41-comma - Revision history

Eufalesio: Updated color notation

2026-05-01T14:46:22Z

Updated color notation

← Older revision		Revision as of 14:46, 1 May 2026
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	\| Monzo = 65 -41		\| Monzo = 65 -41
	\| Name = 41-comma, Pythagorean countercomma, countercomp comma		\| Name = 41-comma, Pythagorean countercomma, countercomp comma
	\| Color name = ~~Tribisawa 5th~~, ~~Wa-41~~		\| Color name = 41wM, fowowama
	\| Comma = yes		\| Comma = yes
	}}		}}

FloraC: Undo revision 211175 by M1k1 H2tsun2 (talk)

2025-09-27T12:01:17Z

Undo revision 211175 by M1k1 H2tsun2 (talk)

← Older revision		Revision as of 12:01, 27 September 2025
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	\| Ratio = 36 893 488 147 419 103 232 / <br>36 472 996 377 170 786 403		\| Ratio = 36 893 488 147 419 103 232 / <br>36 472 996 377 170 786 403
	\| Monzo = 65 -41		\| Monzo = 65 -41
	\| Name = ~~Threerish 41-tone's comma,~~ 41-comma, Pythagorean countercomma, countercomp comma		\| Name = 41-comma, Pythagorean countercomma, countercomp comma
	\| Color name = Tribisawa 5th, Wa-41		\| Color name = Tribisawa 5th, Wa-41
	\| Comma = yes		\| Comma = yes

M1k1 H2tsun2: add it them

2025-09-27T11:58:11Z

add it them

← Older revision		Revision as of 11:58, 27 September 2025
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	\| Ratio = 36 893 488 147 419 103 232 / <br>36 472 996 377 170 786 403		\| Ratio = 36 893 488 147 419 103 232 / <br>36 472 996 377 170 786 403
	\| Monzo = 65 -41		\| Monzo = 65 -41
	\| Name = 41-comma, Pythagorean countercomma, countercomp comma		\| Name = Threerish 41-tone's comma, 41-comma, Pythagorean countercomma, countercomp comma
	\| Color name = Tribisawa 5th, Wa-41		\| Color name = Tribisawa 5th, Wa-41
	\| Comma = yes		\| Comma = yes

ArrowHead294 at 16:01, 11 December 2024

2024-12-11T16:01:37Z

← Older revision		Revision as of 16:01, 11 December 2024
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	== See also ==		== See also ==
	* [[Small comma]]		* [[Small comma]]
	* [[~~Schismic-countercommatic~~ equivalence continuum]]		* [[Schismic–countercommatic equivalence continuum]]

	[[Category:Countercomp]]		[[Category:Countercomp]]
	[[Category:Commas named systematically]]		[[Category:Commas named systematically]]
	[[Category:Commas named for their regular temperament properties]]		[[Category:Commas named for their regular temperament properties]]

BudjarnLambeth at 08:47, 3 November 2024

2024-11-03T08:47:31Z

← Older revision		Revision as of 08:47, 3 November 2024
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	[[Category:Countercomp]]		[[Category:Countercomp]]
			[[Category:Commas named systematically]]
			[[Category:Commas named for their regular temperament properties]]

FloraC: +a useful way to think of this interval. Clarify on the names.

2024-07-27T09:50:59Z

+a useful way to think of this interval. Clarify on the names.

← Older revision		Revision as of 09:50, 27 July 2024
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	\| Comma = yes		\| Comma = yes
	}}		}}
	The '''41-comma''', '''Pythagorean countercomma''', or '''countercomp comma''' ([[monzo]]: {{monzo\| 65 -41 }}), is a [[3-limit]] interval of 19.845 [[cent]]s. It is the amount by which a stack of 41 perfect fifths ([[3/2]]) falls short of 24 [[octave]]s, in other words 2<sup>24</sup>/(3/2)<sup>41</sup>.		The '''41-comma''', '''Pythagorean countercomma''', or '''countercomp comma''' ([[monzo]]: {{monzo\| 65 -41 }}), is a [[3-limit]] interval of 19.845 [[cent]]s. It is the amount by which a stack of 41 [[3/2\|perfect fifths (3/2)]] falls short of 24 [[octave]]s, in other words 2<sup>24</sup>/(3/2)<sup>41</sup>. It can also be described as the difference between a perfect fifth and a stack of six [[2187/2048\|apotomes]], or equivalently as the small gap between the Pythagorean triple-augmented unison and the triple-diminished fifth.

