24/1

Interval information

Ratio	24/1
Factorization	23 × 3
Monzo	[3 1⟩
Size in cents	5501.955¢
Name	24th harmonic
FJS name	[math]\displaystyle{ \text{P33} }[/math]
Special properties	harmonic, highly composite harmonic
Tenney height (log2 nd)	4.58496
Weil height (log2 max(n, d))	9.16993
Wilson height (sopfr(nd))	9
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24/1, the 24th harmonic, is the harmonic past 23/1 and before 25/1. It is about four octaves and seven semitones in size. Used in harmony, it sounds particularly wide: if the lower note is C2, the higher note will be about G6. Think of a soprano and a bass at their extremes. Since 24 is a highly composite number, this harmonic can be approached in various ways of stacking, all the components being Pythagorean intervals. For example, stacking with octaves, fifths and fourths gives a consonant but simplistic skeleton across multiple registers: 1-2-3-4-6-8-12-24, on which higher-limit intervals can be added to enrich its colors.

See also

• Gallery of just intervals