In this paper we present Aligned Scores and Performances (ASAP): a new dataset of 222 digital musical scores aligned with 1068 performances (more than 92 hours) of Western classical piano music. The scores are provided as paired MusicXML files and quantized MIDI files, and the performances as paired MIDI files and partially as audio recordings. Scores and performances are aligned with downbeat, beat, time signature, and key signature annotations. ASAP has been obtained thanks to a new annotation workflow that combines score analysis and alignment algorithms, with the goal of reducing the time for manual annotation. The dataset itself is, to our knowledge, the largest that includes an alignment of music scores to MIDI and audio performance data. As such, it is a useful resource for a wide variety of MIR applications, from those that target the complete audio-to-score Automatic Music Transcription task, to others that target more specific aspects (e.g., key signature estimation and beat or downbeat tracking from both MIDI and audio representations).