Resonant metamaterials and phononic crystals are widely studied, with the aim of controlling and altering elastic wave propagation in solids. Beams with varying stiffness along the length are an archetypal example of a phononic crystal for bending waves, since the resulting nontrivial dispersion relation can be modeled analytically. In this work, the complex dispersion curve over the complete audible frequency range is measured using the inhomogeneous wave-correlation (IWC) technique, and compared to a unitcell model and an explicit model of the finite beam. Multiple band gaps, each with a different attenuation coefficient, are predicted and validated. An iterative implementation of IWC allows the identification of a spatial spectrum of wave numbers, responsible for the intricate beam displacement shape. The energy carried by the fundamental wave number and its Bloch (sub)harmonics are determined, showing that the main dispersion branch is monotonically increasing. It is shown that only a small fraction of the wave energy travels along branches with a negative slope in the first Brillouin zone. Additionally, in band gaps affecting only bending waves, energy is converted to other wave types, such as longitudinal waves. This approach offers some important insights into the physics of the wave propagation, which cannot be gathered from unit-cell modeling alone.