1429edo: Difference between revisions

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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|1429}}
{{EDO intro|1429}}
== Theory ==
== Theory ==
1429et tempers out [[4375/4374]] in the 7-limit; 2657205/2656192, 759375/758912, 1953125/1951488, 2359296/2358125, [[131072/130977]], 369140625/369098752, 184549376/184528125, 645922816/645700815 and 3294225/3294172 in the 11-limit. It supports the [[gross]] temperament and the [[trillium]] temperament.
1429et tempers out [[4375/4374]] in the 7-limit; [[131072/130977]], 759375/758912, 1953125/1951488, 2359296/2358125, 2657205/2656192, and 3294225/3294172 in the 11-limit; [[2080/2079]], [[4096/4095]], [[4225/4224]], 78125/78078, and [[123201/123200]] in the 13-limit; [[2500/2499]], [[5832/5831]], [[11016/11011]], and [[12376/12375]] in the 17-limit. It supports the [[gross]] temperament and provides the [[optimal patent val]] for the 11- and 13-limit [[trillium]] temperament.
===Subsets and supersets===
 
=== Prime harmonics ===
{{Harmonics in equal|1429}}
 
=== Subsets and supersets ===
1429edo is the 226th [[prime edo]].
1429edo is the 226th [[prime edo]].
===Prime harmonics===
{{Harmonics in equal|1429}}


==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|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]] (¢)
![[TE simple badness|Relative]] (%)
! [[TE simple badness|Relative]] (%)
|-
|-
|2.3
| 2.3
|{{monzo|2265 -1429}}
| {{monzo| 2265 -1429 }}
|{{val|1429 2265}}
| {{mapping| 1429 2265 }}
| -0.0235
| -0.0235
| 0.0234
| 0.0234
| 2.80
| 2.80
|-
|-
|2.3.5
| 2.3.5
|{{monzo|39 -29 3}}, {{monzo|-66 -36 53}}
| {{monzo| 39 -29 3 }}, {{monzo| -66 -36 53 }}
|{{val|1429 2265 3318}}
| {{mapping| 1429 2265 3318 }}
| -0.0114
| -0.0114
| 0.0257
| 0.0257
| 3.06
| 3.06
|-
|-
|2.3.5.7
| 2.3.5.7
|4375/4374, {{monzo|41 -15 -5 -2}}, {{monzo|-16 12 12 -11}}
| 4375/4374, {{monzo| 26 4 -3 -14 }}, {{monzo| 40 -22 -1 -1 }}
|{{val|1429 2265 3318 4012}}
| {{mapping| 1429 2265 3318 4012 }}
| -0.0302
| -0.0302
| 0.0395
| 0.0395
| 4.70
| 4.70
|-
|-
|2.3.5.7.11
| 2.3.5.7.11
|4375/4374, 131072/130977, 759375/758912, 3294225/3294172
| 4375/4374, 131072/130977, 759375/758912, 3294225/3294172
|{{val|1429 2265 3318 4012 4944}}
| {{mapping| 1429 2265 3318 4012 4944 }}
| -0.0471
| -0.0471
| 0.0488
| 0.0488
| 5.81
| 5.81
|-
|-
|2.3.5.7.11.13
| 2.3.5.7.11.13
|2080/2079, 4225/4224, 59319/59290, 67392/67375, 91125/91091, 27227340/27217619
| 2080/2079, 4096/4095, 4375/4374, 78125/78078, 3294225/3294172
|{{val|1429 2265 3318 4012 4944 5288}}
| {{mapping| 1429 2265 3318 4012 4944 5288 }}
| -0.0420
| -0.0420
| 0.0460
| 0.0460
| 5.48
| 5.48
|-
|-
|2.3.5.7.11.13.17
| 2.3.5.7.11.13.17
|2080/2079, 2500/2499, 4225/4224, 12376/12375, 14875/14872, 108086/108045, 149175/149072, 1783600/1783419
| 2080/2079, 2500/2499, 4096/4095, 4375/4374, 11016/11011, 108086/108045
|{{val|1429 2265 3318 4012 4944 5288 5841}}
| {{mapping| 1429 2265 3318 4012 4944 5288 5841 }}
| -0.0364
| -0.0364
| 0.0447
| 0.0447
Line 66: Line 69:
|+Table of rank-2 temperaments by generator
|+Table of rank-2 temperaments by generator
! Periods<br>per 8ve
! Periods<br>per 8ve
! Generator<br>(reduced)
! Generator*
! Cents<br>(reduced)
! Cents*
! Associated<br>ratio
! Associated<br>Ratio
! Temperaments
! Temperaments
|-
|-
|1
| 1
|109\1429
| 109\1429
|91.533
| 91.533
|{{monzo|144 -22 -47}}
| {{monzo| 144 -22 -47 }}
|[[Gross]]
| [[Gross]]
|-
|-
|1
| 1
|674\1429
| 674\1429
|565.990
| 565.990
|25/18
| 25/18
|[[Tricot]]
| [[Trillium]]
|}
|}
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct


