Sqrt(2/1): Difference between revisions

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== In temperaments ==
== In temperaments ==
Many temperaments equate a just interval (or more accurately, a pair of just intervals) to the semioctave. The semioctave appears in every even equal temperament.
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 ==
== See also ==

Revision as of 02:27, 26 March 2025

Interval information
Expression [math]\displaystyle{ \sqrt{2} }[/math]
Size in cents 600¢
Names semioctave,
(hemipythagorean) tritone,
perfect four-and-a-halfth
Special properties reduced

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