The A exciton feature at 6.025 eV is observed directly in the low temperature (1.8 K) reflectance spectra of AlN for the first time, using a bulk AlN single crystal which has a relatively flat m-face that allows both σ and π configurations. Features involving unresolved B and C excitons are also observed around 6.25 eV from this sample and in three c-oriented MOCVD AlN films. Transmission measurements on the thickest film reveal a clear but weak A excitonic absorption feature at 6.080 eV. The results are explained by theoretical calculations of exciton energies and oscillator strengths. The calculations suggest that AlGaN light-emitting devices will emit light mainly in the π polarization for wavelengths shorter than 320 nm.