source file: mills2.txt Date: Sun, 29 Sep 1996 10:55:26 -0700 Subject: Re: 88CET Variants and Their Approximations From: Gary Morrison <71670.2576@compuserve.com> For you folks out there who have also been experimenting with 88CET, the two cases in Manuel's 88CET calculations that struck me as especially interesting were: ------------------------------------------------------------------------------ 1: 4 2: 7 3: 10 88.2160 cents, 13.6030/oct. Std. dev: 2.9412 cents 1: 11/9 -5.4561 undecimal neutral third 2: 10/7 -0.0242 septimal augmented fourth, Euler's tritone 3: 5/3 2.1987 major sixth 1: 3 2: 4 3: 10 88.2707 cents, 13.5946/oct. Std. dev: 3.1293 cents 1: 7/6 2.0588 septimal minor third 2: 11/9 -5.6749 undecimal neutral third 3: 5/3 1.6517 major sixth ------------------------------------------------------------------------------ I found them particularly interesting, because stretching the step size to 88 1/4 cents or thereabouts, would make the 41-step triple-octave approximation pretty far off. It would be sufficiently far off to make that tuning pretty much unequivocally different from simply every third step of 41TET. Perhaps that's something of an ignoble goal - making it different just to be different. I suppose that's a matter of perspective. But it's a thought anyway. Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Sun, 29 Sep 1996 20:00 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA01056; Sun, 29 Sep 1996 18:59:43 +0100 Received: from eartha.mills.edu by ns (smtpxd); id XA04542 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id KAA06769; Sun, 29 Sep 1996 10:59:37 -0700 Date: Sun, 29 Sep 1996 10:59:37 -0700 Message-Id: <960929174918_71670.2576_HHB73-2@CompuServe.COM> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu