source file: mills2.txt Date: Tue, 19 Nov 1996 10:09:54 -0800 Subject: Re: Reply to Gary Morrison; Meeting in NYC From: Paul Hahn On Mon, 18 Nov 1996, PAULE wrote: > Of course the major mode was not one > of the favorite modes of the diatonic scale until triadic harmony had been > in use for some time -- the tritone resolves to the tonic triad only in the > major and minor modes. A minor quibble--this is true if the voices are led in contrary motion, but using oblique motion the tritones in the Phrygian and Lydian modes resolve to the tonic fifth. > My paper is an attempt to find a set of pitches > which, like the diatonic scale, stands up on a melodic basis alone, but > leads as naturally to 7-limit harmony and 7-limit tonality, as the diatonic > scale leads to 5-limit harmony and tonality, and (if you believe Yasser was > on the right track) as the pentatonic scale leads to 3-limit harmony and > tonality. The attempt succeeds even though I look no farther than the first > 34 equal temperaments (the solution is found in 22-equal). As others have said, this sounds like a very interesting paper. (And once again, it seems to dovetail with some concepts I've been playing with myself. Maybe it's something about guys named Paul. 8-)> ) --pH (manynote@library.wustl.edu or http://library.wustl.edu/~manynote) O /\ "How about that? The guy can't run six balls, -\-\-- o and they make him president." Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Tue, 19 Nov 1996 19:39 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA18186; Tue, 19 Nov 1996 19:40:52 +0100 Received: from eartha.mills.edu by ns (smtpxd); id XA17858 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id KAA19438; Tue, 19 Nov 1996 10:40:48 -0800 Date: Tue, 19 Nov 1996 10:40:48 -0800 Message-Id: <41961119183814/0005695065PK4EM@MCIMAIL.COM> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu