251edo: Difference between revisions

ArrowHead294 (talk | contribs)
mNo edit summary
m Cleanup
Line 3: Line 3:


== 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.  
Line 21: Line 21:
! rowspan="2" | [[Comma list]]
! rowspan="2" | [[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
|-
|-
Line 28: Line 28:
|-
|-
| 2.3
| 2.3
| {{monzo| 398 -251 }}
| {{Monzo| 398 -251 }}
| {{mapping| 251 398 }}
| {{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 }}
| {{Monzo| 9 -13 5 }}, {{monzo| 49 -6 -17 }}
| {{mapping| 251 398 583 }}
| {{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 }}
| {{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 />per 8ve
! Periods<br>per 8ve
! Generator*
! Generator*
! Cents*
! Cents*
! Associated<br />ratio*
! 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 lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
<nowiki/>* [[Normal forms|Octave-reduced form]], reduced to the first half-octave, and [[Normal forms|minimal form]] in parentheses if distinct


== Music ==
== Music ==