source file: mills2.txt Date: Mon, 23 Jun 1997 10:29:52 +0200 Subject: Re: the 6th chord and odd-limit theory (Paul E) From: Paul Hahn On Fri, 20 Jun 1997, it was written: > 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. Once again I correct myself: 7 is unusual in this regard because it is smaller than 9, the smallest odd composite; actually in the example Paul gave the chord overall was 15-limit, while each individual interval in it was 9-limit, which shows that strictly speaking it _is_ possible for larger primes, such 11 and 13. However, it would not be possible to construct a chord which included a (say) 11-limit interval, but none higher, such that the chord overall had a higher limit. --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 10:38 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA01702; Mon, 23 Jun 1997 10:38:21 +0200 Date: Mon, 23 Jun 1997 10:38:21 +0200 Received: from ella.mills.edu by ns (smtpxd); id XA01700 Received: (qmail 11646 invoked from network); 20 Jun 1997 21:20:53 -0000 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 20 Jun 1997 21:20:53 -0000 Message-Id: Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu