source file: mills3.txt Date: Thu, 25 Sep 1997 20:32:59 +0200 Subject: Blackwood's proof From: James Kukula Mark Nowitzky writes: > It was something about Helmholtz' > and Ellis' attempt to use just intonation to get better harmony than equal > temperament being proved impossible by Easley Blackwood in "The Structure of > Recognizable Diatonic Tunings". I don't know how familiar folks are with Blackwood's book. I'm not any kind of musician. But I really loved the book, because it built a bridge between my own thinking and more conventional musical ideas. Before I read Blackwood I had tried taking a couple of Bach harmonized chorales and figuring out how they should be played in j.t., I think 5-limit is the right term. Basically the problem is just to figure out which of a set of nearby pitches to use for each note, the pitches differing by the 80/81 comma. Being a musical ignoramus I'm sure I made tons of errors. But the exercise really opened up for me the structure of the Bach pieces, or seemed to anyway. I found, though, that the pieces seemed to turn on a kind of musical pun, to take advantage of the blurring of harmonic distinctions provided by temperament. As I read Blackwood, the point is not so much that e.t. or any temperament is so much better than j.t. in any universal or absolute sense, but that mainstream European musical practise at least in the 18th & 19th Centuries was really structured around temperament, and you can't just slide j.t. into the classics and make them better. A different kind of music based on j.t. might be better in some sense, but the structure of composition is strongly connected to tuning, so you can't change one without some adjustment in the other. Jim SMTPOriginator: tuning@eartha.mills.edu From: clumma@nni.com Subject: Barbershop and Equal-Step Tuning PostedDate: 25-09-97 21:31:24 SendTo: CN=coul1358/OU=AT/O=EZH ReplyTo: tuning@eartha.mills.edu $UpdatedBy: CN=notesrv2/OU=Server/O=EZH,CN=coul1358/OU=AT/O=EZH,CN=Manuel op de Coul/OU=AT/O=EZH RouteServers: CN=notesrv2/OU=Server/O=EZH,CN=notesrv1/OU=Server/O=EZH RouteTimes: 25-09-97 21:31:11-25-09-97 21:31:12,25-09-97 21:30:15-25-09-97 21:30:16 DeliveredDate: 25-09-97 21:30:16 Categories: $Revisions: Received: from ns.ezh.nl by notesrv2.ezh.nl (Lotus SMTP MTA v1.1 (385.6 5-6-1997)) with SMTP id C125651D.006B350D; Thu, 25 Sep 1997 21:30:59 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA31095; Thu, 25 Sep 1997 21:31:24 +0200 Date: Thu, 25 Sep 1997 21:31:24 +0200 Received: from ella.mills.edu by ns (smtpxd); id XA31090 Received: (qmail 23892 invoked from network); 25 Sep 1997 12:31:21 -0700 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 25 Sep 1997 12:31:21 -0700 Message-Id: <19970925193227218.AAB352@NIETZSCHE> Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu