201edo: Difference between revisions

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'''201edo''' is the [[EDO|equal division of the octave]] into 201 parts of 5.9701 [[cent]]s each. Using the patent val, it tempers out 393216/390625 ([[würschmidt comma]]) and 2621440000000/2541865828329 in the 5-limit; 245/243, 50421/50000, and 2100875/2097152 in the 7-limit; 385/384, 896/891, 1331/1323, and 47432/46875 in the 11-limit; 196/195, 325/324, 2080/2079, 2200/2197, and 3146/3125 in the 13-limit. Using the 201b val, it tempers out 1990656/1953125 and 282429536481/268435456000 in the 5-limit; 126/125, 1029/1024, and 1162261467/1129900996 in the 7-limit; 540/539, 1944/1925, 2835/2816, and 483153/480200 in the 11-limit; 1287/1280, 1575/1573, 1716/1715, 2200/2197, and 3146/3125 in the 13-limit. Using the 201bcf val, it tempers out 15625/15552 and |-56 31 3> in the 5-limit; 1029/1024, 250047/250000, and 273375/268912 in the 7-limit; 385/384, 441/440, 4000/3993, and 295245/290521 in the 11-limit; 351/350, 975/968, 1287/1280, 1573/1568, and 10935/10816 in the 13-limit. Using the 201de val, it tempers out 4000/3969, 10976/10935, and 4194304/4134375 in the 7-limit; 540/539, 896/891, 1375/1372, and 234375/234256 in the 11-limit; 325/324, 352/351, 364/363, 640/637, and 4394/4375 in the 13-limit (supporting the [[Mirkwai clan|pluto temperament]]). Using the 201e val, it tempers out 441/440, 2200/2187, 3388/3375, and 65536/65219 in the 11-limit; 196/195, 325/324, 352/351, 1001/1000, and 106496/105875 in the 13-limit.

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

201edo is only [[consistent]] to the [[5-odd-limit]], and [[harmonic]] [[3/1|3]] is about halfway between its steps.

Using the [[patent val]], it [[tempering out|tempers out]] 393216/390625 ([[würschmidt comma]]) and {{monzo| 25 -26 7 }} in the 5-limit; [[245/243]], [[50421/50000]], and [[2100875/2097152]] in the 7-limit; [[385/384]], [[896/891]], 1331/1323, and 47432/46875 in the 11-limit; [[196/195]], [[325/324]], [[2080/2079]], [[2200/2197]], and 3146/3125 in the 13-limit.

Using the 201e val, it tempers out [[441/440]], [[2200/2187]], [[3388/3375]], and [[65536/65219]] in the 11-limit; 196/195, 325/324, [[352/351]], [[1001/1000]], and 106496/105875 in the 13-limit.

Using the 201de val, it tempers out [[4000/3969]], [[10976/10935]], and 4194304/4134375 in the 7-limit; [[540/539]], 896/891, 1375/1372, and 234375/234256 in the 11-limit; 325/324, 352/351, [[364/363]], [[640/637]], and [[4394/4375]] in the 13-limit (supporting the [[pluto]] temperament).

Using the 201b val, it tempers out 1990656/1953125 (valentine comma) and {{monzo| -31 24 -3 }} in the 5-limit; [[126/125]], [[1029/1024]], and {{monzo| -2 19 0 -10 }} in the 7-limit; 540/539, 1944/1925, 2835/2816, and 483153/480200 in the 11-limit; [[1287/1280]], [[1575/1573]], [[1716/1715]], 2200/2197, and 3146/3125 in the 13-limit.

Using the 201bcf val, it tempers out 15625/15552 ([[15625/15552|kleisma]]) and {{monzo| -56 31 3 }} in the 5-limit; 1029/1024, [[250047/250000]], and 273375/268912 in the 7-limit; 385/384, 441/440, [[4000/3993]], and 295245/290521 in the 11-limit; [[351/350]], 975/968, 1287/1280, [[1573/1568]], and 10935/10816 in the 13-limit.

=== Odd harmonics ===

=== Subsets and supersets ===

Since 201 factors into {{factorization|201}}, 201edo contains [[3edo]] and [[67edo]] as its subsets. [[402edo]], which doubles it, provides a good correction to the approximation of harmonic 3.

