source file: mills2.txt Date: Wed, 15 Nov 1995 22:30:00 -0800 Subject: Re: Tritriadics, etc. From: Gary Morrison <71670.2576@compuserve.com> Aha! 3:5:7:9 harmonies for Pierce-Bohlen. Excellent. I've been wondering for a long time, but never had the time to sit down and crank out, what ratio approximations Pierce-Bohlen makes available. Thanks for pointing that out, John. That makes sense in light of Brian M's observation that Pierce-Bohlen is essentially every fifth step of 41TET, and that 88CET is essentially every third step. That of course means that 3 PB steps ~= 5 88CET steps, which is a pretty good approximation to 9:7 (checko). And 6 PB steps ~= 10 88CET steps, which is a good approximation to 5:3 (checko again). Oh, by the way, the corresponding harmonic series fragment for 88CET is 4:6:7:9:10:11:15. And as with Pierce-Bohlen's 3:5:7:9 fragment John mentioned, it can be taken in retrograde to form a subharmonic series fragment. One very valuable difference that falls out of those two harmonic series fragments is that 88CET has a 10:7 tritone, whereas Pierce-Bohlen has a 7:5 tritone. I personally have always liked 7:5 better than 10:7, although that's kind of like saying that I carrots more than potatoes. They both have value in their own right. Sorry to keep prattling on about 88CET, or even more importantly, to relate an observation about Pierce-Bohlen, to 88CET as though 88CET were some sort of universal tuning reference. I blabber about 88CET because it's my current "thing". But anyway, a number of you have experimented with both tunings, so I thought some of you might find that relationship interesting. Received: from eartha.mills.edu [144.91.3.20] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Fri, 17 Nov 1995 01:55 +0100 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id PAA00648; Thu, 16 Nov 1995 15:55:48 -0800 Date: Thu, 16 Nov 1995 15:55:48 -0800 Message-Id: <9511161555.ZM7862@frollo> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu