The spectral centroid is the frequency-domain centre of mass of a sound spectrum and correlates with perceived brightness

The spectral centroid is computed as the weighted mean frequency of a spectrum: sum of (frequency times magnitude) divided by sum of magnitudes. It is among the most used audio features in timbre research and music information retrieval because it correlates well with perceived brightness. A higher spectral centroid means more energy in higher frequencies: a brighter, thinner sound. A lower centroid means more bass energy: a darker, fuller sound. In an interactive music system, spectral centroid can drive visual or synthesis parameters for audio-reactive mappings. It is typically extracted per frame from STFT magnitudes and can be smoothed across time.

Examples

A cymbal has a high spectral centroid (around 5 to 10 kHz). A bass drum has a low spectral centroid (around 100 to 200 Hz). In audio-reactive visuals: map centroid to colour hue or particle speed.

Assessment

What is the spectral centroid formula and what perceptual quality does it correlate with? How could you use spectral centroid as a mapping signal in an audio-reactive performance?