  A model for ac-driven systems, based on the
Tang-Wiesenfeld-Bak-Coppersmith-Littlewood automaton for an elastic medium,
exhibits mode-locked steps with frequencies that are irrational multiples of
the drive frequency, when the pinning is spatially quasiperiodic. Detailed
numerical evidence is presented for the large-system-size convergence of such a
mode-locked step. The irrational mode locking is stable to small thermal noise
and weak disorder. Continuous time models with irrational mode locking and
possible experimental realizations are discussed.
