Why can a slightly mistuned octave or fifth sound dissonant?

A slightly mistuned octave or fifth sounds dissonant because of the production of beats, which are pulsations or throbs caused by the interference between sound waves of slightly different frequencies.12

In music, consonance is achieved when the ratio between the frequencies of two tones is numerically simple, such as the 2:1 ratio of an octave or the 3:2 ratio of a fifth. When these intervals are perfectly tuned, there is an absence of beats, resulting in a stable, consonant sound.13

However, when these intervals are slightly mistuned, the frequencies no longer align in these simple ratios. This discrepancy creates interference, resulting in audible beats—a periodic rise and fall in the intensity of the sound. The human ear perceives this interference as dissonance, which is often judged as being "out of tune". While these beats are sometimes intentionally introduced in systems of tempered tuning, they remain the primary physical mechanism that causes a listener to perceive an interval as clashing or unstable.14