Sqrt(3/2) - Revision history

FloraC: Cleanup

2025-04-03T17:30:19Z

Cleanup

← Older revision		Revision as of 17:30, 3 April 2025
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	''"Hemififth" redirects here; this page is about the irrational interval. For the regular temperament, see [[Hemififths]].''		: ''"Hemififth" redirects here; this page is about the irrational interval. For the regular temperament, see [[Hemififths]].''

	{{Infobox interval~~\|ratio=/sqrt{3/2}\|cents=350.9775\|name=neutral third~~\|Name=(hemipythagorean) neutral third\|Ratio=\sqrt{3/2}\|Cents=350.9775}}		{{Infobox interval
			\| Name = (hemipythagorean) neutral third
	'''√(3/2)''', the ~~[[Hemipyth\|~~'''hemipythagorean~~''']] '''~~neutral third''' or '''perfect hemififth''', is a [[radical interval]] of about 351 cents, in the √2.√3 subgroup. It appears in [[hemipyth]] as one of the generators, alongside [[√2/1]]~~'''~~.~~'''~~ It is the unique interval with the property that when stacked twice, it leads to a perfect fifth [[3/2]], and as such it naturally lends itself to building "neutral triads" with an ambiguous sound between major and minor.		\| Ratio = \sqrt{3/2}
			\| Cents = 350.9775
			}}
			'''sqrt(3/2)''', the '''hemipythagorean neutral third''' or '''perfect hemififth''', is a [[radical interval]] of about 351 cents, in the [[hemipyth\|sqrt(2).sqrt(3) subgroup]]. It appears in [[hemipyth]] as one of the generators, alongside [[sqrt(2/1)]]. It is the unique interval with the property that when stacked twice, it leads to a perfect fifth [[3/2]], and as such it naturally lends itself to building "neutral triads" with an ambiguous sound between major and minor.

	== In temperaments ==		== In temperaments ==
	Many temperaments equate a just interval (or more accurately, a pair of just intervals) to the hemififth; the most common interval pairs to be merged this way are [[11/9]] and [[27/22]] (which differ by [[243/242]]), and [[49/40]] and [[60/49]] (which differ by [[2401/2400]]). Equal temperaments in which the fifth is mapped to an even number of steps (i.e. [[24edo]], [[41edo]]) have an approximation to √(3/2).		Many temperaments equate a just interval (or more accurately, a pair of just intervals) to the hemififth; the most common interval pairs to be merged this way are [[11/9]] and [[27/22]] (which differ by [[243/242]]), and [[49/40]] and [[60/49]] (which differ by [[2401/2400]]). Equal temperaments in which the fifth is mapped to an even number of steps (i.e. [[24edo]], [[41edo]]) have an approximation to sqrt(3/2).

FloraC: FloraC moved page √(3/2) to Sqrt(3/2) over redirect: It's fine to write out the name of the function!

2025-04-03T17:25:37Z

FloraC moved page √(3/2) to Sqrt(3/2) over redirect: It's fine to write out the name of the function!

← Older revision	Revision as of 17:25, 3 April 2025
(No difference)

Lériendil at 02:25, 26 March 2025

2025-03-26T02:25:27Z

← Older revision		Revision as of 02:25, 26 March 2025
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			''"Hemififth" redirects here; this page is about the irrational interval. For the regular temperament, see [[Hemififths]].''

	{{Infobox interval\|ratio=/sqrt{3/2}\|cents=350.9775\|name=neutral third\|Name=(hemipythagorean) neutral third\|Ratio=\sqrt{3/2}\|Cents=350.9775}}		{{Infobox interval\|ratio=/sqrt{3/2}\|cents=350.9775\|name=neutral third\|Name=(hemipythagorean) neutral third\|Ratio=\sqrt{3/2}\|Cents=350.9775}}

Lériendil at 01:52, 26 March 2025

2025-03-26T01:52:32Z

← Older revision		Revision as of 01:52, 26 March 2025
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	== In temperaments ==		== In temperaments ==
	Many temperaments equate a just interval (or more accurately, a pair of just intervals) to the hemififth; the most common are [[11/9]] and [[27/22]] (which differ by [[243/242]]), and [[49/40]] and [[60/49]] (which differ by [[2401/2400]]). Equal temperaments in which the fifth is mapped to an even number of steps (i.e. [[24edo]], [[41edo]]) have an approximation to √(3/2).		Many temperaments equate a just interval (or more accurately, a pair of just intervals) to the hemififth; the most common interval pairs to be merged this way are [[11/9]] and [[27/22]] (which differ by [[243/242]]), and [[49/40]] and [[60/49]] (which differ by [[2401/2400]]). Equal temperaments in which the fifth is mapped to an even number of steps (i.e. [[24edo]], [[41edo]]) have an approximation to √(3/2).

