Arrays of artificial spin ices exhibit reconfigurable ferromagnetic resonance modes that can be leveraged and designed for potential applications. However, analytical and numerical studies of the frequency response of artificial spin ices have been restricted in scope due to the need of take into account nonlocal dipole fields in theoretical calculations or by long computation times in micromagnetic simulations. Here, we introduce Gænice, a framework to compute magnon dispersion relations of arbitrary artificial spin ice configurations. Gænice makes use of a tight-binding approach to compute the magnon bands. It also provides the user control over the interaction terms included, e.g., external field, shape anisotropy, exchange, and dipole, making Gænice useful for computing ferromagnetic resonances for a variety of structures, such as multilayers and ensembles of weakly or non-interacting nanoparticles. Because it relies on a semi-analytical model, Gænice is computationally inexpensive and efficient. This makes it an attractive tool for the exploration of large parameter spaces. We expect Gænice to help guide the development of novel artificial spin ices geometries and specific micromagnetic simulations for full quantitative verification.