Sqrt(2/1): Difference between revisions

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{{Infobox interval

| Name = semioctave, (hemipythagorean) tritone, perfect four-and-a-halfth~~, perfect median~~

| Name = semioctave, (hemipythagorean) tritone, perfect four-and-a-halfth

| Ratio =\sqrt{2}

| Cents = 600

}}

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

'''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.

~~== Name ==~~

~~"Semioctave" corresponds to its construction as the logarithmic division of an octave into 2. "Median" is a term for a tritone as a distinct interval degree borrowed from [[Leriendil]]'s parlance.~~

== See also ==

@@ Line 1: / Line 1: @@
 {{Infobox interval
-| Name = semioctave, (hemipythagorean) tritone, perfect four-and-a-halfth, perfect median
+| Name = semioctave, (hemipythagorean) tritone, perfect four-and-a-halfth
 | Ratio =\sqrt{2}
 | Cents = 600
 }}
-'''sqrt(2/1)''', the '''semioctave''' or '''perfect median''', is an important [[radical interval]] of exactly 600 cents. It appears in [[hemipyth]] as one of the generators, alongside [[sqrt(3/2)]].
+'''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.
-== Name ==
-"Semioctave" corresponds to its construction as the logarithmic division of an octave into 2. "Median" is a term for a tritone as a distinct interval degree borrowed from [[Leriendil]]'s parlance.
 == See also ==