Sqrt(3/2): Difference between revisions
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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). | ||
Revision as of 01:48, 26 March 2025
| Interval information |
√(3/2), the 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
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).