Programming Arvo Pärt

 

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Aesthetic Complexity

Tintinnabuli Mathematica is an experiment in programming Arvo Pärt’s tintinnabuli method of composition. The process has two stages. Firstly, a melodic part (or M-voice) is created by generating a string of notes and timings. Then harmonic tintinnabuli parts (T-voices) are generated by applying transformation rules to the melody.

To generate a melody, a program was written to select notes from a scale, which in this case is A natural minor, i.e. all the white notes on a piano starting from A. Two types of generative method are used: random selection and series based on integer sequences (e.g. the Fibonacci sequence or the series of prime numbers). The random methods include equal-weighted choice of pitch and duration which generates notes scattered all over the scale, and a random walk method which produces wandering melodies of close pitches, varying in closeness depending on the maximum size of interval. In the random walk method…

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