Quantifying Aesthetic Preference and Perceived Complexity for Fractal Melodies

PARTICIPANTS RATED THE PERCEIVED complexity and melodiousness of fractal (1/f ) tone sequences with specific ß values. Plotting the mean complexity and melodicity ratings against each other and against ß indicated that: (1) a melody’s spectral power density slope ( ß) can be used as an objective measure of its perceived complexity; (2) ß ≈ 1.50 for optimally preferred melodies; (3) perceived complexity is determined by the distribution of pitch intervals such that optimally preferred melodies have a preponderance of small intervals compared to large ones; (4) the poor quadratic fits found in music-preference studies are due to the use of an independent-subjects design or the stimuli not covering the whole possible range of complexity; (5) ß < 2 for most music stimuli; and (6) ecologically valid melodies only exist over the ß range 0.67 to 2.35, with melodies whose ß values lie outside this range not being perceived as musical due to their extreme complexity or simplicity. Finally, converging experimental and neurophysiological evidence is discussed that suggests that these results are a consequence of the auditory system being optimally tuned to the statistical properties of speech.