31/1

Interval information

Ratio	31/1
Subgroup monzo	31 [1⟩
Size in cents	5945.036¢
Name	31st harmonic
Color name	c431o7, quadcothiwo 7th
FJS name	[math]\displaystyle{ \text{M35}^{31} }[/math]
Special properties	harmonic, prime harmonic
Tenney height (log2 nd)	4.9542
Weil height (log2 max(n, d))	9.90839
Wilson height (sopfr(nd))	31
Harmonic entropy (Shannon, [math]\displaystyle{ \sqrt{nd} }[/math])	~1.94389 bits
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31/1, the 31st harmonic, is the harmonic past 30/1 and before 32/1. It is about four octaves and eleven and a half semitones in size. Used in harmony, it sounds particularly wide: if the base note is F1, the higher note will be about Et6 or Fd6. That is for all practical purposes beyond the range of choral music. However, it remains useful in some instrumental solos and ensembles. It is the basis of 31-limit harmony, as many 31-limit intervals can be expressed as the difference between this and another harmonic.

See also

• 31/16 – its octave-reduced form