source file: mills2.txt Date: Sun, 9 Feb 1997 19:31:06 -0800 Subject: Re: Neil's Post in 980 From: John Starrett G'Night John Boy- Neil Haverstick stated that the harmonic series is a natural phenomenon, and that deviation from it is deviation from the "pure" in some way. I disagree, and I agree. In nature, there are no physical objects that vibrate with a pure harmonic series of partials above the fundamental. The harmonic series is a construct of our mathematical minds, modeling a phenomenon first observed with our nonlinear hearing mechanism, and later with lab instruments. The harmonic series is an idea, just as is the beatlessness of simultaneously sounding simple tones. Making a scale from a pitch set of harmonic partials divided down into the octave is no more natural than making a scale from a pitch set whose elements are related by small number ratios. They are both constructs of the mind, and in my view perfectly natural things (we are not in the world, we are the world). We may have, hardwired into the structure of our brains, an innate musical understanding of the harmonic series, but we may be hardwired for understanding small number ratios as well. For that matter, we may be hardwired for mathematical understanding of all that we can understand mathematically, and that may spill over into musical understanding, even of tempered and non-octave scales. In short, I don't think we are in any position to say what is natural to our musical understanding and what is not. Further psychoacoustic research may shed some light on what musical structures are more primal, but I haven't seen anything convincing yet. I'll bet Brian Mclaren has an opinion on this. John Starrett Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Mon, 10 Feb 1997 12:43 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA00941; Mon, 10 Feb 1997 12:43:36 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA00939 Received: from by ella.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) id DAA13714; Mon, 10 Feb 1997 03:41:34 -0800 Date: Mon, 10 Feb 1997 03:41:34 -0800 Message-Id: Errors-To: madole@mills.edu Reply-To: tuning@ella.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@ella.mills.edu