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829edo: Difference between revisions

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Created page with "{{Infobox ET}} {{EDO intro|829}} == Theory == 829et is consistent to the 11-odd-limit. The equal temperament tempers out 4375/4374, 7710244864/7688671875 and 4202..."
 
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}}
{{EDO intro|829}}
{{ED intro}}


== Theory ==
== Theory ==
829et is [[consistent]] to the [[11-odd-limit]]. The equal temperament tempers out [[4375/4374]], 7710244864/7688671875 and 4202539929/4194304000 in the 7-limit; 4375/4374, [[200704/200475]], [[41503/41472]] and 3750705/3748096 in the 11-limit. It [[support]]s [[squarschmidt]], [[senior]] and [[acrokleismic]].
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" |[[Comma list|Comma List]]
! rowspan="2" |[[Mapping]]
! rowspan="2" |Optimal<br>8ve Stretch (¢)
! colspan="2" |Tuning Error
|-
![[TE error|Absolute]] (¢)
![[TE simple badness|Relative]] (%)
|-
|-
|2.3
! rowspan="2" | [[Subgroup]]
|{{monzo|1314 -829}}
! rowspan="2" | [[Comma list]]
|{{val|829 1314}}
! rowspan="2" | [[Mapping]]
| -0.0302
! rowspan="2" | Optimal<br>8ve stretch (¢)
! colspan="2" | Tuning error
|-
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
| 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}}
| {{Monzo| 39 -29 3 }}, {{monzo| 61 4 -29 }}
|{{val|829 1314 1925}}
| {{Mapping| 829 1314 1925 }}
| -0.0454
| −0.0454
| 0.0327
| 0.0327
| 2.26
| 2.26
|-
|-
|2.3.5.7
| 2.3.5.7
|4375/4374, 7710244864/7688671875, 4202539929/4194304000
| 4375/4374, {{monzo| -25 6 -3 8 }}, {{monzo| 16 -9 -8 6 }}
|{{val|829 1314 1925 2327}}
| {{Mapping| 829 1314 1925 2327 }}
| +0.0043
| +0.0043
| 0.0906
| 0.0906
| 6.25
| 6.25
|-
|-
|2.3.5.7.11
| 2.3.5.7.11
|4375/4374, 200704/200475, 41503/41472, 3750705/3748096
| 4375/4374, 41503/41472, 200704/200475, 3750705/3748096
|{{val|829 1314 1925 2327 2868}}
| {{Mapping| 829 1314 1925 2327 2868 }}
| -0.0076
| −0.0076
| 0.0844
| 0.0844
| 5.83
| 5.83
|-
|-
|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
|{{val|829 1314 1925 2327 2868 3068}}
| {{Mapping| 829 1314 1925 2327 2868 3068 }}
| -0.0282
| −0.0282
| 0.0898
| 0.0898
| 6.20
| 6.20
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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
|-
|-
|1
| 1
|218\829
| 218\829
|315.561
| 315.561
|6/5
| 6/5
|[[Acrokleismic]]
| [[Acrokleismic]]
|-
|-
|1
| 1
|223\829
| 223\829
|322.799
| 322.799
|3087/2560
| 3087/2560
|[[Senior]] / [[Seniority]]
| [[Senior]] / [[seniority]]
|-
|-
|1
| 1
|274\829
| 274\829
|396.622
| 396.622
|98304/78125
| 98304/78125
|[[Squarschmidt]]
| [[Squarschmidt]]
|-
|-
|1
| 1
|391\829
| 391\829
|565.983
| 565.983
|59049/40960
| 59049/40960
|[[Tricot]]
| [[Alphatrillium]]
|}
|}
<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


<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is 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
Retrieved from "https://en.xen.wiki/w/829edo"