%0 Journal Article %1 5174333020100301 %A Walton, Adrian %D 2010 %J Journal of Mathematics & Music %K Cayley_Graph Faktorisierung %N 1 %P 45 - 56 %T A graph theoretic approach to tonal modulation. %U http://search.ebscohost.com/login.aspx?direct=true&db=a9h&AN=51743330&site=ehost-live %V 4 %X Tonal modulation is discussed in the context of graph theory with the aim of applying its fundamental ideas and theorems to solve or pose musically interesting problems. Mathematical ideas such as connectivity of graphs, group structure, graph colouring, metrics, Hamiltonian paths and Euler tours are used to prove the existence of special sequences of modulations and chord progressions, as well as to investigate the possibilities and limitations of tonal modulation. ABSTRACT FROM AUTHOR

@article{5174333020100301, abstract = {Tonal modulation is discussed in the context of graph theory with the aim of applying its fundamental ideas and theorems to solve or pose musically interesting problems. Mathematical ideas such as connectivity of graphs, group structure, graph colouring, metrics, Hamiltonian paths and Euler tours are used to prove the existence of special sequences of modulations and chord progressions, as well as to investigate the possibilities and limitations of tonal modulation. [ABSTRACT FROM AUTHOR]}, added-at = {2011-05-03T15:33:28.000+0200}, author = {Walton, Adrian}, biburl = {https://www.bibsonomy.org/bibtex/2944011fd5a35d3b5254ae4bf77ed155e/keinstein}, file = {:Walton/A graph theoretic approach to tonal modulation.pdf:PDF;:51743330.pdf:PDF}, groups = {public}, interhash = {8ecd9c25b9843c188c55b74f38e9f91a}, intrahash = {944011fd5a35d3b5254ae4bf77ed155e}, issn = {17459737}, journal = {Journal of Mathematics \& Music}, keywords = {Cayley_Graph Faktorisierung}, number = 1, pages = {45 - 56}, timestamp = {2013-01-20T19:14:59.000+0100}, title = {A graph theoretic approach to tonal modulation.}, url = {http://search.ebscohost.com/login.aspx?direct=true&db=a9h&AN=51743330&site=ehost-live}, username = {keinstein}, volume = 4, year = 2010 }