 703125/702464 and 283115520/282475249 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.
+edo is distinctly [[consistent]] through the [[25-odd-limit]]. It tempers out the [[schisma]], 32805/32768, and {{monzo| 8 77 -5 }} 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 a 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 35 50/49s equal with the octave. In addition, it suppors 21st-octave period called [[akjayland]].
+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}}.
+=== Prime harmonics ===
+{{Harmonics in equal|525|columns=11}}
-'s divisors are {{EDOs|1, 3, 5, 7, 15, 21, 25, 35, 75, 105, 175.}}
-{{Harmonics in equal|525}}
 [[Category:Equal divisions of the octave|###]]
 [[Category:Akjayland]]