429edo: Difference between revisions
Created page with "{{Infobox ET}} {{EDO intro|429}} == Theory == 429et is consistent to the 11-odd-limit. It tempers out 48828125/48771072, 65625/65536, 250047/250000, 359661568/358..." |
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== Theory == | == Theory == | ||
429et is consistent to the [[11-odd-limit]]. | 429et is [[consistent]] to the [[11-odd-limit]]. The equal temperament [[tempering out|tempers out]] [[65625/65536]], [[250047/250000]], and 823543/820125 in the 7-limit; [[3025/3024]], 12005/11979, [[19712/19683]], 42875/42768, and 102487/102400 in the 11-limit. It [[support]]s [[vavoom]], [[turkey]], [[counterhanson]] and [[aluminium]]. | ||
=== Prime harmonics === | === Prime harmonics === | ||
| Line 13: | Line 13: | ||
== 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|680 -429}} | | {{monzo| 680 -429 }} | ||
|{{mapping|429 680}} | | {{mapping| 429 680 }} | ||
| -0.0451 | | -0.0451 | ||
| 0.0451 | | 0.0451 | ||
| 1.61 | | 1.61 | ||
|- | |- | ||
|2.3.5 | | 2.3.5 | ||
|{{monzo|24 -21 4}}, {{monzo|-20 -24 25}} | | {{monzo| 24 -21 4 }}, {{monzo| -20 -24 25 }} | ||
|{{mapping|429 680 996}} | | {{mapping| 429 680 996 }} | ||
| +0.0130 | | +0.0130 | ||
| 0.0900 | | 0.0900 | ||
| 3.22 | | 3.22 | ||
|- | |- | ||
|2.3.5.7 | | 2.3.5.7 | ||
|250047/250000, 823543/820125 | | 65625/65536, 250047/250000, 823543/820125 | ||
|{{mapping|429 680 996 1204}} | | {{mapping| 429 680 996 1204 }} | ||
| +0.0982 | | +0.0982 | ||
| 0.1670 | | 0.1670 | ||
| 5.97 | | 5.97 | ||
|- | |- | ||
|2.3.5.7.11 | | 2.3.5.7.11 | ||
|3025/3024, | | 3025/3024, 12005/11979, 19712/19683, 102487/102400 | ||
|{{mapping|429 680 996 1204 1484}} | | {{mapping| 429 680 996 1204 1484 }} | ||
| +0.0941 | | +0.0941 | ||
| 0.1496 | | 0.1496 | ||
| 5.35 | | 5.35 | ||
|- | |- | ||
|2.3.5.7.11.13 | | 2.3.5.7.11.13 | ||
|1001/1000 | | 676/675, 1001/1000, 3025/3024, 12005/11979, 19712/19683 | ||
|{{mapping|429 680 996 1204 1484 1587}} | | {{mapping| 429 680 996 1204 1484 1587 }} | ||
| +0.1400 | | +0.1400 | ||
| 0.1708 | | 0.1708 | ||
| Line 67: | Line 67: | ||
! Temperaments | ! Temperaments | ||
|- | |- | ||
|1 | | 1 | ||
|40\429 | | 40\429 | ||
|111.89 | | 111.89 | ||
|16/15 | | 16/15 | ||
|[[Vavoom]] | | [[Vavoom]] | ||
|- | |- | ||
|1 | | 1 | ||
|113\429 | | 113\429 | ||
|316.08 | | 316.08 | ||
|6/5 | | 6/5 | ||
|[[Counterhanson]] | | [[Counterhanson]] | ||
|- | |- | ||
|1 | | 1 | ||
|170\429 | | 170\429 | ||
|475.52 | | 475.52 | ||
|320/243 | | 320/243 | ||
|[[Vulture]] | | [[Vulture]] | ||
|- | |- | ||
|3 | | 3 | ||
|138\429<br>(5\429) | | 138\429<br>(5\429) | ||
|386.01<br>(13.99) | | 386.01<br>(13.99) | ||
|5/4<br>( | | 5/4<br>(126/125) | ||
|[[Mutt]] | | [[Mutt]] | ||
|} | |} | ||
<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 | ||