  This paper presents a novel approach to understanding the role of harmonic
dynamics and gaining a deeper appreciation for its impact within and outside of
quantum mechanics. This includes consequences of harmonic dynamics and the
uncertainty principle for anomalous diffusion and for the time-frequency
analysis of chirp signals. In this approach, we consider a contact
transformation to view a system of canonical variables with coordinate $x$ and
momentum $p_x$ in the context of a new system of "generalized" coordinates and
momentum. This new system is first studied in the context of non-relativistic
quantum mechanics. The classical analog is then explored by use of the Poisson
bracket equation. From this, new implications are demonstrated in classical
phenomena. One is for a new model of Anomalous and Normal Diffusion. In
another, we introduce the concept of the "Mixed Fourier Transform" which
explores a new Gaussian Fourier Transform kernel in terms of the generalized
variables. This has the ultimate objective of "harmonizing" chirp signals or
producing a harmonic signal from an otherwise non-harmonic chirp.
