99/80 - Revision history

Overthink at 23:10, 24 September 2025

2025-09-24T23:10:09Z

← Older revision		Revision as of 23:10, 24 September 2025
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	\| Color name = logu 3rd, 1og3		\| Color name = logu 3rd, 1og3
	}}		}}
	'''99/80''', the '''undecimal submajor third''', also known as the '''cake third''', is [[45/44]] flat of the [[81/64\|Pythagorean major third (81/64)]], and also [[100/99]] flat of the [[5/4\|classical major third (5/4)]], while being [[8019/8000]] sharp of the [[100/81\|grave major third (100/81)]]. The alternate name, ''cake third'', refers to the fact that tempering out 45/44, the cake comma, leads to a temperament that slices 99/80 exactly in half (into two [[11/10]]'s). It arises in [[just intonation]] as the sum of a [[9/8]] whole tone and an [[11/10]] submajor second.		'''99/80''', the '''undecimal submajor third''', also known as the '''cake third''', is [[45/44]] flat of the [[81/64\|Pythagorean major third (81/64)]], and also [[100/99]] flat of the [[5/4\|classical major third (5/4)]], while being [[8019/8000]] sharp of the [[100/81\|grave major third (100/81)]]. The alternate name, ''cake third'', refers to the fact that tempering out 45/44, the cake comma, leads to a temperament that slices 99/80 exactly in half (into two [[11/10]]'s). It arises in [[just intonation]] as the sum of a [[9/8]] whole tone and an [[11/10]] submajor second. It is also [[2080/2079]] flat of [[26/21]].

	== Approximation ==		== Approximation ==

FloraC: Rework +1

2024-12-15T16:50:18Z

Rework +1

← Older revision		Revision as of 16:50, 15 December 2024
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	\| Color name = logu 3rd, 1og3		\| Color name = logu 3rd, 1og3
	}}		}}
			'''99/80''', the '''undecimal submajor third''', also known as the '''cake third''', is [[45/44]] flat of the [[81/64\|Pythagorean major third (81/64)]], and also [[100/99]] flat of the [[5/4\|classical major third (5/4)]], while being [[8019/8000]] sharp of the [[100/81\|grave major third (100/81)]]. The alternate name, ''cake third'', refers to the fact that tempering out 45/44, the cake comma, leads to a temperament that slices 99/80 exactly in half (into two [[11/10]]'s). It arises in [[just intonation]] as the sum of a [[9/8]] whole tone and an [[11/10]] submajor second.
	'''99/80''', the '''undecimal submajor third''', also known as the '''cake third''' is [[45/44]] flat of the [[81/64\|Pythagorean major third (81/64)]], and also [[100/99]] flat of the [[5/4\|classical major third (5/4)]], while being [[8019/8000]] sharp of the [[100/81\|grave major third (100/81)]]. The alternate name, ''cake third'', refers to the fact that tempering out 45/44, the cake comma, leads to a temperament that slices 99/80 exactly in half (into two [[11/10]]s).

	It arises in [[just intonation]] as the sum of a [[9/8]] whole tone and an [[11/10]] submajor second.

	== Approximation ==		== Approximation ==

FloraC: Rework

2024-12-15T16:47:42Z

Rework

← Older revision		Revision as of 16:47, 15 December 2024
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	}}		}}

	'''99/80''', the '''undecimal submajor third''', also known as the '''cake third'''~~, is exactly [[8/7]] flat of the very accurate half-octave of [[99/70]], and so is accurately represented in any even edo with a good 7, such as [[26edo]]. It~~ is [[45/44]] flat of the [[81/64\|Pythagorean major third (81/64)]], and also [[100/99]] flat of the [[5/4\|classical major third (5/4)]]. The alternate name, ''cake third'', refers to the fact that tempering out 45/44, the cake comma, leads to a temperament that slices 99/80 exactly in half (into two [[11/10]]s).		'''99/80''', the '''undecimal submajor third''', also known as the '''cake third''' is [[45/44]] flat of the [[81/64\|Pythagorean major third (81/64)]], and also [[100/99]] flat of the [[5/4\|classical major third (5/4)]], while being [[8019/8000]] sharp of the [[100/81\|grave major third (100/81)]]. The alternate name, ''cake third'', refers to the fact that tempering out 45/44, the cake comma, leads to a temperament that slices 99/80 exactly in half (into two [[11/10]]s).

