203edo: Difference between revisions

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'''203edo''' is the [[EDO|equal division of the octave]] into 203 parts of 5.9113 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 7-limit: <203 322 471 570| (patent val), <203 321 471 569| (203bd), and <203 322 472 570| (203c). Using the patent val, it tempers out the semicomma, 2109375/2097152 and 97656250000/94143178827 in the 5-limit; 4000/3969, 10976/10935, and 2100875/2097152 in the 7-limit; 385/384, 1331/1323, and 4000/3993 in the 11-limit; 352/351, 676/675, 1573/1568, and 1625/1617 in the 13-limit. Using the 203c val, it tempers out the sensipent comma, 78732/78125 and [[29-comma]] in the 5-limit; 5120/5103, 50421/50000, and 110592/109375 in the 7-limit; 176/175, 1331/1323, 8019/8000, and 26411/26244 in the 11-limit. Using the 203ce val, it tempers out 441/440, 896/891, and 3388/3375 in the 11-limit. Using the 203cef val, it tempers out 196/195, 352/351, 364/363, 676/675, and 78732/78125 in the 13-limit.

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

Since {{nowrap|203 {{=}} 7 × 29}}, 203edo shares its [[3/2|fifth]] with [[29edo]]. It is in[[consistent]] to the [[5-odd-limit]] and higher limits, with two mappings possible for the 7-limit: {{val| 203 322 471 570 }} ([[patent val]]), {{val| 203 322 '''472''' 570 }} (203c). Using the patent val, it [[tempering out|tempers out]] 2109375/2097152 ([[semicomma]]) and {{monzo| 4 -23 14 }} in the 5-limit; [[4000/3969]], [[10976/10935]], and [[2100875/2097152]] in the 7-limit; [[385/384]], 1331/1323, and [[4000/3993]] in the 11-limit; [[352/351]], [[676/675]], [[1573/1568]], and 1625/1617 in the 13-limit. Using the 203c val, it tempers out 78732/78125 ([[sensipent comma]]) in the 5-limit; [[5120/5103]], [[50421/50000]], and 110592/109375 in the 7-limit; [[176/175]], 1331/1323, [[8019/8000]], and 26411/26244 in the 11-limit. The alternative 203cef val is also worth considering, which tempers out [[441/440]], [[896/891]], and [[3388/3375]] in the 11-limit; and [[196/195]], 352/351, [[364/363]], and 676/675 in the 13-limit.

=== Odd harmonics ===

=== Subsets and supersets ===

Since 203 factors into {{factorization|203}}, 203edo contains [[7edo]] and [[29edo]] as its subsets.

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-'''203edo''' is the [[EDO|equal division of the octave]] into 203 parts of 5.9113 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 7-limit: &lt;203 322 471 570| (patent val), &lt;203 321 471 569| (203bd), and &lt;203 322 472 570| (203c). Using the patent val, it tempers out the semicomma, 2109375/2097152 and 97656250000/94143178827 in the 5-limit; 4000/3969, 10976/10935, and 2100875/2097152 in the 7-limit; 385/384, 1331/1323, and 4000/3993 in the 11-limit; 352/351, 676/675, 1573/1568, and 1625/1617 in the 13-limit. Using the 203c val, it tempers out the sensipent comma, 78732/78125 and [[29-comma]] in the 5-limit; 5120/5103, 50421/50000, and 110592/109375 in the 7-limit; 176/175, 1331/1323, 8019/8000, and 26411/26244 in the 11-limit. Using the 203ce val, it tempers out 441/440, 896/891, and 3388/3375 in the 11-limit. Using the 203cef val, it tempers out 196/195, 352/351, 364/363, 676/675, and 78732/78125 in the 13-limit.
+{{Infobox ET}}
+{{ED intro}}
-[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
+Since {{nowrap|203 {{=}} 7 × 29}}, 203edo shares its [[3/2|fifth]] with [[29edo]]. It is in[[consistent]] to the [[5-odd-limit]] and higher limits, with two mappings possible for the 7-limit: {{val| 203 322 471 570 }} ([[patent val]]), {{val| 203 322 '''472''' 570 }} (203c). Using the patent val, it [[tempering out|tempers out]] 2109375/2097152 ([[semicomma]]) and {{monzo| 4 -23 14 }} in the 5-limit; [[4000/3969]], [[10976/10935]], and [[2100875/2097152]] in the 7-limit; [[385/384]], 1331/1323, and [[4000/3993]] in the 11-limit; [[352/351]], [[676/675]], [[1573/1568]], and 1625/1617 in the 13-limit. Using the 203c val, it tempers out 78732/78125 ([[sensipent comma]]) in the 5-limit; [[5120/5103]], [[50421/50000]], and 110592/109375 in the 7-limit; [[176/175]], 1331/1323, [[8019/8000]], and 26411/26244 in the 11-limit. The alternative 203cef val is also worth considering, which tempers out [[441/440]], [[896/891]], and [[3388/3375]] in the 11-limit; and [[196/195]], 352/351, [[364/363]], and 676/675 in the 13-limit.
+=== Odd harmonics ===
+{{Harmonics in equal|203}}
+=== Subsets and supersets ===
+Since 203 factors into {{factorization|203}}, 203edo contains [[7edo]] and [[29edo]] as its subsets.