<html><head></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; ">By the way there is a book devoted to the application of category theory to music.<div>I didn't read it so I can't go deeper about it, but maybe somebody out there might be interested in it.</div><div>It is "The topos of music" written by Guerino Mazzola.</div><div><br></div><div><a href="http://www.amazon.com/Topos-Music-Geometric-Concepts-Performance/dp/3764357312">http://www.amazon.com/Topos-Music-Geometric-Concepts-Performance/dp/3764357312</a></div><div><br></div><div><br></div><div><br><div><div>Il giorno 23/dic/2009, alle ore 05.43, Justin Glenn Smith ha scritto:</div><br class="Apple-interchange-newline"><blockquote type="cite"><div>I have heard the claim that Bach wrote out the entirety of possible music composition - that every possible variation was present in his music, and nothing could be new after him.<br><br>This, of course, is laughably false.<br><br>But I was thinking about a context in which this could be made a true statement. In category theory there is the concept of a functor, which is a structure-preserving mapping from one category to another. If we treated two genres of composition as categories, we could define a functor to take a composition in one of these genres and get a composition in the other, without losing structural information (ie. analogous patterns would exist).<br><br>Did I make this up? Am I remembering it from somewhere? Has someone tried it already? I am imagining mapping the sequence of pitches in a bach piece to spectral densities, and the durations to amplitude, and amplitude to pitch center, and timbre to duration. For example. With enough of a clinamen, of course, to keep things interesting (or maybe just keeping the clinamen of the original figured bass for example, but mapping it to a different part of the composition?).<br>_______________________________________________<br>microsound mailing list<br><a href="mailto:microsound@microsound.org">microsound@microsound.org</a><br>http://or8.net/mailman/listinfo/microsound<br><br></div></blockquote></div><br></div><br><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; "><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; "><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; "><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; "><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; "><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; "><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; "><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; "><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><div><div>__________________________________</div><div>M a s s i m i l i a n o V i e l </div><div></div><div><font class="Apple-style-span" color="#0000EE"><span class="Apple-style-span" style="-webkit-text-decorations-in-effect: underline; "><span class="Apple-style-span" style="color: rgb(0, 0, 0); ">MAIN SITE! -------------></span><span class="Apple-style-span" style="text-decoration: underline; color: rgb(0, 0, 0); "> <a href="http://www.maxviel.it">http://www.maxviel.it</a></span></span></font></div><div><span class="Apple-style-span"><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><font face="Arial" size="3" color="#000cee" style="font: normal normal normal 12px/normal Arial; color: rgb(0, 12, 238); "><u style="text-decoration: none; "><span class="Apple-style-span" style="color: rgb(0, 0, 0); font-family: Helvetica; ">BLOG! -------></span><span class="Apple-style-span" style="text-decoration: underline; color: rgb(0, 0, 0); font-family: Helvetica; "> </span><span class="Apple-style-span" style="text-decoration: underline; "><a href="http://maxviel.wordpress.com/">http://maxviel.wordpress.com/</a></span></u></font></div><div style="text-align: left; margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><a href="http://www.myspace.com/massimilianoviel"> http://www.myspace.com/massimilianoviel</a></div><div style="text-align: left; margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><br></div></span></div><div style="text-align: left; "><font class="Apple-style-span" color="#0000EE"><span class="Apple-style-span" style="-webkit-text-decorations-in-effect: underline; "><span class="Apple-style-span" style="color: rgb(0, 0, 0); "> </span><a href="http://www.ssim-el.net">http://www.ssim-el.net</a></span></font></div><div style="text-align: left; "> <a href="http://www.otolab.net">http://www.otolab.net</a></div><div style="text-align: left; "> <a href="http://www.sincronie.org">http://www.sincronie.org</a></div><div style="text-align: left; ">__________________________________</div></div></div></span></span></span></span></span></span></span></span></span>
</div>
<br></body></html>