From PErlich@acadian-asset.com Thu Apr 15 14:47:00 1999 Received: from siren.shore.net ([207.244.124.5]) by clinch.math.niu.edu (8.9.1a/8.9.1) with ESMTP id OAA17145 for ; Thu, 15 Apr 1999 14:46:55 -0500 (CDT) Received: from mail.acadian-asset.com [207.244.72.210] by siren.shore.net with smtp (Exim) id 10Xs62-00053S-00; Thu, 15 Apr 1999 15:46:46 -0400 Received: from MARS by mail.acadian-asset.com via smtpd (for relay1.shore.net [207.244.124.129]) with SMTP; 15 Apr 1999 19:46:45 UT Received: by MARS with Internet Mail Service (5.5.2448.0) id <28JDZSPJ>; Thu, 15 Apr 1999 15:44:01 -0400 Message-ID: From: "Paul H. Erlich" To: "'bhammel@graham.main.nc.us'" Cc: "'rusin@math.niu.edu'" Subject: music and math Date: Thu, 15 Apr 1999 15:44:00 -0400 MIME-Version: 1.0 X-Mailer: Internet Mail Service (5.5.2448.0) Content-Type: text/plain Status: R Hi Bill and David, and thanks for having such great web pages up. There is a _great_ deal of mathematics surrounding microtonal music theory, falling into many, many different categories. Your pages barely scratch the surface of this stuff, though the connection with the Riemann zetafunction is interesting and I'd love to learn more. If either of you are interested in discussing this stuff, please contact me (it's my lifelong obsession) -- I have much to share but also many open problems that perhaps one of you could help me along a path to solving. Or, you could join the mailing list tuning@onelist.com (this recently moved from tuning@eartha.mills.edu; the discussions since the move, and directions for subscribing, are at http://www.onelist.com/arcindex.cgi?listname=tuning). Here are some www links: First, a shameless plug for my paper on 22-tone equal temperament: http://www-math.cudenver.edu/~jstarret/22ALL.pdf. Please note that page 20 is riddled with errors and should be deleted. This paper was published in volume 17 of Xenharmonikon, a journal of microtonal music that often gets very mathematical. Second, Graham Breed's page http://www.cix.co.uk/~gbreed/tuning.htm is excellent overall, and quite mathematical. It features his tuning matrices which allow for great formal simplicity in much microtonal theory. A unique and popular non-octave scale, the Bohlen-Pierce scale, is studied at http://members.aol.com/bpsite/index.html Erv Wilson was one of the geniuses of microtonal theory and many of his papers, featuring beautiful but mathematically rigorous diagrams, are collected at http://www.anaphoria.com/wilson.html. John Allen's page http://www.tiac.net/users/jsallen/tunings/tunintro.htm is good too. A discussion of equal-tempered musical scales: http://uq.net.au/~zzdkeena/Music/EqualTemperedMusicalScales.htm. Georg Hajdu's mathematically-oriented paper on tuning systems: http://www.uni-muenster.de/Musikhochschule/Dozenten/Hajdu/Articles/LowEnergy .pdf There's so much more . . . Thanks again, Paul