Various methods have been proposed for detecting the onset times of musical notes in audio signals. We examine recent work on onset detection using spectral features such as the magnitude, phase and complex domain representations, and propose improvements to these methods: a weighted phase deviation function and a halfwave rectified complex difference. These new algorithms are compared with several state-of-the-art algorithms from the literature, and these are tested using a standard data set of short excerpts from a range of instruments (1060 onsets), plus a much larger data set of piano music (106054 onsets). Some of the results contradict previously published results and suggest that a similarly high level of performance can be obtained with a magnitude-based (spectral flux), a phase-based (weighted phase deviation) or a complex domain (complex difference) onset detection function.