HexaChord swMATH ID: 22120 Software Authors: Bigo, Louis; Andreatta, Moreno Description: Topological structures in computer-aided music analysis. We propose a spatial approach to musical analysis based on the notion of a chord complex. A chord complex is a labelled simplicial complex which represents a set of chords. The dimension of the elements of the complex and their neighbourhood relationships highlight the size of the chords and their intersections. Following a well-established tradition in set-theoretical and neo-Riemannian music analysis, we present the family of T/I complexes which represent classes of chords which are transpositionally and inversionally equivalent and which relate to the notion of Generalized Tonnetze. A musical piece is represented by a trajectory within a given chord complex. We propose a method to compute the compactness of a trajectory in any chord complex. Calculating the trajectory compactness of a piece in T/I complexes provides valuable information for music analysis and classification. We introduce different geometrical transformations on trajectories that correspond to different musical transformations. Finally, we present HexaChord, a software package dedicated to computer-aided music analysis with chord complexes, which implements most of the concepts discussed in this chapter. Homepage: https://link.springer.com/chapter/10.1007/978-3-319-25931-4_3 Related Software: MGS Cited in: 4 Documents all top 5 Cited by 6 Authors 3 Andreatta, Moreno 2 Bigo, Louis 1 Amiot, Emmanuel 1 Arias-Valero, Juan Sebastián 1 Lluis-Puebla, Emilio 1 Yust, Jason Cited in 1 Serial 2 Journal of Mathematics and Music Cited in 4 Fields 4 General and overarching topics; collections (00-XX) 1 Combinatorics (05-XX) 1 Category theory; homological algebra (18-XX) 1 Computer science (68-XX) Citations by Year