Sqrt(2/1): Difference between revisions

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m FloraC moved page √2/1 to Sqrt(2/1): It's fine to write out the name of the function!
Cleanup. -Wikipedia box (This article isn't about the number)
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{{Infobox interval|Name=semioctave, (hemipythagorean) tritone, perfect four-and-a-halfth|Ratio=\sqrt{2}|Cents=600}}
{{Infobox interval
{{Wikipedia|Square root of 2}}
| Name = semioctave, (hemipythagorean) tritone, perfect four-and-a-halfth
 
| Ratio =\sqrt{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)]].'''
| 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 ==

Revision as of 17:27, 3 April 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

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