26th-octave temperaments - Revision history

Eliora: link sentences

2026-08-02T16:32:59Z

link sentences

← Older revision		Revision as of 16:32, 2 August 2026
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	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.

	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]]~~. However, 7/4 is frequently inherited~~.		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]].

	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]]).		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]]).

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

Eliora: nonetheless expand whithin limits of "not cataloging edos" - [-41 26] is technically a 26th-octave temperament, just a really bad one, and precisely clarify what it means that "3/2 is not that of 26edo"

2026-08-02T16:27:40Z

nonetheless expand whithin limits of "not cataloging edos" - [-41 26] is technically a 26th-octave temperament, just a really bad one, and precisely clarify what it means that "3/2 is not that of 26edo"

← Older revision		Revision as of 16:27, 2 August 2026
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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.

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

	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]]).

FloraC: Do not name/catalog equal temps. Refer to them by 2.7-subgroup 26et, etc.

2026-08-02T08:36:39Z

Do not name/catalog equal temps. Refer to them by *2.7-subgroup 26et*, etc.

@@ 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.
 == 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

Eliora: +26/7 comma, or fynn if following naming logic, + style

2026-08-01T23:55:13Z

+26/7 comma, or fynn if following naming logic, + style

← Older revision		Revision as of 23:55, 1 August 2026
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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]]).		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 ==		== 26-commatic ==
	{{Mathematical interest}}		{{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 }}		{{mapping\|legend=2\| 37 28 }}
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	[[Support]]ing [[ET]]s: {{EDOs\|26, 52}}		[[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 ==
	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		[[Subgroup]]: 2.3.5.7

Eliora: 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

2026-08-01T23:48:41Z

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

← Older revision		Revision as of 23:48, 1 August 2026
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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 ==

FloraC: - bosonic (more properly addressed in varunismic temps)

2026-07-21T04:18:01Z

- bosonic (more properly addressed in varunismic temps)

@@ Line 3: / Line 3: @@
 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]]).
-== Bosonic ==
+Temperaments discussed elsewhere include [[varunismic temperaments #Bosonic|bosonic]]. Considered below is iron.
 == Iron ==

FloraC: Switch to Sintel's badness, WE & CWE tunings

2026-07-21T03:31:14Z

Switch to Sintel's badness, WE & CWE tunings

Show changes

FloraC: Units & misc. cleanup

2026-07-21T03:15:06Z

Units & misc. cleanup

Show changes

Hotcrystal0: fix link

2026-06-03T01:45:56Z

fix link

← Older revision		Revision as of 01:45, 3 June 2026
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	== Bosonic ==		== Bosonic ==
	{{See also\| ~~High badness~~ temperaments #Tridecatonic }}		{{See also\| Miscellaneous 5-limit temperaments #Tridecatonic }}

	Subgroup: 2.3.5.7		Subgroup: 2.3.5.7

VectorGraphics at 05:13, 12 June 2025

2025-06-12T05:13:14Z

← Older revision		Revision as of 05:13, 12 June 2025
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	Mapping generators: ~36/35, ~3		Mapping generators: ~36/35, ~3

	~~{{Multival\|legend=1\|26 52 0 22 -73 -146}}~~

	[[POTE generator]]: ~3/2 = 701.250		[[POTE generator]]: ~3/2 = 701.250