We study the measurement of the atmospheric neutrino oscillation parameters, θ 23 and ∆m 2 23 , at the ν µ disappearance channel at three conventional beam facilities, the SPL, T2K-phase I and NOνA. These two parameters have been shown to be of crucial importance in the measurement of two of the unknowns of the PMNS mixing matrix, θ 13 and the leptonic CP-violating phase δ. In our analyis, the effect of the two discrete ambiguities, sign(∆m 2 23 ) and sign(tan 2θ 23 ), is explicitly taken into account. We analyse also the ν µ disappearance channel at the Neutrino Factory, and combine it with the "golden" ν e → ν µ and "silver" ν e → ν τ appearance channels to study its impact on the measurement of θ 13 and δ. Eventually, we present the sensitivity of the four facilities to different observables: θ 13 , δ, maximal θ 23 , the sign of the atmospheric mass difference, s atm , and the θ 23 -octant, s oct .