Sqrt(3/2): Difference between revisions

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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}}

'''√(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 ==

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).

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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}}
-'''√(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 ==
 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).