source file: mills2.txt Date: Fri, 11 Jul 1997 14:13:15 +0200 Subject: Re: Multi-Dimensionality From: Daniel Wolf David Finnamore wrote: ''But I think it's a different kind of dimensionality, if you will, from the prime type. I can't fully explain this concept yet, but to me, prime, odd, and scale-interval-generator are three distinctly different and equally valid kinds of dimensionality'' I believe that definitions like these have a lot to do with what exactly you want your music theory to do. If you are making a pre-compositional theory, then you will probably want to locate and organize aspects of the materials that you intend to project structurally, so as to make these aspects them audible throughthe way that you articulate them. If you are making a theory for interpreting (asa listener or a performer) an existing work, then the theory should explain how the surface articulations reflect physical characteristics of the materials. Both of these kinds of theories are based upon the assumption that the way musical materials are articulated is essential to their interpretation. On the other hand, if your intention is to make a claim for the psychophysical status of your materials, you are initially freed from accounting for such personal or cultural constructions as described above, but the completion of a psychophysical approach depends upon eventually being able to address these concerns. In my experience, existing psychophysical theories are either weak or culturally local. (There are some minor innate behavior mechanisms associated with sounds - my favorite example is the taste of Carlsberg Beer while listening to particular sine wave frequencies - but the culturally aquired patterns seem to be overriding; see, for example, Gilbert Rouget _Music and Trance_). Let's look at some real examples: (1) I compose a piece consisting only of chromatically planed (parallel) Major ninth chords without fifths in just intonation. If the orchestration is such that a listener can hear the individual voices of these chords, then 9 is being articulated independently of 3. Since 9 is here relatively prime, how could 9 be here distinguished a 'real' prime? (2) I write a chorale in triads that goes I - IV - V - I. There is a 9:8 relationship between IV and V chords, but this is usually weakly articulated and the Vof V (3^2) relationship is heard as more important. (3) I compose a sound installation consisting of standing sine waves using only prime multiples of a given fundamental and 9 times that fundamental. Depending upon where I am in the room, I will hear the 9 as either an independent entity or inconnection with 3. (4) Using a TX81Z (with a resolution of 1.56 cent deviations from 12tet),I perform a melody based upon random walks over a lattice with two dimensions: 3s and 9s. The best approximation of 9 does not coincide with the best approximation of 3^2. For all practical purposes, 3 and 9, in this temperament, are relatively prime. (5) A composition is played one day on a gamelan tuned to a 7 pitches outof 9TET, on the next to a Lou Harrison-style just intonation pelog, on the next to a Wilson style linear series in just intonation, and finally on a real unsystematically-tuned Javanese instrument. To what degree is the composition intonation-transparent? Itis interesting to hear how certain structures survive radically differentmappings intact as well as to hear what features are projected differently under alternative intonations. Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Fri, 11 Jul 1997 16:03 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA30509; Fri, 11 Jul 1997 16:03:47 +0200 Date: Fri, 11 Jul 1997 16:03:47 +0200 Received: from ella.mills.edu by ns (smtpxd); id XA30382 Received: (qmail 23600 invoked from network); 11 Jul 1997 14:02:40 -0000 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 11 Jul 1997 14:02:40 -0000 Message-Id: Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu