769edo: Difference between revisions
Created page with "{{Infobox ET}} {{EDO intro|769}} == Theory == 769edo is consistent to the 9-odd-limit, despite of a large error in its harmonic 5. As an equal temperament..." |
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== 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" |[[Comma list | ! rowspan="2" | [[Subgroup]] | ||
! rowspan="2" |[[Mapping]] | ! rowspan="2" | [[Comma list]] | ||
! rowspan="2" |Optimal<br>8ve | ! rowspan="2" | [[Mapping]] | ||
! colspan="2" |Tuning | ! rowspan="2" | Optimal<br />8ve stretch (¢) | ||
|- | ! colspan="2" | Tuning error | ||
![[TE error|Absolute]] (¢) | |- | ||
![[TE simple badness|Relative]] (%) | ! [[TE error|Absolute]] (¢) | ||
! [[TE simple badness|Relative]] (%) | |||
|- | |- | ||
| 2.3 | | 2.3 | ||
| {{monzo|1219 -769}} | | {{monzo|1219 -769}} | ||
| {{mapping|769 1219}} | | {{mapping|769 1219}} | ||
| | | −0.0807 | ||
| 0.0806 | | 0.0806 | ||
| 5.17 | | 5.17 | ||
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| {{monzo|8 14 -13}}, {{monzo|103 -43 -15}} | | {{monzo|8 14 -13}}, {{monzo|103 -43 -15}} | ||
| {{mapping|769 1219 1786}} | | {{mapping|769 1219 1786}} | ||
| | | −0.1517 | ||
| 0.1202 | | 0.1202 | ||
| 7.70 | | 7.70 | ||
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| 2401/2400, 359661568/358722675, 1224440064/1220703125 | | 2401/2400, 359661568/358722675, 1224440064/1220703125 | ||
| {{mapping|769 1219 1786 2159}} | | {{mapping|769 1219 1786 2159}} | ||
| | | −0.1338 | ||
| 0.1086 | | 0.1086 | ||
| 6.96 | | 6.96 | ||
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=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{| class="wikitable center-all left-5" | {| class="wikitable center-all left-5" | ||
|+Table of rank-2 temperaments by generator | |+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | ||
! Periods<br>per 8ve | |- | ||
! Periods<br />per 8ve | |||
! Generator* | ! Generator* | ||
! Cents* | ! Cents* | ||
! Associated<br> | ! Associated<br />ratio* | ||
! Temperaments | ! Temperaments | ||
|- | |- | ||
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| [[Maviloid]] | | [[Maviloid]] | ||
|} | |} | ||
<nowiki />* [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct | |||
<nowiki>* | |||