193edo: Difference between revisions
+data for the 23-limit |
ArrowHead294 (talk | contribs) mNo edit summary |
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== Regular temperament properties == | == Regular temperament properties == | ||
{ | {{comma basis begin}} | ||
|- | |- | ||
| 2.3 | | 2.3 | ||
| {{monzo| 306 -193 }} | | {{monzo| 306 -193 }} | ||
| {{mapping| 193 306 }} | | {{mapping| 193 306 }} | ||
| | | −0.2005 | ||
| 0.2005 | | 0.2005 | ||
| 3.23 | | 3.23 | ||
Line 36: | Line 28: | ||
| 15625/15552, {{monzo| 50 -33 1 }} | | 15625/15552, {{monzo| 50 -33 1 }} | ||
| {{mapping| 193 306 448 }} | | {{mapping| 193 306 448 }} | ||
| | | −0.0158 | ||
| 0.3084 | | 0.3084 | ||
| 4.96 | | 4.96 | ||
Line 43: | Line 35: | ||
| 5120/5103, 15625/15552, 16875/16807 | | 5120/5103, 15625/15552, 16875/16807 | ||
| {{mapping| 193 306 448 542 }} | | {{mapping| 193 306 448 542 }} | ||
| | | −0.1118 | ||
| 0.3146 | | 0.3146 | ||
| 5.06 | | 5.06 | ||
Line 50: | Line 42: | ||
| 540/539, 1375/1372, 4375/4356, 5120/5103 | | 540/539, 1375/1372, 4375/4356, 5120/5103 | ||
| {{mapping| 193 306 448 542 668 }} | | {{mapping| 193 306 448 542 668 }} | ||
| | | −0.2080 | ||
| 0.3408 | | 0.3408 | ||
| 5.48 | | 5.48 | ||
Line 57: | Line 49: | ||
| 325/324, 364/363, 540/539, 625/624, 4096/4095 | | 325/324, 364/363, 540/539, 625/624, 4096/4095 | ||
| {{mapping| 193 306 448 542 668 714 }} | | {{mapping| 193 306 448 542 668 714 }} | ||
| | | −0.1216 | ||
| 0.3662 | | 0.3662 | ||
| 5.89 | | 5.89 | ||
Line 64: | Line 56: | ||
| 325/324, 364/363, 375/374, 442/441, 595/594, 4096/4095 | | 325/324, 364/363, 375/374, 442/441, 595/594, 4096/4095 | ||
| {{mapping| 193 306 448 542 668 714 789 }} | | {{mapping| 193 306 448 542 668 714 789 }} | ||
| | | −0.1302 | ||
| 0.3397 | | 0.3397 | ||
| 5.46 | | 5.46 | ||
Line 71: | Line 63: | ||
| 325/324, 364/363, 375/374, 400/399, 442/441, 595/594, 1216/1215 | | 325/324, 364/363, 375/374, 400/399, 442/441, 595/594, 1216/1215 | ||
| {{mapping| 193 306 448 542 668 714 789 820 }} | | {{mapping| 193 306 448 542 668 714 789 820 }} | ||
| | | −0.1414 | ||
| 0.3191 | | 0.3191 | ||
| 5.13 | | 5.13 | ||
Line 78: | Line 70: | ||
| 325/324, 364/363, 375/374, 400/399, 442/441, 460/459, 507/506, 529/528 | | 325/324, 364/363, 375/374, 400/399, 442/441, 460/459, 507/506, 529/528 | ||
| {{mapping| 193 306 448 542 668 714 789 820 873 }} | | {{mapping| 193 306 448 542 668 714 789 820 873 }} | ||
| | | −0.1184 | ||
| 0.3078 | | 0.3078 | ||
| 4.95 | | 4.95 | ||
{{comma basis end}} | |||
* 193et has a lower relative error in the 23-limit than any previous equal temperaments, past [[190edo|190g]] and followed by [[217edo|217]]. | * 193et has a lower relative error in the 23-limit than any previous equal temperaments, past [[190edo|190g]] and followed by [[217edo|217]]. | ||
* 193et is also notable in the 19-limit, where it has a lower absolute error than any previous equal temperaments, past 190g and followed by [[212edo|212gh]]. | * 193et is also notable in the 19-limit, where it has a lower absolute error than any previous equal temperaments, past 190g and followed by [[212edo|212gh]]. | ||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{ | {{rank-2 begin}} | ||
|- | |- | ||
| 1 | | 1 | ||
Line 147: | Line 133: | ||
| 4/3 | | 4/3 | ||
| [[Kwai]] | | [[Kwai]] | ||
{{rank-2 end}} | |||
{{orf}} | |||
== Scales == | == Scales == |