23/1

Interval information

Ratio	23/1
Subgroup monzo	23 [1⟩
Size in cents	5428.274¢
Name	23rd harmonic
Color name	c423o5, quadcotwetho 5th
FJS name	[math]\displaystyle{ \text{A32}^{23} }[/math]
Special properties	harmonic, prime harmonic
Tenney height (log2 nd)	4.52356
Weil height (log2 max(n, d))	9.04712
Wilson height (sopfr(nd))	23
Harmonic entropy (Shannon, [math]\displaystyle{ \sqrt{nd} }[/math])	~2.07667 bits
Open this interval in xen-calc

23/1, the 23rd harmonic, is the harmonic past 22/1 and before 24/1. It is about four octaves and six semitones in size. Used in harmony, it sounds particularly wide: if the lower note is C2, the higher note will be about F#6 or Gb6. Think of a soprano and a bass at their extremes. It is however, the basis of 23-limit harmony, as many 23-limit intervals can be expressed as the difference between this and another harmonic.

See also

• 23/16 – its octave-reduced form