429edo: 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
| {{monzo| 680 -429 }}
| {{monzo| 680 -429 }}
| {{mapping| 429 680 }}
| {{mapping| 429 680 }}
| -0.0451
| &minus;0.0451
| 0.0451
| 0.0451
| 1.61
| 1.61
Line 56: Line 48:
| 0.1708
| 0.1708
| 6.11
| 6.11
|}
{{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
Line 86: Line 72:
|-
|-
| 3
| 3
| 138\429<br>(5\429)
| 138\429<br />(5\429)
| 386.01<br>(13.99)
| 386.01<br />(13.99)
| 5/4<br>(126/125)
| 5/4<br />(126/125)
| [[Mutt]]
| [[Mutt]]
|}
{{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 02:31, 16 November 2024

← 428edo 429edo 430edo →
Prime factorization 3 × 11 × 13
Step size 2.7972 ¢ 
Fifth 251\429 (702.098 ¢)
Semitones (A1:m2) 41:32 (114.7 ¢ : 89.51 ¢)
Consistency limit 11
Distinct consistency limit 11

Template:EDO intro

Theory

429et is consistent to the 11-odd-limit. The equal temperament tempers out 65625/65536, 250047/250000, and 823543/820125 in the 7-limit; 3025/3024, 12005/11979, 19712/19683, 42875/42768, and 102487/102400 in the 11-limit. It supports vavoom, turkey, counterhanson and aluminium.

Prime harmonics

Approximation of prime harmonics in 429edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.00 +0.14 -0.30 -0.99 -0.27 -1.37 +1.34 -1.01 +1.10 -0.21 -0.98
Relative (%) +0.0 +5.1 -10.7 -35.5 -9.6 -48.9 +47.8 -36.1 +39.2 -7.4 -35.0
Steps
(reduced) 		429
(0) 		680
(251) 		996
(138) 		1204
(346) 		1484
(197) 		1587
(300) 		1754
(38) 		1822
(106) 		1941
(225) 		2084
(368) 		2125
(409)

Subsets and supersets

429 factors into 3 × 11 × 13, with subset edos 3, 11, 13, 33, 39, and 143.

Regular temperament properties

Template:Comma basis begin |- | 2.3 | [680 -429⟩ | [⟨429 680]] | −0.0451 | 0.0451 | 1.61 |- | 2.3.5 | [24 -21 4⟩, [-20 -24 25⟩ | [⟨429 680 996]] | +0.0130 | 0.0900 | 3.22 |- | 2.3.5.7 | 65625/65536, 250047/250000, 823543/820125 | [⟨429 680 996 1204]] | +0.0982 | 0.1670 | 5.97 |- | 2.3.5.7.11 | 3025/3024, 12005/11979, 19712/19683, 102487/102400 | [⟨429 680 996 1204 1484]] | +0.0941 | 0.1496 | 5.35 |- | 2.3.5.7.11.13 | 676/675, 1001/1000, 3025/3024, 12005/11979, 19712/19683 | [⟨429 680 996 1204 1484 1587]] | +0.1400 | 0.1708 | 6.11 Template:Comma basis end

Rank-2 temperaments

Template:Rank-2 begin |- | 1 | 40\429 | 111.89 | 16/15 | Vavoom |- | 1 | 113\429 | 316.08 | 6/5 | Counterhanson |- | 1 | 170\429 | 475.52 | 320/243 | Vulture |- | 3 | 138\429
(5\429) | 386.01
(13.99) | 5/4
(126/125) | Mutt Template:Rank-2 end Template:Orf

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