Sqrt(2/1)

Interval information

Expression	[math]\displaystyle{ \sqrt{2} }[/math]
Size in cents	600¢
Names	semioctave, (hemipythagorean) tritone, perfect four-and-a-halfth
Special properties	reduced
Harmonic entropy (Shannon, [math]\displaystyle{ \sqrt{nd} }[/math])	~4.22587 bits

sqrt(2/1), the semioctave, is an important radical interval of exactly 600 cents. It appears in hemipyth as one of the generators, alongside sqrt(3/2).

In temperaments

Many temperaments equate a just interval (or more accurately, a pair of just intervals) to the semioctave; among the most common to be merged this way are 7/5 and 10/7 (which differ by 50/49), 17/12 and 24/17 (which differ by 289/288), and 99/70 and 140/99 (which differ by 9801/9800). The semioctave appears in every even equal temperament.

See also

• 2edo