	== Temperaments ==		== Temperaments ==
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	== Terminology ==		== Terminology ==
	''Pythagorean countercomma'' is derived by analogy to ''Pythagorean comma''. ''Countercomp comma'' is derived from the temperament name, which was changed from ''counterpyth'' as in earlier materials, where this comma was also called ''counterpyth comma''. It was renamed after the convention was established that the temperament of the [[Pythagorean comma]] should be [[compton]], and never ''Pythagorean'', for fear of confusion with [[Pythagorean tuning]].		The names were given by [[Flora Canou]] in 2022. ''Pythagorean countercomma'' was derived by analogy to ''Pythagorean comma'' as part of a series of Pythagorean interval names. ''Countercomp comma'' was derived from the temperament name, ''countercomp'', which was changed from ''counterpyth'' as in earlier materials, where this comma was also called ''counterpyth comma''. It was renamed after the convention was established that the temperament of the [[Pythagorean comma]] should be [[compton]] and never ''Pythagorean'', for fear of confusion with [[Pythagorean tuning]].

	== See also ==		== See also ==

FloraC: +terminology section; name of the equivalence continuum

2022-12-22T05:52:07Z

+terminology section; name of the equivalence continuum

← Older revision		Revision as of 05:52, 22 December 2022
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	== Temperaments ==		== Temperaments ==
	Tempering out this comma leads to the [[countercomp]] temperament, which splits the octave into 41 equal parts and maps the harmonic 3 to 24\41. For equal divisions ''N'' up to 1230, the comma is tempered out if and only if 41 divides ''N''. Examples are [[41edo]], [[164edo]], [[205edo]], [[246edo]], [[328edo]] and [[369edo]]. See [[countercomp family]] for a number of rank-2 temperaments where it is tempered out.		Tempering out this comma leads to the [[countercomp]] temperament, which splits the octave into 41 equal parts and maps the harmonic 3 to 24\41. For equal divisions ''N'' up to 1230, the comma is tempered out if and only if 41 divides ''N''. Examples are [[41edo]], [[164edo]], [[205edo]], [[246edo]], [[328edo]] and [[369edo]]. See [[countercomp family]] for a number of rank-2 temperaments where it is tempered out.

			== Terminology ==
			''Pythagorean countercomma'' is derived by analogy to ''Pythagorean comma''. ''Countercomp comma'' is derived from the temperament name, which was changed from ''counterpyth'' as in earlier materials, where this comma was also called ''counterpyth comma''. It was renamed after the convention was established that the temperament of the [[Pythagorean comma]] should be [[compton]], and never ''Pythagorean'', for fear of confusion with [[Pythagorean tuning]].

	== See also ==		== See also ==
	* [[Small comma]]		* [[Small comma]]
	* [[Schismic-~~countercomp~~ equivalence continuum]]		* [[Schismic-countercommatic equivalence continuum]]

	[[Category:Countercomp]]		[[Category:Countercomp]]

FloraC: Name change following pythagorean -> compton

2022-12-22T04:51:21Z

Name change following pythagorean -> compton

← Older revision		Revision as of 04:51, 22 December 2022
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	\| Ratio = 36 893 488 147 419 103 232 / <br>36 472 996 377 170 786 403		\| Ratio = 36 893 488 147 419 103 232 / <br>36 472 996 377 170 786 403
	\| Monzo = 65 -41		\| Monzo = 65 -41
	\| Name = 41-comma, ~~counterpyth~~ comma		\| Name = 41-comma, Pythagorean countercomma, countercomp comma
	\| Color name = Tribisawa 5th, Wa-41		\| Color name = Tribisawa 5th, Wa-41
	\| Comma = yes		\| Comma = yes
	}}		}}
			The '''41-comma''', '''Pythagorean countercomma''', or '''countercomp comma''' ([[monzo]]: {{monzo\| 65 -41 }}), is a [[3-limit]] interval of 19.845 [[cent]]s. It is the amount by which a stack of 41 perfect fifths ([[3/2]]) falls short of 24 [[octave]]s, in other words 2<sup>24</sup>/(3/2)<sup>41</sup>.
	~~{{monzo\|65 -41}}, the~~ '''41-comma''' or '''~~counterpyth~~ comma''', is an interval of 19.845 [[cent]]s. It is the amount by which 41 fifths ([[3/2]]) ~~fall~~ short of 24 [[octave]]s, in other words 2<sup>24</sup>/(3/2)<sup>41</sup>.

	== Temperaments ==		== Temperaments ==
	Tempering out this comma splits the octave into 41 equal parts and maps the harmonic 3 to 24\41~~. It leads to a number of regular temperaments in the [[counterpyth family]]~~. For equal divisions ''N'' up to 1230, the comma is tempered out if and only if 41 divides ''N''. Examples are [[41edo~~\|41EDO~~]], [[164edo~~\|164EDO~~]], [[205edo~~\|205EDO~~]], [[246edo~~\|246EDO~~]], [[328edo~~\|328EDO~~]] and [[369edo~~\|369EDO~~]].		Tempering out this comma leads to the [[countercomp]] temperament, which splits the octave into 41 equal parts and maps the harmonic 3 to 24\41. For equal divisions ''N'' up to 1230, the comma is tempered out if and only if 41 divides ''N''. Examples are [[41edo]], [[164edo]], [[205edo]], [[246edo]], [[328edo]] and [[369edo]]. See [[countercomp family]] for a number of rank-2 temperaments where it is tempered out.

	~~=== Counterpyth (41&205) ===~~
	~~Subgroup: 2.3.5~~

	[[~~Comma list~~]]~~: {{monzo\|65~~ -~~41}}~~

	~~[[Mapping]]: [{{val\| 41 65 0 }}, {{val\| 0 0 1 }}]~~

	~~Mapping generators: ~531441/524288, ~5~~

	~~[[POTE generator]]: ~5/4 = 386.668~~

	~~{{Val list\|legend=1\| 41, 123, 164, 205, 369, 574, 779, 2132bc }}~~

	~~[[Badness]]: 0~~.~~934310~~

	== See also ==		== See also ==
	* [[Small comma]]		* [[Small comma]]
	* [[Schismic-~~counterpyth~~ equivalence continuum]]		* [[Schismic-countercomp equivalence continuum]]

	[[Category:~~Counterpyth~~]]		[[Category:Countercomp]]

Plumtree: Normalising usage of Infobox Interval

2022-10-25T15:44:24Z

Normalising usage of Infobox Interval

← Older revision		Revision as of 15:44, 25 October 2022
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	{{Infobox Interval		{{Infobox Interval
	~~\| Icon =~~
	\| Ratio = 36 893 488 147 419 103 232 / <br>36 472 996 377 170 786 403		\| Ratio = 36 893 488 147 419 103 232 / <br>36 472 996 377 170 786 403
	\| Monzo = 65 -41		\| Monzo = 65 -41
	~~\| Cents = 19.84496~~		\| Name = 41-comma, counterpyth comma
	\| Name = 41-comma, ~~<br>~~counterpyth comma
	\| Color name = Tribisawa 5th, Wa-41		\| Color name = Tribisawa 5th, Wa-41
	\| ~~FJS name =~~		\| Comma = yes
	~~\| Sound~~ =
	}}		}}

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	* [[Schismic-counterpyth equivalence continuum]]		* [[Schismic-counterpyth equivalence continuum]]

	~~[[Category:3-limit]]~~
	~~[[Category:Small commas]]~~
	[[Category:Counterpyth]]		[[Category:Counterpyth]]

Fredg999 category edits: Moving from Category:Small comma to Category:Small commas using Cat-a-lot

2022-03-20T21:59:56Z

Moving from Category:Small comma to Category:Small commas using Cat-a-lot

← Older revision		Revision as of 21:59, 20 March 2022
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	[[Category:3-limit]]		[[Category:3-limit]]
	[[Category:Small ~~comma~~]]		[[Category:Small commas]]
	[[Category:Counterpyth]]		[[Category:Counterpyth]]