Sqrt(3/2)

"Hemififth" redirects here; this page is about the irrational interval. For the regular temperament, see Hemififths.

Interval information

Expression	[math]\displaystyle{ \sqrt{3/2} }[/math]
Size in cents	350.9775¢
Name	(hemipythagorean) neutral third
Special properties	reduced
Harmonic entropy (Shannon, [math]\displaystyle{ \sqrt{nd} }[/math])	~4.26168 bits

sqrt(3/2), the hemipythagorean neutral third or perfect hemififth, is a radical interval of about 351 cents, in the 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 sqrt(3/2).