Why saturation sounds good

Saturation adds harmonics, and harmonics can make a sound more interesting.¹ Harmonic saturation is mathematically the same as the harmonic series present in instrument’s timbre.² Harmonics are what make an instrument sound like itself. Harmonics are the reason why a flute and a violin can both play A 440, yet sound entirely different from one another.

Harmonics can also make the fundamental be perceived as more present, as demonstrated by the Missing fundamental principle. Thus, it stands to reason, that adding subtle saturation can make an instrument sound more like itself. Not only is the instrument’s fundamental strengthened, but also its harmonics, by the same principle. Also, Partials make sounds more interesting.