352edo: Difference between revisions
Created page with "{{Infobox ET}} {{EDO intro|352}} == Theory == 352et is consistent to the 7-odd-limit. Using the patent val, it tempers out 156250000/155649627, 33554432/33480783, 359..." |
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== Theory == | == Theory == | ||
352edo is [[consistent]] to the [[7-odd-limit]]. Using the [[patent val]], the equal temperament [[tempering out|tempers out]] [[2401/2400]], [[15625/15552]], [[390625/388962]], and [[33554432/33480783]] in the 7-limit; [[3025/3024]], 4375/4356, 14700/14641, [[19712/19683]], [[41503/41472]], and [[131072/130977]] in the 11-limit. It [[support]]s [[newt]], [[world calendar]], [[septiruthenic]], [[enki]] and [[fortune]]. | |||
=== Prime harmonics === | === Prime harmonics === | ||
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=== Subsets and supersets === | === Subsets and supersets === | ||
352 factors into 2<sup>5</sup> × 11, with subset edos {{EDOs|2, 4, 8, 11, 16, 22, 32, 44, 88, and 176}} | 352 factors into 2<sup>5</sup> × 11, with subset edos {{EDOs| 2, 4, 8, 11, 16, 22, 32, 44, 88, and 176 }}. | ||
== 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 | |||
| 15625/15552, {{monzo| 95 -57 -2 }} | |||
| {{mapping| 352 558 817 }} | |||
|2.3.5 | |||
|15625/15552, {{monzo|95 -57 -2}} | |||
|{{mapping|352 558 817}} | |||
| +0.0891 | | +0.0891 | ||
| 0.2801 | | 0.2801 | ||
| 8.22 | | 8.22 | ||
|- | |- | ||
|2.3.5.7 | | 2.3.5.7 | ||
|2401/2400, 15625/15552, | | 2401/2400, 15625/15552, 33554432/33480783 | ||
|{{mapping|352 558 817 988}} | | {{mapping| 352 558 817 988 }} | ||
| +0.1242 | | +0.1242 | ||
| 0.2500 | | 0.2500 | ||
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|+Table of rank-2 temperaments by generator | |+Table of rank-2 temperaments by generator | ||
! Periods<br>per 8ve | ! Periods<br>per 8ve | ||
! Generator | ! Generator* | ||
! Cents | ! Cents* | ||
! Associated<br>Ratio* | ! Associated<br>Ratio* | ||
! Temperaments | ! Temperaments | ||
|- | |- | ||
|1 | | 1 | ||
|35\352 | | 35\352 | ||
|119.32 | | 119.32 | ||
|15/14 | | 15/14 | ||
|[[Septidiasemi]] | | [[Septidiasemi]] | ||
|- | |- | ||
|1 | | 1 | ||
|65\352 | | 65\352 | ||
|221.59 | | 221.59 | ||
|8388608/7381125 | | 8388608/7381125 | ||
|[[Fortune]] | | [[Fortune]] | ||
|- | |- | ||
|1 | | 1 | ||
|93\352 | | 93\352 | ||
|317.05 | | 317.05 | ||
|6/5 | | 6/5 | ||
|[[Hanson]] | | [[Hanson]] | ||
|- | |- | ||
|1 | | 1 | ||
|103\352 | | 103\352 | ||
|351.14 | | 351.14 | ||
|49/40 | | 49/40 | ||
|[[Newt]] | | [[Newt]] | ||
|- | |- | ||
|4 | | 4 | ||
|93\352<br>(5\352) | | 93\352<br>(5\352) | ||
|317.05<br>(17.05) | | 317.05<br>(17.05) | ||
|6/5<br>(126/125) | | 6/5<br>(126/125) | ||
|[[Quadritikleismic]] | | [[Quadritikleismic]] | ||
|- | |||
| 4 | |||
| 117\352<br>(29\352) | |||
| 398.86<br>(98.86) | |||
| 34/27<br>(18/17) | |||
| [[World calendar]] | |||
|} | |} | ||
<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 | ||