MIDI serves as an important symbolic representation of performance and sheet music. With the availability of millions of MIDI files in public datasets, content-based analysis of MIDI files has become increasingly important. In this extended abstract, we present a self-supervised approach for chord and key estimation in score MIDI files. The core idea is extremely simple: We locate MIDI tracks that look useful to the task and create noisy psuedo-labels, which are used to fine-tune a MIDI foundation model. Our method achieves state-of-the-art performance entirely without human annotation or MIDI metadata.