source file: mills2.txt Date: Mon, 24 Feb 1997 09:46:07 -0800 Subject: RE: Reply to Neil from Paul From: Manuel.Op.de.Coul@ezh.nl (Manuel Op de Coul) From: PAULE Gary wrote, >>>I probably ought to let Neil speak for himself, but I suspect that he meant >>>less specifically than the harmonic series itself, but JI in general. I wrote, >>I see no difference here. I could say, "19 consistenly represents 9-limit JI >>and 34 consistenly represents 5-limit JI," but I didn't want to start the >>odd vs. prime debate on the definition of "limit" again. Gary wrote, >I'm not sure about 19 or 34 right off the top of my head, but there is a >difference: >Approximating the harmonic series itself forces them to be represented >relative to the fundamental of that series. Two harmonic approximations in >some equal-temperament could, for example, be way flat of the harmonics >they are closest to, but if they are nearly equally flat, then that tuning >will have a pretty good approximation to that frequency ratio, but not of >either of those harmonics. Gary, Yes, you are correct. There is a difference. My comments are meaningless with respect to a "relations between the fundamental and other members of the harmonic series" viewpoint, but they do apply to a "small-integer-ratio" viewpoint. So why your comment above (first quote above)? By the way, the difference between the two viewpoints leads to two different JI lattice constructions. The RBFAOMOHS view leads to rectangular lattices, while the SIR viewpoint leads to triangular lattices. Exploring the relationship between these views in 5-dimensional lattices led me to some interesting discoveries about the tiling of 5-dimensional space with regular hyperpolyhedra (which happen to be various Wilson CPSs from [1,3,5,7,11]). Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Mon, 24 Feb 1997 18:49 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA17776; Mon, 24 Feb 1997 18:49:41 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA17772 Received: from by ella.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) id JAA10291; Mon, 24 Feb 1997 09:47:37 -0800 Date: Mon, 24 Feb 1997 09:47:37 -0800 Message-Id: <009B060B13FE003D.3465@vbv40.ezh.nl> Errors-To: madole@mills.edu Reply-To: tuning@ella.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@ella.mills.edu