This article presents new spectral analysis-synthesis approaches to musical signal transformation. The analysis methods presented here involve the use of a superior quality technique of frequency estimation, the Instantaneous Frequency Distribution (IFD), and partial tracking. We discuss the theory behind the IFD, comparing it to other existing methods. The partial tracking analysis employed in this process is explained fully. This is followed by a look into the three resynthesis methods proposed by this work, based on different approaches to additive synthesis. A number of transformations of musical signals are proposed to take advantage of the analysis-synthesis techniques. Performance details and specific aspects of this implementation are discussed. This is complemented by a look at some of the results of these methods in the time-stretching of audio signals, where they will be shown to perform better than many of the currently available techniques.