The variform musical creation of Xenakis, as it is understood by the brain instead of the heart, has been classified in the Pythagorean School. Xenakis expresses his intellectual thoughts by turning his interest and his research as well to the structure of his musical compositions. Xenakis’ music has not been charged by strong emotions. It is not dramatic or it is not committed to ideologies. Xenakis’ music is erotic and not sensual at all. It is witty and not comic. It contains elements of play and struggle. Xenakis’ music is a hymn to freedom. It is loaded by ancient Greek philosophy. It contains elements of ancient Greek prosody. Xenakis uses randomness in his music, without anything to be accidental in it. The harmony in Xenakis’ music is not constructed according to the European patterns, but it is a many-stranded monophony, especially influenced by the traditional music of Epirus.Xenakis’ music is based on a variety of mathematical theories, i.e. mathematical analogies, Algebra, Set Theory, Group Theory, Combinatorial Analysis, Probabilities, Statistics, Game Theory, Fourier analysis, Topology, etc.The following musical parameters could also be highlighted in Xenakis’ musical works: micro-intervals, modes, melodic forms, basic rhythmic patterns, counterpoint, tonality, atonality, musical instruments, dynamic chains, multidimensional musical ensembles, multimedia forms, non instrumental music, communication and, finally, polyagogy.