191edo: Difference between revisions

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'''191edo''' is the [[EDO|equal division of the octave]] into 191 parts of 6.2827 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with two mappings possible for the 5-limit: <191 303 443| (optimal patent val) and <191 303 444| (191c). Using the optimal patent val, it tempers out the [[Tetracot family|tetracot comma]], 20000/19683 and |-52, 5, 19> in the 5-limit; 245/243, 2401/2400, and 68359375/67108864 in the 7-limit. Using the 191c val, it tempers out the [[Amity family|amity comma]], 1600000/1594323 and 549755813888/533935546875 in the 5-limit; 4375/4374, 5120/5103, and 823543/810000 in the 7-limit. Using the alternative 191cd val, 1728/1715, 3136/3125, and 1605632/1594323 are tempered out in the 7-limit.

191edo is the ~~43th~~ [[~~prime EDO~~]].

191edo is in[[consistent]] to the [[5-odd-limit]] and higher limits, with two mappings possible for the 5-limit: {{val| 191 303 443 }} ([[patent val]]) and {{val| 191 303 444 }} (191c). Using the patent val, it tempers out the [[tetracot comma]], 20000/19683 and {{monzo| -52 5 19 }} in the 5-limit; [[245/243]], [[2401/2400]], and 68359375/67108864 in the 7-limit; [[385/384]], [[896/891]], 1375/1372, and 118125/117128 in the 11-limit; [[352/351]], [[364/363]], 1625/1617, 1875/1859, and [[2197/2187]] in the 13-limit. Using the 191c val, it tempers out the [[amity comma]], 1600000/1594323 and {{monzo| 39 -7 -12 }} in the 5-limit; [[4375/4374]], [[5120/5103]], and 823543/810000 in the 7-limit; [[441/440]], 896/891, 6912/6875, and [[14641/14580]] in the 11-limit; [[196/195]], 352/351, 364/363, 2197/2187, and 3146/3125 in the 13-limit. Using the alternative 191cd val, it tempers out [[1728/1715]], [[3136/3125]], and 1605632/1594323 in the 7-limit; [[176/175]], [[540/539]], 1331/1323, and 655360/649539 in the 11-limit; [[351/350]], 352/351, [[640/637]], [[1573/1568]], and 2197/2187 in the 13-limit, [[support]]ing the [[semisept]] temperament.

~~[[Category:Edo]]~~

=== Odd harmonics ===

[[~~Category:Prime EDO~~]]

=== Subsets and supersets ===

191edo is the 43rd [[prime edo]].

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-'''191edo''' is the [[EDO|equal division of the octave]] into 191 parts of 6.2827 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with two mappings possible for the 5-limit: &lt;191 303 443| (optimal patent val) and &lt;191 303 444| (191c). Using the optimal patent val, it tempers out the [[Tetracot family|tetracot comma]], 20000/19683 and |-52, 5, 19&gt; in the 5-limit; 245/243, 2401/2400, and 68359375/67108864 in the 7-limit. Using the 191c val, it tempers out the [[Amity family|amity comma]], 1600000/1594323 and 549755813888/533935546875 in the 5-limit; 4375/4374, 5120/5103, and 823543/810000 in the 7-limit. Using the alternative 191cd val, 1728/1715, 3136/3125, and 1605632/1594323 are tempered out in the 7-limit.
+{{Infobox ET}}
+{{ED intro}}
-edo is the 43th [[prime EDO]].
+edo is in[[consistent]] to the [[5-odd-limit]] and higher limits, with two mappings possible for the 5-limit: {{val| 191 303 443 }} ([[patent val]]) and {{val| 191 303 444 }} (191c). Using the patent val, it tempers out the [[tetracot comma]], 20000/19683 and {{monzo| -52 5 19 }} in the 5-limit; [[245/243]], [[2401/2400]], and 68359375/67108864 in the 7-limit; [[385/384]], [[896/891]], 1375/1372, and 118125/117128 in the 11-limit; [[352/351]], [[364/363]], 1625/1617, 1875/1859, and [[2197/2187]] in the 13-limit. Using the 191c val, it tempers out the [[amity comma]], 1600000/1594323 and {{monzo| 39 -7 -12 }} in the 5-limit; [[4375/4374]], [[5120/5103]], and 823543/810000 in the 7-limit; [[441/440]], 896/891, 6912/6875, and [[14641/14580]] in the 11-limit; [[196/195]], 352/351, 364/363, 2197/2187, and 3146/3125 in the 13-limit. Using the alternative 191cd val, it tempers out [[1728/1715]], [[3136/3125]], and 1605632/1594323 in the 7-limit; [[176/175]], [[540/539]], 1331/1323, and 655360/649539 in the 11-limit; [[351/350]], 352/351, [[640/637]], [[1573/1568]], and 2197/2187 in the 13-limit, [[support]]ing the [[semisept]] temperament.
-[[Category:Edo]]
+=== Odd harmonics ===
-[[Category:Prime EDO]]
+{{Harmonics in equal|191}}
+=== Subsets and supersets ===
+edo is the 43rd [[prime edo]].