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1429edo: Difference between revisions

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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|1429}}
{{ED intro}}
 
== 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.
1429edo has a reasonable approximation of the full [[17-limit]]. It is [[consistent]] to the [[9-odd-limit]] with only [[11/10]] barely missing the line. The 11-limit [[TE tuning|optimal tuning]] of the equal temperament is consistent to the 18-integer-limit; however, the 13- and 17-limit optimal tunings, which have less of octave compression, are not, so one might want to keep the compression tight.
 
As an equal temperament, it [[tempering out|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 [[support]]s the [[gross]] temperament and provides the [[optimal patent val]] for the 11- and 13-limit [[alphatrillium]] temperament.  
 
=== Prime harmonics ===
{{Harmonics in equal|1429}}
 
=== Subsets and supersets ===
1429edo is the 226th [[prime edo]].
1429edo is the 226th [[prime edo]].
{{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" |[[Comma list|Comma List]]
! rowspan="2" |[[Mapping]]
! rowspan="2" |Optimal<br>8ve Stretch (¢)
! colspan="2" |Tuning Error
|-
|-
![[TE error|Absolute]] (¢)
! rowspan="2" | [[Subgroup]]
![[TE simple badness|Relative]] (%)
! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br>8ve stretch (¢)
! colspan="2" | Tuning error
|-
|-
|2.3
! [[TE error|Absolute]] (¢)
|{{monzo|2265 -1429}}
! [[TE simple badness|Relative]] (%)
|{{val|1429 2265}}
|-
| -0.0235
| 2.3
| {{Monzo| 2265 -1429 }}
| {{Mapping| 1429 2265 }}
| −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
| 5.32
| 5.32
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=== Rank-2 temperaments ===
=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
{| class="wikitable center-all left-5"
|+Table of rank-2 temperaments by generator
|+ style="font-size: 105%;" | 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
|91.5325
| 91.533
|{{monzo|144 -22 -47}}
| {{monzo| 144 -22 -47 }}
|Gross
| [[Gross]]
|-
| 1
| 674\1429
| 565.990
| 104/75
| [[Alphatrillium]]
|}
|}
<nowiki/>* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
== Scales ==
* [[Gross13]]
== Music ==
; [[Francium]]
* "Gross Pattern" from ''Gross temperament EP'' (2023) [https://open.spotify.com/track/1BwMVnnrzfug6pSLUJ0jSG Spotify] | [https://francium223.bandcamp.com/track/gross-pattern Bandcamp] | [https://youtu.be/ttQVdzSy96M YouTube] – gross in 1429edo tuning
[[Category:Listen]]
Retrieved from "https://en.xen.wiki/w/1429edo"