http://www.scivee.tv/node/28524 en http://www.scivee.tv/node/32365 <p>The musical notion of rhythmic canons has proved to be relevant to some non-trivial mathematical problems.<br /> After a survey of the main concepts of tiling rhythmic canons, we discuss recent developments that enable<br /> to make, or expect, definite progress on several open mathematical conjectures.</p> <div class="og_rss_groups"><ul class="links"><li class="first last og_links"><a href="/node/28524" class="og_links">Journal of Mathematics and Music</a></li> </ul></div> algorithm Fuglede’s conjecture music rhythmic canons spectral conjecture tiling Vuza Journal of Mathematics and Music Tue, 19 Jul 2011 02:35:44 -0700 CLDouglas 32365 at http://www.scivee.tv http://www.scivee.tv/node/32173 <p>The present work originated from purely musical topics, namely the notion of ‘selfRep melody’ as defined by the composer Tom Johnson in his work Self-similar Melodies published in 1996, and reaped interesting mathematical as well as musical rewards. It is about melodies that contain themselves in augmentation, and some generalizations thereof. Some of the mathematical by-results are new to the best of the author's knowledge. Applications range from melodies to rhythms, and include some new results on mosaics.</p> <div class="og_rss_groups"><ul class="links"><li class="first last og_links"><a href="/node/28524" class="og_links">Journal of Mathematics and Music</a></li> </ul></div><p><a href="http://www.scivee.tv/node/32173">read more</a></p> affine map augmentation autosimilar Autosimilarity cyclic group melody mosaic orbit ratio tiling Journal of Mathematics and Music Wed, 13 Jul 2011 03:09:58 -0700 CLDouglas 32173 at http://www.scivee.tv