Sqrt(3/2)
"Hemififth" redirects here; this page is about the irrational interval. For the regular temperament, see Hemififths.
| Interval information |
√(3/2), the 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 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).