470edo: Difference between revisions
Created page with "{{Infobox ET}} {{EDO intro|470}} == Theory == 470et is enfactored in the 3-limit and only consistent to the 5-odd-limit. Using the patent val, it tempers out 703125..." |
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== Theory == | == Theory == | ||
470 = 5 × 94, and 470edo shares the [[perfect fifth|fifth]] with [[94edo]]. Unlike 94edo, however, 470edo is only [[consistent]] to the [[5-odd-limit]]. Using the [[patent val]], the equal temperament [[tempering out|tempers out]] [[703125/702464]], 823543/820125, and 1500625/1492992 in the 7-limit; [[3025/3024]], [[4000/3993]], [[6250/6237]], [[19712/19683]], and 117649/117128 in the 11-limit. It [[support]]s [[uniwiz]] and [[decimetra]]. | |||
=== Prime harmonics === | === Prime harmonics === | ||
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=== Subsets and supersets === | === Subsets and supersets === | ||
470 factors into 2 × 5 × 47, | Since 470 factors into 2 × 5 × 47, 470edo has subset edos {{EDOs| 2, 5, 10, 47, 94, and 235 }}. | ||
== 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]] (%) | ||
|- | |- | ||
| 2.3.5 | |||
| 1600000/1594323, {{monzo|-77 -10 40}} | |||
| {{mapping| 470 745 1091 }} | |||
|2.3.5 | |||
|1600000/1594323, {{monzo|-77 -10 40}} | |||
|{{mapping|470 745 1091}} | |||
| +0.0759 | | +0.0759 | ||
| 0.1897 | | 0.1897 | ||
| 7.43 | | 7.43 | ||
|- | |- | ||
|2.3.5.7 | | 2.3.5.7 | ||
|1500625/1492992 | | 703125/702464, 1500625/1492992, 1600000/1594323 | ||
|{{mapping|470 745 1091 1319}} | | {{mapping| 470 745 1091 1319 }} | ||
| +0.1608 | | +0.1608 | ||
| 0.2205 | | 0.2205 | ||
| 8.64 | | 8.64 | ||
|- | |- | ||
|2.3.5.7.11 | | 2.3.5.7.11 | ||
|3025/3024, | | 3025/3024, 4000/3993, 19712/19683, 117649/117128 | ||
|{{mapping|470 745 1091 1319 1626}} | | {{mapping| 470 745 1091 1319 1626 }} | ||
| +0.1187 | | +0.1187 | ||
| 0.2144 | | 0.2144 | ||
| 8.40 | | 8.40 | ||
|- | |- | ||
|2.3.5.7.11.13 | | 2.3.5.7.11.13 | ||
|1575/1573, 2080/2079 | | 625/624, 1575/1573, 2080/2079, 13720/13689, 15379/15360 | ||
|{{mapping|470 745 1091 1319 1626 1739}} | | {{mapping| 470 745 1091 1319 1626 1739 }} | ||
| +0.1227 | | +0.1227 | ||
| 0.1959 | | 0.1959 | ||
| 7.67 | | 7.67 | ||
|- | |- | ||
|2.3.5.7.11.13.17 | | 2.3.5.7.11.13.17 | ||
|595/594, | | 595/594, 625/624, 833/832, 1575/1573, 3185/3179, 8624/8619 | ||
|{{mapping|470 745 1091 1319 1626 1739 1921}} | | {{mapping| 470 745 1091 1319 1626 1739 1921 }} | ||
| +0.1148 | | +0.1148 | ||
| 0.1824 | | 0.1824 | ||
| Line 74: | Line 67: | ||
! Temperaments | ! Temperaments | ||
|- | |- | ||
|1 | | 1 | ||
|133\470 | | 133\470 | ||
|339.57 | | 339.57 | ||
|243/200 | | 243/200 | ||
|[[Amity]] | | [[Amity]] (5-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 | ||