- 325 -Enders, Bernd / Stange-Elbe, Joachim (Hrsg.): Global Village - Global Brain - Global Music 
  Erste Seite (1) Vorherige Seite (324)Nächste Seite (326) Letzte Seite (507)      Suchen  Nur aktuelle Seite durchsuchen Gesamtes Dokument durchsuchen     Aktuelle Seite drucken Hilfe 

  • Step 2: Define vectors a,b  (- M. Create a pattern C in M consisting of elements B + na + mb, (m,n  (- Z), modulo a preditermined integer p (in our case p was 71).
  • Step 3: Define a set G of main 2-dimensional transformations g : p2(M) --> p2(M), where p2 =projection of M on T P, T L, T D, P L, P D or L D.
  • Step 4: Apply certain transformations g  (- G to local parts (subsets) of C. Note that the transformations are applied to any two-dimensional projection.
  • Step 5: Apply other freely chosen transformations h  (- Gc to local parts (subsets) of C.
  • Step 6: Shape a detailed tempo curve.
  • Step 7: Define an instrumentation.
  • Steps 2–7 are applied repeatedly, and not necessarily in the given sequence.
  • A few remarks need to be made at this point, since at first the construction given above may appear completely abstract and too mathematical:

    1. The composition was done using “musical intuition”, without conscious application of mathematics. Only a vague global plan existed – the description above is an a posteriori analysis that is much more precise than the original plan. This corresponds to the usual compositional process. A global plan is used, consciously or subconsciously, in most composed (and even in improvised) music. (Also, for traditional music it is not unusual that an a posteriori analysis reveals structural features the composer was not quite aware of.)
    2. An intuitive musical application of transforms was made possible by the graphical MIDI-software PRESTO (Mazzola 1989–94). No mathematical knowledge was required. Due to the help of the software, a vast variety musical possibilities could be tried out by listening. This allowed “controlled improvisation” leading to an enormously fast, intuitive and spontaneous way of composing.
    3. It should be emphasized that the software used here does not compose, The computer is here “only” a tool that enables us to pursue new musical ideas in an efficient way.

    1.3.  Basic principles

    The following basic principles were used:

    • Representation of basic aspects of the composition (excluding e.g. instrumentation, microtuning etc.) as a “point cloud” in an algebraic module (linear space).
    • Transformations.
    • Hierarchy (global structures, local structures).
    • Exchangibility of musical parameters (time, pitch, loudness, duration).


    Erste Seite (1) Vorherige Seite (324)Nächste Seite (326) Letzte Seite (507)      Suchen  Nur aktuelle Seite durchsuchen Gesamtes Dokument durchsuchen     Aktuelle Seite drucken Hilfe 
    - 325 -Enders, Bernd / Stange-Elbe, Joachim (Hrsg.): Global Village - Global Brain - Global Music