Evolutionary Music and the Zipf-Mandelbrot Law: Developing Fitness Functions for Pleasant Music

Abstract

Abstract.A study on a 220-piece corpus (baroque, classical, romantic, 12-tone, jazz, rock, DNA strings, and random music) reveals that aesthetically pleasing music may be describable under the Zipf-Mandelbrot law. Various Zipf-based metrics have been developed and evaluated. Some focus on musictheoretic attributes such as pitch, pitch and duration, melodic intervals, and harmonic intervals. Others focus on higher-order attributes and fractal aspects of musical balance. Zipf distributions across certain dimensions appear to be a necessary, but not sufficient condition for pleasant music. Statistical analyses suggest that combinations of Zipf-based metrics might be used to identify genre and/or composer. This is supported by a preliminary experiment with a neural network classifier. We describe an evolutionary music framework under development, which utilizes Zipf-based metrics as fitness functions.

Emotional task-dependent low-frequency fluctuations and methylphenidate: Wavelet scaling analysis of 1/f-type fluctuations in fMRI of the cerebellar vermis

“…Schizophrenia and autism, both psychiatric conditions associated with various forms of midline cerebellar pathology (Heath et al, 1982;Deicken et al, 2001), are also associated with defects in the perception and transmission of emotional information (Ornitz, 1970;Schmahmann, 2000). Our finding of a significant correlation between changes in emotional state and wavelet exponent unique to PIV supports an observation by Shaffer (1981;cited in Wing et al, 2004) that emotions are expressed by intended variations in movement timing (e.g., vocal porosity; musical production; dance: Juslin and Laukka, 2003;Madison, 2000;Manaris et al, 2003) aspects of which display power-laws (Tuller et al, 1997;Voss and Clarke, 1975). Is 1/f-type emotional-motor production variability perceived (Bhattacharya et al, 2001, Jeong et al, 1998 and if so, then does it serve the brain as a neurobiological broad-band carrier wave Teich and Lowen, 1994;Teich et al, 1996) for the reception, translation and retransmission of emotional experience (Jeong et al, 1998)?…”

A Music Information Retrieval Approach Based on Power Laws

“…the slopes for least preferred pieces indicate more chaotic proportions (average of -0.8846). This is consistent with slopes seen in earlier studies [7,8,24].…”

“…Empirical studies demonstrate connections between power laws and human aesthetics [8,19,20,21]. For instance, "socially-sanctioned" (popular) music exhibits power laws across various attributes [7,21,22,24].…”

Fitness in evolutionary art and music: a taxonomy and future prospects

“…Sometimes, more structure is put into the design of the fitness function by the system designer. For example, in the work of Manaris et al (2003), the fitness function is in the form of a Zipf-Mandlebrot law, the parameters of which are tuned so that the function would give a high value when applied to a specific corpus of musical material. This latter approach combines the corpus-based approach with the aesthetic measure approach discussed above; the system designer is asserting that the functional form of the fitness function is a meaningful measure, and then the parameter details are learned from the corpus.…”