A Thesis Submitted to the Faculty of Graduate Studies and Research In Partial Fulfillment of the Requirements for the Degree of Master of Science in Computer Science, University of Regina. ix , 70 p. An isomorphic keyboard layout is an arrangement of notes of a scale such that any musical construct has the same shape regardless of the root note. The mathematics of some speci c isomorphisms have been explored since the 1700s, however, only recently has a general theory of isomorphisms been developed such that any set of musical intervals can be used to generate a valid layout. These layouts have been implemented in the design of electronic musical instruments and software applications. This thesis presents a new extension to the theory of isomorphic layouts, taking advantage of the repetition of notes in these layouts to produce a three-dimensional representational mapping onto a cylinder. Isomorphic layouts can be produced using rectangular or hexagonal grids, and the mathematics of Fullerene molecules from organic chemistry is borrowed to regularize the mapping of hexagonal isomorphisms onto cylinders. This new cylindrical mapping model is also applied to the study of tonal pitch space models, a branch of musicology which seeks to explore the underlying perceptual relationships between harmonically related pitches. Tonal pitch space models are spatial networks of the perceptual \closeness" of pitches, and researchers have experimented with at networks, cylindrical arrangements, and even torus (or donut) shaped models. Cylindrical models are often helical or spiral in nature, and the new cylindrical isomorphic model developed in this thesis is applied to existing helical tonal pitch space models. Student yes