Sqrt(2/1): Difference between revisions

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Created page with "{{Infobox interval|Name=semioctave, (hemipythagorean) tritone, perfect four-and-a-halfth|Ratio=\sqrt{2}|Cents=600}} '''√2/1''', the '''semioctave''', is an important radi..."
 
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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}}


'''√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]].'''
'''√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 ==
== 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. The semioctave appears in every even equal temperament.

Revision as of 00:53, 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. The semioctave appears in every even equal temperament.