32/31 - Revision history

Lériendil at 04:01, 8 August 2025

2025-08-08T04:01:11Z

← Older revision		Revision as of 04:01, 8 August 2025
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	== See also ==		== See also ==
	* [[31/16]] – its [[octave complement]]		* [[31/16]] – its [[octave complement]]
	* [[31/24]] – its [[~~fifth~~ complement]]		* [[31/24]] – its [[fourth complement]]
	* [[Gallery of just intervals]]		* [[Gallery of just intervals]]

	[[Category:Quartertone]]		[[Category:Quartertone]]

FloraC: Clarify

2025-07-12T13:44:32Z

Clarify

← Older revision		Revision as of 13:44, 12 July 2025
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	'''32/31''' is the '''small tricesimoprimal quartertone''' measuring about 55{{cent}}. It differs from [[33/32]], the undecimal quartertone, by [[1024/1023]] (approx. 1.69{{cent}}). It differs from [[31/30]], another tricesimoprimal quartertone, by [[961/960]] (approx. 1.80{{cent}}); they together make [[16/15]]. This interval is approximated well (about 0.4{{cent}} off) by [[22edo\|1\22]] and extremely closely (about 0.0025{{cent}} off) by [[131edo\|6\131]]. It can also serve as a generator for the [[escapade]] temperament (which both 22 and 131edo, among others, support).		'''32/31''' is the '''small tricesimoprimal quartertone''' measuring about 55{{cent}}. It differs from [[33/32]], the undecimal quartertone, by [[1024/1023]] (approx. 1.69{{cent}}). It differs from [[31/30]], another tricesimoprimal quartertone, by [[961/960]] (approx. 1.80{{cent}}); they together make [[16/15]]. This interval is approximated well (about 0.4{{cent}} off) by [[22edo\|1\22]] and extremely closely (about 0.0025{{cent}} off) by [[131edo\|6\131]]. It can also serve as a generator for the [[escapade]] temperament (which both 22 and 131edo, among others, support).

	This interval is significant in [[~~Helmholtz-Ellis~~ notation]] as the formal comma to translate a Pythagorean interval to a nearby tricesimoprimal (31-limit) interval. The symbols ~~being used~~ are ~~virtually identical to~~ Persian quartertones accidentals invented by {{w\|Ali-Naqi Vaziri}}.		== Notation ==
			This interval is significant in [[Helmholtz–Ellis notation]] as the formal comma to translate a Pythagorean interval to a nearby tricesimoprimal (31-limit) interval. The symbols are adapted from Persian quartertones accidentals invented by {{w\|Ali-Naqi Vaziri}}.

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

Lériendil at 01:59, 25 March 2025

2025-03-25T01:59:13Z

← Older revision		Revision as of 01:59, 25 March 2025
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	}}		}}

	'''32/31''' is the '''small tricesimoprimal quartertone''' measuring about 55{{cent}}. It differs from [[33/32]], the undecimal quartertone, by [[1024/1023]] (approx. 1.69{{cent}}). It differs from [[31/30]], another tricesimoprimal quartertone, by [[961/960]] (approx. 1.80{{cent}}); they together make [[16/15]]. This interval is approximated well (about 0.4{{cent}} off) by [[22edo\|1\22]] and extremely closely (about 0.0025{{cent}} off) by [[131edo\|6\131]]. It can also serve as a generator for the [[escapade]] temperament.		'''32/31''' is the '''small tricesimoprimal quartertone''' measuring about 55{{cent}}. It differs from [[33/32]], the undecimal quartertone, by [[1024/1023]] (approx. 1.69{{cent}}). It differs from [[31/30]], another tricesimoprimal quartertone, by [[961/960]] (approx. 1.80{{cent}}); they together make [[16/15]]. This interval is approximated well (about 0.4{{cent}} off) by [[22edo\|1\22]] and extremely closely (about 0.0025{{cent}} off) by [[131edo\|6\131]]. It can also serve as a generator for the [[escapade]] temperament (which both 22 and 131edo, among others, support).

	This interval is significant in [[Helmholtz-Ellis notation]] as the formal comma to translate a Pythagorean interval to a nearby tricesimoprimal (31-limit) interval. The symbols being used are virtually identical to Persian quartertones accidentals invented by {{w\|Ali-Naqi Vaziri}}.		This interval is significant in [[Helmholtz-Ellis notation]] as the formal comma to translate a Pythagorean interval to a nearby tricesimoprimal (31-limit) interval. The symbols being used are virtually identical to Persian quartertones accidentals invented by {{w\|Ali-Naqi Vaziri}}.

