Sqrt(3/2): Difference between revisions

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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.

== 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).

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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.
 == 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).