Transmission coefficient for a staircase embedded in a stably stratified medium, in an inclined box with and Θ = π/ 4, for different number of steps a) m = 2; b) m = 5 and c) m = 10, as a function of dimensionless frequency and horizontal wave number (upper panel) or vertical wave number (bottom panel). The white arrow indicates the frequency ω = f. A set of bands extending vertically depart from f = 2ΩcosΘ (). In addition, m bands of perfect transmission appear in the regions ω<f and ω>f, each becoming narrower with increasing m.