Abstract
This article draws on Jonathan De Souza's (2018) notion of generalized fretboard space and Julian Hook's (2023) mathematical descriptions of pitch spaces to study intervallic relationships between the instrumental space of the violin and abstract pitch space. Since both fingerboard space (fgbd) and pitch space (pitch) can be formalized as Lewinian GISes (Lewin [1987] 2007), the article employs transformational theory—specifically the concept of a GIS homomorphism—to examine the properties of intervals and transformations (transposition and inversion) in these two spaces. The final section explores a notion of equivalence between certain kinds of intervals based on their layout on the fingerboard. This leads to the construction of fingerboard-class space (fbc) and a consideration of its voice-leading properties. These theoretical topics are explored through brief analyses of works by Eugène Ysaÿe, Wolfgang Amadeus Mozart, Ross Lee Finney, and Augusta Read Thomas.
