This note summarizes certain properties common to Macdonald, Koornwinder and Arthamonov-Shakirov q-difference operators, relating to the duality or bi-spectrality properties of their eigenfunctions. This results in Pieri operators which, in the q-Whittaker limit, are relativistic difference Toda type Hamiltonians which have a related quantum cluster algebra structure known as the quantum Q-system. The genus-2 result explained here is new.