Music exemplifies the repetitive patterns in nature. These patterns lend a distinctiveness to sound sources that make them identifiable. In audio analysis, this information can be accessed by using a process called spectral decomposition. This dissertation evaluates the ways in which spectral decomposition techniques can yield a different way to understand music. Using an interdisciplinary framework incorporating Albert Bregman's Auditory Scene Analysis with traditional music and computational analysis methods, spectral decomposition techniques are employed in the following four activities: a digital-musicology study of Grisey's Partiels, and John Cage's Sonatas and Interludes; a timbre-rhythm groove retrieval analysis on a new dataset named ISHKUR, a discussion of a repertoire of music written using spectral decomposition techniques, and future directions for music research and aesthetics. The main conclusions drawn from this research illustrate the versatility of latent structure analysis to activities beyond source separation and argues for a perceptual foundation for a post-spectralist approach to music.