320edo: Difference between revisions

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Rank-2 temperaments: new mercury notated
Improve intro and +divisors
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{{Infobox ET}}
{{Infobox ET}}
The '''320 equal divisions of the octave''' ('''320edo'''), or the '''320(-tone) equal temperament''' ('''320tet''', '''320et''') when viewed from a [[regular temperament]] perspective, divides the [[octave]] into 320 [[equal]] parts of precisely 3.75 [[cent]]s each.
{{EDO intro|320}}


== Theory ==
== Theory ==
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=== Prime harmonics ===
=== Prime harmonics ===
{{Harmonics in equal|320|intervals=prime|columns=11}}
{{Harmonics in equal|320|intervals=prime|columns=11}}
=== Divisors ===
Since 320 factors into 2<sup>6</sup> × 5, 320edo has subset edos {{EDOs| 2, 4, 5, 10, 16, 20, 32, 40, 64, 80, and 160 }}.


== Regular temperament properties ==
== Regular temperament properties ==
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! 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]] (¢)
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{| class="wikitable center-all left-5"
{| class="wikitable center-all left-5"
|+Table of rank-2 temperaments by generator
|+Table of rank-2 temperaments by generator
! Periods<br>per Octave
! Periods<br>per 8ve
! Generator<br>(Reduced)
! Generator<br>(Reduced)
! Cents<br>(Reduced)
! Cents<br>(Reduced)
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| [[Untriton]] (5-limit)
| [[Untriton]] (5-limit)
|-
|-
|1
| 1
|93\320
| 93\320
|348.75
| 348.75
|6144/3757
| 6144/3757
|[[Hectosaros leap week]] (no-5, no-11)
| [[Hectosaros leap week]]
|-
|-
| 2
| 2
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| [[Decal]]
| [[Decal]]
|-
|-
|80
| 80
|99\320<br>(3\320)
| 99\320<br>(3\320)
|371.25<br>(11.25)
| 371.25<br>(11.25)
|2275/1836<br>(?)
| 2275/1836<br>(?)
|[[Mercury]]
| [[Mercury]]
|-
|-
| 80
| 80
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|}
|}


[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
[[Category:Varuna]]
[[Category:Varuna]]
[[Category:Werckismic]]
[[Category:Werckismic]]