Average all the frequencies in a sound, weighted by their energy, and the result is the spectral centroid: one number for where the spectrum balances. Dark sounds sit low, bright ones high, and listeners’ judgments of brightness track it closely.
It is the workhorse of timbre analysis because it is cheap, stable, and perceptually honest. A closing filter sweep is visible as a falling centroid; a distorted guitar’s aggression as a raised one.
For visuals, centroid is the natural driver of color temperature and altitude: let brightness of sound pull brightness of image and the mapping reads as obvious, which in cross-modal design is the highest compliment.