251edo: Difference between revisions
m Added "harmonics in equal" table |
No edit summary |
||
| Line 1: | Line 1: | ||
{{Infobox ET}} | {{Infobox ET}} | ||
{{EDO intro|251}} | |||
== Theory == | |||
251et tempers out 1600000/1594323 (amity comma) and 562949953421312/556182861328125 (maquila comma) in the 5-limit; 4375/4374, 5120/5103, and 40500000/40353607 in the 7-limit. | |||
Using the patent val, it tempers out 1331/1323, 1375/1372, 16896/16807, and 24057/24010 in the 11-limit; 352/351, 676/675, 847/845, and 1573/1568 in the 13-limit. | Using the patent val, it tempers out 1331/1323, 1375/1372, 16896/16807, and 24057/24010 in the 11-limit; 352/351, 676/675, 847/845, and 1573/1568 in the 13-limit. | ||
| Line 8: | Line 8: | ||
Using the 251e val, it tempers out 540/539, 5632/5625, 6250/6237, and 12005/11979 in the 11-limit; 364/363, 676/675, 1716/1715, and 3584/3575 in the 13-limit. | Using the 251e val, it tempers out 540/539, 5632/5625, 6250/6237, and 12005/11979 in the 11-limit; 364/363, 676/675, 1716/1715, and 3584/3575 in the 13-limit. | ||
=== Odd harmonics === | |||
{{Harmonics in equal|251}} | |||
=== Subsets and supersets === | |||
251edo is the 54th [[prime EDO]]. | 251edo is the 54th [[prime EDO]]. | ||
{{ | ==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|398 -251}} | |||
|{{val|251 398}} | |||
| -0.2630 | |||
| 0.2630 | |||
| 5.50 | |||
|- | |||
|2.3.5 | |||
|{{monzo|9 -13 5}}, {{monzo|49 -6 -17}} | |||
|{{val|251 398 583}} | |||
| -0.3099 | |||
| 0.2247 | |||
| 4.70 | |||
|- | |||
|2.3.5.7 | |||
|4375/4374, 5120/5103, 6144/6125 | |||
|{{val|251 398 583 705}} | |||
| -0.3830 | |||
| 0.2322 | |||
| 4.86 | |||
|} | |||
=== 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 | |||
|71\251 | |||
|339.44 | |||
|243/200 | |||
|[[Amity]] | |||
|- | |||
|1 | |||
|75\251 | |||
|358.57 | |||
|315/256 | |||
|[[Restles]] | |||
|- | |||
|1 | |||
|91\251 | |||
|435.06 | |||
|9/7 | |||
|[[Supermajor]] | |||
|- | |||
|1 | |||
|96\251 | |||
|458.96 | |||
|125/96 | |||
|[[Majvam]] | |||
|- | |||
|1 | |||
|112\251 | |||
|535.46 | |||
|512/375 | |||
|[[Maquila]] | |||
|- | |||
|1 | |||
|117\251 | |||
|559.26 | |||
|864/625 | |||
|[[Tritriple]] | |||
|} | |||
[[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | [[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | ||
[[Category:Prime EDO]] | [[Category:Prime EDO]] | ||