20480/19683 - Revision history

FloraC: Sectioning. Linking. - 17edo in favor of 49edo. + category

2026-05-01T06:21:31Z

Sectioning. Linking. - 17edo in favor of 49edo. + category

← Older revision		Revision as of 06:21, 1 May 2026
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	\| Color name = sayo 2nd, sy2, Sayo comma		\| Color name = sayo 2nd, sy2, Sayo comma
	}}		}}
	'''20480/19683''', the '''retroptolemaic minor second''', is a [[5-limit]] [[interval]] measuring about 68.7{{cent}}. It gets its name from being equal to being one [[81/80\|syntonic comma (81/80)]] flatter than the [[256/243\|Pythagorean limma (256/243)]], in contrast to [[16/15]] which is a syntonic comma ''sharper'' than a Pythagorean limma. When treated as a [[comma]] to be tempered out, it is the '''superpyth comma''', and is the difference between 5/4 and an [[~~Octave~~ reduction\|octave-reduced]] stack of nine [[3/2]]'s, as well as [[25/24]] minus a [[~~Schisma~~\|schisma (32805/32768)]]. Tempering it out by itself defines [[~~Archytas_clan~~#Superpyth\|~~the~~ 5-limit version of superpyth temperament]]. Notable [[edo]]s that temper it out include [[~~17edo~~\|17]], [[~~22edo~~\|22]], and [[~~27edo~~\|27]].		'''20480/19683''', the '''retroptolemaic minor second''', is a [[5-limit]] [[interval]] measuring about 68.7{{cent}}. It gets its name from being equal to being one [[81/80\|syntonic comma (81/80)]] flatter than the [[256/243\|Pythagorean limma (256/243)]], in contrast to [[16/15]] which is a syntonic comma ''sharper'' than a Pythagorean limma.

			== Temperaments ==
			When treated as a [[comma]] to be [[tempering out\|tempered out]], it is the '''superpyth comma''', and is the difference between [[5/4]] and an [[octave reduction\|octave-reduced]] stack of nine [[3/2]]'s, as well as [[25/24]] minus a [[schisma\|schisma (32805/32768)]]. Tempering it out by itself defines the [[syntonic–diatonic equivalence continuum #Superpyth (5-limit)\|5-limit version of superpyth temperament]]. Notable [[edo]]s that temper it out include [[22edo\|22]], [[27edo\|27]], and [[49edo\|49]].

	== Comma pump example ==		== Comma pump example ==

	[[File:Akselai superpyth comma pump (JI).wav\|thumb\|5-limit JI]]		[[File:Akselai superpyth comma pump (JI).wav\|thumb\|5-limit JI]]
	[[File:Akselai superpyth comma pump (22edo).wav\|thumb\|22edo]]		[[File:Akselai superpyth comma pump (22edo).wav\|thumb\|22edo]]

	The progression returns to the original chord in 22edo, but modulates downward by 20480/19683 in JI.		The progression returns to the original chord in 22edo, but modulates downward by 20480/19683 in JI.

	[[File:Superpyth comma pump.png\|thumb\|Superpyth comma pump in JI and 22edo.]]		[[File:Superpyth comma pump.png\|thumb\|Superpyth comma pump in JI and 22edo.]]

			[[Category:Superpyth]]
	[[Category:Second]]		[[Category:Second]]
	[[Category:Semitone]]		[[Category:Semitone]]

ArrowHead294 at 16:00, 11 December 2024

2024-12-11T16:00:51Z

← Older revision		Revision as of 16:00, 11 December 2024
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	\| Color name = sayo 2nd, sy2, Sayo comma		\| Color name = sayo 2nd, sy2, Sayo comma
	}}		}}
	'''20480/19683''', the '''retroptolemaic minor second''', is a [[5-limit]] [[interval]] measuring about 68.7{{cent}}. It is equal to the [[256/243\|Pythagorean ~~minor second~~ (256/243)]] ~~flattened by a~~ [[81/~~80\|~~syntonic comma ~~(81/80)]]~~. When treated as a [[comma]] to be tempered out, it is the '''superpyth comma''', and is the difference between 5/4 and an [[Octave reduction\|octave-reduced]] stack of nine [[3/2]]'s, as well as [[25/24]] minus a [[Schisma\|schisma (32805/32768)]]. Tempering it out by itself defines [[Archytas_clan#Superpyth\|the 5-limit version of superpyth temperament]]. Notable [[edo]]s that temper it out include [[17edo\|17]], [[22edo\|22]], and [[27edo\|27]].		'''20480/19683''', the '''retroptolemaic minor second''', is a [[5-limit]] [[interval]] measuring about 68.7{{cent}}. It gets its name from being equal to being one [[81/80\|syntonic comma (81/80)]] flatter than the [[256/243\|Pythagorean limma (256/243)]], in contrast to [[16/15]] which is a syntonic comma ''sharper'' than a Pythagorean limma. When treated as a [[comma]] to be tempered out, it is the '''superpyth comma''', and is the difference between 5/4 and an [[Octave reduction\|octave-reduced]] stack of nine [[3/2]]'s, as well as [[25/24]] minus a [[Schisma\|schisma (32805/32768)]]. Tempering it out by itself defines [[Archytas_clan#Superpyth\|the 5-limit version of superpyth temperament]]. Notable [[edo]]s that temper it out include [[17edo\|17]], [[22edo\|22]], and [[27edo\|27]].

