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482edo: Difference between revisions

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Created page with "{{EDO intro|482}} == Theory == {{Harmonics in equal|482}} Prime harmonics with less than 17% (1 standard deviation error) in 482edo are 3, 5, 7, 17, 31, 37. 11 and 13 have ra..."
 
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{{EDO intro|482}}
{{Infobox ET}}
{{ED intro}}


== Theory ==
== Theory ==
482edo has good approximations of [[harmonic]]s [[3/1|3]], [[5/1|5]], [[7/1|7]], [[17/1|17]], [[31/1|31]], and [[37/1|37]]. [[11/1|11]] and [[13/1|13]] have rather large errors, but they are reasonable to work with.
In the 7-limit, 482edo provides excellent tuning for the [[tertiaseptal]] temperament.
=== Prime harmonics ===
{{Harmonics in equal|482}}
{{Harmonics in equal|482}}
Prime harmonics with less than 17% (1 standard deviation error) in 482edo are 3, 5, 7, 17, 31, 37. 11 and 13 have rather large errors, but they are reasonable to work with.


In the 7-limit, 482edo provides excellent tuning for the [[tertiaseptal]] temperament.  
=== Subsets and supersets ===
Since 482 factors into {{factorization|482}}, 482edo contains [[2edo]] and [[241edo]] as subsets.  


== 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]]
! rowspan="2" |[[Mapping]]
! rowspan="2" |Optimal
8ve stretch (¢)
! colspan="2" |Tuning error
|-
|-
![[TE error|Absolute]] (¢)
! rowspan="2" | [[Subgroup]]
![[TE simple badness|Relative]] (%)
! rowspan="2" | [[Comma list|Comma List]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br>8ve Stretch (¢)
! colspan="2" | Tuning Error
|-
|-
|2.3.5
! [[TE error|Absolute]] (¢)
|[24, -21, 4⟩, [-59, 5, 22⟩
! [[TE simple badness|Relative]] (%)
|[{{val| 482 764 1119}}]
|0.035344
|0.058672
|
|-
|-
|2.3.5.7
| 2.3.5
|[-6, 3, 9, -7⟩, [-26, -1, 1, 9⟩, [8, -20, 9, 1⟩
| {{monzo| 24 -21 4 }}, {{monzo| -59 5 22 }}
|[{{val| 482 764 1119 1353}}]
| {{mapping| 482 764 1119 }}
|0.058672
| +0.0353
|0.101802
| 0.0587
|4.089
| 4.33
|-
|-
|2.3.5.7.11
| 2.3.5.7
|2401/2400, 9801/9800, 19712/19683, 65625/65536
| 2401/2400, 65625/65536, {{monzo| 8 -20 9 1 }}
|[{{val| 482 764 1119 1353 1667}}]
| {{mapping| 482 764 1119 1353 }}
|0.111136
| +0.0587
|0.138937
| 0.1018
|
| 4.09
|-
|-
|2.3.5.7.11.13
| 2.3.5.7.11
|625/624, 847/845, 2401/2400, 9801/9800, 35750/35721
| 2401/2400, 9801/9800, 19712/19683, 65625/65536
|[{{val| 482 764 1119 1353 1667 1784}}]
| {{mapping| 482 764 1119 1353 1667 }}
|0.049077
| +0.1111
|0.187961
| 0.1389
|
| 5.58
|- style="border-top: double;"
| 2.3.5.7.11.13
| 676/675, 1001/1000, 1716/1715, 10648/10647, 65625/65536
| {{mapping| 482 764 1119 1353 1667 1783 }} (482f)
| +0.1612
| 0.1692
| 6.80
|- style="border-top: double;"
| 2.3.5.7.11.13
| 625/624, 847/845, 2401/2400, 9801/9800, 35750/35721
| {{mapping| 482 764 1119 1353 1667 1784 }} (482)
| +0.0491
| 0.1880
| 7.55
|}
|}
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