263edo: Difference between revisions
m Added "harmonics in equal" table and rearranged the order of sentences. |
+regular temperament properties |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{EDO intro|263}} | |||
==Theory== | |||
263et tempers out 393216/390625 (Würschmidt comma) and |50 -33 1> in the 5-limit. Using the patent val, it tempers out 4375/4374, 50421/50000, and 458752/455625 in the 7-limit; 441/440, 3388/3375, 16384/16335, and 26411/26244 in the 11-limit; 364/363, 2080/2079, 2197/2187, and 3584/3575 in the 13-limit; 595/594, 833/832, 936/935, and 1156/1155 in the 17-limit. | |||
Using the 263d val, it tempers out 5120/5103, 16875/16807, and 1959552/1953125 in the 7-limit; 540/539, 1375/1372, 16384/16335, and 43923/43750 in the 11-limit; 351/350, 1001/1000, 1573/1568, 2197/2187, and 4225/4224 in the 13-limit. | Using the 263d val, it tempers out 5120/5103, 16875/16807, and 1959552/1953125 in the 7-limit; 540/539, 1375/1372, 16384/16335, and 43923/43750 in the 11-limit; 351/350, 1001/1000, 1573/1568, 2197/2187, and 4225/4224 in the 13-limit. | ||
Using the 263df val, it tempers out 352/351, 640/637, 729/728, and 3584/3575 in the 13-limit. | Using the 263df val, it tempers out 352/351, 640/637, 729/728, and 3584/3575 in the 13-limit. | ||
===Prime harmonics=== | |||
{{Harmonics in equal|263}} | {{Harmonics in equal|263}} | ||
===Subsets and supersets=== | |||
263edo is the 56th [[prime EDO]]. It is accurate for the 17th harmonic, as the denominator of a convergent to log<sub>2</sub>17, after [[80edo|80]] and before [[343edo|343]]. | |||
==Regular temperament properties== | |||
{| class="wikitable center-4 center-5 center-6" | |||
! rowspan="2" |[[Subgroup]] | |||
! rowspan="2" |[[Comma list|Comma List]] | |||
! rowspan="2" |[[Mapping]] | |||
! rowspan="2" |Optimal<br>8ve Stretch (¢) | |||
! colspan="2" |Tuning Error | |||
|- | |||
![[TE error|Absolute]] (¢) | |||
![[TE simple badness|Relative]] (%) | |||
|- | |||
|2.3 | |||
|{{monzo|417 -263}} | |||
|{{val|263 417}} | |||
| -0.2229 | |||
| 0.2229 | |||
| 4.89 | |||
|- | |||
|2.3.5 | |||
|393216/390625, {{monzo|50 -33 1}} | |||
|{{val|263 417 611}} | |||
| -0.3666 | |||
| 0.2728 | |||
| 5.98 | |||
|} | |||
=== Rank-2 temperaments === | |||
{| class="wikitable center-all left-5" | |||
|+Table of rank-2 temperaments by generator | |||
! Periods<br>per 8ve | |||
! Generator<br>(reduced) | |||
! Cents<br>(reduced) | |||
! Associated<br>ratio | |||
! Temperaments | |||
|- | |||
|1 | |||
|40\263 | |||
|182.51 | |||
|10/9 | |||
|[[Minortone]] | |||
|- | |||
|1 | |||
|85\263 | |||
|387.83 | |||
|5/4 | |||
|[[Würschmidt]] | |||
|} | |||
[[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | [[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | ||
[[Category:Prime EDO]] | [[Category:Prime EDO]] | ||