	== Comma pump example ==		== Comma pump example ==

Akselai at 13:55, 23 March 2024

2024-03-23T13:55:08Z

← Older revision		Revision as of 13:55, 23 March 2024
Line 4:		Line 4:
	}}		}}
	'''20480/19683''', the '''retroptolemaic minor second''', is a [[5-limit]] [[interval]] measuring about 68.7{{cent}}. It is equal to the [[256/243\|Pythagorean minor second (256/243)]] flattened by a [[81/80\|syntonic comma (81/80)]]. When treated as a [[comma]] to be tempered out, it is the '''superpyth comma''', and is the difference between 5/4 and an [[Octave reduction\|octave-reduced]] stack of nine [[3/2]]'s, as well as [[25/24]] minus a [[Schisma\|schisma (32805/32768)]]. Tempering it out by itself defines [[Archytas_clan#Superpyth\|the 5-limit version of superpyth temperament]]. Notable [[edo]]s that temper it out include [[17edo\|17]], [[22edo\|22]], and [[27edo\|27]].		'''20480/19683''', the '''retroptolemaic minor second''', is a [[5-limit]] [[interval]] measuring about 68.7{{cent}}. It is equal to the [[256/243\|Pythagorean minor second (256/243)]] flattened by a [[81/80\|syntonic comma (81/80)]]. When treated as a [[comma]] to be tempered out, it is the '''superpyth comma''', and is the difference between 5/4 and an [[Octave reduction\|octave-reduced]] stack of nine [[3/2]]'s, as well as [[25/24]] minus a [[Schisma\|schisma (32805/32768)]]. Tempering it out by itself defines [[Archytas_clan#Superpyth\|the 5-limit version of superpyth temperament]]. Notable [[edo]]s that temper it out include [[17edo\|17]], [[22edo\|22]], and [[27edo\|27]].

			== Comma pump example ==

			[[File:Akselai superpyth comma pump (JI).wav\|thumb\|5-limit JI]]
			[[File:Akselai superpyth comma pump (22edo).wav\|thumb\|22edo]]
			The progression returns to the original chord in 22edo, but modulates downward by 20480/19683 in JI.

			[[File:Superpyth comma pump.png\|thumb\|Superpyth comma pump in JI and 22edo.]]

	[[Category:Second]]		[[Category:Second]]
	[[Category:Semitone]]		[[Category:Semitone]]

Cmloegcmluin at 05:04, 25 February 2024

2024-02-25T05:04:36Z

← Older revision		Revision as of 05:04, 25 February 2024
Line 3:		Line 3:
	\| Color name = sayo 2nd, sy2, Sayo comma		\| Color name = sayo 2nd, sy2, Sayo comma
	}}		}}
	'''20480/19683''', the '''retroptolemaic minor second''', is a [[5-limit]] [[interval]] measuring about 68.7{{cent}}. It is equal to the [[256/243\|Pythagorean minor second (256/243)]] flattened by a [[81/80\|syntonic comma (81/80)]]. When treated as a [[comma]] to be tempered out, it is the '''superpyth comma''', and is the difference between 5/4 and an [[Octave reduction\|octave-reduced]] stack of nine [[3/2]]'s, as well as [[25/24]] minus a [[Schisma\|schisma (32805/32768)]]. Tempering it out by itself defines the 5-limit version of [[superpyth]] ~~temperament~~. Notable [[edo]]s that temper it out include [[17edo\|17]], [[22edo\|22]], and [[27edo\|27]].		'''20480/19683''', the '''retroptolemaic minor second''', is a [[5-limit]] [[interval]] measuring about 68.7{{cent}}. It is equal to the [[256/243\|Pythagorean minor second (256/243)]] flattened by a [[81/80\|syntonic comma (81/80)]]. When treated as a [[comma]] to be tempered out, it is the '''superpyth comma''', and is the difference between 5/4 and an [[Octave reduction\|octave-reduced]] stack of nine [[3/2]]'s, as well as [[25/24]] minus a [[Schisma\|schisma (32805/32768)]]. Tempering it out by itself defines [[Archytas_clan#Superpyth\|the 5-limit version of superpyth temperament]]. Notable [[edo]]s that temper it out include [[17edo\|17]], [[22edo\|22]], and [[27edo\|27]].