Lériendil at 02:10, 16 March 2025

2025-03-16T02:10:42Z

← Older revision		Revision as of 02:10, 16 March 2025
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	}}		}}

	'''32/31''' is the '''small tricesimoprimal quartertone''' measuring about 55{{cent}}. It differs from [[33/32]], the undecimal quartertone, by [[1024/1023]] (approx. 1.69{{cent}}). It differs from [[31/30]], another tricesimoprimal quartertone, by [[961/960]] (approx. 1.80{{cent}}); they together make [[16/15]].		'''32/31''' is the '''small tricesimoprimal quartertone''' measuring about 55{{cent}}. It differs from [[33/32]], the undecimal quartertone, by [[1024/1023]] (approx. 1.69{{cent}}). It differs from [[31/30]], another tricesimoprimal quartertone, by [[961/960]] (approx. 1.80{{cent}}); they together make [[16/15]]. This interval is approximated well (about 0.4{{cent}} off) by [[22edo\|1\22]] and extremely closely (about 0.0025{{cent}} off) by [[131edo\|6\131]]. It can also serve as a generator for the [[escapade]] temperament.

	This interval is significant in [[Helmholtz-Ellis notation]] as the formal comma to translate a Pythagorean interval to a nearby tricesimoprimal (31-limit) interval. The symbols being used are virtually identical to Persian quartertones accidentals invented by {{w\|Ali-Naqi Vaziri}}.		This interval is significant in [[Helmholtz-Ellis notation]] as the formal comma to translate a Pythagorean interval to a nearby tricesimoprimal (31-limit) interval. The symbols being used are virtually identical to Persian quartertones accidentals invented by {{w\|Ali-Naqi Vaziri}}.

FloraC: +short explanation on its look in HEJI

2024-11-28T18:00:03Z

+short explanation on its look in HEJI

← Older revision		Revision as of 18:00, 28 November 2024
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	'''32/31''' is the '''small tricesimoprimal quartertone''' measuring about 55{{cent}}. It differs from [[33/32]], the undecimal quartertone, by [[1024/1023]] (approx. 1.69{{cent}}). It differs from [[31/30]], another tricesimoprimal quartertone, by [[961/960]] (approx. 1.80{{cent}}); they together make [[16/15]].		'''32/31''' is the '''small tricesimoprimal quartertone''' measuring about 55{{cent}}. It differs from [[33/32]], the undecimal quartertone, by [[1024/1023]] (approx. 1.69{{cent}}). It differs from [[31/30]], another tricesimoprimal quartertone, by [[961/960]] (approx. 1.80{{cent}}); they together make [[16/15]].

	This interval is significant in [[Helmholtz-Ellis notation]] as the formal comma to translate a Pythagorean interval to a nearby tricesimoprimal (31-limit) interval.		This interval is significant in [[Helmholtz-Ellis notation]] as the formal comma to translate a Pythagorean interval to a nearby tricesimoprimal (31-limit) interval. The symbols being used are virtually identical to Persian quartertones accidentals invented by {{w\|Ali-Naqi Vaziri}}.

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

FloraC: +significance in HEJI and correct the name

2024-11-28T17:13:56Z

+significance in HEJI and correct the name

← Older revision		Revision as of 17:13, 28 November 2024
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	{{Infobox Interval		{{Infobox Interval
	\| Name = 31st subharmonic, small tricesimoprimal quartertone		\| Name = octave-reduced 31st subharmonic, small tricesimoprimal quartertone
	\| Color name = 31u2, thiwu 2nd		\| Color name = 31u2, thiwu 2nd
	\| Sound = Ji-32-31-csound-foscil-220hz.mp3		\| Sound = Ji-32-31-csound-foscil-220hz.mp3
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	'''32/31''' is the '''small tricesimoprimal quartertone''' measuring about 55{{cent}}. It differs from [[33/32]], the undecimal quartertone, by [[1024/1023]] (approx. 1.69{{cent}}). It differs from [[31/30]], another tricesimoprimal quartertone, by [[961/960]] (approx. 1.80{{cent}}); they together make [[16/15]].		'''32/31''' is the '''small tricesimoprimal quartertone''' measuring about 55{{cent}}. It differs from [[33/32]], the undecimal quartertone, by [[1024/1023]] (approx. 1.69{{cent}}). It differs from [[31/30]], another tricesimoprimal quartertone, by [[961/960]] (approx. 1.80{{cent}}); they together make [[16/15]].

			This interval is significant in [[Helmholtz-Ellis notation]] as the formal comma to translate a Pythagorean interval to a nearby tricesimoprimal (31-limit) interval.

