Sqrt(2/1): Difference between revisions
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{{Infobox interval|Name=semioctave, (hemipythagorean) tritone, perfect four-and-a-halfth|Ratio=\sqrt{2}|Cents=600}} | {{Infobox interval | ||
| Name = semioctave, (hemipythagorean) tritone, perfect four-and-a-halfth | |||
''' | | Ratio =\sqrt{2} | ||
| Cents = 600 | |||
}} | |||
'''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 == | == 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 == | ||
* [[2edo]] | * [[2edo]] | ||
* [[Tritone#Tritones_as_approximations_of_the_semioctave|Tritones as approximations of the semioctave]] | |||
[[Category:2edo]] | |||