source file: mills2.txt Date: Fri, 6 Dec 1996 08:43:01 -0800 Subject: Three views on the fourth From: Daniel Wolf <106232.3266@compuserve.com> Without any number crunching, my spacing model - which was a result of compositional, rather than analytic thinking - has used a **compacting** function, where successions of chords **resolve** by seeking optimal density. For example, of the three chords 6/4, 5/3, 4/2 over a given tonic, the first is not dense enough, the third is too dense, and the middle is just right. Thus either the first or third chord will **resolve** to the second. This function does vary with register (I have assumed with critical band width), but in apparently all voicings available in the conventional vocal ranges, the example works as given. I have marked **resolve** with quotes, because this is clearly a local, cultural feature. In my own work, something like **optimize spacing** might be more correct, but I am not hung up on terminology. Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Fri, 6 Dec 1996 17:42 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA02036; Fri, 6 Dec 1996 17:44:52 +0100 Received: from eartha.mills.edu by ns (smtpxd); id XA02039 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id IAA22303; Fri, 6 Dec 1996 08:44:49 -0800 Date: Fri, 6 Dec 1996 08:44:49 -0800 Message-Id: <199612061139_MC1-CBF-41A@compuserve.com> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu