We explore a novel way of conceptualising the task of polyphonic music transcription, using so-called invertible neural networks. Invertible models unify both discriminative and generative aspects in one function, sharing one set of parameters. Introducing invertibility enables the practitioner to directly inspect what the discriminative model has learned, and exactly determine which inputs lead to which outputs. For the task of transcribing polyphonic audio into symbolic form, these models may be especially useful as they allow us to observe, for instance, to what extent the concept of single notes could be learned from a corpus of polyphonic music alone (which has been identified as a serious problem in recent research). This is an entirely new approach to audio transcription, which first of all necessitates some groundwork. In this paper, we begin by looking at the simplest possible invertible transcription model, and then thoroughly investigate its properties. Finally, we will take first steps towards a more sophisticated and capable version. We use the task of piano transcription, and specifically the MAPS dataset, as a basis for these investigations.