source file: mills2.txt Date: Sat, 14 Oct 1995 10:11:58 -0700 Subject: Re: Computing Nth Roots From: Gary Morrison <71670.2576@compuserve.com> As John (C) briefly aluded here, graphical methods can place frets, toneholes, lengths of bars, or most any other physical dimension to pretty decent precision. In the case of 12TET, once you precisely calculate whatever dimensions you're interested in for the square root (tritone), the square root of that (minor third), and the product of the two (minor sixth), you've got a 4TET scale. You can graph those points and "french curve" in the rest of the notes' dimensions to pretty decent accuracy. Certainly far greater accuracy than the "lipping" range of a wind instrument. Fixed pitch instruments like the bells mentioned here would have a little error here and there, but not a whole lot more than you get from typical well-temperament schemes. (Now of course the "error" from ET in well temperament schemes are intentional and desirable, but I'm sure you get my point.) Received: from eartha.mills.edu [144.91.3.20] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Sun, 15 Oct 1995 17:00 +0100 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id HAA26733; Sun, 15 Oct 1995 07:59:42 -0700 Date: Sun, 15 Oct 1995 07:59:42 -0700 Message-Id: <9510150758.aa10492@cyber.cyber.net> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu