source file: mills2.txt Date: Tue, 1 Oct 1996 10:28:17 -0700 Subject: Equal tempered approximations to just in From: PAULE I thought I'd put together a table showing how closely the just 7-limit intervals are approximated by equal temperaments. The octave inversions and extensions of these intervals will be approximated just as well as the intervals themselves. Each ET is the smallest required to improve on the rms error of the previous ET. Notes per octave Interval Ratio 12 15 19 22 27 31 68 72 Error in Cents for this ET: perf.4th 4/3 2 -18 7 -7 -9 5 -4 2 maj.3rd 5/4 14 14 -7 -4 13 1 2 -3 min.3rd 6/5 -16 4 0 12 -5 -6 2 1 tritone 7/5 17 -23 -14 17 -5 -2 -0 1 sub.3rd 7/6 33 -27 -14 6 -0 4 -2 -0 sup.2nd 8/7 -31 9 21 -13 -9 1 -2 2 rootmeansquare 22 18 13 11 8 4 2 2 Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Wed, 2 Oct 1996 11:44 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA02851; Wed, 2 Oct 1996 10:44:52 +0100 Received: from eartha.mills.edu by ns (smtpxd); id XA02857 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id CAA13068; Wed, 2 Oct 1996 02:44:49 -0700 Date: Wed, 2 Oct 1996 02:44:49 -0700 Message-Id: <199610020542_MC1-9F7-C9C3@compuserve.com> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu