Sqrt(3/2): Difference between revisions

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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 ==

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).

@@ Line 1: / Line 1: @@
-''"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 ==
-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).