9801/9800 - Revision history

Overthink: also this

2026-04-12T01:55:22Z

also this

← Older revision		Revision as of 01:55, 12 April 2026
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	* [[245/243]] and [[121/120]]		* [[245/243]] and [[121/120]]
	* [[245/242]] and [[81/80]]		* [[245/242]] and [[81/80]]
			* [[176/175]] and [[896/891]]

	It also factors into the two smallest 13-limit superparticular commas: 9801/9800 = ([[10648/10647]])⋅([[123201/123200]]).		It also factors into the two smallest 13-limit superparticular commas: 9801/9800 = ([[10648/10647]])⋅([[123201/123200]]).

Lucius Chiaraviglio: Add another difference that this comma corresponds to

2026-04-12T01:50:02Z

Add another difference that this comma corresponds to

← Older revision		Revision as of 01:50, 12 April 2026
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	\| Comma = yes		\| Comma = yes
	}}		}}
	'''9801/9800''', the '''kalisma''', sometimes described as ''Gauss' comma'', is an [[unnoticeable comma\|unnoticeable]] [[11-limit]] [[comma]] measuring about 0.18{{cent}}. It is the smallest 11-limit [[superparticular]] interval. It can be described as the difference between [[99/70]] and its [[octave complement]] [[140/99]], or between ([[35/33]])<sup>2</sup> and [[9/8]].		'''9801/9800''', the '''kalisma''', sometimes described as ''Gauss' comma'', is an [[unnoticeable comma\|unnoticeable]] [[11-limit]] [[comma]] measuring about 0.18{{cent}}. It is the smallest 11-limit [[superparticular]] interval. It can be described as the difference between [[99/70]] and its [[octave complement]] [[140/99]], between ([[35/33]])<sup>2</sup> and [[9/8]], or between ([[176/175]])<sup>2</sup> and [[2048/2025]].

	In terms of superparticular commas, it is the difference between:		In terms of superparticular commas, it is the difference between:

Eufalesio: Mention of pythcomma split

2026-04-09T08:37:21Z

Mention of pythcomma split

← Older revision		Revision as of 08:37, 9 April 2026
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	== Temperaments ==		== Temperaments ==
	[[Tempering out]] this comma leads to the '''kalismic temperament''', which splits the [[octave]] into two equal parts, each representing 99/70~140/99. Tempering it out also means that [[10/9]] and [[11/7]] are ~~1/2-octave~~ apart, as well as are [[11/10]] and [[14/9]]. Odd-numbered edos cannot temper it out, as they do not have a semioctave.		[[Tempering out]] this comma leads to the '''kalismic temperament''', which splits the [[octave]] into two equal parts, each representing 99/70~140/99. Tempering it out also means that the [[pythagorean comma]] is split into two [[2835/2816]] halves, [[10/9]] and [[11/7]] are a semioctave apart, as well as are [[11/10]] and [[14/9]]. Odd-numbered edos cannot temper it out, as they do not have a semioctave.

	See [[Rank-4 temperament #Kalismic (9801/9800)]] for some technical details. See [[Kalismic temperaments]] for a collection of rank-3 temperaments where it is tempered out.		See [[Rank-4 temperament #Kalismic (9801/9800)]] for some technical details. See [[Kalismic temperaments]] for a collection of rank-3 temperaments where it is tempered out.

Squib: add 13-limit difference, not 11-limit but probably still notable

2026-03-01T06:19:23Z

add 13-limit difference, not 11-limit but probably still notable

← Older revision		Revision as of 06:19, 1 March 2026
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	In terms of superparticular commas, it is the difference between:		In terms of superparticular commas, it is the difference between:
	* [[99/98]] and [[100/99]]		* [[99/98]] and [[100/99]]
			* [[351/350]] and [[364/363]]
	* [[1716/1715]] and [[2080/2079]]		* [[1716/1715]] and [[2080/2079]]
	* [[3025/3024]] and [[4375/4374]]		* [[3025/3024]] and [[4375/4374]]

Overthink: add one differencce

2026-02-28T00:32:26Z

add one differencce

← Older revision		Revision as of 00:32, 28 February 2026
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	In terms of superparticular commas, it is the difference between:		In terms of superparticular commas, it is the difference between:
	* [[99/98]] and [[100/99]]		* [[99/98]] and [[100/99]]
			* [[1716/1715]] and [[2080/2079]]
	* [[3025/3024]] and [[4375/4374]]		* [[3025/3024]] and [[4375/4374]]

Overthink: /* Temperaments */ split paragraph, + reasoning

2026-02-28T00:31:09Z

Temperaments: split paragraph, + reasoning

← Older revision		Revision as of 00:31, 28 February 2026
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	== Temperaments ==		== Temperaments ==
	[[Tempering out]] this comma leads to the '''kalismic temperament''', which splits the [[octave]] into two equal parts, each representing 99/70~140/99. Tempering it out also means that [[10/9]] and [[11/7]] are 1/2-octave apart, as well as are [[11/10]] and [[14/9]]. Odd-numbered edos cannot temper it out. See [[Rank-4 temperament #Kalismic (9801/9800)]] for some technical details. See [[Kalismic temperaments]] for a collection of rank-3 temperaments where it is tempered out.		[[Tempering out]] this comma leads to the '''kalismic temperament''', which splits the [[octave]] into two equal parts, each representing 99/70~140/99. Tempering it out also means that [[10/9]] and [[11/7]] are 1/2-octave apart, as well as are [[11/10]] and [[14/9]]. Odd-numbered edos cannot temper it out, as they do not have a semioctave.

			See [[Rank-4 temperament #Kalismic (9801/9800)]] for some technical details. See [[Kalismic temperaments]] for a collection of rank-3 temperaments where it is tempered out.

	== Etymology ==		== Etymology ==

FloraC at 10:19, 24 February 2026

2026-02-24T10:19:13Z

← Older revision		Revision as of 10:19, 24 February 2026
Line 4:		Line 4:
	\| Comma = yes		\| Comma = yes
	}}		}}

	'''9801/9800''', the '''kalisma''', sometimes described as ''Gauss' comma'', is an [[unnoticeable comma\|unnoticeable]] [[11-limit]] [[comma]] measuring about 0.18{{cent}}. It is the smallest 11-limit [[superparticular]] interval. It can be described as the difference between [[99/70]] and its [[octave complement]] [[140/99]], or between ([[35/33]])<sup>2</sup> and [[9/8]].		'''9801/9800''', the '''kalisma''', sometimes described as ''Gauss' comma'', is an [[unnoticeable comma\|unnoticeable]] [[11-limit]] [[comma]] measuring about 0.18{{cent}}. It is the smallest 11-limit [[superparticular]] interval. It can be described as the difference between [[99/70]] and its [[octave complement]] [[140/99]], or between ([[35/33]])<sup>2</sup> and [[9/8]].

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	* [[List of superparticular intervals]]		* [[List of superparticular intervals]]

	== ~~Notes~~ ==		== References ==

	[[Category:Kalismic]]		[[Category:Kalismic]]
	[[Category:Commas named by translating something into another language]]		[[Category:Commas named by translating something into another language]]
	[[Category:Commas named after mathematicians]]		[[Category:Commas named after mathematicians]]

Squib: as s33/s35, it splits 9/8 (=36/32) in two

2026-02-22T17:52:46Z

as s33/s35, it splits 9/8 (=36/32) in two

← Older revision		Revision as of 17:52, 22 February 2026
Line 5:		Line 5:
	}}		}}

	'''9801/9800''', the '''kalisma''', sometimes described as ''Gauss' comma'', is an [[unnoticeable comma\|unnoticeable]] [[11-limit]] [[comma]] measuring about 0.18{{cent}}. It is the smallest 11-limit [[superparticular]] interval. It can be described as the difference between [[99/70]] and its [[octave complement]] [[140/99]].		'''9801/9800''', the '''kalisma''', sometimes described as ''Gauss' comma'', is an [[unnoticeable comma\|unnoticeable]] [[11-limit]] [[comma]] measuring about 0.18{{cent}}. It is the smallest 11-limit [[superparticular]] interval. It can be described as the difference between [[99/70]] and its [[octave complement]] [[140/99]], or between ([[35/33]])<sup>2</sup> and [[9/8]].

