  We study spanning properties of a family of functions translated along simple
model sets. We characterize tight frame and dual frame generators for such
irregular translates and we apply the results to Gabor systems. We use the
connection between model sets and almost periodic functions and rely strongly
on a Poisson summations formula for model sets to introduce the so-called
bracket product, which then plays a crucial role in our approach. As a
corollary to our main results we obtain a density statement for semi-regular
Gabor frames.
