569edo: Difference between revisions
Created page with "{{Infobox ET}} {{EDO intro|569}} == Theory == 569et is only consistent to the 5-odd-limit. Using the patent val, it tempers out 1220703125/1219784832, 33554432/33480783..." |
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== Theory == | == Theory == | ||
569edo is only [[consistent]] to the [[5-odd-limit]]. The equal temperament [[tempering out|tempers out]] 1600000/1594323 ([[amity comma]]) in the 5-limit. Using the [[patent val]], it [[tempering out|tempers out]] [[65625/65536]], 823543/820125, and [[33554432/33480783]] in the 7-limit; 42592/42525, 42875/42768, 43923/43904, and 151263/151250 in the 11-limit. | |||
=== Prime harmonics === | === Prime harmonics === | ||
| Line 9: | Line 9: | ||
=== Subsets and supersets === | === Subsets and supersets === | ||
569edo is the 104th [[prime | 569edo is the 104th [[prime edo]]. | ||
== Regular temperament properties == | == Regular temperament properties == | ||
{| class="wikitable center-4 center-5 center-6" | {| class="wikitable center-4 center-5 center-6" | ||
! rowspan="2" |[[Subgroup]] | ! rowspan="2" | [[Subgroup]] | ||
! rowspan="2" |[[Comma list|Comma List]] | ! rowspan="2" | [[Comma list|Comma List]] | ||
! rowspan="2" |[[Mapping]] | ! rowspan="2" | [[Mapping]] | ||
! rowspan="2" |Optimal<br>8ve Stretch (¢) | ! rowspan="2" | Optimal<br>8ve Stretch (¢) | ||
! colspan="2" |Tuning Error | ! colspan="2" | Tuning Error | ||
|- | |- | ||
![[TE error|Absolute]] (¢) | ! [[TE error|Absolute]] (¢) | ||
![[TE simple badness|Relative]] (%) | ! [[TE simple badness|Relative]] (%) | ||
|- | |- | ||
|2.3 | | 2.3 | ||
|{{monzo|902 -569}} | | {{monzo| 902 -569 }} | ||
|{{mapping|569 902}} | | {{mapping| 569 902 }} | ||
| -0.1040 | | -0.1040 | ||
| 0.1040 | | 0.1040 | ||
| 4.93 | | 4.93 | ||
|- | |- | ||
|2.3.5 | | 2.3.5 | ||
|1600000/1594323, {{monzo|-94 -11 48}} | | 1600000/1594323, {{monzo| -94 -11 48 }} | ||
|{{mapping|569 902 1321}} | | {{mapping| 569 902 1321 }} | ||
| -0.0157 | | -0.0157 | ||
| 0.1510 | | 0.1510 | ||
| 7.16 | | 7.16 | ||
|- | |- | ||
|2.3.5.7 | | 2.3.5.7 | ||
|823543/820125 | | 65625/65536, 823543/820125, 1600000/1594323 | ||
|{{mapping|569 902 1321 1597}} | | {{mapping| 569 902 1321 1597 }} | ||
| +0.0605 | | +0.0605 | ||
| 0.1858 | | 0.1858 | ||
| 8.81 | | 8.81 | ||
|- | |- | ||
|2.3.5.7.11 | | 2.3.5.7.11 | ||
|42875/42768, | | 42592/42525, 42875/42768, 43923/43904, 151263/151250 | ||
|{{mapping|569 902 1321 1597 1968}} | | {{mapping| 569 902 1321 1597 1968 }} | ||
| +0.0992 | | +0.0992 | ||
| 0.1834 | | 0.1834 | ||
| Line 60: | Line 60: | ||
! Temperaments | ! Temperaments | ||
|- | |- | ||
|1 | | 1 | ||
|161\569 | | 161\569 | ||
|339.54 | | 339.54 | ||
|243/200 | | 243/200 | ||
|[[ | | [[Paramity]] | ||
|} | |} | ||
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct | <nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct | ||