<html><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; ">I wonder wether the "discernable strands of the musical texture" are a consequence of the pitch treatment in Christobal's example, – which is extrinsic to "the idea" I mentioned – or wether it is also(!) a consequence of the radical slow-down. It think it would be nice to make more experiments...<div>best wishes</div><div>Thomas Noll </div><div><br></div><div><div>Am 15.10.2009 um 15:09 schrieb Justin London:</div><br class="Apple-interchange-newline"><blockquote type="cite"><div style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; ">This is a nifty idea, but I don't think it works. For the periodicities one tracks in the ritardando illusion are invidividual, discernable strands of the musical texture (so to speak), as these stream separately from the other periodicities at different rates in different registers. Whereas in the case of the shepherd tones, the components tend to fuse into a single tone percept, which enables the illusion. <div><br></div><div>Best,</div><div>Justin London</div><div><br><div><div>On Oct 15, 2009, at 1:42 AM, Thomas Noll wrote:</div><br class="Apple-interchange-newline"><div style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; ">Dear colleages,<div>with students in theory class we have been working on the idea of an infinite accellerando (or ritardando) in analogy to the illusion of infinite ascend (or descend) in pitch height in the Shepard scale (or glissando). The solution we came up with is a combination of </div><div>(1) a non-periodic self-similar rhythm (such as investigated by Norman Carey and David Clampitt in their 1996 PNM article: "Self-similar pitch structures, their duals, and rhythmic analogues"), which is played simultaneously at several speeds, where "old" levels fade out and new levels fade in through a Gaussian envelope for the amplitude, and</div><div>(2) an exponential time flow (which is the physical time of performance as a function of symbolic score time). All of the (infinitely many) voices silently start simultaenously at minus infinity ;-)</div><div>One of the students, Christobal Massis Valencia (percussionist), realized a ritardando (in combination with an "infinite" descend) as a homework on that class:</div><div><a href="http://user.cs.tu-berlin.de/~noll/sqrt2">http://user.cs.tu-berlin.de/~noll/sqrt2</a></div><div>Thomas Noll</div><div><br></div><div><div><div><div><br></div></div><div apple-content-edited="true"><span class="Apple-style-span" style="border-collapse: separate; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-align: auto; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0; "><div style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><span class="Apple-style-span" style="border-collapse: separate; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; "><div style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><div><div><div><div>*********************************************************</div><div>Thomas Noll</div><div><a href="http://flp.cs.tu-berlin.de/~noll">http://flp.cs.tu-berlin.de/~noll</a></div><div><a href="mailto:noll@cs.tu-berlin.de">noll@cs.tu-berlin.de</a></div><div>Escola Superior de Musica de Catalunya, Barcelona </div><div>Departament de Teoria i Composició </div><div><br class="khtml-block-placeholder"></div><div>*********************************************************</div></div></div></div><div><br></div></div></span><br class="Apple-interchange-newline"></div></span><br class="Apple-interchange-newline"> </div><br></div></div></div>_______________________________________________<br>Smt-talk mailing list<br><a href="mailto:Smt-talk@societymusictheory.org">Smt-talk@societymusictheory.org</a><br><a href="http://lists.societymusictheory.org/listinfo.cgi/smt-talk-societymusictheory.org">http://lists.societymusictheory.org/listinfo.cgi/smt-talk-societymusictheory.org</a><br></div><br><div apple-content-edited="true"> <span class="Apple-style-span" style="border-collapse: separate; color: rgb(0, 0, 0); font-family: Helvetica; font-size: medium; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-align: auto; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; "><div style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><span class="Apple-style-span" style="border-collapse: separate; color: rgb(0, 0, 0); font-family: Helvetica; font-size: medium; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; "><div style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><div><div>*************************************************</div><div>Justin London, Professor of Music (and other stuff)</div><div>President, Society for Music Theory</div><div>Carleton College</div><div>Department of Music</div><div>One North College St.</div><div>Northfield, MN 55057 USA</div><div>507-222-4397</div><div>fax 507-222-5561</div><div><a href="mailto:jlondon@carleton.edu">jlondon@carleton.edu</a></div><div><br></div></div></div></span><br class="Apple-interchange-newline"></div></span><br class="Apple-interchange-newline"> </div><br></div></div></blockquote></div><br><div> <span class="Apple-style-span" style="border-collapse: separate; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-align: auto; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0; "><div style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><span class="Apple-style-span" style="border-collapse: separate; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; "><div style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><div>PS: My other mail <a href="mailto:tnoll@iua.upf.edu">tnoll@iua.upf.edu</a> doesn't exist any longer.<div><br><div><div>*********************************************************</div><div>Thomas Noll</div><div><a href="http://flp.cs.tu-berlin.de/~noll">http://flp.cs.tu-berlin.de/~noll</a></div><div><a href="mailto:noll@cs.tu-berlin.de">noll@cs.tu-berlin.de</a></div><div>Escola Superior de Musica de Catalunya, Barcelona </div><div>Departament de Teoria i Composició </div><div><br class="khtml-block-placeholder"></div><div>*********************************************************</div></div></div></div><div><br></div></div></span><br class="Apple-interchange-newline"></div></span><br class="Apple-interchange-newline"> </div><br></body></html>