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

Tristanbay: 31th to 31st

2024-08-18T01:58:04Z

31th to 31st

← Older revision		Revision as of 01:58, 18 August 2024
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	{{Infobox Interval		{{Infobox Interval
	\| Name = ~~31th~~ subharmonic, small tricesimoprimal quartertone		\| Name = 31st subharmonic, small tricesimoprimal quartertone
	\| Color name = 31u2, thiwu 2nd		\| Color name = 31u2, thiwu 2nd
	\| Sound = Ji-32-31-csound-foscil-220hz.mp3		\| Sound = Ji-32-31-csound-foscil-220hz.mp3
	}}		}}

	'''32/31''' is the '''small tricesimoprimal quartertone''' measuring about 55{{cent}}. It differs from [[33/32]], the undecimal quartertone, by [[1024/1023]] (approx. 1.69{{cent}}). It differs from [[31/30]], another tricesimoprimal quartertone, by [[961/960]] (approx. 1.80{{cent}}); they together make [[16/15]].		'''32/31''' is the '''small tricesimoprimal quartertone''' measuring about 55{{cent}}. It differs from [[33/32]], the undecimal quartertone, by [[1024/1023]] (approx. 1.69{{cent}}). It differs from [[31/30]], another tricesimoprimal quartertone, by [[961/960]] (approx. 1.80{{cent}}); they together make [[16/15]].

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

TallKite: added color name

2022-12-29T01:27:24Z

added color name

← Older revision		Revision as of 01:27, 29 December 2022
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	{{Infobox Interval		{{Infobox Interval
	\| Name = 31th subharmonic, small tricesimoprimal quartertone		\| Name = 31th subharmonic, small tricesimoprimal quartertone
			\| Color name = 31u2, thiwu 2nd
	\| Sound = Ji-32-31-csound-foscil-220hz.mp3		\| Sound = Ji-32-31-csound-foscil-220hz.mp3
	}}		}}

Plumtree: Normalising usage of Infobox Interval

2022-10-25T15:02:04Z

Normalising usage of Infobox Interval

← Older revision		Revision as of 15:02, 25 October 2022
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	{{Infobox Interval		{{Infobox Interval
	~~\| Ratio = 32/31~~		\| Name = 31th subharmonic, small tricesimoprimal quartertone
	~~\| Monzo = 5 0 0 0 0 0 0 0 0 0 -1~~
	~~\| Cents = 54.96443~~
	\| Name = 31th subharmonic, ~~<br>~~small tricesimoprimal quartertone
	~~\| Color name =~~
	\| Sound = Ji-32-31-csound-foscil-220hz.mp3		\| Sound = Ji-32-31-csound-foscil-220hz.mp3
	}}		}}
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	* [[Gallery of just intervals]]		* [[Gallery of just intervals]]

	~~[[Category:31-limit]]~~
	[[Category:Quartertone]]		[[Category:Quartertone]]
	~~[[Category:Superparticular]]~~
	~~[[Category:Octave-reduced subharmonics]]~~

	~~{{todo\|expand\|add color name}}~~

Fredg999: Misc. edits, categories

2022-03-23T12:49:55Z

Misc. edits, categories

← Older revision		Revision as of 12:49, 23 March 2022
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	{{Infobox Interval		{{Infobox Interval
	~~\| Icon =~~
	\| Ratio = 32/31		\| Ratio = 32/31
	\| Monzo = 5 0 0 0 0 0 0 0 0 0 -1		\| Monzo = 5 0 0 0 0 0 0 0 0 0 -1
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	}}		}}

	'''32/31''' is the '''small tricesimoprimal quartertone''' measuring about 55 ~~cents~~. It differs from [[33/32]], the undecimal quartertone, by [[1024/1023]] (~~''c''~~. 1.69 ~~cents~~). It differs from [[31/30]], another tricesimoprimal quartertone, by [[961/960]] (~~''c''~~. 1.80 ~~cents~~); they together make [[16/15]].		'''32/31''' is the '''small tricesimoprimal quartertone''' measuring about 55{{cent}}. It differs from [[33/32]], the undecimal quartertone, by [[1024/1023]] (approx. 1.69{{cent}}). It differs from [[31/30]], another tricesimoprimal quartertone, by [[961/960]] (approx. 1.80{{cent}}); they together make [[16/15]].

	== See also ==		== See also ==
Line 17:		Line 16:

	[[Category:31-limit]]		[[Category:31-limit]]
	~~[[Category:Interval ratio]]~~
	[[Category:Quartertone]]		[[Category:Quartertone]]
	[[Category:Superparticular]]		[[Category:Superparticular]]
	[[Category:Octave-reduced subharmonics]]		[[Category:Octave-reduced subharmonics]]

	~~[[Category:Todo:~~expand]]		{{todo\|expand\|add color name}}
	~~[[Category:Todo:~~add color name]]