426edo: Difference between revisions

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== Regular temperament properties ==
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
{{comma basis begin}}
! rowspan="2" | [[Subgroup]]
! rowspan="2" | [[Comma list|Comma List]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br>8ve Stretch (¢)
! colspan="2" | Tuning Error
|-
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
|-
| 2.3
| 2.3
Line 42: Line 34:
| 0.1600
| 0.1600
| 5.68
| 5.68
|}
{{comma basis end}}


=== Rank-2 temperaments ===
=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
{{rank-2 begin}}
|+Table of rank-2 temperaments by generator
! Periods<br>per 8ve
! Generator*
! Cents*
! Associated<br>Ratio*
! Temperaments
|-
|-
| 1
| 1
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|-
|-
| 3
| 3
| 137\426<br>(5\426)
| 137\426<br />(5\426)
| 385.92<br>(14.08)
| 385.92<br />(14.08)
| 5/4<br>(126/125)
| 5/4<br />(126/125)
| [[Mutt]] (7-limit)
| [[Mutt]] (7-limit)
|}
{{rank-2 end}}
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct
{{orf}}

Revision as of 01:33, 16 November 2024

← 425edo 426edo 427edo →
Prime factorization 2 × 3 × 71
Step size 2.8169 ¢ 
Fifth 249\426 (701.408 ¢) (→ 83\142)
Semitones (A1:m2) 39:33 (109.9 ¢ : 92.96 ¢)
Consistency limit 9
Distinct consistency limit 9

Template:EDO intro

Theory

426edo is consistent to the 9-odd-limit. Using the patent val, the equal temperament tempers out 65625/65536, 118098/117649, 250047/250000 in the 7-limit; 540/539, 4000/3993, 9801/9800, 24057/24010, 137781/137500, and 151263/151250 in the 11-limit. It supports the 5-limit version of untriton.

Prime harmonics

Approximation of prime harmonics in 426edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.00 -0.55 -0.40 +0.19 +0.79 -1.09 -0.73 +1.08 -0.11 -1.41 -1.37
Relative (%) +0.0 -19.4 -14.1 +6.7 +28.2 -38.7 -25.9 +38.3 -3.7 -50.0 -48.8
Steps
(reduced) 		426
(0) 		675
(249) 		989
(137) 		1196
(344) 		1474
(196) 		1576
(298) 		1741
(37) 		1810
(106) 		1927
(223) 		2069
(365) 		2110
(406)

Subsets and supersets

Since 426 factors into 2 × 3 × 71, 426edo has subset edos 2, 3, 6, 71, 142, and 213.

Regular temperament properties

Template:Comma basis begin |- | 2.3 | [-225 142⟩ | [⟨426 675]] | +0.1724 | 0.1724 | 6.12 |- | 2.3.5 | [-7 22 -12⟩, [-44 -3 21⟩ | [⟨426 675 989]] | +0.1721 | 0.1408 | 5.00 |- | 2.3.5.7 | 65625/65536, 118098/117649, 250047/250000 | [⟨426 675 989 1196]] | +0.1123 | 0.1600 | 5.68 Template:Comma basis end

Rank-2 temperaments

Template:Rank-2 begin |- | 1 | 199\426 | 560.56 | 864/625 | Whoosh |- | 1 | 209\426 | 588.73 | 45/32 | Untriton (5-limit) |- | 3 | 137\426
(5\426) | 385.92
(14.08) | 5/4
(126/125) | Mutt (7-limit) Template:Rank-2 end Template:Orf

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