469edo: Difference between revisions
Created page with "{{Infobox ET}} {{EDO intro|469}} == Theory == 469et is only consistent to the 5-odd-limit and the error of the harmonic 3 is quite large. It can be considered..." |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
469et is only consistent to the [[5-odd-limit]] and the error of the [[harmonic]] [[3/1|3]] is quite large. It can be considered for the 2.9.5.7.13.17 [[subgroup]], tempering out [[2601/2600]], 7616/7605, [[5832/5831]], 60112/60025 and 265625/264992. It [[support]]s [[gravity]] and [[french decimal]]. | 469et is only [[consistent]] to the [[5-odd-limit]] and the error of the [[harmonic]] [[3/1|3]] is quite large. It can be considered for the 2.9.5.7.13.17 [[subgroup]], tempering out [[2601/2600]], 7616/7605, [[5832/5831]], 60112/60025 and 265625/264992. It [[support]]s [[gravity]] and [[french decimal]]. | ||
=== Odd harmonics === | === Odd harmonics === | ||
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=== Subsets and supersets === | === Subsets and supersets === | ||
469 factors into 7 × 67, | Since 469 factors into 7 × 67, 469edo has [[7edo]] and [[67edo]] as its subset edos. [[938edo]], which doubles it, gives a good correction to the harmonics 3 and 5. | ||
== Regular temperament properties == | == Regular temperament properties == | ||
{| class="wikitable center-4 center-5 center-6" | {| class="wikitable center-4 center-5 center-6" | ||
|- | |- | ||
|2.9 | ! rowspan="2" | [[Subgroup]] | ||
|{{monzo|1487 -469}} | ! rowspan="2" | [[Comma list]] | ||
|{{mapping|469 1487}} | ! rowspan="2" | [[Mapping]] | ||
| | ! rowspan="2" | Optimal<br />8ve stretch (¢) | ||
! colspan="2" | Tuning error | |||
|- | |||
! [[TE error|Absolute]] (¢) | |||
! [[TE simple badness|Relative]] (%) | |||
|- | |||
| 2.9 | |||
| {{monzo| 1487 -469 }} | |||
| {{mapping| 469 1487 }} | |||
| −0.1232 | |||
| 0.1232 | | 0.1232 | ||
| 4.82 | | 4.82 | ||
|- | |- | ||
|2.9.5 | | 2.9.5 | ||
|{{monzo|38 -1 -15}}, {{monzo|13 -29 34}} | | {{monzo| 38 -1 -15 }}, {{monzo| 13 -29 34 }} | ||
|{{mapping|469 1487 1089}} | | {{mapping| 469 1487 1089 }} | ||
| | | −0.0879 | ||
| 0.1122 | | 0.1122 | ||
| 4.39 | | 4.39 | ||
|} | |} | ||