source file: mills3.txt Date: Wed, 17 Dec 1997 20:30:33 +0100 Subject: Re: 22-tone exhortations From: gbreed@cix.compulink.co.uk (Graham Breed) I wrote: >}I haven't investigated Paul Erlich's decatonic >}modes enough to decide if they can be treated as 10 pitch classes. >}I don't like the theory because it clings to the idea of diatonic >}harmony -- that all notes used in harmony must belong to the same key. >}I'd rather work out a chord sequence, and fit a melody to it. Or, >}define a melodic mode, write a tune in it, and harmonise it >}chromatically. and Paul replied: >You can't deny that most Western music derives much of its beauty and >contrapuntal versatility from having both vertical and horizontal sonorities >taken from the same pitch set. These pitch sets have characteristic dissonant >intervals which allow a "tonic" to be defined and when the pitch set changes, >so does the tonic. In this way non-diatonic notes can anticipate a change of >tonality before that tonality also arrives. Actually, my statement looks stronger than I intended. There are a number of reasons for which I like Paul's theory, and some for which I don't. I mentioned diatonic harmony (is there a better term that doesn't imply a 7-note scale?) because it's an assumption that isn't explicitly justified in the paper. I'm no expert on Western classical music, but I don't feel full blown tonality is for me. There are a number of personal reasons for this. I like the idea of decentered harmony in a post-relativistic world. I feel that harmony, which grew out of modality, is mature enough to stand on it's own. Now I've been put on the spot, I suppose I'll have to justify my other objections, so here goes ... The criteria under "scale structure" are dispensable, but do have some value. I'd rather the scale worked with triads, as even just 4:5:6:7 chords aren't consonant enough for me to use as a tonic. This means the tonic has to be a 5-limit chord, as septimal diminished triads don't work that well either, and other 7-limit chords will tend to share their root with a 5-limit one. I don't like more than 7 notes in a key. I can accept additional chromatic notes, but 10 is too many for me as the reference against which the chromaticism is added. I expect the scale, in its consonant limit, to be significantly _better_ than 12 equal in the 5-limit. To my ears, a 5-limit chord progressing to a 7-limit one will almost always sound like an increase in dissonance in 22 equal, although the 7-limit chords are still tuned well enough to be contrasted against stronger dissonances. With these restrictions, I don't think 7-limit tonality will work. The best theory we have is that of the decatonic modes, and there is the potential for some great music to be written using it. It just won't be written by me. SMTPOriginator: tuning@eartha.mills.edu From: gbreed@cix.compulink.co.uk (Graham Breed) Subject: Reply to Gregg Gibson PostedDate: 17-12-97 20:31:49 SendTo: CN=coul1358/OU=AT/O=EZH ReplyTo: tuning@eartha.mills.edu $MessageStorage: 0 $UpdatedBy: CN=notesrv2/OU=Server/O=EZH,CN=coul1358/OU=AT/O=EZH,CN=Manuel op de Coul/OU=AT/O=EZH RouteServers: CN=notesrv2/OU=Server/O=EZH,CN=notesrv1/OU=Server/O=EZH RouteTimes: 17-12-97 20:29:49-17-12-97 20:29:50,17-12-97 20:29:27-17-12-97 20:29:28 DeliveredDate: 17-12-97 20:29:28 Categories: $Revisions: Received: from ns.ezh.nl ([137.174.112.59]) by notesrv2.ezh.nl (Lotus SMTP MTA SMTP v4.6 (462.2 9-3-1997)) with SMTP id C1256570.006B15B9; Wed, 17 Dec 1997 20:31:35 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA18328; Wed, 17 Dec 1997 20:31:49 +0100 Date: Wed, 17 Dec 1997 20:31:49 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA18333 Received: (qmail 3548 invoked from network); 17 Dec 1997 10:42:58 -0800 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 17 Dec 1997 10:42:58 -0800 Message-Id: Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu