525edo: Difference between revisions

@@ Line 1: / Line 1: @@
-'''525edo''' is the [[EDO|equal division of the octave]] into 525 parts of 2.28571 [[cent]]s each. 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 intro|525}}
-[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
+== 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.
+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]].
+'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]]