100/99 - Revision history

FloraC: + link

2025-11-05T08:39:38Z

+ link

← Older revision		Revision as of 08:39, 5 November 2025
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	* [[List of superparticular intervals]]		* [[List of superparticular intervals]]
	* [[Gallery of just intervals]]		* [[Gallery of just intervals]]
			* [[:File: Demo 100 99 tempered.pdf]]

	[[Category:Ptolemismic]]		[[Category:Ptolemismic]]
	[[Category:Commas named after polymaths]]		[[Category:Commas named after polymaths]]

FloraC: Move stuff to the appropriate sections. Improve linking

2025-01-07T08:42:26Z

Move stuff to the appropriate sections. Improve linking

← Older revision		Revision as of 08:42, 7 January 2025
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	\| Comma = yes		\| Comma = yes
	}}		}}
	In [[just intonation]], '''100/99''', the '''ptolemisma''' or '''Ptolemy's comma''', is a [[small comma\|small]] [[superparticular ratio\|superparticular]] [[comma]] of around 17.4¢ which makes the difference between [[11/10]], the greater undecimal neutral second of about 165¢, and [[10/9]], the 5-limit minor whole tone of about 182.4¢.		In [[just intonation]], '''100/99''', the '''ptolemisma''' or '''Ptolemy's comma''', is a [[small comma\|small]] [[superparticular ratio\|superparticular]] [[comma]] of around 17.4¢ which makes the difference between [[11/10]], the greater undecimal neutral second of about 165¢, and [[10/9]], the 5-limit minor whole tone of about 182.4¢. It is also the difference between [[25/24]] and [[33/32]]. In terms of commatic relations it notably factors into [[225/224]] and [[896/891]].

	== Temperaments ==		== Temperaments ==
	Tempering out this interval in the 11-limit results in the rank-4 ptolemismic temperament (→ [[Rank-4 temperament #Ptolemismic (100/99)]]). Equal ~~temperaments~~ in which 100/99 is tempered out include [[22edo]], [[41edo]] and others. In such systems, 11/10 and 10/9 are equated. This is in contrast to the more familiar tempering out of [[81/80]], which results in meantone and other temperaments, in which 10/9 is equated, not with 11/10, but with [[9/8]]. However, meantone and ptolemismic are not necessarily mutually exclusive–the [[flattone]] temperament (known as "hypnotone" in the 2.3.5.11 subgroup) merges both and has [[11/10]], [[10/9]] and [[9/8]] all tempered to a 10/9-like interval. Along with being the difference between 11/10 and 10/9, 100/99 is the amount by which an [[11/8]] and two [[6/5]]'s fall short of an octave, so that tempering out 100/99 allows for the [[ptolemismic triad]] which has intervals of 11/8, 6/5, 6/5~~. It is also the difference between [[25/24]] and [[33/32]]. In terms of commatic relations it notably factors into [[225/224]] and [[896/891]]~~.		[[Tempering out]] this interval in the 11-limit results in the rank-4 ptolemismic temperament (→ [[Rank-4 temperament #Ptolemismic (100/99)]]). [[Equal temperament]]s in which 100/99 is tempered out include [[22edo]], [[41edo]] and others. In such systems, 11/10 and 10/9 are equated. This is in contrast to the more familiar tempering out of [[81/80]], which results in meantone and other temperaments, in which 10/9 is equated, not with 11/10, but with [[9/8]]. However, meantone and ptolemismic are not necessarily mutually exclusive–the [[flattone]] temperament (known as "hypnotone" in the 2.3.5.11 subgroup) merges both and has [[11/10]], [[10/9]] and [[9/8]] all tempered to a 10/9-like interval. Along with being the difference between 11/10 and 10/9, 100/99 is the amount by which an [[11/8]] and two [[6/5]]'s fall short of an octave, so that tempering out 100/99 allows for the [[ptolemismic triad]] which has intervals of 11/8, 6/5, 6/5.

	See [[Ptolemismic clan]] for the clan of rank-3 temperaments where it is tempered out.		See [[Ptolemismic clan]] for the clan of rank-3 temperaments where it is tempered out.

	== Approximation ==		== Approximation ==
	If the interval is not tempered and instead treated as an identity, it is extremely closely represented by one step of [[69edo]]. The associated unnoticeable comma, [[ptolemi-nicema]], represents the difference between 69 100/~~99s~~ and the octave, is only 0.56 cents wide. Nice.		If the interval is not tempered out and instead treated as an identity, it is extremely closely represented by one step of [[69edo]]. The associated unnoticeable comma, [[ptolemi-nicema]], represents the difference between 69 100/99's and the octave, is only 0.56 cents wide. Nice.

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

FloraC: Rework to absorb some of the links in the see also section to the main text

2025-01-07T08:38:33Z

Rework to absorb some of the links in the see also section to the main text

← Older revision		Revision as of 08:38, 7 January 2025
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	[[de:100/99]]		[[de:100/99]]
	{{Infobox Interval		{{Infobox Interval
	\| Name = Ptolemy's comma~~, ptolemisma~~		\| Name = ptolemisma, Ptolemy's comma
	\| Color name = 1uyy1, luyoyo 1sn,<br>Luyoyo comma		\| Color name = 1uyy1, luyoyo 1sn,<br>Luyoyo comma
	\| Comma = yes		\| Comma = yes
	}}		}}
	In [[just intonation]], '''100/99''', the '''~~Ptolemy~~'~~s comma~~''' or '''~~ptolemisma~~''', is a [[superparticular]] ~~interval~~ of around 17.4¢ which makes the difference between [[11/10]], the greater undecimal neutral second of about 165¢, and [[10/9]], the 5-limit minor whole tone of about 182.4¢.		In [[just intonation]], '''100/99''', the '''ptolemisma''' or '''Ptolemy's comma''', is a [[small comma\|small]] [[superparticular ratio\|superparticular]] [[comma]] of around 17.4¢ which makes the difference between [[11/10]], the greater undecimal neutral second of about 165¢, and [[10/9]], the 5-limit minor whole tone of about 182.4¢.

			== Temperaments ==
			Tempering out this interval in the 11-limit results in the rank-4 ptolemismic temperament (→ [[Rank-4 temperament #Ptolemismic (100/99)]]). Equal temperaments in which 100/99 is tempered out include [[22edo]], [[41edo]] and others. In such systems, 11/10 and 10/9 are equated. This is in contrast to the more familiar tempering out of [[81/80]], which results in meantone and other temperaments, in which 10/9 is equated, not with 11/10, but with [[9/8]]. However, meantone and ptolemismic are not necessarily mutually exclusive–the [[flattone]] temperament (known as "hypnotone" in the 2.3.5.11 subgroup) merges both and has [[11/10]], [[10/9]] and [[9/8]] all tempered to a 10/9-like interval. Along with being the difference between 11/10 and 10/9, 100/99 is the amount by which an [[11/8]] and two [[6/5]]'s fall short of an octave, so that tempering out 100/99 allows for the [[ptolemismic triad]] which has intervals of 11/8, 6/5, 6/5. It is also the difference between [[25/24]] and [[33/32]]. In terms of commatic relations it notably factors into [[225/224]] and [[896/891]].

			See [[Ptolemismic clan]] for the clan of rank-3 temperaments where it is tempered out.

