The electronic supplementary material provides videos illustrating the waveforms associated with the gyroscopic periodic waveguides. The paper presents new work on gravity-induced wave motion of gyroscopic systems composed of gyropendulums connected by elastic springs. Classification of trajectories of a single gyropendulum is given, followed by the Floquet-Bloch analysis of the dispersion and localisation for waves within a periodic gyroscopic chain. We construct Green's matrices to identify regimes of propagating modes and wave localisation, which correspond to elliptical motions of the nodal elements. The waveforms subjected to gravity for localised defect modes are discussed in addition to the effect of no pre-tension along the chiral chain.