source file: m1496.txt Date: Fri, 7 Aug 1998 13:32:23 -0400 (EDT) Subject: Re: Numbers and a new tuning From: Johnny Reinhard Thanks Paul. When one is composing the theoretical wing of the mind takes a back seat to the creation muse. :) Johnny Reinhard Director American Festival of Microtonal Music 318 East 70th Street, Suite 5FW New York, New York 10021 USA (212)517-3550/fax (212) 517-5495 reinhard@idt.net http://www.echonyc.com/~jhhl/AFMM On Fri, 7 Aug 1998, Paul Hahn wrote: > On Thu, 6 Aug 1998, Johnny Reinhard wrote: > >The Harmonic-17 tuning I'm working with for my new work _Trespass_ uses > >the following notes, based on a 1/1 fundamental: > > > > 1/1 17/18 17/16 34/31 19/17 17/15 20/17 17/14 22/17 > ^^^^^ > >cents: 0 99 105 160 193 217 281 336 447 > > That's got to be 18/17, right Johnny? > > >17/13 24/17 26/17 17/11 28/17 34/20 62/34 34/17 > ^^^^^ ^^^^^ > >464 597 735 754 864 919 1040 1095 > > I.e. 17/10 and 31/17. > > I think the best way to diagram this is as two intersecting Otonal and > Utonal identities, with a few members missing: > > 31/17 > 28/17 > 26/17 > 24/17 > 22/17 > 20/17 > 19/17 > 17/16 18/17 > 17/17 > 17/10 > 17/11 > 17/13 > 17/14 > 17/15 > 34/31 > > > [snip] > >I have not noticed any 3/2's. Can you map it out the way you think best? > > Hate to break it to you, Johnny, but there's a couple of lovely 3/2s > (4/3s): 17/10 to 17/15, and 18/17 to 24/17. > > --pH http://library.wustl.edu/~manynote > O > /\ "Churchill? Can he run a hundred balls?" > -\-\-- o > NOTE: dehyphenate node to remove spamblock. <*> >