	~~== Tempering ==~~
	Temperaments in which 100/99 is tempered out include [[22edo]], [[41edo]] and others; in such systems, 11/10 and 10/9 are equated. This is in contrast to the more familiar tempering out of [[81/80]], which results in meantone and other temperaments, in which 10/9 is equated, not with 11/10, but with [[9/8]]. However, meantone and ptolemismic are not necessarily mutually exclusive–the [[flattone]] temperament (known as "hypnotone" in the 2.3.5.11 subgroup) merges both and has [[11/10]], [[10/9]] and [[9/8]] all tempered to a 10/9-like interval. Along with being the difference between 11/10 and 10/9, 100/99 is the amount by which an [[11/8]] and two [[6/5]]s fall short of an octave, so that tempering out 100/99 allows for the [[ptolemismic triad]] which has intervals of 11/8, 6/5, 6/5. It is also the difference between [[25/24]] and [[33/32]]. In terms of commatic relations it notably factors into [[225/224]] and [[896/891]].
	== Approximation ==		== Approximation ==
	If the interval is not tempered and instead treated as an identity, it is extremely closely represented by one step of [[69edo]]. The associated unnoticeable comma, [[ptolemi-nicema]], represents the difference between 69 100/99s and the octave, is only 0.56 cents wide. Nice.		If the interval is not tempered and instead treated as an identity, it is extremely closely represented by one step of [[69edo]]. The associated unnoticeable comma, [[ptolemi-nicema]], represents the difference between 69 100/99s and the octave, is only 0.56 cents wide. Nice.

	== See also ==		== See also ==
	* [[Ptolemismic triad]]
	* [[Rank-4 temperament #Ptolemismic (100/99)]]
	* [[Ptolemismic clan]], the clan of rank-3 temperaments where it is tempered out
	* [[Small comma]]
	* [[List of superparticular intervals]]		* [[List of superparticular intervals]]
	* [[Gallery of just intervals]]		* [[Gallery of just intervals]]

Fitzgerald Lee: /* Approximation */:3

2025-01-07T05:12:51Z

Approximation: :3

← Older revision		Revision as of 05:12, 7 January 2025
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	Temperaments in which 100/99 is tempered out include [[22edo]], [[41edo]] and others; in such systems, 11/10 and 10/9 are equated. This is in contrast to the more familiar tempering out of [[81/80]], which results in meantone and other temperaments, in which 10/9 is equated, not with 11/10, but with [[9/8]]. However, meantone and ptolemismic are not necessarily mutually exclusive–the [[flattone]] temperament (known as "hypnotone" in the 2.3.5.11 subgroup) merges both and has [[11/10]], [[10/9]] and [[9/8]] all tempered to a 10/9-like interval. Along with being the difference between 11/10 and 10/9, 100/99 is the amount by which an [[11/8]] and two [[6/5]]s fall short of an octave, so that tempering out 100/99 allows for the [[ptolemismic triad]] which has intervals of 11/8, 6/5, 6/5. It is also the difference between [[25/24]] and [[33/32]]. In terms of commatic relations it notably factors into [[225/224]] and [[896/891]].		Temperaments in which 100/99 is tempered out include [[22edo]], [[41edo]] and others; in such systems, 11/10 and 10/9 are equated. This is in contrast to the more familiar tempering out of [[81/80]], which results in meantone and other temperaments, in which 10/9 is equated, not with 11/10, but with [[9/8]]. However, meantone and ptolemismic are not necessarily mutually exclusive–the [[flattone]] temperament (known as "hypnotone" in the 2.3.5.11 subgroup) merges both and has [[11/10]], [[10/9]] and [[9/8]] all tempered to a 10/9-like interval. Along with being the difference between 11/10 and 10/9, 100/99 is the amount by which an [[11/8]] and two [[6/5]]s fall short of an octave, so that tempering out 100/99 allows for the [[ptolemismic triad]] which has intervals of 11/8, 6/5, 6/5. It is also the difference between [[25/24]] and [[33/32]]. In terms of commatic relations it notably factors into [[225/224]] and [[896/891]].
	== Approximation ==		== Approximation ==
	If the interval is not tempered and instead treated as an identity, it is extremely closely represented by one step of [[69edo]]. The associated unnoticeable comma, [[ptolemi-nicema]], represents the difference between 69 100/99s and the octave, is only 0.56 cents wide.		If the interval is not tempered and instead treated as an identity, it is extremely closely represented by one step of [[69edo]]. The associated unnoticeable comma, [[ptolemi-nicema]], represents the difference between 69 100/99s and the octave, is only 0.56 cents wide. Nice.

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

BudjarnLambeth at 01:55, 4 November 2024

2024-11-04T01:55:47Z

← Older revision		Revision as of 01:55, 4 November 2024
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	[[Category:Ptolemismic]]		[[Category:Ptolemismic]]
	[[Category:Commas named after ~~individuals~~]]		[[Category:Commas named after polymaths]]

BudjarnLambeth at 10:00, 3 November 2024

2024-11-03T10:00:18Z

← Older revision		Revision as of 10:00, 3 November 2024
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	[[Category:Ptolemismic]]		[[Category:Ptolemismic]]
			[[Category:Commas named after individuals]]

Eliora: sectoning + approximation and relationship to 69edo

2024-10-09T19:12:43Z

sectoning + approximation and relationship to 69edo

← Older revision		Revision as of 19:12, 9 October 2024
Line 5:		Line 5:
	\| Comma = yes		\| Comma = yes
	}}		}}
	In [[just intonation]], '''100/99''', the '''Ptolemy's comma''' or '''ptolemisma''', is a [[superparticular]] interval of around 17.4¢ which makes the difference between [[11/10]], the greater undecimal neutral second of about 165¢, and [[10/9]], the 5-limit minor whole tone of about 182.4¢. Temperaments in which 100/99 is tempered out include [[22edo]], [[41edo]] and others; in such systems, 11/10 and 10/9 are equated. This is in contrast to the more familiar tempering out of [[81/80]], which results in meantone and other temperaments, in which 10/9 is equated, not with 11/10, but with [[9/8]]. However, meantone and ptolemismic are not necessarily mutually exclusive–the [[flattone]] temperament (known as "hypnotone" in the 2.3.5.11 subgroup) merges both and has [[11/10]], [[10/9]] and [[9/8]] all tempered to a 10/9-like interval. Along with being the difference between 11/10 and 10/9, 100/99 is the amount by which an [[11/8]] and two [[6/5]]s fall short of an octave, so that tempering out 100/99 allows for the [[ptolemismic triad]] which has intervals of 11/8, 6/5, 6/5. It is also the difference between [[25/24]] and [[33/32]]. In terms of commatic relations it notably factors into [[225/224]] and [[896/891]].		In [[just intonation]], '''100/99''', the '''Ptolemy's comma''' or '''ptolemisma''', is a [[superparticular]] interval of around 17.4¢ which makes the difference between [[11/10]], the greater undecimal neutral second of about 165¢, and [[10/9]], the 5-limit minor whole tone of about 182.4¢.

			== Tempering ==
			Temperaments in which 100/99 is tempered out include [[22edo]], [[41edo]] and others; in such systems, 11/10 and 10/9 are equated. This is in contrast to the more familiar tempering out of [[81/80]], which results in meantone and other temperaments, in which 10/9 is equated, not with 11/10, but with [[9/8]]. However, meantone and ptolemismic are not necessarily mutually exclusive–the [[flattone]] temperament (known as "hypnotone" in the 2.3.5.11 subgroup) merges both and has [[11/10]], [[10/9]] and [[9/8]] all tempered to a 10/9-like interval. Along with being the difference between 11/10 and 10/9, 100/99 is the amount by which an [[11/8]] and two [[6/5]]s fall short of an octave, so that tempering out 100/99 allows for the [[ptolemismic triad]] which has intervals of 11/8, 6/5, 6/5. It is also the difference between [[25/24]] and [[33/32]]. In terms of commatic relations it notably factors into [[225/224]] and [[896/891]].
			== Approximation ==
			If the interval is not tempered and instead treated as an identity, it is extremely closely represented by one step of [[69edo]]. The associated unnoticeable comma, [[ptolemi-nicema]], represents the difference between 69 100/99s and the octave, is only 0.56 cents wide.