	In terms of superparticular commas, it is the difference between:		In terms of superparticular commas, it is the difference between:

FloraC: Not all of these are notable.

2026-02-22T14:57:32Z

Not all of these are notable.

← Older revision		Revision as of 14:57, 22 February 2026
Line 5:		Line 5:
	}}		}}

	'''9801/9800''', the '''kalisma''', sometimes described as ''Gauss' comma'', is an [[unnoticeable comma\|unnoticeable]] [[11-limit]] [[comma]] measuring about 0.18{{cent}}. It is the smallest 11-limit [[superparticular]] interval.		'''9801/9800''', the '''kalisma''', sometimes described as ''Gauss' comma'', is an [[unnoticeable comma\|unnoticeable]] [[11-limit]] [[comma]] measuring about 0.18{{cent}}. It is the smallest 11-limit [[superparticular]] interval. It can be described as the difference between [[99/70]] and its [[octave complement]] [[140/99]].

	~~It can be described as~~ the difference between:		In terms of superparticular commas, it is the difference between:
			* [[99/98]] and [[100/99]]
			* [[3025/3024]] and [[4375/4374]]

	* [[99/98]] and [[100/99]]		It is also the difference between the following notable non-superparticular commas:
	* [[99/70]] and [[140/99]]
	* [[245/243]] and [[121/120]]		* [[245/243]] and [[121/120]]
	* [[245/242]] and [[81/80]]		* [[245/242]] and [[81/80]]
	* [[125/121]] and [[405/392]]
	* [[4375/4374]] and [[3025/3024]]
	* [[250047/250000]] and [[151263/151250]]

	It also factors into the two smallest 13-limit superparticular commas: 9801/9800 = ([[10648/10647]])([[123201/123200]]).		It also factors into the two smallest 13-limit superparticular commas: 9801/9800 = ([[10648/10647]])⋅([[123201/123200]]).

	== Temperaments ==		== Temperaments ==

Eufalesio: More differences!

2026-02-22T12:52:09Z

More differences!

← Older revision		Revision as of 12:52, 22 February 2026
Line 7:		Line 7:
	'''9801/9800''', the '''kalisma''', sometimes described as ''Gauss' comma'', is an [[unnoticeable comma\|unnoticeable]] [[11-limit]] [[comma]] measuring about 0.18{{cent}}. It is the smallest 11-limit [[superparticular]] interval.		'''9801/9800''', the '''kalisma''', sometimes described as ''Gauss' comma'', is an [[unnoticeable comma\|unnoticeable]] [[11-limit]] [[comma]] measuring about 0.18{{cent}}. It is the smallest 11-limit [[superparticular]] interval.

	It can be described as the difference between ~~[[99/98]] and [[100/99]], and between [[99/70]] and its octave complement, [[140/99]]. It is also the difference between [[245/243]] and [[121/120]], and between [[245/242]] and [[81/80]].~~		It can be described as the difference between:

	It factors into the two smallest 13-limit superparticular commas: 9801/9800 = ([[10648/10647]])([[123201/123200]]).		* [[99/98]] and [[100/99]]
			* [[99/70]] and [[140/99]]
			* [[245/243]] and [[121/120]]
			* [[245/242]] and [[81/80]]
			* [[125/121]] and [[405/392]]
			* [[4375/4374]] and [[3025/3024]]
			* [[250047/250000]] and [[151263/151250]]

			It also factors into the two smallest 13-limit superparticular commas: 9801/9800 = ([[10648/10647]])([[123201/123200]]).

	== Temperaments ==		== Temperaments ==