179edo: Difference between revisions
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+regular temperament properties |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{EDO intro|179}} | {{EDO intro|179}} | ||
== Theory == | |||
179edo doesn't approximate well any odd harmonic up to 23, best being [[21/16]] with 22% error. Nonetheless, it is consistent in the 7-limit and there are anumber of temperaments to be considered. | 179edo doesn't approximate well any odd harmonic up to 23, best being [[21/16]] with 22% error. Nonetheless, it is consistent in the 7-limit and there are anumber of temperaments to be considered. | ||
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=== Odd harmonics === | === Odd harmonics === | ||
{{Harmonics in equal|179}} | {{Harmonics in equal|179}} | ||
=== Subsets and supersets === | === Subsets and supersets === | ||
179edo is the 41st [[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|284 -179}} | |||
|{{val|179 284}} | |||
| -0.6169 | |||
| 0.6166 | |||
| 9.20 | |||
|- | |||
|2.3.5 | |||
|{{monzo|20 -17 3}}, {{monzo|28 -3 -10}} | |||
|{{val|179 284 416}} | |||
| -0.7718 | |||
| 0.5490 | |||
| 8.19 | |||
|- | |||
|2.3.5.7 | |||
|3136/3125, 4375/4374, 10976/10935 | |||
|{{val|179 284 416 503}} | |||
| -0.8673 | |||
| 0.5034 | |||
| 7.51 | |||
|} | |||
=== 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 | |||
|35\179 | |||
|234.64 | |||
|8/7 | |||
|[[Rodan]] | |||
|- | |||
|1 | |||
|47\179 | |||
|315.08 | |||
|6/5 | |||
|[[Parakleismic]] | |||
|- | |||
|1 | |||
|79\167 | |||
|529.61 | |||
|512/375 | |||
|[[Mabila]] | |||
|} | |||
[[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | [[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | ||
[[Category:Prime EDO]] | [[Category:Prime EDO]] | ||