612edo: Difference between revisions
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== Regular temperament properties == | == Regular temperament properties == | ||
{ | {{comma basis begin}} | ||
|- | |- | ||
| 2.3.5 | | 2.3.5 | ||
| Line 52: | Line 44: | ||
| 1331/1330, 1540/1539, 2200/2197, 2376/2375, 2926/2925, 4096/4095 | | 1331/1330, 1540/1539, 2200/2197, 2376/2375, 2926/2925, 4096/4095 | ||
| {{mapping| 612 970 1421 1718 2117 2265 2600 }} | | {{mapping| 612 970 1421 1718 2117 2265 2600 }} | ||
| | | −0.0168 | ||
| 0.0917 | | 0.0917 | ||
| 4.68 | | 4.68 | ||
{{comma basis end}} | |||
* 612et has a lower relative error than any previous equal temperaments in the 5-limit. Not until [[1171edo|1171]] do we find a better equal temperament in terms of either absolute error or relative error. | * 612et has a lower relative error than any previous equal temperaments in the 5-limit. Not until [[1171edo|1171]] do we find a better equal temperament in terms of either absolute error or relative error. | ||
* | * It also has a lower absolute error in the 7- and 11-limit than any previous equal temperaments, and is only bettered by [[935edo|935]] and [[836edo|836]], respectively. | ||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{ | {{rank-2 begin}} | ||
|- | |- | ||
| 1 | | 1 | ||
| Line 87: | Line 73: | ||
|- | |- | ||
| 4 | | 4 | ||
| 194\612<br>(41\612) | | 194\612<br />(41\612) | ||
| 380.39<br>(80.39) | | 380.39<br />(80.39) | ||
| 81/65<br>(22/21) | | 81/65<br />(22/21) | ||
| [[Quasithird]] | | [[Quasithird]] | ||
|- | |- | ||
| 9 | | 9 | ||
| 133\612<br>(25\612) | | 133\612<br />(25\612) | ||
| 315.69<br>(49.02) | | 315.69<br />(49.02) | ||
| 6/5<br>(36/35) | | 6/5<br />(36/35) | ||
| [[Ennealimmal]] | | [[Ennealimmal]] | ||
|- | |- | ||
| 12 | | 12 | ||
| 124\612<br>(22\612) | | 124\612<br />(22\612) | ||
| 243.137<br>(43.14) | | 243.137<br />(43.14) | ||
| 3145728/2734375<br>(?) | | 3145728/2734375<br />(?) | ||
| [[Magnesium]] | | [[Magnesium]] | ||
|- | |- | ||
| 12 | | 12 | ||
| 254\612<br>(1\612) | | 254\612<br />(1\612) | ||
| 498.04<br>(1.96) | | 498.04<br />(1.96) | ||
| 4/3<br>(32805/32768) | | 4/3<br />(32805/32768) | ||
| [[Atomic]] | | [[Atomic]] | ||
|- | |- | ||
| 17 | | 17 | ||
| 127\612<br>(17\612) | | 127\612<br />(17\612) | ||
| 249.02<br>(33.33) | | 249.02<br />(33.33) | ||
| {{monzo| -23 5 9 -2 }}<br>(100352/98415) | | {{monzo| -23 5 9 -2 }}<br />(100352/98415) | ||
| [[Chlorine]] | | [[Chlorine]] | ||
|- | |- | ||
| 18 | | 18 | ||
| 127\612<br>(9\612) | | 127\612<br />(9\612) | ||
| 249.02<br>(17.65) | | 249.02<br />(17.65) | ||
| 231/200<br>(99/98) | | 231/200<br />(99/98) | ||
| [[Hemiennealimmal]] (11-limit) | | [[Hemiennealimmal]] (11-limit) | ||
{{rank-2 end}} | |||
{{orf}} | |||
== Music == | == Music == | ||