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The classic Fux exercises are a way to learn counterpoint, but they use old styles of tonality. I want to do the same thing using modern styles without a tonal center. In Fux exercises only certain melodic and harmonic patterns are permitted.
But what should the rules for atonal counterpoint be? What are the permitted harmonies and melodies? In short, I'm doing what sounds good to me, without many contraints. Perhaps it's not a beginner's exercise, if there are no guiding rules. I feel that these exercises are helping me to take my intuition about what sounds good and connect it up with a variety of melodic and harmonic patterns. By working within the constraint of a cantus firmus, I am forced to innovate and variety is injected into my vocabulary.
After picking a cantus firmus, usually something atonal resembling early Schoenberg, I add accompanying notes, in any of the following manners:
In each of these sound files, you hear the cantus firmus alone first and then played together with the accompaniment.