563edo: Difference between revisions
Created page with "{{Infobox ET}} {{EDO intro|563}} == Theory == 563et is only consistent to the 5-odd-limit and the harmonic 3 is about halfway its steps. It is suitable for th..." |
Review |
||
| Line 3: | Line 3: | ||
== Theory == | == Theory == | ||
563edo is only [[consistent]] to the [[5-odd-limit]] and the error of [[harmonic]] [[3/1|3]] is quite large. It is suitable for the 2.9.7.11.19.23 [[subgroup]], [[tempering out]] [[1863/1862]], [[3971/3969]], 3449952/3447493, 7901568/7891499 and 4333568/4322241. | |||
=== Odd harmonics === | === Odd harmonics === | ||
| Line 9: | Line 9: | ||
=== Subsets and supersets === | === Subsets and supersets === | ||
563edo is the 103rd [[prime edo]]. [[ | 563edo is the 103rd [[prime edo]]. [[1689edo]], which triples it, gives a good correction to the harmonic 3. | ||
== 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]] (%) | ||
|- | |- | ||
|2.9 | | 2.9 | ||
|{{monzo|1785 -563}} | | {{monzo| 1785 -563 }} | ||
|{{mapping|563 1785}} | | {{mapping| 563 1785 }} | ||
| -0.1117 | | -0.1117 | ||
| 0.1117 | | 0.1117 | ||
|5.24 | | 5.24 | ||
|} | |} | ||
| Line 39: | Line 39: | ||
! Temperaments | ! Temperaments | ||
|- | |- | ||
|1 | | 1 | ||
|263\563 | | 263\563 | ||
|560.57 | | 560.57 | ||
|864/625 | | 864/625 | ||
|[[Whoosh]] | | [[Whoosh]] | ||
|} | |} | ||
<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 | ||