"The vector space structure of intervals of certain sound characteristics permits us to treat their elements mathematically and to express them by the set of numbers, which is indispensable for dialogue with computers, or by the set of points on a straight line, graphic expression often being very convenient." [211]
"A new and rich work of visual art could arise, whose evolution would be ruled by huge computers (tools vital not only for the calculation of bombs or price indexes, but also for the artistic life of the future), a total audiovisual manifestation ruled in its compositional intelligence by machines serving other machines, which are, thanks to the scientific arts, directed by man." [179]
"In reality formalization and axiomatization constitute a procedural guide, better suited to modern thought. They permit, at the outset, the placing of sonic art on a more universal plane. Once more it can be considered on the same level as the stars, the numbers, and the riches of the human brain, as it was in the great periods of the ancient civilizations. The movements of sounds that cause movements in us in agreement with them 'procure a common pleasure for those who do not know how to reason; and for those who do know, a reasoned joy through the imitation of the divine harmony which they realize in perishable movements' (Plato, Timaeus)." [179]
"... I have all along continued to develop certain theses and to open up some new ones. The new chapter on "Sieves" is an example of this ... Another approach to the mystery of sounds in the use of cellular automata which I have employed in several instrumental compositions these past few years. This can be explained by an observation which I made: scales of pitch (sieves) automatically establish a kind of global musical style, a sort of macroscopic 'synthesis' of musical works, much like a 'spectrum of frequencies, or iterations,' of the physics of particles. Internal symmetries or their dissymmetries are the reason behind this. Therefore, through a discerning logico-aesthetic choice of 'non-octave' scales, we can obtain very rich simultaneities (chords) or linear successions which revive and generalize tonal, modal or serial aspects. It is on this basis of sieves that cellular automata can be useful in harmonic progressions which create new and rich timbric fusions with orchestral instruments. Examples of this can be found in works of mine such as Ata, Horos, etc." [xii]