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 {{Infobox ET}}
-'''201edo''' is the [[EDO|equal division of the octave]] into 201 parts of 5.9701 [[cent]]s each. Using the patent val, it tempers out 393216/390625 ([[würschmidt comma]]) and 2621440000000/2541865828329 in the 5-limit; 245/243, 50421/50000, and 2100875/2097152 in the 7-limit; 385/384, 896/891, 1331/1323, and 47432/46875 in the 11-limit; 196/195, 325/324, 2080/2079, 2200/2197, and 3146/3125 in the 13-limit. Using the 201b val, it tempers out 1990656/1953125 and 282429536481/268435456000 in the 5-limit; 126/125, 1029/1024, and 1162261467/1129900996 in the 7-limit; 540/539, 1944/1925, 2835/2816, and 483153/480200 in the 11-limit; 1287/1280, 1575/1573, 1716/1715, 2200/2197, and 3146/3125 in the 13-limit. Using the 201bcf val, it tempers out 15625/15552 and |-56 31 3&gt; in the 5-limit; 1029/1024, 250047/250000, and 273375/268912 in the 7-limit; 385/384, 441/440, 4000/3993, and 295245/290521 in the 11-limit; 351/350, 975/968, 1287/1280, 1573/1568, and 10935/10816 in the 13-limit. Using the 201de val, it tempers out 4000/3969, 10976/10935, and 4194304/4134375 in the 7-limit; 540/539, 896/891, 1375/1372, and 234375/234256 in the 11-limit; 325/324, 352/351, 364/363, 640/637, and 4394/4375 in the 13-limit (supporting the [[Mirkwai clan|pluto temperament]]). Using the 201e val, it tempers out 441/440, 2200/2187, 3388/3375, and 65536/65219 in the 11-limit; 196/195, 325/324, 352/351, 1001/1000, and 106496/105875 in the 13-limit.
+{{ED intro}}
-[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
+edo is only [[consistent]] to the [[5-odd-limit]], and [[harmonic]] [[3/1|3]] is about halfway between its steps.
+Using the [[patent val]], it [[tempering out|tempers out]] 393216/390625 ([[würschmidt comma]]) and {{monzo| 25 -26 7 }} in the 5-limit; [[245/243]], [[50421/50000]], and [[2100875/2097152]] in the 7-limit; [[385/384]], [[896/891]], 1331/1323, and 47432/46875 in the 11-limit; [[196/195]], [[325/324]], [[2080/2079]], [[2200/2197]], and 3146/3125 in the 13-limit.
+Using the 201e val, it tempers out [[441/440]], [[2200/2187]], [[3388/3375]], and [[65536/65219]] in the 11-limit; 196/195, 325/324, [[352/351]], [[1001/1000]], and 106496/105875 in the 13-limit.
+Using the 201de val, it tempers out [[4000/3969]], [[10976/10935]], and 4194304/4134375 in the 7-limit; [[540/539]], 896/891, 1375/1372, and 234375/234256 in the 11-limit; 325/324, 352/351, [[364/363]], [[640/637]], and [[4394/4375]] in the 13-limit (supporting the [[pluto]] temperament).
+Using the 201b val, it tempers out 1990656/1953125 (valentine comma) and {{monzo| -31 24 -3 }} in the 5-limit; [[126/125]], [[1029/1024]], and {{monzo| -2 19 0 -10 }} in the 7-limit; 540/539, 1944/1925, 2835/2816, and 483153/480200 in the 11-limit; [[1287/1280]], [[1575/1573]], [[1716/1715]], 2200/2197, and 3146/3125 in the 13-limit.
+Using the 201bcf val, it tempers out 15625/15552 ([[15625/15552|kleisma]]) and {{monzo| -56 31 3 }} in the 5-limit; 1029/1024, [[250047/250000]], and 273375/268912 in the 7-limit; 385/384, 441/440, [[4000/3993]], and 295245/290521 in the 11-limit; [[351/350]], 975/968, 1287/1280, [[1573/1568]], and 10935/10816 in the 13-limit.
+=== Odd harmonics ===
+{{Harmonics in equal|201}}
+=== Subsets and supersets ===
+Since 201 factors into {{factorization|201}}, 201edo contains [[3edo]] and [[67edo]] as its subsets. [[402edo]], which doubles it, provides a good correction to the approximation of harmonic 3.