26th-octave temperaments: Difference between revisions

Line 1:

All temperaments on this page have a period that is 1/26th of an octave.

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.

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]].

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

~~== 26-commatic ==~~

~~{{Mathematical interest}}~~

~~The ''26-commatic'' temperament tempers out the [[26-comma]], {{monzo|-41 26}}. 26edo~~ is notable for having a flattone, even if innacurate, fifth, which has seen some attention in music theory. 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}}~~

~~== Fynn ==~~

~~{{Main|Fynn's comma}}~~

~~''Fynn'', or systematically, 26-7-commatic, tempers out the [[Fynn's comma]] or the 26-7-comma.~~

~~[[Subgroup]]: 2~~.3

~~[[Comma list]]: {{monzo| 73 -26 }}~~

~~{{mapping|legend=2| 26 73 }}~~

~~: mapping generators: ~ 16807/16384 = 1\26~~

~~[[Support]]ing [[ET]]s: 26N, N = 1 to 56~~

== Iron ==

''Iron'' may be described as the {{nowrap| 130 & 494 }} temperament. It was named by [[Eliora]] in 2023 after the 26th element.

Iron may be described as the {{nowrap| 130 & 494 }} temperament. It was named by [[Eliora]] in 2023 after the 26th element.

[[Subgroup]]: 2.3.5.7

@@ Line 1: / Line 1: @@
 {{Technical data page}}
 {{Infobox fractional-octave|26}}
-All temperaments on this page have a period that is 1/26th of an octave.
+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.
 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]]).
-Temperaments discussed elsewhere include [[varunismic temperaments #Bosonic|bosonic]].
+Temperaments discussed elsewhere include [[varunismic temperaments #Bosonic|bosonic]]. Considered below is iron.
-== 26-commatic ==
-{{Mathematical interest}}
-The ''26-commatic'' temperament tempers out the [[26-comma]], {{monzo|-41 26}}. 26edo is notable for having a flattone, even if innacurate, fifth, which has seen some attention in music theory. 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}}
-== Fynn ==
-{{Main|Fynn's comma}}
-''Fynn'', or systematically, 26-7-commatic, tempers out the [[Fynn's comma]] or the 26-7-comma.
-[[Subgroup]]: 2.3
-[[Comma list]]: {{monzo| 73 -26 }}
-{{mapping|legend=2| 26 73 }}
-: mapping generators: ~	16807/16384 = 1\26
-[[Support]]ing [[ET]]s: 26N, N = 1 to 56
 == Iron ==
-''Iron'' may be described as the {{nowrap| 130 & 494 }} temperament. It was named by [[Eliora]] in 2023 after the 26th element.
+Iron may be described as the {{nowrap| 130 & 494 }} temperament. It was named by [[Eliora]] in 2023 after the 26th element.
 [[Subgroup]]: 2.3.5.7