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1429edo: Difference between revisions

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Comma bases; cleanup; clarify the title row of the rank-2 temp table
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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
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|+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)
Retrieved from "https://en.xen.wiki/w/1429edo"