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..."
 
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== 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]]. The equal temperament [[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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== 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]] (%)
|-
|-
|2.3
| 2.3
|{{monzo|1314 -829}}
| {{monzo| 1314 -829 }}
|{{val|829 1314}}
| {{mapping| 829 1314 }}
| -0.0302
| -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
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! 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]]
| [[Tricot]]
|}
|}
<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 09:30, 13 May 2024

← 828edo 829edo 830edo →
Prime factorization 829 (prime)
Step size 1.44753 ¢ 
Fifth 485\829 (702.051 ¢)
Semitones (A1:m2) 79:62 (114.4 ¢ : 89.75 ¢)
Consistency limit 11
Distinct consistency limit 11

Template:EDO intro

Theory

829edo is consistent to the 11-odd-limit. The equal temperament tempers out 4375/4374, [-25 6 -3 8⟩, and [16 -9 -8 6⟩ in the 7-limit; 41503/41472, 200704/200475, and 3750705/3748096 in the 11-limit. It supports squarschmidt, senior and acrokleismic.

Prime harmonics

Approximation of prime harmonics in 829edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000 +0.096 +0.176 -0.430 +0.190 +0.486 +0.714 +0.678 -0.048 -0.385 -0.042
Relative (%) +0.0 +6.6 +12.2 -29.7 +13.1 +33.5 +49.3 +46.8 -3.3 -26.6 -2.9
Steps
(reduced) 		829
(0) 		1314
(485) 		1925
(267) 		2327
(669) 		2868
(381) 		3068
(581) 		3389
(73) 		3522
(206) 		3750
(434) 		4027
(711) 		4107
(791)

Subsets and supersets

829edo is the 145th prime edo.

Regular temperament properties

Subgroup Comma List Mapping Optimal
8ve Stretch (¢) 		Tuning Error
Absolute (¢) Relative (%)
2.3 [1314 -829⟩ [⟨829 1314]] -0.0302 0.0302 2.09
2.3.5 [39 -29 3⟩, [61 4 -29⟩ [⟨829 1314 1925]] -0.0454 0.0327 2.26
2.3.5.7 4375/4374, [-25 6 -3 8⟩, [16 -9 -8 6⟩ [⟨829 1314 1925 2327]] +0.0043 0.0906 6.25
2.3.5.7.11 4375/4374, 41503/41472, 200704/200475, 3750705/3748096 [⟨829 1314 1925 2327 2868]] -0.0076 0.0844 5.83
2.3.5.7.11.13 4096/4095, 4375/4374, 4459/4455, 47432/47385, 59535/59488 [⟨829 1314 1925 2327 2868 3068]] -0.0282 0.0898 6.20

Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per 8ve 		Generator* Cents* Associated
Ratio* 		Temperaments
1 218\829 315.561 6/5 Acrokleismic
1 223\829 322.799 3087/2560 Senior / seniority
1 274\829 396.622 98304/78125 Squarschmidt
1 391\829 565.983 59049/40960 Tricot

* octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct

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