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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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== 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. | 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. | In the 7-limit, 482edo provides excellent tuning for the [[tertiaseptal]] temperament. | ||
=== Prime harmonics === | |||
{{Harmonics in equal|482}} | |||
== 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]] | ||
! rowspan="2" |[[Mapping]] | ! rowspan="2" | [[Mapping]] | ||
! rowspan="2" |Optimal | ! rowspan="2" | Optimal<br>8ve stretch (¢) | ||
8ve stretch (¢) | ! colspan="2" | Tuning error | ||
! 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 }} | ||
|[{{val| 482 764 1119}}] | | [{{val| 482 764 1119}}] | ||
|0. | | 0.0353 | ||
|0. | | 0.0587 | ||
| | | | ||
|- | |- | ||
|2.3.5.7 | | 2.3.5.7 | ||
| | | {{monzo| -6 3 9 -7}}, {{monzo| -26 -1 1 9 }}, {{monzo| 8 -20 9 1 }} | ||
|[{{val| 482 764 1119 1353}}] | | [{{val| 482 764 1119 1353 }}] | ||
|0. | | 0.0587 | ||
|0. | | 0.1018 | ||
|4. | | 4.09 | ||
|- | |- | ||
|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}}] | | [{{val| 482 764 1119 1353 1667 }}] | ||
|0. | | 0.1111 | ||
|0. | | 0.1389 | ||
| | | | ||
|- | |- | ||
|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 | ||
|[{{val| 482 764 1119 1353 1667 1784}}] | | [{{val| 482 764 1119 1353 1667 1784 }}] | ||
|0. | | 0.0491 | ||
|0. | | 0.1880 | ||
| | | | ||
|} | |} | ||
[[Category:Equal divisions of the octave]] | |||
Revision as of 17:11, 22 April 2022
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.
In the 7-limit, 482edo provides excellent tuning for the tertiaseptal temperament.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | +0.12 | -0.42 | -0.36 | -1.11 | +0.97 | -0.39 | +1.24 | -0.89 | +1.13 | +0.19 |
| Relative (%) | +0.0 | +4.8 | -16.9 | -14.5 | -44.6 | +38.8 | -15.7 | +49.9 | -35.7 | +45.3 | +7.7 | |
| Steps (reduced) |
482 (0) |
764 (282) |
1119 (155) |
1353 (389) |
1667 (221) |
1784 (338) |
1970 (42) |
2048 (120) |
2180 (252) |
2342 (414) |
2388 (460) | |
Regular temperament properties
| Subgroup | Comma list | Mapping | Optimal 8ve stretch (¢) |
Tuning error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3.5 | [24 -21 4⟩, [-59 5 22⟩ | [⟨482 764 1119]] | 0.0353 | 0.0587 | |
| 2.3.5.7 | [-6 3 9 -7⟩, [-26 -1 1 9⟩, [8 -20 9 1⟩ | [⟨482 764 1119 1353]] | 0.0587 | 0.1018 | 4.09 |
| 2.3.5.7.11 | 2401/2400, 9801/9800, 19712/19683, 65625/65536 | [⟨482 764 1119 1353 1667]] | 0.1111 | 0.1389 | |
| 2.3.5.7.11.13 | 625/624, 847/845, 2401/2400, 9801/9800, 35750/35721 | [⟨482 764 1119 1353 1667 1784]] | 0.0491 | 0.1880 | |