26th-octave temperaments: Difference between revisions

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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 are 26-commatic and iron~~.

Temperaments discussed elsewhere include [[varunismic temperaments #Bosonic|bosonic]].

== 26-commatic ==

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.

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

[[Subgroup]]: 2.3

Comma list: {{monzo|-41 26}}

[[Comma list]]: {{monzo|-41 26}}

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[[Support]]ing [[ET]]s: {{EDOs|26, 52}}

== Fynn ==

''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 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 5: / Line 5: @@
 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]]. Considered below are 26-commatic and iron.
+Temperaments discussed elsewhere include [[varunismic temperaments #Bosonic|bosonic]].
 == 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.
+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
+[[Subgroup]]: 2.3
-Comma list: {{monzo|-41 26}}
+[[Comma list]]: {{monzo|-41 26}}
 {{mapping|legend=2| 37 28 }}
@@ Line 20: / Line 20: @@
 [[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