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352edo: Difference between revisions

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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..."
 
m Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"
 
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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|352}}
{{ED intro}}


== Theory ==
== Theory ==
352et is consistent to the [[7-odd-limit]]. Using the patent val, it tempers out 156250000/155649627, [[33554432/33480783]], 359661568/358722675 and [[2401/2400]] in the 7-limit; [[214990848/214358881]], 78121827/77948684, 100663296/100656875, 10333575/10307264, 2097152/2096325, 1366875/1362944, 125000/124509, [[536870912/535869675]], 151263/151250, 104857600/104825259, [[131072/130977]], 1265625/1261568, [[200704/200475]], 5788125/5767168, [[19712/19683]], 1479016/1476225, [[3025/3024]], [[41503/41472]], [[532400/531441]] and 67110351/67108864 in the 11-limit. It [[support]]s [[world calendar]], [[septiruthenic]], [[enki]] and [[fortune]].
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}}. [[2112edo]], which sextuples it, gives a good correction to the harmonic 11.
352 factors into {{factorisation|352}}, 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" |[[Comma list|Comma List]]
! rowspan="2" |[[Mapping]]
! rowspan="2" |Optimal<br>8ve Stretch (¢)
! colspan="2" |Tuning Error
|-
![[TE error|Absolute]] (¢)
![[TE simple badness|Relative]] (%)
|-
|-
|2.3
! rowspan="2" | [[Subgroup]]
|{{monzo|279 -176}}
! rowspan="2" | [[Comma list]]
|{{mapping|352 558}}
! rowspan="2" | [[Mapping]]
| -0.1002
! rowspan="2" | Optimal<br />8ve stretch (¢)
| 0.1002
! colspan="2" | Tuning error
| 2.94
|-
|-
|2.3.5
! [[TE error|Absolute]] (¢)
|15625/15552, {{monzo|95 -57 -2}}   
! [[TE simple badness|Relative]] (%)
|{{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, 359661568/358722675
| 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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=== Rank-2 temperaments ===
=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
{| class="wikitable center-all left-5"
|+Table of rank-2 temperaments by generator
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
! Periods<br>per 8ve
|-
! Generator<br>(reduced)*
! Periods<br />per 8ve
! Cents<br>(reduced)*
! Generator*
! Associated<br>Ratio*
! Cents*
! Associated<br />ratio*
! Temperaments
! Temperaments
|-
|-
|1
| 1
|35\352
| 35\352
|119.32
| 119.32
|15/14
| 15/14
|[[Septidiasemi]]
| [[Septidiasemi]]
|-
| 1
| 65\352
| 221.59
| 8388608/7381125
| [[Fortune]]
|-
|-
|1
| 1
|65\352
| 93\352
|221.59
| 317.05
|8388608/7381125
| 6/5
|[[Fortune]]
| [[Hanson]]
|-
|-
|1
| 1
|93\352
| 103\352
|317.05
| 351.14
|6/5
| 49/40
|[[Hanson]]
| [[Newt]]
|-
|-
|1
| 4
|103\352
| 93\352<br />(5\352)
|351.14
| 317.05<br />(17.05)
|49/40
| 6/5<br />(126/125)
|[[Newt]]
| [[Quadritikleismic]]
|-
|-
|4
| 4
|93\352<br>(5\352)
| 117\352<br />(29\352)
|317.05<br>(17.05)
| 398.86<br />(98.86)
|6/5<br>(126/125)
| 34/27<br />(18/17)
|[[Quadritikleismic]]
| [[World calendar]]
|}
|}
 
<nowiki />* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if 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
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