source file: mills2.txt Date: Sat, 1 Mar 1997 07:29:29 -0800 Subject: Re: Reply to Matt Nathan From: Manuel.Op.de.Coul@ezh.nl (Manuel Op de Coul) From: PAULE >The diatonic symbol ii is a case of >confounded rational structures however. No, rational structures are a case of confounded diatonic theory. >There are at >least two distinct rational structures which suffer >lossy compression in a diatonic assumption and get >lumped under "ii". You can sometimes tell by context which >of these is being implied. The ii chord can function >in context as either the relative minor of IV, which comes >from the rational structure n/4 n/5 n/6 where n is 5/3, >or as the secondary v (minor) of V, which comes from the >rational structure n/4 n/5 n/6 where n is 27/16. The ii chord must often be both or neither. In a I-ii-I progression (common in popular music), it is definitely neither. Rational structures fail in these cases. Here, Matt, I wrote a piece where the chord progression is I-IV-ii-V-I-IV-ii-V-(ad infinitum). Analyze this piece in Just Intonation. How many pitches are implied here? When does the piece return to the home key? Are these results going to make any sense for musicians and composers working in a meantone temperament (including 12-tET)? Do your interpretations have any psychoacoustical manifestations? If not, I maintain it's nothing more than playing with numbers. Composing in Just Intonation, on the other hand, is a valid enterprise and I have no objection to trying to produce diatonic structures in JI. Doing so requires extra care, however. Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Sat, 1 Mar 1997 16:32 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA01445; Sat, 1 Mar 1997 16:32:11 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA01437 Received: from by ella.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) id HAA13521; Sat, 1 Mar 1997 07:30:25 -0800 Date: Sat, 1 Mar 1997 07:30:25 -0800 Message-Id: <009B09E5B06E437A.582E@vbv40.ezh.nl> Errors-To: madole@mills.edu Reply-To: tuning@ella.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@ella.mills.edu