Lériendil at 01:52, 26 March 2025

2025-03-26T01:52:05Z

← Older revision		Revision as of 01:52, 26 March 2025
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	'''√(3/2)''', the [[Hemipyth\|'''hemipythagorean''']] '''neutral third''' or '''perfect hemififth''', is a [[radical interval]] of about 351 cents, in the √2.√3 subgroup. It appears in [[hemipyth]] as one of the generators, alongside [[√2/1]]'''.''' It is the unique interval with the property that when stacked twice, it leads to a perfect fifth [[3/2]], and as such it naturally lends itself to building "neutral triads" with an ambiguous sound between major and minor.		'''√(3/2)''', the [[Hemipyth\|'''hemipythagorean''']] '''neutral third''' or '''perfect hemififth''', is a [[radical interval]] of about 351 cents, in the √2.√3 subgroup. It appears in [[hemipyth]] as one of the generators, alongside [[√2/1]]'''.''' It is the unique interval with the property that when stacked twice, it leads to a perfect fifth [[3/2]], and as such it naturally lends itself to building "neutral triads" with an ambiguous sound between major and minor.


	== In temperaments ==		== In temperaments ==
	Many temperaments equate a just interval (or more accurately, a pair of just intervals) to the ~~hemipyth neutral third~~. Equal temperaments in which the fifth is mapped to an even number of steps (i.e. [[24edo]], [[41edo]]) have an approximation to √(3/2).		Many temperaments equate a just interval (or more accurately, a pair of just intervals) to the hemififth; the most common are [[11/9]] and [[27/22]] (which differ by [[243/242]]), and [[49/40]] and [[60/49]] (which differ by [[2401/2400]]). Equal temperaments in which the fifth is mapped to an even number of steps (i.e. [[24edo]], [[41edo]]) have an approximation to √(3/2).

Lériendil at 01:49, 26 March 2025

2025-03-26T01:49:16Z

← Older revision		Revision as of 01:49, 26 March 2025
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	{{Infobox interval\|ratio=/sqrt{3/2}\|cents=350.9775\|name=neutral third\|Name=(hemipythagorean) neutral third\|Ratio=\sqrt{3/2}\|Cents=350.9775}}		{{Infobox interval\|ratio=/sqrt{3/2}\|cents=350.9775\|name=neutral third\|Name=(hemipythagorean) neutral third\|Ratio=\sqrt{3/2}\|Cents=350.9775}}

	'''√(3/2)''', the [[Hemipyth\|'''hemipythagorean''']] '''neutral third''', is a [[radical interval]] of about 351 cents, in the √2.√3 subgroup. It appears in [[hemipyth]] as one of the generators, alongside [[√2/1]]'''.''' It is the unique interval with the property that when stacked twice, it leads to a perfect fifth [[3/2]], and as such it naturally lends itself to building "neutral triads" with an ambiguous sound between major and minor.		'''√(3/2)''', the [[Hemipyth\|'''hemipythagorean''']] '''neutral third''' or '''perfect hemififth''', is a [[radical interval]] of about 351 cents, in the √2.√3 subgroup. It appears in [[hemipyth]] as one of the generators, alongside [[√2/1]]'''.''' It is the unique interval with the property that when stacked twice, it leads to a perfect fifth [[3/2]], and as such it naturally lends itself to building "neutral triads" with an ambiguous sound between major and minor.


	== In temperaments ==		== In temperaments ==
	Many temperaments equate a just interval (or more accurately, a pair of just intervals) to the hemipyth neutral third. Equal temperaments in which the fifth is mapped to an even number of steps (i.e. [[24edo]], [[41edo]]) have an approximation to √(3/2).		Many temperaments equate a just interval (or more accurately, a pair of just intervals) to the hemipyth neutral third. Equal temperaments in which the fifth is mapped to an even number of steps (i.e. [[24edo]], [[41edo]]) have an approximation to √(3/2).

VectorGraphics at 01:49, 26 March 2025

2025-03-26T01:49:04Z

← Older revision		Revision as of 01:49, 26 March 2025
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	== In temperaments ==		== In temperaments ==
	Many temperaments equate a just interval (or more accurately, a pair of just intervals) to the neutral third. Equal temperaments in which the fifth is mapped to an even number of steps (i.e. [[24edo]], [[41edo]]) have an approximation to √(3/2).		Many temperaments equate a just interval (or more accurately, a pair of just intervals) to the hemipyth neutral third. Equal temperaments in which the fifth is mapped to an even number of steps (i.e. [[24edo]], [[41edo]]) have an approximation to √(3/2).

