Ab initio density functional theory calculations for ethanal and muonium, using the projector augmented-wave technique, are described. The potential binding sites for the muonium are evaluated from total-energy-minimization calculations. At these preferred sites the associated (bond-stretching) vibrational frequencies, Einstein coefficients and isotropic hyperfine coupling constants are then calculated. It is found that the hyperfine parameter at each site depends on the vibrational state, and so muon vibrational spectroscopy of ethanal is predicted to be possible. The effect of a rigid-muonium-bond rotation is also considered. It is found that this can change the sign of the predicted hyperfine coupling constant at certain sites, which is necessary to get reasonable agreement with experimental values. The temperature dependence of the hyperfine coupling constant was calculated from a Boltzmann population of rotational states. This was found to be insufficient to explain the experimentally observed temperature dependence. This is probably due to the neglect of coupling between vibrational and rotational modes. Therefore this common interpretation of the experimental temperature dependence of the hyperfine coupling constant must be reconsidered.