source file: mills3.txt Date: Tue, 23 Dec 1997 21:11:36 +0100 Subject: Mathematics and Tuning From: Gregg Gibson Anyone who compares the musical theory of the past to that of the present, and especially musical theory as it relates to tuning questions, will be immediately impressed by one great difference. The theorists of the past used mathematics only very charily, but language copiously. In some cases this may have been due to mathematical ignorance; no doubt it was. But in other cases it seems to have been highly deliberate. It was felt that mathematics, if applied before one's _assumptions_ had been presented with the utmost clarity, could lead only to mistaken conclusions. Modern theorists on the other hand, painfully trained in mathematical habits of thought, but little accustomed to think profoundly in language, and often under the vague impression that to state anything mathematically is to gain public respect, very often pass over their musical assumptions with an apologetic air, then turn to the most involved calculations with an audible sigh of relief. >From such persons using such a method, musical truth is most unlikely to emerge. For it is in the assumptions which should be made, and not in the mathematical methods, which are, in comparison, trivial, that the true difficulties arise. None of this is to disparage mathematics or abate its just claims; mathematical truths compare in beauty to the highest conceptions of art, and without mathematics there can be no sure foundation for musical speculation at all. Used with circumspection, this science can stimulate and condense thought in a very wonderful manner. SMTPOriginator: tuning@eartha.mills.edu From: Paul Hahn Subject: Re: Paul E[h]rlich (sic) PostedDate: 23-12-97 21:29:59 SendTo: CN=coul1358/OU=AT/O=EZH ReplyTo: tuning@eartha.mills.edu $MessageStorage: 0 $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: 23-12-97 21:27:51-23-12-97 21:27:52,23-12-97 21:27:22-23-12-97 21:27:23 DeliveredDate: 23-12-97 21:27:23 Categories: $Revisions: Received: from ns.ezh.nl ([137.174.112.59]) by notesrv2.ezh.nl (Lotus SMTP MTA SMTP v4.6 (462.2 9-3-1997)) with SMTP id C1256576.007065C4; Tue, 23 Dec 1997 21:29:37 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA24610; Tue, 23 Dec 1997 21:29:59 +0100 Date: Tue, 23 Dec 1997 21:29:59 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA24638 Received: (qmail 29387 invoked from network); 23 Dec 1997 12:29:56 -0800 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 23 Dec 1997 12:29:56 -0800 Message-Id: Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu