source file: mills2.txt Date: Thu, 3 Jul 1997 21:16:00 +0200 Subject: Re: Definitions From: Edward Remler The responses to my ‘Historical Questions’ indicate that, not surprisingly, terms referring to tuning are defined in different ways by different people. I would like to check that my usage and understanding of them is not outside generally accepted bounds. Here they are, and I would appreciate any comments and criticisms you may have: 1. Tempering initially referred to how one deviated about the system of Pythagorean tuning (ascending|descending fifths|fourths with frequency ratios of 3/2|4/3) in order to temper sour and howling intervals. Nowadays, however, temperament and tuning seem to be synonymous. 2. The circle of fifths seems to have generally been started on middle C. This at least is what is suggested by both von Helmholtz’s book and the piano keyboard’s layout. 3. Mean Temperament has two general meanings. First it means a system of tuning by fifths such that four ascending fifths and two descending octaves make up a perfect third. It also means any one of many slight variations about this basic system. 4. Bach’s WTC refers to a mean tempered clavichord; in particular, well-tempered means mean tempered. Since the WTC starts in the key of C, it seems that Bach’s thought of mean tempered in terms of ascending fifths started on C. Ed Remler Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Thu, 3 Jul 1997 21:26 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA04316; Thu, 3 Jul 1997 21:26:28 +0200 Date: Thu, 3 Jul 1997 21:26:28 +0200 Received: from ella.mills.edu by ns (smtpxd); id XA04258 Received: (qmail 19302 invoked from network); 3 Jul 1997 14:37:36 -0000 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 3 Jul 1997 14:37:36 -0000 Message-Id: Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu