source file: mills2.txt Date: Thu, 20 Feb 1997 11:30:51 -0800 Subject: Reply to Matt Nathan From: Manuel.Op.de.Coul@ezh.nl (Manuel Op de Coul) From: PAULE Sorry, I disagree with you about comma shifts. Melody is historically and aesthetically prior to harmony. If the unaccompanied melody uses equal-sized whole tones and no comma shifts, then the harmonized melody should too. >Will you explain this dissonance function with >figures please? It sounds interesting but I'm >not sure what you mean by derivative. "Derivative" means "rate of change" of a function in calculus. What I was getting at is that if you assume that dissonance has a local minima at certain simple just ratios (I believe this is certainly true at least for 5-limit intervals smaller than one octave), and make the additional assumption that the rate of change of the rate of change is finite and not zero at these minima, then a quadratic function is appropriate: the dissonance function must be shaped like a parabola if you are close to the just ratio. >In JI, I prefer to think of the "complexity" (or something, >rather than "dissonance") of an interval or sonority, which >I measure not by multiplying the members of a ratio or >chord, but by adding them! As an example, 4/1 is about as >"complex" as 3/2 by my rule of thumb, and 8/5 is about as >"complex" as 9/4. This may be a valid issue but is irrelevant here, since we are merely comparing representations of the same interval(s). >In systems which deviate from just by small amounts, >I'm not really sure how to calculate dissonance, >except that it may have something to do with the >speed of beating (faster beating, more dissonance). That is the issue and I assume a quadratic function as justified above. Many, many other justifications are possible. >I'm afraid I'd still classify >weighted mean-tone as an error-spreading and pitch-class- >confounding system though. Its main value would be >in the tuning of instruments whose pitch sets are finite >and not manually adjustable during performance, especially >for period music. Very well. Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Fri, 21 Feb 1997 01:41 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA13226; Fri, 21 Feb 1997 01:41:22 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA13228 Received: from by ella.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) id QAA11444; Thu, 20 Feb 1997 16:39:29 -0800 Date: Thu, 20 Feb 1997 16:39:29 -0800 Message-Id: <3.0.32.19970220161838.0068b080@adnc.com> Errors-To: madole@mills.edu Reply-To: tuning@ella.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@ella.mills.edu