829edo: Difference between revisions
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 == | ||
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 }} | ||
|{{ | | {{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 }} | ||
|{{ | | {{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, | | 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 | ||
| 6.25 | | 6.25 | ||
|- | |- | ||
|2.3.5.7.11 | | 2.3.5.7.11 | ||
|4375/4374, 200704/200475 | | 4375/4374, 41503/41472, 200704/200475, 3750705/3748096 | ||
|{{ | | {{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 | ||
|{{ | | {{mapping| 829 1314 1925 2327 2868 3068 }} | ||
| -0.0282 | | -0.0282 | ||
| 0.0898 | | 0.0898 | ||
| Line 67: | Line 67: | ||
! 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]] / [[ | | [[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 | ||