source file: mills2.txt Date: Sun, 25 May 1997 20:33:02 +0200 Subject: Re: Harmonics & beats are better .. (Paul E) From: Manuel.Op.de.Coul@ezh.nl (Manuel Op de Coul) From: PErlich Ray Tomes wrote, >I would suggest that it would be possible to make some tempered tunings >which are not too far from equitempered tunings, but which have beats >that are reasonably well in tune. Has anyone ever investigated this? >It might be a fruitful exercise. First, let's get some acoustics straight. Beats only occur between tones that are very close (within a critical bandwidth) and are never heard as musical tones, even when they are rapid enough to match the frequency of audible tones. Helmholtz is a good reference for all this, and should be quite readable to a 19th century mind like Ray's :). However, at loud volumes, nonlinearities in our ears cause "difference tones" as well as other, weaker "combination tones" to be heard. So Ray's analysis is mathematically valid but applies not to "beats" at all but to difference tones. Difference tones are important (Heinz Bohlen believes difference tones to be the foundation of all harmony) while matching beat rates to scale pitches can have no musical significance whatsoever. Now, to answer the question, with "beats" changed to "difference tones," I believe Erv Wilson's meta-meantone tuning has some difference tones that are in tune with each other. It should also be possible to devise meantone tunings where some difference tones are in tune with some scale tones. Perhaps John Chalmers or Manuel Op de Coul have compiled a list of such tunings? The nice thing about meantone tuning, of course, is that re-la is what it "wants to be." -- P.S. (MOdC) Interesting thought but I haven't. Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Sun, 25 May 1997 21:50 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA09612; Sun, 25 May 1997 21:50:26 +0200 Date: Sun, 25 May 1997 21:50:26 +0200 Received: from ella.mills.edu by ns (smtpxd); id XA09608 Received: (qmail 10678 invoked from network); 25 May 1997 19:50:11 -0000 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 25 May 1997 19:50:11 -0000 Message-Id: <199705251549_MC2-1742-F714@compuserve.com> Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu