Gabor transforms and scalograms are used for mathematically analysing music,
identifying patterns in the time-frequency structure of music
at multiple time scales, and providing insight into the nature of
music.  Musical passages from classical music, popular song, bird song, and
fractal music are analysed using a synthesis of the generative theory
of tonal music and the mathematical methods of Gabor transforms and
scalograms.  Applications to musical processing, and musical synthesis are described using
inversion of Gabor transforms.