We show the coexistence of discrete modes and turbulence in numerical experiments of magnetohydrodynamics with a strong background magnetic field. The particular system we consider is a model of an open magnetic region which we have previously used in coronal heating studies. In the simulations shown here, Alfven waves at discrete frequencies with values corresponding to solar g-modes and p-modes are injected at the boundary (although the question of how those modes could generate Alfven waves is not addressed). Numerical probes are used to compute the magnetic field fluctuations at the output. The frequency spectra obtained from those probes are broadband, but with peaks at the driving frequencies. The perpendicular (to the mean magnetic field) wavenumber energy spectrum is of a turbulent Kolmogorov-like type, and formation of small scale structures is observed. This shows, numerically, the possibility of persistence of discrete modes in a turbulent system.