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1051edo: Difference between revisions

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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|1051}}
{{ED intro}}
 
== Theory ==
== Theory ==
1051et tempers out 2460375/2458624 in the 7-limit; 820125/819896, 2097152/2096325, 514714375/514434888, 180224/180075, 184549376/184528125, 43923/43904 and 20614528/20588575 in the 11-limit.  
1051edo only has a [[consistency]] limit of 3 and does poorly with approximating the harmonic 5. However, it has a reasonable representation of the 2.3.7.11.17.19 subgroup.
From a regular temperament perspective, 1051edo only has a consistency limit of 3 and does poorly with approximating the harmonics 5 and 7. However, 1051edo has a good representation of the 2.3.11.13.15.17.19.35 subgroup.
 
===Odd harmonics===
Assume the [[patent val]], 1051et tempers out 2460375/2458624 in the 7-limit; 820125/819896, 2097152/2096325, 514714375/514434888, 180224/180075, 184549376/184528125, 43923/43904 and 20614528/20588575 in the 11-limit.  
 
=== Odd harmonics ===
{{Harmonics in equal|1051}}
{{Harmonics in equal|1051}}
===Subsets and supersets===
 
1051edo is the 177th [[prime edo]]. 2102edo, which doubles it, gives a good correction to the harmonic 5. 4212edo, which quadruples it, gives a good correction to the harmonic 7.
=== Subsets and supersets ===
==Regular temperament properties==
1051edo is the 177th [[prime edo]]. 2102edo, which doubles it, gives a good correction to the harmonic 5 and 7. 4212edo, which quadruples it, gives a good correction to the harmonic 3.
 
== 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|1666 -1051}}
! [[TE simple badness|Relative]] (%)
|{{val|1051 1666}}
|-
| -0.0736
| 2.3
| {{monzo| 1666 -1051 }}
| {{mapping| 1051 1666 }}
| −0.0736
| 0.0736
| 0.0736
| 6.45
| 6.45
|-
|-
|2.3.15
| 2.3.5
|{{monzo|-68 1 17}}, {{monzo|42 -61 14}}
| {{monzo| -68 18 17 }}, {{monzo| -26 -29 31 }}
|{{val|1051 1666 4106}}
| {{mapping| 1051 1666 2440 }} (1051)
| -0.0353
| +0.0077
| 0.0810
| 0.1298
| 7.09
| 11.4
|-
|2.3.15.35
|2460375/2458624, 4096000/4084101, 299072265625/297538935552
|{{val|1051 1666 4106 5391}}
| -0.0333
| 0.0702
| 6.15
|-
|2.3.15.35.11
|6250/6237, 180224/180075, 2460375/2458624, 43923/43904
|{{val|1051 1666 4106 5391 3636}}
| -0.0357
| 0.0630
| 5.52
|-
|2.3.15.35.11.13
|1716/1715, 4096/4095, 6250/6237, 91125/91091, 6656/6655
|{{val|1051 1666 4106 5391 3636 3889}}
| -0.0214
| 0.0658
| 5.76
|-
|2.3.15.35.11.13.17
|1275/1274, 1716/1715, 2431/2430, 4096/4095, 6250/6237, 6656/6655
|{{val|1051 1666 4106 5391 3636 3889 4296}}
| -0.0214
| 0.0609
| 5.33
|-
|-
|2.3.15.35.11.13.17.19
| 2.3.5
|1540/1539, 1275/1274, 1716/1715, 2431/2430, 4096/4095, 6250/6237, 41800/41769
| {{monzo| 40 7 -22 }}, {{monzo| 63 -50 7 }}
|{{val|1051 1666 4106 5391 3636 3889 4296 4465}}
| {{mapping| 1051 1666 2441 }} (1051c)
| -0.0331
| −0.1562
| 0.0648
| 0.1313
| 5.68
| 11.5
|}
|}
 
<!--
=== 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
|-
! Generator<br>(reduced)
! Periods<br />per 8ve
! Cents<br>(reduced)
! Generator*
! Associated<br>ratio
! Cents*
! Associated<br />ratio*
! Temperaments
! Temperaments
|-
|1
|435\1051
|496.67
|5457/4096
|Edson
|}
|}
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
-->
== Music ==
; [[Francium]]
* [https://www.youtube.com/watch?v=e1lARtnPl1E ''you have to run!''] (2023) – [[edson]] in 1051edo tuning


==  Music ==
[[Category:Listen]]
*[https://www.youtube.com/watch?v=e1lARtnPl1E you have to run!] by [[User:Francium|Francium]]
Retrieved from "https://en.xen.wiki/w/1051edo"