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A Multi-Dimensional Model
Average: Spectral Centroid/Brightness
Spectral centroid is formulated as the weighted mean of the time-frequency spectrum. It characterize the spectrum by specifying where the frequency center of the spectrum is located. Brightness is defined to be the proportion of the overall magnitude above certain frequency. Both could be used for the analysis of the average of the spectrum
Variation: Spectral Flux
Spectral flux is defined to be the fluctuations of the time-frequency spectrum. Different norms are used for different purposes and the most widely-accepted definition is 2-norm. In this case, spectral flux is calculated as the sum of squared differences between different frame's (or timepoint's) frequency diagram.
Attack time is defined to be the temporal duration of rise of a peak in a novel curve or a detection curve. A detection curve is the curve of energy throughout time and each peak in the detection curve corresponds to an event such as a note. It could characterize the type of instrument or the timbre of the preformance.