251edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{EDO intro|251}} | {{EDO intro|251}} | ||
== Theory == | == Theory == | ||
251et tempers out 1600000/1594323 (amity comma) and | 251et [[tempering out|tempers out]] 1600000/1594323 ([[amity comma]]) and {{monzo| 49 -6 -17 }} ([[maquila comma]]) in the 5-limit; [[4375/4374]], [[5120/5103]], and 40500000/40353607 in the 7-limit, [[support]]ing [[amity]], [[supermajor]], and [[acrokleismic]]. | ||
Using the patent val, it tempers out 1331/1323, 1375/1372, 16896/16807, and 24057/24010 in the 11-limit; 352/351, 676/675, 847/845, and 1573/1568 in the 13-limit. | Using the [[patent val]] {{val| 251 398 583 705 '''868''' }}, it tempers out 1331/1323, 1375/1372, 16896/16807, and 24057/24010 in the 11-limit; [[352/351]], [[676/675]], [[847/845]], and [[1573/1568]] in the 13-limit. | ||
Using the 251e val, it tempers out 540/539, 5632/5625, 6250/6237, and 12005/11979 in the 11-limit; 364/363, 676/675, 1716/1715, and 3584/3575 in the 13-limit. | Using the 251e val {{val| 251 398 583 705 '''869''' }}, it tempers out [[540/539]], [[5632/5625]], [[6250/6237]], and 12005/11979 in the 11-limit; [[364/363]], [[676/675]], [[1716/1715]], and 3584/3575 in the 13-limit. | ||
=== Odd harmonics === | === Odd harmonics === | ||
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=== Subsets and supersets === | === Subsets and supersets === | ||
251edo is the 54th [[prime | 251edo is the 54th [[prime edo]]. | ||
==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|398 -251}} | | {{monzo| 398 -251 }} | ||
|{{ | | {{mapping| 251 398 }} | ||
| -0.2630 | | -0.2630 | ||
| 0.2630 | | 0.2630 | ||
| 5.50 | | 5.50 | ||
|- | |- | ||
|2.3.5 | | 2.3.5 | ||
|{{monzo|9 -13 5}}, {{monzo|49 -6 -17}} | | {{monzo| 9 -13 5 }}, {{monzo| 49 -6 -17 }} | ||
|{{ | | {{mapping| 251 398 583 }} | ||
| -0.3099 | | -0.3099 | ||
| 0.2247 | | 0.2247 | ||
| 4.70 | | 4.70 | ||
|- | |- | ||
|2.3.5.7 | | 2.3.5.7 | ||
|4375/4374, 5120/5103, | | 4375/4374, 5120/5103, 40500000/40353607 | ||
|{{ | | {{mapping| 251 398 583 705 }} | ||
| -0.3830 | | -0.3830 | ||
| 0.2322 | | 0.2322 | ||
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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 | ! Generator* | ||
! Cents | ! Cents* | ||
! Associated<br> | ! Associated<br>Ratio* | ||
! Temperaments | ! Temperaments | ||
|- | |- | ||
|1 | | 1 | ||
| | | 66\251 | ||
| | | 315.54 | ||
| 6/5 | |||
| [[Acrokleismic]] | |||
| | |||
|[[ | |||
|- | |- | ||
|1 | | 1 | ||
| | | 71\251 | ||
| | | 339.44 | ||
| | | 243/200 | ||
|[[ | | [[Amity]] | ||
|- | |- | ||
|1 | | 1 | ||
| | | 91\251 | ||
| | | 435.06 | ||
| | | 9/7 | ||
|[[ | | [[Supermajor]] | ||
|- | |- | ||
|1 | | 1 | ||
| | | 96\251 | ||
| | | 458.96 | ||
| | | 125/96 | ||
|[[ | | [[Majvam]] | ||
|- | |- | ||
|1 | | 1 | ||
| | | 112\251 | ||
| | | 535.46 | ||
| | | 512/375 | ||
|[[ | | [[Maquila]] | ||
|} | |} | ||
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct | |||
== Music == | == Music == | ||
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* "hope in dark times" from ''hope in dark times'' (2024) – [https://open.spotify.com/track/1zSiYXz46ugWAmqySaEN2A Spotify] | [https://francium223.bandcamp.com/track/hope-in-dark-times Bandcamp] | [https://www.youtube.com/watch?v=yHl3oku_NmY YouTube] | * "hope in dark times" from ''hope in dark times'' (2024) – [https://open.spotify.com/track/1zSiYXz46ugWAmqySaEN2A Spotify] | [https://francium223.bandcamp.com/track/hope-in-dark-times Bandcamp] | [https://www.youtube.com/watch?v=yHl3oku_NmY YouTube] | ||
[[Category:Listen]] | [[Category:Listen]] | ||