While the unique gamut of the Musica and Scolica enchiriadis is highly systematic and self-consistent, it proves an imperfect fit for the polyphony notated in the treatises themselves. The author(s) variously ignore, amend, conceal, explain by way of miracle, or simply omit passages of noncongruence between theory and practice. This paper seeks to address two well-known deficiencies with the enchiriadis gamut: its infamous lack of octave equivalency and the absence of common pitches in practice. Drawing upon musical examples from the treatises, I will show how contemporaneous polyphonic practice involved palpable tension between theory, practice, and musical notation. I will then expand the enchiriadis gamut into a Tonnetz that solves its practical problems while maintaining its theoretical strengths. Yet for its size and scope, this pitch space is firmly rooted in medieval pitch modelling, merely extending 9^th-c. methods to their logical conclusion.