source file: mills3.txt Date: Tue, 29 Jul 1997 00:37:41 +0200 Subject: talk about music From: "Paul H. Erlich" Christopher Smith wanted to hear about our compositions. Unfortunately, I'm not much of a composer -- I'm more of an improviser. I can sit in on anything diatonic and throw in chorale-style harmonies, motivically structured melodies, and flashy solo sections. However, I've only composed a relatively small amount of music. I developed my ear for harmony for keyboard but now play guitar. 22-tone equal temperament does not conform to traditional diatonic thinking the way meantone tunings like 19 and 31 do. I have a theory (soon to appear in Xenharmonikon 17 and on the Web) about what will work in 22, and I've begun playing 22-tone keyboard and guitar as a result. Although my theory may end up having a lot to do with how I translate my improvisational skills to 22-TET music, so far my one real composition has nothing to do with it. I can talk about the composition in diatonic terms, even though it is nothing if not microtonal. The main melodic motif is a descending ultrachromatic scale spanning a perfect fourth. If the harmony is analyzed in JI, the melodic intervals (descending) are 25 36 49 36 25 256 36 49 36 4 -- * -- * -- * -- * -- * --- * -- * -- * -- = - 24 35 48 35 24 243 35 48 35 3 Relative to the initial tonic at 1/1, this gives the pitches 5 6 7 8 10 16 81 63 27 15 -, -, -, -, --, --, --, --, --, -- 4 5 6 7 9 15 80 64 28 16 15/16 is interpreted as the 5/4 of the dominant. The 256/243 interval comes from the circle of fifths, which is the source for most of the root progressions. In JI, some of the inner voices lose their integrity, and the fact that it's in 22 means that you only have to learn one melodic interval to sing it, instead of four intervals ranging from 36 to 90 cents. I can only sing it if I'm imagining the chords in my head (and taking a shower). It doesn't really stand up as a melody all by itself. This composition was created with no theory or mathematics in mind; they were used later to analyse it. If you meet me in person I'll tell you more about how I wrote this piece. I often suspect that I might be just as good a musician if deprived of all mathematical abilities, but I'm not going to test this theory. SMTPOriginator: tuning@eartha.mills.edu From: mr88cet@texas.net Subject: Re: theories PostedDate: 29-07-97 04:18:21 SendTo: CN=coul1358/OU=AT/O=EZH ReplyTo: tuning@eartha.mills.edu $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: 29-07-97 04:18:16-29-07-97 04:18:16,29-07-97 04:17:15-29-07-97 04:17:15 DeliveredDate: 29-07-97 04:17:15 Categories: $Revisions: Received: from ns.ezh.nl by notesrv2.ezh.nl (Lotus SMTP MTA v1.1 (385.6 5-6-1997)) with SMTP id C12564E3.000CA705; Tue, 29 Jul 1997 04:18:11 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA23712; Tue, 29 Jul 1997 04:18:21 +0200 Date: Tue, 29 Jul 1997 04:18:21 +0200 Received: from ella.mills.edu by ns (smtpxd); id XA24314 Received: (qmail 4905 invoked from network); 29 Jul 1997 02:12:58 -0000 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 29 Jul 1997 02:12:58 -0000 Message-Id: Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu