482edo: Difference between revisions

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{{novelty}}{{stub}}{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|482}}
{{ED intro}}


== 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
|-
|- style="border-top: double;"
| 2.3.5.7.11.13
| 2.3.5.7.11.13
| 676/675, 1001/1000, 1716/1715, 10648/10647, 65625/65536
| 676/675, 1001/1000, 1716/1715, 10648/10647, 65625/65536
| [{{val| 482 764 1119 1353 1667 1783 }}] (482f)
| {{mapping| 482 764 1119 1353 1667 1783 }} (482f)
| +0.1612
| +0.1612
| 0.1692
| 0.1692
| 6.80
| 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
| [{{val| 482 764 1119 1353 1667 1784 }}] (482)
| {{mapping| 482 764 1119 1353 1667 1784 }} (482)
| +0.0491
| +0.0491
| 0.1880
| 0.1880
| 7.55
| 7.55
|}
|}
[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->

Latest revision as of 23:04, 20 February 2025

← 481edo 482edo 483edo →
Prime factorization 2 × 241
Step size 2.48963 ¢ 
Fifth 282\482 (702.075 ¢) (→ 141\241)
Semitones (A1:m2) 46:36 (114.5 ¢ : 89.63 ¢)
Consistency limit 9
Distinct consistency limit 9

482 equal divisions of the octave (abbreviated 482edo or 482ed2), also called 482-tone equal temperament (482tet) or 482 equal temperament (482et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 482 equal parts of about 2.49 ¢ each. Each step represents a frequency ratio of 21/482, or the 482nd root of 2.

Theory

482edo has good approximations of harmonics 3, 5, 7, 17, 31, and 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

Approximation of prime harmonics in 482edo
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)

Subsets and supersets

Since 482 factors into 2 × 241, 482edo contains 2edo and 241edo as subsets.

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 4.33
2.3.5.7 2401/2400, 65625/65536, [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 5.58
2.3.5.7.11.13 676/675, 1001/1000, 1716/1715, 10648/10647, 65625/65536 [⟨482 764 1119 1353 1667 1783]] (482f) +0.1612 0.1692 6.80
2.3.5.7.11.13 625/624, 847/845, 2401/2400, 9801/9800, 35750/35721 [⟨482 764 1119 1353 1667 1784]] (482) +0.0491 0.1880 7.55
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