Musical Actions of Dihedral Groups Export

@article{citeulike:1914760, abstract = {The sequence of pitches which form a musical melody can be transposed or inverted. Since the 1970s, music theorists have modeled musical transposition and inversion in terms of an action of the dihedral group of order 24. More recently music theorists have found an intriguing second way that the dihedral group of order 24 acts on the set of major and minor chords. We illustrate both geometrically and algebraically how these two actions are {\it dual}. Both actions and their duality have been used to analyze works of music as diverse as Hindemith and the Beatles.}, archivePrefix = {arXiv}, author = {Crans, Alissa S. and Fiore, Thomas M. and Satyendra, Ramon}, citeulike-article-id = {1914760}, citeulike-linkout-0 = {http://arxiv.org/abs/0711.1873}, citeulike-linkout-1 = {http://arxiv.org/pdf/0711.1873}, day = {13}, eprint = {0711.1873}, keywords = {group-theory, music}, month = {Jun}, posted-at = {2009-11-08 16:51:15}, priority = {2}, title = {Musical Actions of Dihedral Groups}, url = {http://arxiv.org/abs/0711.1873}, year = {2008} }

TY - JOUR ID - citeulike:1914760 L3 - citeulike-article-id:1914760 N2 - The sequence of pitches which form a musical melody can be transposed or inverted. Since the 1970s, music theorists have modeled musical transposition and inversion in terms of an action of the dihedral group of order 24. More recently music theorists have found an intriguing second way that the dihedral group of order 24 acts on the set of major and minor chords. We illustrate both geometrically and algebraically how these two actions are {\it dual}. Both actions and their duality have been used to analyze works of music as diverse as Hindemith and the Beatles. TI - Musical Actions of Dihedral Groups KW - group-theory KW - music AU - Crans, Alissa AU - Fiore, Thomas AU - Satyendra, Ramon PY - 2008/Jun/13/ UR - http://arxiv.org/abs/0711.1873 ER -