220edo: Difference between revisions
m Added "harmonics in equal" table |
No edit summary |
||
| Line 1: | Line 1: | ||
{{Infobox ET}} | {{Infobox ET}} | ||
{{EDO intro|220}} | |||
== Theory == | |||
Using the patent val, it tempers out 131072000/129140163 (rodan comma) and 6115295232/6103515625 (vishnuzma) in the 5-limit; 6144/6125, 10976/10935, and 390625/388962 in the 7-limit; 1331/1323, 1375/1372, 2200/2187, and 16384/16335 in the 11-limit; 325/324, 352/351, 1001/1000, 1573/1568, and 2704/2695 in the 13-limit. | Using the patent val, it tempers out 131072000/129140163 (rodan comma) and 6115295232/6103515625 (vishnuzma) in the 5-limit; 6144/6125, 10976/10935, and 390625/388962 in the 7-limit; 1331/1323, 1375/1372, 2200/2187, and 16384/16335 in the 11-limit; 325/324, 352/351, 1001/1000, 1573/1568, and 2704/2695 in the 13-limit. | ||
=== Odd harmonics === | |||
{{Harmonics in equal|220}} | |||
=== Subsets and supersets === | |||
220 factors into 2<sup>2</sup> × 5 × 11, with subset edos {{EDOs| 2, 4, 5, 10, 11, 20, 22, 44, 55, and 110}} | |||
==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|349 -220}} | |||
|{{val|220 349}} | |||
| -0.5304 | |||
| 0.5302 | |||
| 9.72 | |||
|- | |||
|2.3.5 | |||
|{{monzo|20 -17 3}}, {{monzo|23 6 -14}} | |||
|{{val|220 349 511}} | |||
| -0.4912 | |||
| 0.4364 | |||
| 8.00 | |||
|- | |||
|2.3.5.7 | |||
|6144/6125, 10976/10935, 390625/388962 | |||
|{{val|220 349 511 618}} | |||
| -0.5538 | |||
| 0.3932 | |||
| 7.21 | |||
|} | |||
=== 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 | |||
|43\220 | |||
|234.55 | |||
|8/7 | |||
|[[Rodan]] | |||
|- | |||
|1 | |||
|83\220 | |||
|452.73 | |||
|125/81 | |||
|[[Maja]] | |||
|- | |||
|2 | |||
|13\220 | |||
|70.91 | |||
|25/24 | |||
|[[Vishnu]] | |||
|- | |||
|11 | |||
|91\220<br>(9\220) | |||
|496.36<br>(49.09) | |||
|4/3<br>(36/35) | |||
|[[Hendecatonic]] | |||
|} | |||
[[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | [[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | ||