source file: mills2.txt Date: Mon, 10 Feb 1997 19:07:16 -0800 Subject: Harmonics From: Gary Morrison > 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. I personally think that that, although essentially correct, is a bit of an exaggeration. First of all, a topic that made its rounds on the list recently: To say that (for example) guitars, orchestral strings, almost all woodwind tones, and most brass tones, have exactly harmonic partials, is only slight oversimplification. The biggest departures from harmonic partials are high- and mid-frequency noise components, from rosiny scrapes or breath blowing through the tube. If you force partials from those sorts of instruments to exact harmonics, they take on a very clearly audible, but usually fairly subtle, "robotic" crustiness. To say that most orchestral instruments have exactly harmonic partials is definitely not pure 100% unadulterated truth, but the amount those instruments deviate from pure harmonic partials is FAR too small to have any significant effect upon tuning considerations. But that's not really a point I want to get too much into, and perhaps it wasn't really John's main issue either. I think it's worth pointing out that whatever framework you build your compositional or psychoacoustical model of musical psychology upon, how you defy that framework is every bit as important as how you use it. I personally believe that Neil is mostly correct in at least one sense: Aside from some very important exceptions (e.g., very low pitch range), simple whole-number ratios usually predict quite accurately what our ears view as significant. They are the navigational bouys in the sea of tuning possibilities. BUuuuut... I don't believe that pitch relationship being significant to our ears means that we must ideally use it, any more than we should sail into collision course with navigation bouys! For example, intentionally missing a 3:2 P5 by about 5 cents produces quarter-comma meantone, which to my ears and those of many others, sounds really fantastic! And it sounds great not (only) because it hits a 5:4 right on, but even more so because of the specific way that it misses 3:2. Obeying well-known ground rules sows the seeds of expectation in your audience's minds, but defying those rules is what makes your audience listen! Really brilliant music comes from cleverly and emotionally using both expectation and defiance of expectation. Simple whole-number ratios, being a pretty good model of what is fundamentally meaningful to our ears, are one example of such a means of using and defying expectation. Regular structures in a tuning system (like circles of fifths) are another, as are consistency of meter and rhythm. Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Tue, 11 Feb 1997 05:24 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA01951; Tue, 11 Feb 1997 05:24:06 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA01949 Received: from by ella.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) id UAA20393; Mon, 10 Feb 1997 20:22:29 -0800 Date: Mon, 10 Feb 1997 20:22:29 -0800 Message-Id: Errors-To: madole@mills.edu Reply-To: tuning@ella.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@ella.mills.edu