5/1

Interval information

Ratio	5/1
Factorization	5
Monzo	[0 0 1⟩
Size in cents	2786.314¢
Names	5th harmonic, pentave, quintuple
Color name	ccy3, cocoyo 3rd
FJS name	[math]\displaystyle{ \text{M17}^{5} }[/math]
Special properties	harmonic, prime harmonic
Tenney height (log2 nd)	2.32193
Weil height (log2 max(n, d))	4.64386
Wilson height (sopfr(nd))	5
Harmonic entropy (Shannon, [math]\displaystyle{ \sqrt{nd} }[/math])	~2.95314 bits
[sound info]
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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 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

References

• OEIS: A081464 – Numbers k such that the fractional part of (3/2)^k decreases monotonically to zero
• OEIS: A267122 – Numbers n such that (3/2)ⁿ is closer to an integer than (3/2)^m for any 0 < m < n