@inproceedings{3e779047710649e6af0c3584fa87e2cd,

title = "Three conceptions of musical distance",

abstract = "This paper considers three conceptions of musical distance (or inverse {"}similarity{"}) that produce three different musico-geometrical spaces: the first, based on voice leading, yields a collection of continuous quotient spaces or orbifolds; the second, based on acoustics, gives rise to the Tonnetz and related {"}tuning lattices{"}; while the third, based on the total interval content of a group of notes, generates a six-dimensional {"}quality space{"} first described by Ian Quinn. I will show that although these three measures are in principle quite distinct, they are in practice surprisingly interrelated. This produces the challenge of determining which model is appropriate to a given music-theoretical circumstance. Since the different models can yield comparable results, unwary theorists could potentially find themselves using one type of structure (such as a tuning lattice) to investigate properties more perspicuously represented by another (for instance, voice-leading relationships).",

keywords = "Fourier transform, Orbifold, Tonnetz, Tuning lattice, Voice leading",

author = "Dmitri Tymoczko",

year = "2009",

doi = "10.1007/978-3-642-02394-1_24",

language = "English (US)",

isbn = "9783642023934",

series = "Communications in Computer and Information Science",

pages = "258--272",

editor = "Elaine Chew and Elaine Chew and Adrian Childs and Ching-Hua Chuan",

booktitle = "Mathematics and Computation in Music",

}