829edo: Difference between revisions
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m Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
829edo is [[consistent]] to the [[11-odd-limit]]. | 829edo is [[consistent]] to the [[11-odd-limit]]. As an equal temperament, it [[tempering out|tempers out]] [[4375/4374]], {{monzo| -25 6 -3 8 }}, and {{monzo| 16 -9 -8 6 }} in the 7-limit; [[41503/41472]], [[200704/200475]], and 3750705/3748096 in the 11-limit. It [[support]]s [[squarschmidt]], [[senior]] and [[acrokleismic]]. | ||
=== Prime harmonics === | === Prime harmonics === | ||
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=== Subsets and supersets === | === Subsets and supersets === | ||
829edo is the 145th [[prime edo]]. | 829edo is the 145th [[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 | ! rowspan="2" | [[Comma list]] | ||
! rowspan="2" | [[Mapping]] | ! rowspan="2" | [[Mapping]] | ||
! rowspan="2" | Optimal<br>8ve | ! rowspan="2" | Optimal<br>8ve stretch (¢) | ||
! colspan="2" | Tuning | ! colspan="2" | Tuning error | ||
|- | |- | ||
! [[TE error|Absolute]] (¢) | ! [[TE error|Absolute]] (¢) | ||
! [[TE simple badness|Relative]] (%) | ! [[TE simple badness|Relative]] (%) | ||
|- | |- | ||
| 2.3 | | 2.3 | ||
| {{ | | {{Monzo| 1314 -829 }} | ||
| {{ | | {{Mapping| 829 1314 }} | ||
| | | –0.0302 | ||
| 0.0302 | | 0.0302 | ||
| 2.09 | | 2.09 | ||
|- | |- | ||
| 2.3.5 | | 2.3.5 | ||
| {{ | | {{Monzo| 39 -29 3 }}, {{monzo| 61 4 -29 }} | ||
| {{ | | {{Mapping| 829 1314 1925 }} | ||
| | | −0.0454 | ||
| 0.0327 | | 0.0327 | ||
| 2.26 | | 2.26 | ||
| Line 38: | Line 39: | ||
| 2.3.5.7 | | 2.3.5.7 | ||
| 4375/4374, {{monzo| -25 6 -3 8 }}, {{monzo| 16 -9 -8 6 }} | | 4375/4374, {{monzo| -25 6 -3 8 }}, {{monzo| 16 -9 -8 6 }} | ||
| {{ | | {{Mapping| 829 1314 1925 2327 }} | ||
| +0.0043 | | +0.0043 | ||
| 0.0906 | | 0.0906 | ||
| Line 45: | Line 46: | ||
| 2.3.5.7.11 | | 2.3.5.7.11 | ||
| 4375/4374, 41503/41472, 200704/200475, 3750705/3748096 | | 4375/4374, 41503/41472, 200704/200475, 3750705/3748096 | ||
| {{ | | {{Mapping| 829 1314 1925 2327 2868 }} | ||
| | | −0.0076 | ||
| 0.0844 | | 0.0844 | ||
| 5.83 | | 5.83 | ||
| Line 52: | Line 53: | ||
| 2.3.5.7.11.13 | | 2.3.5.7.11.13 | ||
| 4096/4095, 4375/4374, 4459/4455, 47432/47385, 59535/59488 | | 4096/4095, 4375/4374, 4459/4455, 47432/47385, 59535/59488 | ||
| {{ | | {{Mapping| 829 1314 1925 2327 2868 3068 }} | ||
| | | −0.0282 | ||
| 0.0898 | | 0.0898 | ||
| 6.20 | | 6.20 | ||
| Line 60: | Line 61: | ||
=== 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 | ||
|- | |- | ||
| Line 89: | Line 91: | ||
| 565.983 | | 565.983 | ||
| 59049/40960 | | 59049/40960 | ||
| [[ | | [[Alphatrillium]] | ||
|} | |} | ||
<nowiki>* | <nowiki/>* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct | ||
== Music == | |||
; [[Francium]] | |||
* "confluencelessness" from ''albumwithoutspaces'' (2024) – [https://open.spotify.com/track/7luOwK0nu7Cq9hmJy6W7L9 Spotify] | [https://francium223.bandcamp.com/track/confluencelessness Bandcamp] | [https://www.youtube.com/watch?v=eKDAs6aHF1s YouTube] – Acrokleismic[19] in 829edo tuning | |||