225edo: Difference between revisions

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'''225edo''' is the [[EDO|equal division of the octave]] into 225 parts of 5.3333 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 7-limit: <225 357 522 632| (patent val), <225 356 522 631| (225bd), and <225 357 523 632| (225c). Using the patent val, it tempers out 20000/19683 and 2109375/2097152 in the 5-limit; 3125/3087, 10976/10935, and 589824/588245 in the 7-limit. Using the 225bd val, it tempers out 78732/78125 (sensipent comma) and |-52 27 4> in the 5-limit; 225/224, 177147/175000, and 40353607/40000000 in the 7-limit. Using the 225c val, it tempers out 131072000/129140163 (rodan comma) and 30958682112/30517578125 (trisedodge comma) in the 5-limit; 2401/2400, 4375/4374, and 2097152/2066715 in the 7-limit.

~~=Scales=~~

*[[Bossier8]]

*[[Bossier11]]

*[[Bossier14]]

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

== Theory ==

225edo is in[[consistent]] to the [[5-odd-limit]] and higher limits, with rather large errors in [[harmonic]]s [[3/1|3]], [[5/1|5]], [[7/1|7]], [[11/1|11]], and [[13/1|13]]. It has three mappings possible for the 7-limit:

* {{val| 225 357 522 632 }} ([[patent val]]),

* {{val| 225 '''356''' 522 '''631''' }} (225bd),

* {{val| 225 357 '''523''' 632 }} (225c).

Using the patent val, it tempers out 20000/19683 and 2109375/2097152 in the 5-limit; 3125/3087, 10976/10935, and 589824/588245 in the 7-limit.

Using the 225bd val, it tempers out 78732/78125 (sensipent comma) and {{monzo| -52 27 4 }} in the 5-limit; 225/224, 177147/175000, and 40353607/40000000 in the 7-limit.

Using the 225c val, it tempers out 131072000/129140163 (rodan comma) and 30958682112/30517578125 (trisedodge comma) in the 5-limit; 2401/2400, 4375/4374, and 2097152/2066715 in the 7-limit.

=== Odd harmonics ===

== Scales ==

* [[Bossier scales]]

[[Category:Bossier]]

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-'''225edo''' is the [[EDO|equal division of the octave]] into 225 parts of 5.3333 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 7-limit: &lt;225 357 522 632| (patent val), &lt;225 356 522 631| (225bd), and &lt;225 357 523 632| (225c). Using the patent val, it tempers out 20000/19683 and 2109375/2097152 in the 5-limit; 3125/3087, 10976/10935, and 589824/588245 in the 7-limit. Using the 225bd val, it tempers out 78732/78125 (sensipent comma) and |-52 27 4&gt; in the 5-limit; 225/224, 177147/175000, and 40353607/40000000 in the 7-limit. Using the 225c val, it tempers out 131072000/129140163 (rodan comma) and 30958682112/30517578125 (trisedodge comma) in the 5-limit; 2401/2400, 4375/4374, and 2097152/2066715 in the 7-limit.
+{{Infobox ET}}
-=Scales=
+{{ED intro}}
-*[[Bossier8]]
-*[[Bossier11]]
-*[[Bossier14]]
-[[Category:Equal divisions of the octave]]
+== Theory ==
+edo is in[[consistent]] to the [[5-odd-limit]] and higher limits, with rather large errors in [[harmonic]]s [[3/1|3]], [[5/1|5]], [[7/1|7]], [[11/1|11]], and [[13/1|13]]. It has three mappings possible for the 7-limit:
+* {{val| 225 357 522 632 }} ([[patent val]]),
+* {{val| 225 '''356''' 522 '''631''' }} (225bd),
+* {{val| 225 357 '''523''' 632 }} (225c).
+Using the patent val, it tempers out 20000/19683 and 2109375/2097152 in the 5-limit; 3125/3087, 10976/10935, and 589824/588245 in the 7-limit.
+Using the 225bd val, it tempers out 78732/78125 (sensipent comma) and {{monzo| -52 27 4 }} in the 5-limit; 225/224, 177147/175000, and 40353607/40000000 in the 7-limit.
+Using the 225c val, it tempers out 131072000/129140163 (rodan comma) and 30958682112/30517578125 (trisedodge comma) in the 5-limit; 2401/2400, 4375/4374, and 2097152/2066715 in the 7-limit.
+=== Odd harmonics ===
+{{Harmonics in equal|225}}
+== Scales ==
+* [[Bossier scales]]
+[[Category:Bossier]]