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 | |||
}} | |||
'''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 == | ||
* [[2edo]] | |||
* [[Tritone#Tritones_as_approximations_of_the_semioctave|Tritones as approximations of the semioctave]] | |||
[[Category:2edo]] | |||
Latest revision as of 09:39, 20 September 2025
| Interval information |
(hemipythagorean) tritone,
perfect four-and-a-halfth
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.