I-Shaped Tiles in the Tonnetz

An I-shaped tile proposed in this paper is used to construct an enharmonically conformed Tonnetz space that preserves more music-theoretic information related to tonality, arguably the original purpose of a Tonnetz, than the standard parallelogram tiles currently used in the literature. The resulting tiling is monohedral, monomorphic and enantiomorphic, giving music-theoretic meaning in particular to the non-horizontal tile boundaries that cross fifths-related regions.