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482edo: Difference between revisions

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== Theory ==
== Theory ==
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.
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.  
In the 7-limit, 482edo provides excellent tuning for the [[tertiaseptal]] temperament.  
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=== Prime harmonics ===
=== Prime harmonics ===
{{Harmonics in equal|482}}
{{Harmonics in equal|482}}
=== 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" | [[Subgroup]]
! rowspan="2" | [[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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| 2.3.5
| 2.3.5
| {{monzo| 24 -21 4 }}, {{monzo| -59 5 22 }}
| {{monzo| 24 -21 4 }}, {{monzo| -59 5 22 }}
| [{{val| 482 764 1119 }}]
| {{mapping| 482 764 1119 }}
| +0.0353
| +0.0353
| 0.0587
| 0.0587
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| 2.3.5.7
| 2.3.5.7
| 2401/2400, 65625/65536, {{monzo| 8 -20 9 1 }}
| 2401/2400, 65625/65536, {{monzo| 8 -20 9 1 }}
| [{{val| 482 764 1119 1353 }}]
| {{mapping| 482 764 1119 1353 }}
| +0.0587
| +0.0587
| 0.1018
| 0.1018
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| 2.3.5.7.11
| 2.3.5.7.11
| 2401/2400, 9801/9800, 19712/19683, 65625/65536
| 2401/2400, 9801/9800, 19712/19683, 65625/65536
| [{{val| 482 764 1119 1353 1667 }}]
| {{mapping| 482 764 1119 1353 1667 }}
| +0.1111
| +0.1111
| 0.1389
| 0.1389
| 5.58
| 5.58
|-
|-
| 2.3.5.7.11.13
| style="border-top: double;" | 2.3.5.7.11.13
| 676/675, 1001/1000, 1716/1715, 10648/10647, 65625/65536
| style="border-top: double;" | 676/675, 1001/1000, 1716/1715, 10648/10647, 65625/65536
| [{{val| 482 764 1119 1353 1667 1783 }}] (482f)
| style="border-top: double;" | {{mapping| 482 764 1119 1353 1667 1783 }} (482f)
| +0.1612
| style="border-top: double;" | +0.1612
| 0.1692
| style="border-top: double;" | 0.1692
| 6.80
| style="border-top: double;" | 6.80
|-
|-
| 2.3.5.7.11.13
| style="border-top: double;" | 2.3.5.7.11.13
| 625/624, 847/845, 2401/2400, 9801/9800, 35750/35721
| style="border-top: double;" | 625/624, 847/845, 2401/2400, 9801/9800, 35750/35721
| [{{val| 482 764 1119 1353 1667 1784 }}] (482)
| style="border-top: double;" | {{mapping| 482 764 1119 1353 1667 1784 }} (482)
| +0.0491
| style="border-top: double;" | +0.0491
| 0.1880
| style="border-top: double;" | 0.1880
| 7.55
| style="border-top: double;" | 7.55
|}
|}
[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
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