251edo: Difference between revisions
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== Theory == | == Theory == | ||
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]]. | 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 (temperament)|supermajor]], and [[acrokleismic]]. | ||
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 [[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. | ||
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! rowspan="2" | [[Comma list]] | ! rowspan="2" | [[Comma list]] | ||
! rowspan="2" | [[Mapping]] | ! rowspan="2" | [[Mapping]] | ||
! rowspan="2" | Optimal<br | ! rowspan="2" | Optimal<br>8ve stretch (¢) | ||
! colspan="2" | Tuning error | ! colspan="2" | Tuning error | ||
|- | |- | ||
| Line 28: | Line 28: | ||
|- | |- | ||
| 2.3 | | 2.3 | ||
| {{ | | {{Monzo| 398 -251 }} | ||
| {{ | | {{Mapping| 251 398 }} | ||
| −0.2630 | | −0.2630 | ||
| 0.2630 | | 0.2630 | ||
| Line 35: | Line 35: | ||
|- | |- | ||
| 2.3.5 | | 2.3.5 | ||
| {{ | | {{Monzo| 9 -13 5 }}, {{monzo| 49 -6 -17 }} | ||
| {{ | | {{Mapping| 251 398 583 }} | ||
| −0.3099 | | −0.3099 | ||
| 0.2247 | | 0.2247 | ||
| Line 43: | Line 43: | ||
| 2.3.5.7 | | 2.3.5.7 | ||
| 4375/4374, 5120/5103, 40500000/40353607 | | 4375/4374, 5120/5103, 40500000/40353607 | ||
| {{ | | {{Mapping| 251 398 583 705 }} | ||
| −0.3830 | | −0.3830 | ||
| 0.2322 | | 0.2322 | ||
| Line 53: | Line 53: | ||
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | |+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | ||
|- | |- | ||
! Periods<br | ! Periods<br>per 8ve | ||
! Generator* | ! Generator* | ||
! Cents* | ! Cents* | ||
! Associated<br | ! Associated<br>ratio* | ||
! Temperaments | ! Temperaments | ||
|- | |- | ||
| Line 75: | Line 75: | ||
| 435.06 | | 435.06 | ||
| 9/7 | | 9/7 | ||
| [[Supermajor]] | | [[Supermajor (temperament)|Supermajor]] | ||
|- | |- | ||
| 1 | | 1 | ||
| Line 89: | Line 89: | ||
| [[Maquila]] | | [[Maquila]] | ||
|} | |} | ||
<nowiki />* [[Normal | <nowiki/>* [[Normal forms|Octave-reduced form]], reduced to the first half-octave, and [[Normal forms|minimal form]] in parentheses if distinct | ||
== Music == | == Music == | ||