source file: mills2.txt Date: Fri, 20 Sep 1996 14:17:37 -0700 Subject: RE: RE: Consistency generalized From: Paul Hahn On Fri, 20 Sep 1996, PAULE wrote: > Your new algorithm is not correct either -- at least it does not reproduce > my definition of consistency. In particular, no tuning can fail to be level > 1 consistent according to your algorithm, and some tunings would be level 2 > consistent according to this algorithm that wouldn't be according to your > original definition. Er, pardon me but it _is_ correct; at least, it is cribbed directly from the code that generated the table at , and I haven't discovered any errors in that table yet. (And that table _doesn't_ claim that all tunings are level 1 consistent. Code it up and run it yourself if you don't believe me.) Don't be misled by the natural language paraphrase that I followed it with--the paraphrase is not exact, but I couldn't think of a concise and non-technical way to say it precisely. [another bigsnip of stuff I have no disagreement with] > > Very weird things can happen in level 1 > >consistent tunings. A simple example: 5TET is consistent at the > >5-limit. A 16/15, represented as a 4/3 less a 5/4, becomes 2-2=0 steps, > >or a unison. However, a 25/24, represented as a 5/4 less a 6/5, becomes > >2-1=1 step. In other words, a larger interval becomes a unison while a > >smaller interval does not. Maybe this doesn't bother you, but for me it > >causes cognitive dissonance. > > Well, the idea of using 5-tET for 5-limit harmony bothers me. Didn't you > read my post? I explained why, even though 7-tET is consistent at the > 5-limit, it is not a good tuning for 5-limit harmony. The same goes for > 5-tET. [snip] Holy cow, it was just an example. The point is that such discrepancies will occur in any tuning that is level 1 but not level 2 consistent, as you demonstrated with 22TET. > "In other words, a larger interval becomes a unison while a smaller interval > does not." This doesn't bother me in the slightest -- in fact I like it. That's absolutely fine with me. More than fine, it's great. Odd structural artifacts like this in low-consistency tunings are features of, for example, several of Easley Blackwood's 12 Microtonal Etudes, and massively cool pieces I think they are. It's just a different path than that which I am attempting to follow. Please understand that I am not trying to talk you out of composing in 22TET or whatever tuning you please; I am simple trying to explain that my preference for higher consistency is _not_ "arbitrary", but justified given certain assumptions which you may not share. I respect your compositional choices; please do me the same courtesy. --pH (manynote@library.wustl.edu or http://library.wustl.edu/~manynote) O /\ "Foul? What the hell for?" -\-\-- o "Because you are chalking your cue with the 3-ball." Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Sat, 21 Sep 1996 03:04 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA21302; Sat, 21 Sep 1996 03:06:09 +0200 Received: from eartha.mills.edu by ns (smtpxd); id XA20209 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id SAA19747; Fri, 20 Sep 1996 18:06:07 -0700 Date: Fri, 20 Sep 1996 18:06:07 -0700 Message-Id: <960920210400_482611093@emout20.mail.aol.com> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu