5/1: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Name = 5th harmonic, pentave | | Name = 5th harmonic, pentave, quintuple | ||
| Color name = ccy3, cocoyo 3rd | | Color name = ccy3, cocoyo 3rd | ||
| Sound = jid_5_1_pluck_adu_dr110.mp3 | | Sound = jid_5_1_pluck_adu_dr110.mp3 | ||
}} | }} | ||
'''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 on a list of integer harmonics that approximate closest a given stack of fifths, the error being the [[81/80|syntonic comma]]. | |||
== See also == | |||
* [[Ed5]] – equal divisions of the 5th harmonic | |||
== References == | == References == | ||
* | * {{OEIS|A081464}} – Numbers ''k'' such that the fractional part of (3/2)<sup>''k''</sup> decreases monotonically to zero | ||
* {{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'' | |||