%0 Book Section %1 springerlink:10.1007/978-3-642-02394-1_24 %A Tymoczko, Dmitri %B Mathematics and Computation in Music %D 2009 %E Chew, Elaine %E Childs, Adrian %E Chuan, Ching-Hua %I Springer Berlin Heidelberg %K Musiktheorie MaMu Tonnetz %P 258-272 %R 10.1007/978-3-642-02394-1_24 %T Three Conceptions of Musical Distance %U http://dmitri.tymoczko.com/publications.html %V 38 %X 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). %@ 978-3-642-02394-1

@incollection{springerlink:10.1007/978-3-642-02394-1_24, 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).}, added-at = {2013-02-02T14:41:40.000+0100}, affiliation = {310 Woolworth Center, Princeton University Princeton NJ 08544}, author = {Tymoczko, Dmitri}, bdsk-file-1 = {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}, bdsk-url-1 = {http://dx.doi.org/10.1007/978-3-642-02394-1_24}, biburl = {https://www.bibsonomy.org/bibtex/230d55243304c1b35a7377822d3ce1a51/ks-plugin-devel}, booktitle = {Mathematics and Computation in Music}, date-added = {2011-08-15 16:53:47 +0200}, date-modified = {2011-08-15 16:55:13 +0200}, doi = {10.1007/978-3-642-02394-1_24}, editor = {Chew, Elaine and Childs, Adrian and Chuan, Ching-Hua}, groups = {public}, interhash = {d0b5b99cd3702bef6e50048ed7162665}, intrahash = {30d55243304c1b35a7377822d3ce1a51}, isbn = {978-3-642-02394-1}, keyword = {Computer Science}, keywords = {Musiktheorie MaMu Tonnetz}, note = {10.1007/978-3-642-02394-1_24}, pages = {258-272}, publisher = {Springer Berlin Heidelberg}, series = {Communications in Computer and Information Science}, timestamp = {2013-02-02T14:41:40.000+0100}, title = {Three Conceptions of Musical Distance}, url = {http://dmitri.tymoczko.com/publications.html}, username = {keinstein}, volume = 38, year = 2009 }