26th-octave temperaments: Difference between revisions

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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~~]]).

The [[26-comma]], {{monzo| -41 26 }}, is technically usable for regular temperament purposes, however it makes a very imprecise temperament, only supported by 26edo itself and [[52edo]]. Thus, 26th-octave temperaments which are of musical interest typically do not inherit the flattone approximation of 3/2 which is found in [[26edo]].

~~Temperaments discussed elsewhere include~~ [[~~varunismic temperaments #Bosonic~~|~~bosonic~~]]~~. Considered below are~~ 26-~~commatic and iron.~~

However, 7/4 is frequently inherited, as 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]]).

== 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.~~

Temperaments discussed elsewhere include [[varunismic temperaments #Bosonic|bosonic]]. Considered below is iron.

~~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 ==

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 {{Technical data page}}
 {{Infobox fractional-octave|26}}
 All temperaments on this page have a period that is 1/26th of an octave.
-edo 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]]).
+The [[26-comma]], {{monzo| -41 26 }}, is technically usable for regular temperament purposes, however it makes a very imprecise temperament, only supported by 26edo itself and [[52edo]]. Thus, 26th-octave temperaments which are of musical interest typically do not inherit the flattone approximation of 3/2 which is found in [[26edo]].
-Temperaments discussed elsewhere include [[varunismic temperaments #Bosonic|bosonic]]. Considered below are 26-commatic and iron.
+However, 7/4 is frequently inherited, as 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]]).
-== 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.
+Temperaments discussed elsewhere include [[varunismic temperaments #Bosonic|bosonic]]. Considered below is iron.
-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 ==