source file: mills2.txt Date: Mon, 23 Jun 1997 10:38:21 +0200 Subject: Re: the 6th chord and odd-limit theory (Paul E) From: Paul Hahn On Tue, 17 Jun 1997, Paul Erlich wrote: > I wonder if there are any 7-limit analogues to these chords (i.e., chords in > which each interval is within the 7-limit but the chord as a whole is in a > higher limit). I think the answer is no. Anyone care to come up with a > counterexample? There will be no counterexamples because Paul's guess is correct. In general, it is only possible to construct such chords for composite limits (such as, in the snipped example, 9). 7 being prime, it is not possible. I have discovered a truly marvelous proof of this, which this bandwidth is unfortunately too narrow to contain . . . (Actually, it's not particularly marvelous; I just haven't figured out how to translate it from my muttering and making henscratches to myself to something a sentient being would understand. If anyone wishes to challenge me on it, though, I'll give it a go.) --pH http://library.wustl.edu/~manynote <*> O /\ "Hey--do you think I need to lose some weight?" -\-\-- o Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Mon, 23 Jun 1997 11:07 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA04343; Mon, 23 Jun 1997 11:07:45 +0200 Date: Mon, 23 Jun 1997 11:07:45 +0200 Received: from ella.mills.edu by ns (smtpxd); id XA04339 Received: (qmail 17199 invoked from network); 22 Jun 1997 23:55:37 -0000 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 22 Jun 1997 23:55:37 -0000 Message-Id: <33d7b09b.400615185@kcbbs.gen.nz> Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu