317edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{EDO intro|317}} | {{EDO intro|317}} | ||
== Theory == | == Theory == | ||
317et tempers out 589824/588245, [[16875/16807]], [[65625/65536]] and 49009212/48828125 in the 7-limit; 1835008/1830125, 14700/14641, 2097152/2096325, [[4000/3993]], 2734375/2725888, 1953125/1951488, 172032/171875, [[441/440]], 5767168/5764801, 825000/823543, 537109375/536870912, 134775333/134217728, 160083/160000, 16808715/16777216, 539055/537824 and 3294225/3294172 in the 11-limit. | 317et is only consistent to the [[5-odd-limit]] and the [[harmonic]] 3 is about halfway its steps. Using the patent val, it tempers out 589824/588245, [[16875/16807]], [[65625/65536]] and 49009212/48828125 in the 7-limit; 1835008/1830125, 14700/14641, 2097152/2096325, [[4000/3993]], 2734375/2725888, 1953125/1951488, 172032/171875, [[441/440]], 5767168/5764801, 825000/823543, 537109375/536870912, 134775333/134217728, 160083/160000, 16808715/16777216, 539055/537824 and 3294225/3294172 in the 11-limit. | ||
===Odd harmonics=== | ===Odd harmonics=== | ||
{{Harmonics in equal|317}} | {{Harmonics in equal|317}} | ||
===Subsets and supersets=== | ===Subsets and supersets=== | ||
317edo is the 66th [[prime edo]]. [[634edo]], which doubles it, gives a good correction to the harmonic 3. | 317edo is the 66th [[prime edo]]. [[634edo]], which doubles it, gives a good correction to the harmonic 3. | ||
==Regular temperament properties== | ==Regular temperament properties== | ||
{| class="wikitable center-4 center-5 center-6" | {| class="wikitable center-4 center-5 center-6" | ||