	It is the sum of a [[9/8]] whole tone and an [[11/10]] submajor second, and so is [[~~8019~~/~~8000~~]] ~~sharp of~~ [[~~100/81~~]].		It arises in [[just intonation]] as the sum of a [[9/8]] whole tone and an [[11/10]] submajor second.

			== Approximation ==
			This interval is exactly [[8/7]] flat of the very accurate half-octave of [[99/70]], and so is accurately represented in any even edo with a good [[7/1\|7]], such as [[26edo]].

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

	* [[26edo]]
	* [[160/99]] – its [[octave complement]]		* [[160/99]] – its [[octave complement]]
	* [[40/33]] – its [[fifth complement]]		* [[40/33]] – its [[fifth complement]]

FloraC: This interval relates back to the Pythagorean major third via the cake comma

2024-12-15T16:40:07Z

This interval relates back to the Pythagorean major third via the cake comma

← Older revision		Revision as of 16:40, 15 December 2024
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	}}		}}

	'''99/80''', the '''undecimal submajor third''', also known as the '''cake third''', is exactly [[8/7]] flat of the very accurate half-octave of [[99/70]], and so is accurately represented in any even edo with a good 7, ~~of which the first truly good example is~~ [[26edo]]. It is also [[100/99]] flat of [[5/4]]. The alternate name, ''cake third'', refers to the fact that tempering out [[45/44]], the cake comma, leads to a temperament that slices 99/80 exactly in half (into two [[11/10]]s).		'''99/80''', the '''undecimal submajor third''', also known as the '''cake third''', is exactly [[8/7]] flat of the very accurate half-octave of [[99/70]], and so is accurately represented in any even edo with a good 7, such as [[26edo]]. It is [[45/44]] flat of the [[81/64\|Pythagorean major third (81/64)]], and also [[100/99]] flat of the [[5/4\|classical major third (5/4)]]. The alternate name, ''cake third'', refers to the fact that tempering out 45/44, the cake comma, leads to a temperament that slices 99/80 exactly in half (into two [[11/10]]s).

	It is the sum of a [[9/8]] whole tone and an [[11/10]] submajor second, and so is [[8019/8000]] sharp of [[100/81]].		It is the sum of a [[9/8]] whole tone and an [[11/10]] submajor second, and so is [[8019/8000]] sharp of [[100/81]].

AraMax at 14:37, 15 December 2024

2024-12-15T14:37:40Z

← Older revision		Revision as of 14:37, 15 December 2024
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	}}		}}

	'''99/80''', the '''undecimal submajor third''', also known as the '''cake third''', is exactly [[8/7]] flat of the very accurate half-octave of [[99/70]], and so is accurately represented in any even edo with a good 7, of which the first truly good example is [[26edo]]. The alternate name, ''cake third'', refers to the fact that tempering out [[45/44]], the cake comma, leads to a temperament that slices 99/80 exactly in half (into two [[11/10]]s).		'''99/80''', the '''undecimal submajor third''', also known as the '''cake third''', is exactly [[8/7]] flat of the very accurate half-octave of [[99/70]], and so is accurately represented in any even edo with a good 7, of which the first truly good example is [[26edo]]. It is also [[100/99]] flat of [[5/4]]. The alternate name, ''cake third'', refers to the fact that tempering out [[45/44]], the cake comma, leads to a temperament that slices 99/80 exactly in half (into two [[11/10]]s).

	It is the sum of a [[9/8]] whole tone and an [[11/10]] submajor second, and so is [[8019/8000]] sharp of [[100/81]].		It is the sum of a [[9/8]] whole tone and an [[11/10]] submajor second, and so is [[8019/8000]] sharp of [[100/81]].

AraMax at 14:33, 15 December 2024

2024-12-15T14:33:13Z

← Older revision		Revision as of 14:33, 15 December 2024
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			{{interwiki
			\| ro = 99/80 (ro)
			\| de =
			\| es =
			\| ja =
			\| ko =
			}}
	{{Infobox Interval		{{Infobox Interval
	\| Name = undecimal submajor third,<br>cake third		\| Name = undecimal submajor third,<br>cake third

AraMax: Added a „See also” section

2024-12-15T11:37:49Z

Added a „See also” section

← Older revision		Revision as of 11:37, 15 December 2024
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	It is the sum of a [[9/8]] whole tone and an [[11/10]] submajor second, and so is [[8019/8000]] sharp of [[100/81]].		It is the sum of a [[9/8]] whole tone and an [[11/10]] submajor second, and so is [[8019/8000]] sharp of [[100/81]].

			== See also ==

			* [[26edo]]
			* [[160/99]] – its [[octave complement]]
			* [[40/33]] – its [[fifth complement]]
			* [[320/297]] – its [[fourth complement]]
			* [[Gallery of just intervals]]

	[[Category:Third]]		[[Category:Third]]
	[[Category:Submajor third]]		[[Category:Submajor third]]

Tristanbay: Added a missing period

2024-12-15T02:33:35Z

Added a missing period

← Older revision		Revision as of 02:33, 15 December 2024
Line 4:		Line 4:
	}}		}}

	'''99/80''', the '''undecimal submajor third''', also known as the '''cake third''', is exactly [[8/7]] flat of the very accurate half-octave of [[99/70]], and so is accurately represented in any even edo with a good 7, of which the first truly good example is [[26edo]]. The alternate name, ''cake third'', refers to the fact that tempering out [[45/44]], the cake comma, leads to a temperament that slices 99/80 exactly in half (into two [[11/10]]s)		'''99/80''', the '''undecimal submajor third''', also known as the '''cake third''', is exactly [[8/7]] flat of the very accurate half-octave of [[99/70]], and so is accurately represented in any even edo with a good 7, of which the first truly good example is [[26edo]]. The alternate name, ''cake third'', refers to the fact that tempering out [[45/44]], the cake comma, leads to a temperament that slices 99/80 exactly in half (into two [[11/10]]s).

	It is the sum of a [[9/8]] whole tone and an [[11/10]] submajor second, and so is [[8019/8000]] sharp of [[100/81]].		It is the sum of a [[9/8]] whole tone and an [[11/10]] submajor second, and so is [[8019/8000]] sharp of [[100/81]].

Tristanbay: explained the aforementioned name

2024-12-14T19:59:14Z

explained the aforementioned name

← Older revision		Revision as of 19:59, 14 December 2024
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	}}		}}

	'''99/80''', the '''undecimal submajor third''', is exactly [[8/7]] flat of the very accurate half-octave of [[99/70]], and so is accurately represented in any even edo with a good 7, of which the first truly good example is [[26edo]].		'''99/80''', the '''undecimal submajor third''', also known as the '''cake third''', is exactly [[8/7]] flat of the very accurate half-octave of [[99/70]], and so is accurately represented in any even edo with a good 7, of which the first truly good example is [[26edo]]. The alternate name, ''cake third'', refers to the fact that tempering out [[45/44]], the cake comma, leads to a temperament that slices 99/80 exactly in half (into two [[11/10]]s)

	It is the sum of a [[9/8]] whole tone and an [[11/10]] submajor second, and so is [[8019/8000]] sharp of [[100/81]].		It is the sum of a [[9/8]] whole tone and an [[11/10]] submajor second, and so is [[8019/8000]] sharp of [[100/81]].

Tristanbay: CAKE THIRD

2024-12-14T19:47:53Z

CAKE THIRD

← Older revision		Revision as of 19:47, 14 December 2024
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	{{Infobox Interval		{{Infobox Interval
	\| Name = undecimal submajor third		\| Name = undecimal submajor third,<br>cake third
	\| Color name = logu 3rd, 1og3		\| Color name = logu 3rd, 1og3
	}}		}}
Line 7:		Line 7:

	It is the sum of a [[9/8]] whole tone and an [[11/10]] submajor second, and so is [[8019/8000]] sharp of [[100/81]].		It is the sum of a [[9/8]] whole tone and an [[11/10]] submajor second, and so is [[8019/8000]] sharp of [[100/81]].



	[[Category:Third]]		[[Category:Third]]
	[[Category:Submajor third]]		[[Category:Submajor third]]