<table cellspacing="0" cellpadding="0" border="0" ><tr><td valign="top" style="font: inherit;">Much depends on what one means by explicitly recognizing octave equivalence.<br><br>The notion that the 2:1 ratio corresponded to the diapason interval seems to have circulated fairly widely by the time that Aristotle, a student of Plato, wrote that "the form and pattern are a cause, that is to say the statement of the essenc e genera to which it belongs; such, for instance, in the case of the octave, are the ratio of two to one, and number in general" (Physics II.3). <br>http://www.wsu.edu/~dee/GREECE/4CAUSES.HTM <br><br>This is more than 400 years earlier than Ptolemy's account.<br><br>Jay Rahn, York University (Toronto) <br><br>--- On <b>Sat, 7/3/10, Martin Braun <i><nombraun@telia.com></i></b> wrote:<br><blockquote style="border-left: 2px solid rgb(16, 16, 255); margin-left: 5px; padding-left: 5px;"><br>From: Martin Braun
<nombraun@telia.com><br>Subject: Re: [Smt-talk] Math-music structure of Plato's Dialogues<br>To: Smt-talk@societymusictheory.org<br>Date: Saturday, July 3, 2010, 8:00 AM<br><br><div class="plainMail">Hello Kyle, and others,<br><br>"if I'm not mistaken, Ptolemy was the first to explicitly recognize octave equivalence"<br><br>Perhaps Ptolomy was the earliest in survived Greek writings. The earliest survived Chinese writings, in the form of cast bell inscriptions in bronze bell ensembles, are at least 500 years older.<br><br><a href="http://www.neuroscience-of-music.se/Zengbells.htm" target="_blank">http://www.neuroscience-of-music.se/Zengbells.htm</a><br><br><br>Martin<br><br><br>---------------------------------------------------------------------<br>Martin Braun<br>Neuroscience of Music<br>S-671 95 Klässbol<br>Sweden<br><br><br><br><br>----- Original Message ----- From: "Kyle adams" <<a ymailto="mailto:adamsk01@yahoo.com"
href="/mc/compose?to=adamsk01@yahoo.com">adamsk01@yahoo.com</a>><br>To: "Soderberg, Stephen" <<a ymailto="mailto:ssod@loc.gov" href="/mc/compose?to=ssod@loc.gov">ssod@loc.gov</a>>; <<a ymailto="mailto:Smt-talk@societymusictheory.org" href="/mc/compose?to=Smt-talk@societymusictheory.org">Smt-talk@societymusictheory.org</a>><br>Sent: Friday, July 02, 2010 4:41 PM<br>Subject: Re: [Smt-talk] Math-music structure of Plato's Dialogues <br>_______________________________________________<br>Smt-talk mailing list<br><a ymailto="mailto:Smt-talk@societymusictheory.org" href="/mc/compose?to=Smt-talk@societymusictheory.org">Smt-talk@societymusictheory.org</a><br><a href="http://lists.societymusictheory.org/listinfo.cgi/smt-talk-societymusictheory.org" target="_blank">http://lists.societymusictheory.org/listinfo.cgi/smt-talk-societymusictheory.org</a><br></div></blockquote></td></tr></table>