Post-tonal/Atonal  - GENERAL TOPICS


post-Romantic chromaticism and the statistical array (Bach-Webern)

"Free" Atonality (composing with intervals)

Joseph Matthias Hauer and Arnold Schonberg: tropes (hexachords) & series.
     basic row-forms - O or P and R x12
     inversional equivalence - I, RI and the row-chart
     combinatoriality and simultaneity
     the Magic Square (PxI matrix)

special practices - Berg.

systematic composition - Webern.

Post-Webernian Serialism - Messiaen (Boulez, etc.).
     integral serialism - parametric serialism

American Serialism - (Sessions) Babbitt, Stravinsky.
     ordered sets rather than series
     rotations

Set-theory - Forte: The Structure...
     pitch-class sets (unordered) - mod 12
          normal order - permutations = n factorial (1x 2x 3x etc)
          transpositional, inversional equivalence
          interval vectors - not 12, but 6 interval classes (ic 1-6)

Computer Applications:
     analysis
     synthesis
     MIDI and pc#s, etc.