482edo: Difference between revisions
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{{ | {{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. | 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 | ! rowspan="2" | Optimal<br>8ve Stretch (¢) | ||
! colspan="2" | Tuning | ! colspan="2" | Tuning Error | ||
|- | |- | ||
![[TE error|Absolute]] (¢) | ! [[TE error|Absolute]] (¢) | ||
![[TE simple badness|Relative]] (%) | ! [[TE simple badness|Relative]] (%) | ||
|- | |- | ||
| 2.3.5 | | 2.3.5 | ||
| {{monzo| 24 -21 4 }}, {{monzo| -59 5 22 }} | | {{monzo| 24 -21 4 }}, {{monzo| -59 5 22 }} | ||
| | | {{mapping| 482 764 1119 }} | ||
| +0.0353 | | +0.0353 | ||
| 0.0587 | | 0.0587 | ||
| Line 29: | Line 34: | ||
| 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 }} | ||
| | | {{mapping| 482 764 1119 1353 }} | ||
| +0.0587 | | +0.0587 | ||
| 0.1018 | | 0.1018 | ||
| Line 36: | Line 41: | ||
| 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 | ||
| | | {{mapping| 482 764 1119 1353 1667 }} | ||
| +0.1111 | | +0.1111 | ||
| 0.1389 | | 0.1389 | ||
| 5.58 | | 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 | | 2.3.5.7.11.13 | ||
| 625/624, 847/845, 2401/2400, 9801/9800, 35750/35721 | | 625/624, 847/845, 2401/2400, 9801/9800, 35750/35721 | ||
| | | {{mapping| 482 764 1119 1353 1667 1784 }} (482) | ||
| +0.0491 | | +0.0491 | ||
| 0.1880 | | 0.1880 | ||
| 7.55 | | 7.55 | ||
|} | |} | ||