We first introduce the notion of chord progressions by describing a particular example (the II-V-I) that is related to the Coltrane changes. Second, we describe the Coltrane changes using a formalism derived from previous musical investigations with neural networks (Yaremchuk & Dawson, 2005, 2008). Finally, we describe how we trained a neural network to generate the Coltrane changes, how we analyzed its internal structure, and the implications of this interpretation. In particular, we discovered that a network represented transitions between chords in a fashion that could be described in terms of a new musical formalism that we had not envisioned. In short, this paper shows that the interpretation of the internal structure of a musical network can provide new formalisms for representing musical regularities, and can suggest new directions for representational research on musical cognition.