5/1: Difference between revisions
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'''5/1''', the '''5th harmonic''', '''pentave''' or '''quintuple''', is the [[harmonic]] past [[4/1]] and before [[6/1]]. It is two [[octave]]s above [[5/4]], and is the basis of [[5-limit]] harmony, as many 5-limit intervals can be expressed as the difference between this and another harmonic. | '''5/1''', the '''5th harmonic''', '''pentave''' or '''quintuple''', is the [[harmonic]] past [[4/1]] and before [[6/1]]. It is two [[octave]]s above [[5/4]], and is the basis of [[5-limit]] harmony, as many 5-limit intervals can be expressed as the difference between this and another harmonic. | ||
5/1 is the third [[prime harmonic]], after [[3/1]] and before [[7/1]]. | |||
5/1 is on a list of integer harmonics that approximate closest a given stack of fifths, the error being the [[81/80|syntonic comma]].<ref>{{OEIS|A081464}} – Numbers ''k'' such that the fractional part of (3/2)<sup>''k''</sup> decreases monotonically to zero</ref><ref>{{OEIS|A267122}} – Numbers ''n'' such that (3/2)<sup>n</sup> is closer to an integer than (3/2)<sup>m</sup> for any 0 < ''m'' < ''n''</ref> | 5/1 is on a list of integer harmonics that approximate closest a given stack of fifths, the error being the [[81/80|syntonic comma]].<ref>{{OEIS|A081464}} – Numbers ''k'' such that the fractional part of (3/2)<sup>''k''</sup> decreases monotonically to zero</ref><ref>{{OEIS|A267122}} – Numbers ''n'' such that (3/2)<sup>n</sup> is closer to an integer than (3/2)<sup>m</sup> for any 0 < ''m'' < ''n''</ref> | ||
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== See also == | == See also == | ||
* [[5/4]] – its [[octave reduced]] form | |||
* [[Ed5]] – equal divisions of the 5th harmonic | * [[Ed5]] – equal divisions of the 5th harmonic | ||
== References == | == References == | ||
<references/> | <references/> | ||