The Filosax dataset is a large collection of specially commissioned recordings of jazz saxophonists playing with commercially available backing tracks. Five participants each recorded themselves playing the melody, interpreting a transcribed solo and improvising on 48 tracks, giving a total of around 24 hours of audio data. The solos are annotated both as individual note events with physical timing, and as sheet music with a metrical interpretation of the timing. In this paper, we outline the criteria used for choosing and sourcing the repertoire, the recording process and the semi-automatic transcription pipeline. We demonstrate the use of the dataset to analyse musical phenomena such as swing timing and dynamics of typical musical figures, as well as for training a source activity detection system and predicting expressive characteristics. Other potential applications include the modelling of jazz improvisation, performer identification, automatic music transcription, source separation and music generation.