A mathematical model for interactive sound synthesis based on the application of Genetic Algorithms (GA) is presented. The Evolutionary Sound Synthesis Method (ESSynth) generates sequences of waveform variants by the application of genetic operators on an initial population of waveforms. We describe how the waveforms can be treated as genetic code, the fitness evaluation methodology and how genetic operations such as crossover and mutation are used to produce generations of waveforms. Finally, we discuss the results evaluating the generated sounds. IV585587Schaeffer, P., "Traité des objets musicaux": Editions du Seuil, Paris 1966 Risset, J.-C., Timbre analysis by synthesis: Representations, imitations, and variants for musical compostion (1991) In Representations of Musical Signals, pp. 7-43. , ed. De Poli, Piccialli & Road, Cambridge, Massachussetts: The MIT Press, ISBN 0-262-04113-8Smalley, D., Spectro-morphology and structuring processes (1990) In the Language of Electroacoustic Music, pp. 61-93. , ed. EmmersonBiles, J.A., GenJam: "A genetic algorithm for generating jazz solos" (1994) Proceedings of the 1994 International Computer Music Conference, (ICMC'94), pp. 131-137Horowitz, D., Generating rhythms with genetic algorithms (1994) Proceedings of the 1994 International Computer Music Conference, pp. 142-143Manzolli, J., Moroni, A., Von Zuben, F., Gudwin, R., An evolutionary approach applied to algorithmic composition (1999) Proceedings of the VI Brazilian Symposium on Computer Music, pp. 201-210. , Rio de JaneiroMoroni, A., Manzolli, J., Von Zuben, F., Gudwin, R., Vox populi: An interactive evolutionary system for algorithmic music composition (2000) San Francisco, USA: Leonardo Music Journal, 10, pp. 49-55. , MIT PressFogel, D.B., Evolutionary computation - Toward a new philosophy of machine intelligence (1995) IEEE Press, USA, pp. 46-47Johnson, C.G., Exploring the sound-space of synthesis algorithms using interactive genetic algorithms in G. A. (1999) Proceedings of the AISB Workshop on Artificial Intelligence and Musical Creativity, , Wiggins, editorEdinburghKoza, J.R., Bennett III, F.H., Andre, D., Keane, M.A., Dunlap, F., Automated synthesis of analog electrical circuits by means of genetic programming (1997) IEEE Transactions on Evolutionary Computation, 1 (2). , JulyCheung, N.M., Horner, A., Group synthesis with genetic algorithms (1996) Journal of the Audio Engineering Society, 44 (3), pp. 130-147Koza, J.R., Genetic programming (1997) Encyclopedia of Computer Science and TechnologyGarcia, R.A., Automatic generation of sound synthesis techniques (2000) Proposal for Degree of Master of Science. MIT, , Fall