563edo: Difference between revisions
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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..." |
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== 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 === | ||
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=== 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 | ||
|} | |} | ||
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! 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 | ||
Revision as of 08:38, 7 February 2024
| ← 562edo | 563edo | 564edo → |
Theory
563edo is only consistent to the 5-odd-limit and the error of harmonic 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
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.712 | -0.523 | +0.979 | +0.708 | +0.725 | -0.741 | +0.896 | -0.515 | +0.888 | +0.267 | +0.500 |
| Relative (%) | -33.4 | -24.6 | +45.9 | +33.2 | +34.0 | -34.8 | +42.1 | -24.2 | +41.7 | +12.5 | +23.5 | |
| Steps (reduced) |
892 (329) |
1307 (181) |
1581 (455) |
1785 (96) |
1948 (259) |
2083 (394) |
2200 (511) |
2301 (49) |
2392 (140) |
2473 (221) |
2547 (295) | |
Subsets and supersets
563edo is the 103rd prime edo. 1689edo, which triples it, gives a good correction to the harmonic 3.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.9 | [1785 -563⟩ | [⟨563 1785]] | -0.1117 | 0.1117 | 5.24 |
Rank-2 temperaments
| Periods per 8ve |
Generator* | Cents* | Associated Ratio* |
Temperaments |
|---|---|---|---|---|
| 1 | 263\563 | 560.57 | 864/625 | Whoosh |
* octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct