426edo: Difference between revisions
Created page with "{{Infobox ET}} {{EDO intro|426}} == Theory == 426et is consistent to the 9-odd-limit. Using the patent val, it tempers out 283115520/282475249, 48828125/48771072, 65625..." |
Review |
||
| Line 3: | Line 3: | ||
== Theory == | == Theory == | ||
426edo is [[consistent]] to the [[9-odd-limit]]. Using the [[patent val]], the equal temperament [[tempering out|tempers out]] [[65625/65536]], 118098/117649, [[250047/250000]] in the 7-limit; [[540/539]], [[4000/3993]], [[9801/9800]], 24057/24010, 137781/137500, and 151263/151250 in the 11-limit. It [[support]]s the 5-limit version of [[untriton]]. | |||
=== Prime harmonics === | === Prime harmonics === | ||
| Line 9: | Line 9: | ||
=== Subsets and supersets === | === Subsets and supersets === | ||
426 factors into 2 × 3 × 71, | Since 426 factors into 2 × 3 × 71, 426edo has subset edos {{EDOs| 2, 3, 6, 71, 142, and 213 }}. | ||
== 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|-225 142}} | | {{monzo| -225 142 }} | ||
|{{mapping|426 675}} | | {{mapping| 426 675 }} | ||
| 0.1724 | | +0.1724 | ||
| 0.1724 | | 0.1724 | ||
| 6.12 | | 6.12 | ||
|- | |- | ||
|2.3.5 | | 2.3.5 | ||
|{{monzo|-7 22 -12}}, {{monzo|-44 -3 21}} | | {{monzo| -7 22 -12 }}, {{monzo| -44 -3 21 }} | ||
|{{mapping|426 675 989}} | | {{mapping| 426 675 989 }} | ||
| 0.1721 | | +0.1721 | ||
| 0.1408 | | 0.1408 | ||
| 5.00 | | 5.00 | ||
|- | |- | ||
|2.3.5.7 | | 2.3.5.7 | ||
| | | 65625/65536, 118098/117649, 250047/250000 | ||
|{{mapping|426 675 989 1196}} | | {{mapping| 426 675 989 1196 }} | ||
| 0.1123 | | +0.1123 | ||
| 0.1600 | | 0.1600 | ||
| 5.68 | | 5.68 | ||
| Line 53: | Line 53: | ||
! Temperaments | ! Temperaments | ||
|- | |- | ||
|1 | | 1 | ||
|199\426 | | 199\426 | ||
|560.56 | | 560.56 | ||
|864/625 | | 864/625 | ||
|[[Whoosh]] | | [[Whoosh]] | ||
|- | |- | ||
|1 | | 1 | ||
|209\426 | | 209\426 | ||
|588.73 | | 588.73 | ||
| | | 45/32 | ||
|[[Untriton]] | | [[Untriton]] (5-limit) | ||
|- | |- | ||
|3 | | 3 | ||
|137\426<br>(5\426) | | 137\426<br>(5\426) | ||
|385.92<br>(14.08) | | 385.92<br>(14.08) | ||
|5/4<br>( | | 5/4<br>(126/125) | ||
|[[Mutt]] | | [[Mutt]] (7-limit) | ||
|} | |} | ||
<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 | ||