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

Lériendil at 14:00, 19 September 2024

2024-09-19T14:00:17Z

← Older revision		Revision as of 14:00, 19 September 2024
Line 5:		Line 5:
	\| Comma = yes		\| Comma = yes
	}}		}}
	In [[just intonation]], '''100/99''', the '''Ptolemy's comma''' or '''ptolemisma''', is a [[superparticular]] interval of around 17.4¢ which makes the difference between [[11/10]], the greater undecimal neutral second of about 165¢, and [[10/9]], the 5-limit minor whole tone of about 182.4¢. Temperaments in which 100/99 is tempered out include [[22edo]], [[41edo]] and others; in such systems, 11/10 and 10/9 are equated. This is in contrast to the more familiar tempering out of [[81/80]], which results in meantone and other temperaments, in which 10/9 is equated, not with 11/10, but with [[9/8]]. However, meantone and ptolemismic are not necessarily mutually exclusive–the [[flattone]] temperament merges both and has [[11/10]], [[10/9]] and [[9/8]] all tempered to a 10/9-like interval. Along with being the difference between 11/10 and 10/9, 100/99 is the amount by which an [[11/8]] and two [[6/5]]s fall short of an octave, so that tempering out 100/99 allows for the [[ptolemismic triad]] which has intervals of 11/8, 6/5, 6/5. It is also the difference between [[25/24]] and [[33/32]]. In terms of commatic relations it notably factors into [[225/224]] and [[896/891]].		In [[just intonation]], '''100/99''', the '''Ptolemy's comma''' or '''ptolemisma''', is a [[superparticular]] interval of around 17.4¢ which makes the difference between [[11/10]], the greater undecimal neutral second of about 165¢, and [[10/9]], the 5-limit minor whole tone of about 182.4¢. Temperaments in which 100/99 is tempered out include [[22edo]], [[41edo]] and others; in such systems, 11/10 and 10/9 are equated. This is in contrast to the more familiar tempering out of [[81/80]], which results in meantone and other temperaments, in which 10/9 is equated, not with 11/10, but with [[9/8]]. However, meantone and ptolemismic are not necessarily mutually exclusive–the [[flattone]] temperament (known as "hypnotone" in the 2.3.5.11 subgroup) merges both and has [[11/10]], [[10/9]] and [[9/8]] all tempered to a 10/9-like interval. Along with being the difference between 11/10 and 10/9, 100/99 is the amount by which an [[11/8]] and two [[6/5]]s fall short of an octave, so that tempering out 100/99 allows for the [[ptolemismic triad]] which has intervals of 11/8, 6/5, 6/5. It is also the difference between [[25/24]] and [[33/32]]. In terms of commatic relations it notably factors into [[225/224]] and [[896/891]].

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

Aura: Added information.

2024-09-19T10:53:55Z

Added information.

