382edo: Difference between revisions
Created page with "{{Infobox ET}} {{EDO intro|382}} == Theory == 382et is consistent to the 7-odd-limit and the harmonic 3 is about halfway between its steps. Using the patent val, it tempe..." |
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== Theory == | == Theory == | ||
382edo is [[consistent]] to the [[7-odd-limit]], but [[harmonic]]s [[3/1|3]] and [[7/1|7]] are about halfway between its steps. It is also bad at approximating [[11/1|11]], [[13/1|13]], [[15/1|15]], and [[17/1|17]], though its [[5/1|5]], [[9/1|9]], [[19/1|19]], [[21/1|21]], and [[23/1|23]] are good, making it suitable for a 2.9.5.21.19.23 [[subgroup]] interpretation. | |||
Using the [[patent val]] nonetheless, the equal temperament [[tempering out|tempers out]] [[65625/65536]] in the 7-limit; [[540/539]], [[4000/3993]], and [[9801/9800]] in the 11-limit. It [[support]]s [[bastille]]. | |||
=== Odd harmonics === | === Odd harmonics === | ||
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=== Subsets and supersets === | === Subsets and supersets === | ||
382 factors into 2 × 191 with [[2edo]] and [[191edo]] as its subset edos. [[764edo]], which doubles it, gives a good correction to the | 382 factors into 2 × 191 with [[2edo]] and [[191edo]] as its subset edos. [[764edo]], which doubles it, gives a good correction to the harmonics 3, 7, 11, 13, and 17. | ||
== 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]] (%) | ||
|- | |- | ||
|2.9 | | 2.9 | ||
|{{monzo|1211 -382}} | | {{monzo| 1211 -382 }} | ||
|{{mapping|382 1211}} | | {{mapping| 382 1211 }} | ||
| -0.0439 | | -0.0439 | ||
| 0.0439 | | 0.0439 | ||
| 1.40 | | 1.40 | ||
|- | |- | ||
|2.9.5 | | 2.9.5 | ||
|{{monzo|38 -1 -15}}, {{monzo|25 -24 22}} | | {{monzo| 38 -1 -15 }}, {{monzo| 25 -24 22 }} | ||
|{{mapping|382 1211 887}} | | {{mapping| 382 1211 887 }} | ||
| -0.0399 | | -0.0399 | ||
| 0.0363 | | 0.0363 | ||
| 1.16 | | 1.16 | ||
|- | |- | ||
|2.9.5. | | 2.9.5.21 | ||
| | | 4375/4374, 52734375/52706752, {{monzo| 31 0 -2 -6 }} | ||
|{{mapping|382 1211 887 | | {{mapping| 382 1211 887 1678 }} | ||
| | | -0.0552 | ||
| 0. | | 0.0412 | ||
| | | 1.31 | ||
|} | |} | ||