482edo: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older editNewer edit →
VisualWikitext
BudjarnLambeth (talk | contribs)
autopatrolled, emailconfirmed
18,279 edits
mNo edit summary
Cleanup; +subsets and supersets
Line 3: Line 3:


== 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.  
Line 9: Line 9:
=== 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]] (¢)
Line 23: Line 26:
| 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
Line 30: Line 33:
| 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
Line 37: Line 40:
| 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 -->

Revision as of 06:20, 3 November 2023

← 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

Template:EDO intro

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
Retrieved from "https://en.xen.wiki/index.php?title=482edo&oldid=126807"