source file: mills2.txt Date: Thu, 16 Nov 1995 15:55:48 -0800 Subject: Re: TUNING digest 561 From: marcus@fa.disney.com > > The 12 tone equal temperament scale is derived from the overtone > > series of a vibrating string. > > Of course most of us tuning listers will be prompt to point out that 12TET > doesn't provide a *really great* harmonic series approximation. The 5th > harmonic is way sharp and it misses some really neat harmonics - 7, 11, and 13 > for example. It does, however, provide a fairly EFFICIENT mapping to the > harmonics it does match - matching the first 5 harmonics reasonably well on as a > coarse resolution as 100 cents, is in my view an impressive feat. Thanks for replying. I'm afraid I'm waaaaay back at Tuning 101. Would you (or anybody on the list) mind elaborating scale construction base on partial frequency formulas? i.e., Given the really neat partial freq ratios that mclaren described, how do I construct a scale from them? I realize that we can do NonJust Equal Temperament, Just Non Equal Temperament (what others are there?). There also seems to be the option of octave transposition. For the harmonic series, and the cylindrical vibration mode series, transposing partials somehow into an octave seems really important, because the series increases too rapidly to construct a scale merely composed of partials. For 12TET, did someone merely lay out the harmonic series to some order, octave transpose them, and then make a best fit to a 2^(n/12) scale (discarding partials 7,11,13 in this case)? Thanks a bujillion, Marcus Received: from eartha.mills.edu [144.91.3.20] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Fri, 17 Nov 1995 06:14 +0100 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id UAA02094; Thu, 16 Nov 1995 20:14:15 -0800 Date: Thu, 16 Nov 1995 20:14:15 -0800 Message-Id: Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu