26th-octave temperaments: Difference between revisions

- bosonic (more properly addressed in varunismic temps)
Eliora (talk | contribs)
correct the "26-comma is not tempered out" - it is by definition also a 26th-octave tempereament, even if a bad one, and document with corresponding style while acknowledging how innacurate it is
Tag: Reverted
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{{Technical data page}}
{{Technical data page}}
{{Infobox fractional-octave|26}}
{{Infobox fractional-octave|26}}
All temperaments on this page have a period that is 1/26th of an octave. However, the {{monzo| -41 26 }} comma is not tempered out. Thus the 3/2 is not that of [[26edo]]. However, 7/4 is, as is 11/8 in the bosonic temperaments.
All temperaments on this page have a period that is 1/26th of an octave.


26edo is very accurate for 7th harmonic, the [[26-7-comma]] ({{monzo| 73 0 0 -26 }}, the amount by which 26 septimal whole tones ([[8/7]]) exceed 5 octaves) is tempered out by 26-fold multiple edos up to 1456 (such as [[26edo|26-]], [[130edo|130-]], [[286edo|286-]] or [[546edo|546edo]]).  
26edo is very accurate for 7th harmonic, the [[26-7-comma]] ({{monzo| 73 0 0 -26 }}, the amount by which 26 septimal whole tones ([[8/7]]) exceed 5 octaves) is tempered out by 26-fold multiple edos up to 1456 (such as [[26edo|26-]], [[130edo|130-]], [[286edo|286-]] or [[546edo|546edo]]).  


Temperaments discussed elsewhere include [[varunismic temperaments #Bosonic|bosonic]]. Considered below is iron.  
Temperaments discussed elsewhere include [[varunismic temperaments #Bosonic|bosonic]]. Considered below are 26-commatic and iron.
== 26-commatic ==
{{Mathematical interest}}
 
The 26-commatic temperament tempers out the [[26-comma]], {{monzo|-41 26}}. 26edo is notable for having a flattone fifth, and due to large error, 26edo and its double, [[52edo]], are the only temperaments tempering out this comma. Hence it primarily serves as an object of mathematical interest.
 
Subgroup: 2.3
 
Comma list: {{monzo|-41 26}}
 
{{mapping|legend=2| 37 28 }}
 
: mapping generators: ~2187/2048 = 1\26
 
[[Support]]ing [[ET]]s: {{EDOs|26, 52}}


== Iron ==
== Iron ==