%0 Generic %1 Crans2007 %A Crans, Alissa S. %A Fiore, Thomas M. %A Satyendra, Ramon %D 2007 %K Musiktheorie Gruppen Mathematik MaMu %T Musical Actions of Dihedral Groups %U http://arxiv.org/abs/0711.1873 %X The sequence of pitches which form a musical melody can be transposed orinverted. Since the 1970s, music theorists have modeled musical transpositionand inversion in terms of an action of the dihedral group of order 24. Morerecently music theorists have found an intriguing second way that the dihedralgroup of order 24 acts on the set of major and minor chords. We illustrate bothgeometrically and algebraically how these two actions are dual. Bothactions and their duality have been used to analyze works of music as diverseas Hindemith and the Beatles.

@misc{Crans2007, abstract = { The sequence of pitches which form a musical melody can be transposed orinverted. Since the 1970s, music theorists have modeled musical transpositionand inversion in terms of an action of the dihedral group of order 24. Morerecently music theorists have found an intriguing second way that the dihedralgroup of order 24 acts on the set of major and minor chords. We illustrate bothgeometrically and algebraically how these two actions are {\it dual}. Bothactions and their duality have been used to analyze works of music as diverseas Hindemith and the Beatles.}, added-at = {2013-02-02T14:42:39.000+0100}, author = {Crans, Alissa S. and Fiore, Thomas M. and Satyendra, Ramon}, biburl = {https://www.bibsonomy.org/bibtex/2628b490883a32d63128e0f3eca7260f0/ks-plugin-devel}, description = {Musical Actions of Dihedral Groups}, file = {:Crans/Musical Actions of Dihedral Groups.pdf:PDF}, groups = {public}, interhash = {5db5e3dfe830e660551b3985737f1467}, intrahash = {628b490883a32d63128e0f3eca7260f0}, keywords = {Musiktheorie Gruppen Mathematik MaMu}, note = {cite arxiv:0711.1873Comment: 27 pages, 11 figures. To appear in the American Mathematical Monthly.}, timestamp = {2013-02-02T14:42:39.000+0100}, title = {Musical Actions of Dihedral Groups}, url = {http://arxiv.org/abs/0711.1873}, username = {keinstein}, year = 2007 }