We report angle-dependent spin-wave spectroscopy on aperiodic quasicrystalline magnetic lattices, i.e., Ammann, Penrose P2 and P3 lattices made of large arrays of interconnected Ni80Fe20 nanobars. Spin-wave spectra obtained in the nearly saturated state contain distinct sets of resonances with characteristic angular dependencies for applied in-plane magnetic fields. Micromagnetic simulations allow us to attribute detected resonances to mode profiles with specific mirror symmetries. Spectra in the reversal regime show systematic emergence and disappearance of spin-wave modes indicating reprogrammable magnonic characteristics.