	[[Category:Second]]		[[Category:Second]]
	[[Category:Semitone]]		[[Category:Semitone]]

TallKite at 22:57, 21 October 2023

2023-10-21T22:57:30Z

← Older revision		Revision as of 22:57, 21 October 2023
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	{{Infobox Interval		{{Infobox Interval
	\| Name = retroptolemaic minor second, superpyth comma		\| Name = retroptolemaic minor second, superpyth comma
	\| Color name = sayo 2nd, ~~sayo~~ comma		\| Color name = sayo 2nd, sy2, Sayo comma
	}}		}}
	'''20480/19683''', the '''retroptolemaic minor second''', is a [[5-limit]] [[interval]] measuring about 68.7{{cent}}. It is equal to the [[256/243\|Pythagorean minor second (256/243)]] flattened by a [[81/80\|syntonic comma (81/80)]]. When treated as a [[comma]] to be tempered out, it is the '''superpyth comma''', and is the difference between 5/4 and an [[Octave reduction\|octave-reduced]] stack of nine [[3/2]]'s, as well as [[25/24]] minus a [[Schisma\|schisma (32805/32768)]]. Tempering it out by itself defines the 5-limit version of [[superpyth]] temperament. Notable [[edo]]s that temper it out include [[17edo\|17]], [[22edo\|22]], and [[27edo\|27]].		'''20480/19683''', the '''retroptolemaic minor second''', is a [[5-limit]] [[interval]] measuring about 68.7{{cent}}. It is equal to the [[256/243\|Pythagorean minor second (256/243)]] flattened by a [[81/80\|syntonic comma (81/80)]]. When treated as a [[comma]] to be tempered out, it is the '''superpyth comma''', and is the difference between 5/4 and an [[Octave reduction\|octave-reduced]] stack of nine [[3/2]]'s, as well as [[25/24]] minus a [[Schisma\|schisma (32805/32768)]]. Tempering it out by itself defines the 5-limit version of [[superpyth]] temperament. Notable [[edo]]s that temper it out include [[17edo\|17]], [[22edo\|22]], and [[27edo\|27]].

FloraC: This interval has a simple name in Pythagorean-commatic naming

2023-10-19T14:40:41Z

This interval has a simple name in Pythagorean-commatic naming

← Older revision		Revision as of 14:40, 19 October 2023
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	{{Infobox Interval\|Name=superpyth comma\|Color name=sayo 2nd, sayo comma}}		{{Infobox Interval
			\| Name = retroptolemaic minor second, superpyth comma
			\| Color name = sayo 2nd, sayo comma
			}}
			'''20480/19683''', the '''retroptolemaic minor second''', is a [[5-limit]] [[interval]] measuring about 68.7{{cent}}. It is equal to the [[256/243\|Pythagorean minor second (256/243)]] flattened by a [[81/80\|syntonic comma (81/80)]]. When treated as a [[comma]] to be tempered out, it is the '''superpyth comma''', and is the difference between 5/4 and an [[Octave reduction\|octave-reduced]] stack of nine [[3/2]]'s, as well as [[25/24]] minus a [[Schisma\|schisma (32805/32768)]]. Tempering it out by itself defines the 5-limit version of [[superpyth]] temperament. Notable [[edo]]s that temper it out include [[17edo\|17]], [[22edo\|22]], and [[27edo\|27]].

	~~20480/19683, the superpyth comma, is the difference between 5/4 and an~~ [[~~Octave reduction\|octave-reduced~~]] ~~stack of nine 3/2s, as well as 25/24 minus a~~ [[~~schisma~~]] ~~(32805/32768). Tempering it out by itself defines the 5-limit version of [[superpyth]] temperament. Notable [[EDO\|EDOs]] that temper it out include [[17edo\|17]], [[22edo\|22]], and [[27edo\|27]].~~		[[Category:Second]]
			[[Category:Semitone]]

Tristanbay: Added a page for the superpyth comma

2023-10-19T05:37:16Z

Added a page for the superpyth comma

New page

{{Infobox Interval|Name=superpyth comma|Color name=sayo 2nd, sayo comma}}

20480/19683, the superpyth comma, is the difference between 5/4 and an [[Octave reduction|octave-reduced]] stack of nine 3/2s, as well as 25/24 minus a [[schisma]] (32805/32768). Tempering it out by itself defines the 5-limit version of [[superpyth]] temperament. Notable [[EDO|EDOs]] that temper it out include [[17edo|17]], [[22edo|22]], and [[27edo|27]].