Fully generalized Fibonacci series modulo n as music sequence generators

In this paper we introduce fully generalized Fibonacci se- quences as useful tools for the generation of integers that can be interpreted in the musical context for algorithmic composition. In particular, we take into account the mod- ulo operation on Fibonacci sequences resulting in various periodic behaviors that we interpret in the pitch class do- main. First we introduce Fibonacci sequences and general- ized Fibonacci sequences, then we discuss the modulo op- erator applied to sequences. We propose various interpre- tations of the resulting sequences in terms of pitches and pitch classes, and describe some possible operations. Fi- nally, we introduce fully generalized Fibonacci sequences and describe a possible implementation in an algorithmic composition environment.