← Older revision		Revision as of 10:53, 19 September 2024
Line 5:		Line 5:
	\| Comma = yes		\| Comma = yes
	}}		}}
	In [[just intonation]], '''100/99''', the '''Ptolemy's comma''' or '''ptolemisma''', is a [[superparticular]] interval of around 17.4¢ which makes the difference between [[11/10]], the greater undecimal neutral second of about 165¢, and [[10/9]], the 5-limit minor whole tone of about 182.4¢. Temperaments in which 100/99 is tempered out include [[22edo]], [[41edo]] and others; in such systems, 11/10 and 10/9 are equated. This is in contrast to the more familiar tempering out of [[81/80]], which results in meantone and other temperaments, in which 10/9 is equated, not with 11/10, but with [[9/8]]. However, meantone and ptolemismic are not necessarily mutually exclusive–the [[flattone]] temperament merges both and has [[11/10]], [[10/9]] and [[9/8]] all tempered to a 10/9-like interval. Along with being the difference between 11/10 and 10/9, 100/99 is the amount by which an [[11/8]] and two [[6/5]]s fall short of an octave, so that tempering out 100/99 allows for the [[ptolemismic triad]] which has intervals of 11/8, 6/5, 6/5. It is also the difference between [[25/24]] and [[33/32]].		In [[just intonation]], '''100/99''', the '''Ptolemy's comma''' or '''ptolemisma''', is a [[superparticular]] interval of around 17.4¢ which makes the difference between [[11/10]], the greater undecimal neutral second of about 165¢, and [[10/9]], the 5-limit minor whole tone of about 182.4¢. Temperaments in which 100/99 is tempered out include [[22edo]], [[41edo]] and others; in such systems, 11/10 and 10/9 are equated. This is in contrast to the more familiar tempering out of [[81/80]], which results in meantone and other temperaments, in which 10/9 is equated, not with 11/10, but with [[9/8]]. However, meantone and ptolemismic are not necessarily mutually exclusive–the [[flattone]] temperament merges both and has [[11/10]], [[10/9]] and [[9/8]] all tempered to a 10/9-like interval. Along with being the difference between 11/10 and 10/9, 100/99 is the amount by which an [[11/8]] and two [[6/5]]s fall short of an octave, so that tempering out 100/99 allows for the [[ptolemismic triad]] which has intervals of 11/8, 6/5, 6/5. It is also the difference between [[25/24]] and [[33/32]]. In terms of commatic relations it notably factors into [[225/224]] and [[896/891]].

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

CompactStar at 02:53, 4 February 2024

2024-02-04T02:53:39Z

← Older revision		Revision as of 02:53, 4 February 2024
Line 5:		Line 5:
	\| Comma = yes		\| Comma = yes
	}}		}}
	In [[just intonation]], '''100/99''', the '''Ptolemy's comma''' or '''ptolemisma''', is a [[superparticular]] interval of around 17.4¢ which makes the difference between [[11/10]], the greater undecimal neutral second of about 165¢, and [[10/9]], the 5-limit minor whole tone of about 182.4¢. Temperaments in which 100/99 is tempered out include [[22edo]], [[41edo]] and others; in such systems, 11/10 and 10/9 are equated. This is in contrast to the more familiar tempering out of [[81/80]], which results in meantone and other temperaments, in which 10/9 is equated, not with 11/10, but with [[9/8]]. However, meantone and ptolemismic are not necessarily mutually exclusive–the [[flattone]] temperament merges both and has [[11/10]], [[10/9]] and [[9/8] all tempered to a 10/9-like interval. Along with being the difference between 11/10 and 10/9, 100/99 is the amount by which an [[11/8]] and two [[6/5]]s fall short of an octave, so that tempering out 100/99 allows for the [[ptolemismic triad]] which has intervals of 11/8, 6/5, 6/5. It is also the difference between [[25/24]] and [[33/32]].		In [[just intonation]], '''100/99''', the '''Ptolemy's comma''' or '''ptolemisma''', is a [[superparticular]] interval of around 17.4¢ which makes the difference between [[11/10]], the greater undecimal neutral second of about 165¢, and [[10/9]], the 5-limit minor whole tone of about 182.4¢. Temperaments in which 100/99 is tempered out include [[22edo]], [[41edo]] and others; in such systems, 11/10 and 10/9 are equated. This is in contrast to the more familiar tempering out of [[81/80]], which results in meantone and other temperaments, in which 10/9 is equated, not with 11/10, but with [[9/8]]. However, meantone and ptolemismic are not necessarily mutually exclusive–the [[flattone]] temperament merges both and has [[11/10]], [[10/9]] and [[9/8]] all tempered to a 10/9-like interval. Along with being the difference between 11/10 and 10/9, 100/99 is the amount by which an [[11/8]] and two [[6/5]]s fall short of an octave, so that tempering out 100/99 allows for the [[ptolemismic triad]] which has intervals of 11/8, 6/5, 6/5. It is also the difference between [[25/24]] and [[33/32]].

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