==Scales==
== Scales ==
* [[Gross13]]
* [[Gross13]]
== Music ==
== Music ==
* [https://www.youtube.com/watch?v=ttQVdzSy96M Gross Pattern] by Francium
; [[User:Francium|Francium]]
* [https://www.youtube.com/watch?v=ttQVdzSy96M ''Gross Pattern''] (2023)

Revision as of 08:04, 17 October 2023

← 1428edo 1429edo 1430edo →
Prime factorization 1429 (prime)
Step size 0.839748 ¢ 
Fifth 836\1429 (702.029 ¢)
Semitones (A1:m2) 136:107 (114.2 ¢ : 89.85 ¢)
Consistency limit 9
Distinct consistency limit 9

Template:EDO intro

Theory

1429et tempers out 4375/4374 in the 7-limit; 131072/130977, 759375/758912, 1953125/1951488, 2359296/2358125, 2657205/2656192, and 3294225/3294172 in the 11-limit; 2080/2079, 4096/4095, 4225/4224, 78125/78078, and 123201/123200 in the 13-limit; 2500/2499, 5832/5831, 11016/11011, and 12376/12375 in the 17-limit. It supports the gross temperament and provides the optimal patent val for the 11- and 13-limit trillium temperament.

Prime harmonics

Approximation of prime harmonics in 1429edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000 +0.074 -0.030 +0.243 +0.397 +0.060 +0.013 -0.242 -0.143 -0.046 +0.381
Relative (%) +0.0 +8.9 -3.5 +29.0 +47.2 +7.2 +1.6 -28.8 -17.0 -5.5 +45.3
Steps
(reduced) 		1429
(0) 		2265
(836) 		3318
(460) 		4012
(1154) 		4944
(657) 		5288
(1001) 		5841
(125) 		6070
(354) 		6464
(748) 		6942
(1226) 		7080
(1364)

Subsets and supersets

1429edo is the 226th prime edo.

Regular temperament properties

Subgroup Comma List Mapping Optimal
8ve Stretch (¢) 		Tuning Error
Absolute (¢) Relative (%)
2.3 [2265 -1429⟩ [⟨1429 2265]] -0.0235 0.0234 2.80
2.3.5 [39 -29 3⟩, [-66 -36 53⟩ [⟨1429 2265 3318]] -0.0114 0.0257 3.06
2.3.5.7 4375/4374, [26 4 -3 -14⟩, [40 -22 -1 -1⟩ [⟨1429 2265 3318 4012]] -0.0302 0.0395 4.70
2.3.5.7.11 4375/4374, 131072/130977, 759375/758912, 3294225/3294172 [⟨1429 2265 3318 4012 4944]] -0.0471 0.0488 5.81
2.3.5.7.11.13 2080/2079, 4096/4095, 4375/4374, 78125/78078, 3294225/3294172 [⟨1429 2265 3318 4012 4944 5288]] -0.0420 0.0460 5.48
2.3.5.7.11.13.17 2080/2079, 2500/2499, 4096/4095, 4375/4374, 11016/11011, 108086/108045 [⟨1429 2265 3318 4012 4944 5288 5841]] -0.0364 0.0447 5.32

Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per 8ve 		Generator* Cents* Associated
Ratio 		Temperaments
1 109\1429 91.533 [144 -22 -47⟩ Gross
1 674\1429 565.990 25/18 Trillium

* octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct

Scales

Music

Francium
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