VectorGraphics at 01:48, 26 March 2025

2025-03-26T01:48:38Z

← Older revision		Revision as of 01:48, 26 March 2025
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	{{Infobox interval\|ratio=/sqrt{3/2}\|cents=350.9775\|name=neutral third\|Name=neutral third\|Ratio=\sqrt{3/2}\|Cents=350.9775}}		{{Infobox interval\|ratio=/sqrt{3/2}\|cents=350.9775\|name=neutral third\|Name=(hemipythagorean) neutral third\|Ratio=\sqrt{3/2}\|Cents=350.9775}}

	'''√(3/2)''', the '''neutral third''', is a [[radical interval]] of about 351 cents, in the √2.√3 subgroup. It appears in [[hemipyth]] as one of the generators, alongside [[√2/1]]'''.''' It is the unique interval with the property that when stacked twice, it leads to a perfect fifth [[3/2]], and as such it naturally lends itself to building "neutral triads" with an ambiguous sound between major and minor.		'''√(3/2)''', the [[Hemipyth\|'''hemipythagorean''']] '''neutral third''', is a [[radical interval]] of about 351 cents, in the √2.√3 subgroup. It appears in [[hemipyth]] as one of the generators, alongside [[√2/1]]'''.''' It is the unique interval with the property that when stacked twice, it leads to a perfect fifth [[3/2]], and as such it naturally lends itself to building "neutral triads" with an ambiguous sound between major and minor.


	== In temperaments ==		== In temperaments ==
	Many temperaments equate a just interval (or more accurately, a pair of just intervals) to the neutral third. Equal temperaments in which the fifth is mapped to an even number of steps (i.e. [[24edo]], [[41edo]]) have an approximation to √(3/2).		Many temperaments equate a just interval (or more accurately, a pair of just intervals) to the neutral third. Equal temperaments in which the fifth is mapped to an even number of steps (i.e. [[24edo]], [[41edo]]) have an approximation to √(3/2).

VectorGraphics at 01:03, 26 March 2025

2025-03-26T01:03:25Z

← Older revision		Revision as of 01:03, 26 March 2025
Line 1:		Line 1:
	{{Infobox interval\|ratio=/sqrt{3/2}\|cents=350.9775\|name=neutral third\|Name=neutral third\|Ratio=/sqrt{3/2}\|Cents=350.9775}}		{{Infobox interval\|ratio=/sqrt{3/2}\|cents=350.9775\|name=neutral third\|Name=neutral third\|Ratio=\sqrt{3/2}\|Cents=350.9775}}

	'''√(3/2)''', the '''neutral third''', is a [[radical interval]] of about 351 cents. It appears in [[hemipyth]] as one of the generators, alongside [[√2/1]]'''.''' It is the unique interval with the property that when stacked twice, it leads to a perfect fifth [[3/2]], and as such it naturally lends itself to building "neutral triads" with an ambiguous sound between major and minor.		'''√(3/2)''', the '''neutral third''', is a [[radical interval]] of about 351 cents, in the √2.√3 subgroup. It appears in [[hemipyth]] as one of the generators, alongside [[√2/1]]'''.''' It is the unique interval with the property that when stacked twice, it leads to a perfect fifth [[3/2]], and as such it naturally lends itself to building "neutral triads" with an ambiguous sound between major and minor.


	== In temperaments ==		== In temperaments ==
	Many temperaments equate a just interval (or more accurately, a pair of just intervals) to the neutral third. Equal temperaments in which the fifth is mapped to an even number of steps (i.e. [[24edo]], [[41edo]]) have an approximation to √(3/2).		Many temperaments equate a just interval (or more accurately, a pair of just intervals) to the neutral third. Equal temperaments in which the fifth is mapped to an even number of steps (i.e. [[24edo]], [[41edo]]) have an approximation to √(3/2).

VectorGraphics: Created page with "{{Infobox interval|ratio=/sqrt{3/2}|cents=350.9775|name=neutral third|Name=neutral third|Ratio=/sqrt{3/2}|Cents=350.9775}} '''√(3/2)''', the '''neutral third''', is a rad..."

2025-03-26T01:02:22Z

Created page with "{{Infobox interval|ratio=/sqrt{3/2}|cents=350.9775|name=neutral third|Name=neutral third|Ratio=/sqrt{3/2}|Cents=350.9775}} '''√(3/2)''', the '''neutral third''', is a rad..."

New page

{{Infobox interval|ratio=/sqrt{3/2}|cents=350.9775|name=neutral third|Name=neutral third|Ratio=/sqrt{3/2}|Cents=350.9775}}

'''√(3/2)''', the '''neutral third''', is a [[radical interval]] of about 351 cents. It appears in [[hemipyth]] as one of the generators, alongside [[√2/1]]'''.''' It is the unique interval with the property that when stacked twice, it leads to a perfect fifth [[3/2]], and as such it naturally lends itself to building "neutral triads" with an ambiguous sound between major and minor.

== In temperaments ==
Many temperaments equate a just interval (or more accurately, a pair of just intervals) to the neutral third. Equal temperaments in which the fifth is mapped to an even number of steps (i.e. [[24edo]], [[41edo]]) have an approximation to √(3/2).