5/1: Difference between revisions
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| Sound = jid_5_1_pluck_adu_dr110.mp3 | | Sound = jid_5_1_pluck_adu_dr110.mp3 | ||
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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]]. | '''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]]. | 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]]. | ||
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== References == | == References == | ||
* {{OEIS|A081464}} | * {{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'' | |||
Latest revision as of 10:11, 29 May 2025
| Interval information |
pentave,
quintuple
prime harmonic
[sound info]
5/1, the 5th harmonic, pentave or quintuple, is the harmonic past 4/1 and before 6/1. It is two octaves 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 syntonic comma.
See also
- Ed5 – equal divisions of the 5th harmonic