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 Ni$_{80}$Fe$_{20}$ 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. (read more)