source file: mills2.txt Date: Sat, 5 Jul 1997 15:03:38 +0200 Subject: RE: the 6th chord and odd-limit theory From: gbreed@cix.compulink.co.uk (Graham Breed) Paul Erlich said: >Graham, I am puzzled by your statement that these two four note chords >are complete chords of a nature which would seem to require them to be >six-note chords. Somehow, you hid two notes under your sleeve. Therefore >I will reserve judgment on your analysis until you clarify. I used the phrase "complete chords" in the literal English sense of "chords from which no notes are missing" rather than specifically Euler complete chords. I also used the word "saturated" in a different sense to you. Sorry for any confusion this caused. >I should add to this post that Erv Wilson's CPS idea is a reflection of >the triangular lattice philosophy, and deserves more attention, while >Euler genera and LCMs are a reflection of the rectangular lattice >philosophy. Symmetrical saturated chords are indeed Wilson CPSs (e.g. 2)1.3.3.5). They are also Euler genera without the first and last notes. I can't make of these definitions work for the non-symmetrical, non-o/utonal chords mentioned in my more recent post. I haven't worked out the implications of triangular lattices yet. Are they what I would call Hexagonal lattices -- that is, is every point directly connected to 6 others? How do you measure distances on them? How do you extend them to multiple dimensions? Do they work without octave invariance? As I haven't received Digest 1122 yet, I can't be sure my message was in it. If it wasn't, I'll re-post: it contains the conclusions I was working towards through looking at octave reduced ROHSs. However, there is a mistake in it; non-square powers of primes cause the same problems as rhubarb numbers. The only such number small enough to be musically relevant is 27. With n', m, for example, the interval 33/1 will arise. Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Sat, 5 Jul 1997 15:04 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA05341; Sat, 5 Jul 1997 15:04:59 +0200 Date: Sat, 5 Jul 1997 15:04:59 +0200 Received: from ella.mills.edu by ns (smtpxd); id XA05324 Received: (qmail 2908 invoked from network); 5 Jul 1997 13:03:58 -0000 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 5 Jul 1997 13:03:58 -0000 Message-Id: Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu