769edo: Difference between revisions

Francium (talk | contribs)
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..."
 
ArrowHead294 (talk | contribs)
mNo edit summary
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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|Comma List]]
! rowspan="2" | [[Subgroup]]
! rowspan="2" |[[Mapping]]
! rowspan="2" | [[Comma list]]
! rowspan="2" |Optimal<br>8ve Stretch (¢)
! rowspan="2" | [[Mapping]]
! colspan="2" |Tuning Error
! 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
| −0.0807
| 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
| −0.1517
| 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
| −0.1338
| 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>Ratio*
! 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>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct