EJTP 8 (2005) 22–34 Electronic Journal of Theoretical Physics Non Linear Assessment of Musical Consonance Lluis Lligo˜ na Trulla 1 , Alessandro Giuliani 2 , Giovanna Zimatore 3 , Alfredo Colosimo 4 ∗ and Joseph P. Zbilut 5 1 Centre de Recerca “Puig Rod´ o”, c/o Darwin 30, 17200 Palafrugell, Girona. Catalonia, Spain 2 Istituto Superiore di Sanit`a, V.le Regina Elena 299, 0016, Rome, Italy 3 Department of Human Communication Science, Research Institute “Tosinvest Sanit`a s.p.a”, 00163, Rome, Italy 4 Department of Human Physiology and Pharmacology, University of Rome “La Sapienza”, 00185, Rome, Italy 5 Department of Molecular Biophysics and Physiology, Rush University Medical Center, 1653 W. Congress, Chicago, 60612 IL, USA Received 30 September 2005, Published 20 December 2005 Abstract: The position of intervals and the degree of musical consonance can be objectively explained by temporal series formed by mixing two pure sounds covering an octave. This result is achieved by means of Recurrence Quantification Analysis (RQA) without considering neither overtones nor physiological hypotheses. The obtained prediction of a consonance can be considered a novel solution to Galileo’s conjecture on the nature of consonance. It constitutes an objective link between musical performance and listeners’ hearing activity. c  Electronic Journal of Theoretical Physics. All rights reserved. Keywords: Musical Consonance, Recurrence Quantification Analysis PACS (2003): 43.25.+y, 43.60.+d, 43.75.+a, 43.66.+y 1. Introduction According to a current definition, consonance is the “intervallic relationships in sound frequencies producing sounds of repose” [1], and a basic problem in the field of musical acoustics concerns the fact that since musical consonance is a graduated criterion, in principle it should be possible: i) to produce an order of merit (ranking) among intervals, and ii) to find an algorithmic derivation of consonance ranking [2]. An excellent example of the consonance-dissonance issue is due to Galileo Galilei [3], * Corresponding author: colosimo@caspur.it