313edo: Difference between revisions
→Regular temperament properties: rework |
Adopt new intro and prime error templates; +categories |
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{{EDO intro|313}} | |||
== Theory == | == Theory == | ||
313edo provides the [[optimal patent val]] for 11- and 13-limit [[hemischis]] temperament and the 13-limit rank-3 temperaments [[madagascar]] and [[hera]]. It tempers out the [[schisma]], 32805/32768, in the 5-limit; [[6144/6125]] and [[19683/19600]] in the 7-limit; [[540/539]], [[5632/5625]], [[8019/8000]] and [[16384/16335]] in the 11-limit; [[351/350]], [[676/675]], [[729/728]], [[1001/1000]], [[2080/2079]] and [[4096/4095]] in the 13-limit. | 313edo provides the [[optimal patent val]] for 11- and 13-limit [[hemischis]] temperament and the 13-limit rank-3 temperaments [[madagascar]] and [[hera]]. It tempers out the [[schisma]], 32805/32768, in the 5-limit; [[6144/6125]] and [[19683/19600]] in the 7-limit; [[540/539]], [[5632/5625]], [[8019/8000]] and [[16384/16335]] in the 11-limit; [[351/350]], [[676/675]], [[729/728]], [[1001/1000]], [[2080/2079]] and [[4096/4095]] in the 13-limit. | ||
313edo is the 65th [[prime | 313edo is the 65th [[prime edo]]. | ||
=== Prime harmonics === | === Prime harmonics === | ||
{{ | {{Harmonics in equal|313}} | ||
== Regular temperament properties == | == Regular temperament properties == | ||
| Line 21: | Line 21: | ||
|- | |- | ||
| 2.3 | | 2.3 | ||
| {{monzo| -496 | | {{monzo| -496 313 }} | ||
| [{{val| 313 496 }}] | | [{{val| 313 496 }}] | ||
| +0.113 | | +0.113 | ||
| Line 70: | Line 70: | ||
| [[9/8]] (-0.715 ¢) | | [[9/8]] (-0.715 ¢) | ||
|- | |- | ||
| 12 | | 12 (65\313) | ||
| 249.201 | | 249.201 | ||
| [[15/13]] (+1.46 ¢) | | [[15/13]] (+1.46 ¢) | ||
| Line 78: | Line 78: | ||
| [[13/10]] (-1,818 ¢) | | [[13/10]] (-1,818 ¢) | ||
|- | |- | ||
| 12 | | 12 (130\313) | ||
| 498.403 | | 498.403 | ||
| [[4/3]] (+0.358 ¢) | | [[4/3]] (+0.358 ¢) | ||
|- | |- | ||
| 53 | | 53 (183\313) | ||
| 701.597 | | 701.597 | ||
| [[3/2]] (-0.358 ¢) | | [[3/2]] (-0.358 ¢) | ||
|- | |- | ||
| 12 | | 12 (195\313) | ||
| 747.604 | | 747.604 | ||
| [[20/13]] (+1.818 ¢) | | [[20/13]] (+1.818 ¢) | ||
|- | |- | ||
| 53 | | 53 (248\313) | ||
| 950.799 | | 950.799 | ||
| [[26/15]] (-1.46 ¢) | | [[26/15]] (-1.46 ¢) | ||
|- | |- | ||
| 12 | | 12 (260\313) | ||
| 996.805 | | 996.805 | ||
| [[16/9]] (+0.715 ¢) | | [[16/9]] (+0.715 ¢) | ||
|- | |- | ||
| 53 | | 53 (313\313) | ||
| 1200.000 | | 1200.000 | ||
| [[2/1]] (±0 ¢) | | [[2/1]] (±0 ¢) | ||
| Line 108: | Line 108: | ||
[[Category:Equal divisions of the octave]] | [[Category:Equal divisions of the octave]] | ||
[[Category:Prime EDO]] | [[Category:Prime EDO]] | ||
[[Category:Hemischis]] | |||
[[Category:Hera]] | |||
[[Category:Albus]] | |||