24/1
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Ratio
24/1
Factorization
23 × 3
Monzo
[3 1⟩
Size in cents
5501.955¢
Name
24th harmonic
Color name
c4w5, quadcowa 5th
FJS name
[math]\text{P33}[/math]
Special properties
harmonic
Tenney height (log2 nd)
4.58496
Weil height (log2 max(n, d))
9.16993
Wilson height (sopfr(nd))
9
Harmonic entropy
(Shannon, [math]\sqrt{nd}[/math])
~2.1531 bits
open this interval in xen-calc
| Interval information |
(Shannon, [math]\sqrt{nd}[/math])
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.