A spectrogram is a tool that belongs to a set of tools called time-frequency representations. Music, on a CD, is a time-vector. Performing an FFT of this time-vector would give us its frequency content. However, a single FFT would lose all time information since it gives us the frequency content of the time-vector as a whole. We need something like an instantaneous frequency response so we have both frequency and time information. A spectrogram essentially breaks a signal up into many different time-vectors and performs FFTs of each. These FFTs are then placed as columns in the spectrogram. In the end, we have a time-frequency representation of our music.

This is a spectrogram of a techno song and a classical song. freqsmooth.m quantifies the differences seen in these spectrograms. To do this, freqsmooth calculates the variance in the indices of the max values of each column. In other words, a song with a clear, loud melody will show small variance in these indices while a song with a harder-to-identify melody will show a large variance.