339edo: Difference between revisions
Created page with "{{Infobox ET}} {{EDO intro|339}} == Theory == 339et is only consistent to the 5-odd-limit. It can be used for the 2.3.5.13.19.23.31.41 subgroup, tempering out 780/779..." |
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== Theory == | == Theory == | ||
339edo is [[enfactoring|enfactored]] in the [[3-limit]] with the same tuning as [[113edo]], and is only [[consistent]] to the [[5-odd-limit]]. Using the 339d val ({{val| 339 537 787 '''951''' }}) in the 7-limit and the 339de val ({{val| 339 537 787 '''951''' '''1172''' }}) in the 11-limit, it [[support]]s [[tritriple]]. | |||
It can be used for the 2.3.5.13.19.23.31.41 [[subgroup]], where it [[tempering out|tempers out]] [[621/620]], 780/779, 1026/1025, 1426/1425, 2945/2944, 14391/14375 and 73853/73800. | |||
=== Odd harmonics === | === Odd harmonics === | ||
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=== Subsets and supersets === | === Subsets and supersets === | ||
339 factors into 3 × 113, | Since 339 factors into 3 × 113, 339edo has [[3edo]] and 113edo as its subsets. [[1017edo]], which triples it, gives a good correction to the harmonics 7 and 11. | ||
== 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 | |||
| {{monzo| -13 17 -6 }}, {{monzo| -44 -3 21 }} | |||
| {{mapping| 339 537 787 }} | |||
|2.3.5 | |||
|{{monzo|-13 17 -6}}, {{monzo|-44 -3 21}} | |||
|{{mapping|339 537 787}} | |||
| 0.2930 | | 0.2930 | ||
| 0.2828 | | 0.2828 | ||
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! Temperaments | ! Temperaments | ||
|- | |- | ||
|1 | | 1 | ||
|32\339 | | 32\339 | ||
|113.27 | | 113.27 | ||
|16/15 | | 16/15 | ||
|[[Misneb]] | | [[Misneb]] | ||
|- | |- | ||
|1 | | 1 | ||
|146\339 | | 146\339 | ||
|516.81 | | 516.81 | ||
|27/20 | | 27/20 | ||
|[[Gravity]] | | [[Gravity]] | ||
|- | |- | ||
|1 | | 1 | ||
|158\339 | | 158\339 | ||
|559.29 | | 559.29 | ||
|864/625 | | 864/625 | ||
|[[Tritriple]] (339d) | | [[Tritriple]] (339d) | ||
|} | |} | ||
<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 | ||