Music, emotion and Zipf's law

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The hypothesis of Zipf concerning a universal Principle of Least Effort, manifested itself in Zipf's law and was modeled by Ferrer i Cancho and Sol´e into a signal-object reference matrix, giving rise to the idea that it may be possible to identify the elements in music that elicit emotional responses in us. The undeniable relation between music and emotion was the reason to consider a possible signal-emotion reference system analogous to the signal-object reference in natural human language. Following Zipf's line of reasoning, music as an exponent of human behavior, is subject to the Principle of Least Effort and is consequently structured in such a way that the distribution pattern of the signals that "communicate the musical message", follow a power law. In this thesis the possibility of deploying the characteristics of the Zipf curve to gain more insight into the relation between music and emotion was investigated. Two of the elements that, viewed in the framework of a signal-emotion reference, could qualify as the signals that elicit emotion, viz. notes and intervals, were investigated.

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[...] This hypothesis would be rejected when Zipf 's law could be confirmed for texts in which the structure of language would be absent. As random texts do not exhibit language structure they are often regarded as the null hypothesis. Based on Mandelbrot's observations that monkey-and-typewriter random texts exhibit Zipfian behaviour Miller concluded that Zipf 's rule a sim- ple consequence of those intermittent silences which we imagine to exist between successive words” (Miller, 1957). Later, Wentian Li showed that random texts in which the relative frequencies of the characters equal those in human languages, obey Zipf 's law 1992), from which Li concluded that “Zipf 's law is not a deep law in natural language as one might first have thought”. [...]

[...] Chapter 6 Discussion and Conclusion Music, emotion and the Zipf curve The relation between music and emotion is evident, but very little is known about how this relation comes about. Various theories have been developed, like, for example, the the- ory that music is a vehicle for the emotions of the composer, a theory that has been criticized because of the subjectivity of music perception, or like the theory of Meyer (mentioned by Krumhansl), that relates the emo- tions evoked by music with the cognition of musical structures (Krumhansl, 2002). [...]

[...] Davies, S. (1994). Musical Meaning and Expression. Cornell University Press. Dellandrea, E., Makris, P., and Vincent, N. (2004). Zipf analysis of audio signals. Fractals [Complex Geometry, Patterns, and Scaling in Nature and Society], 12(1):73–85. Elliot, J. and Atwell, E. (2000). [...]

[...] If further research reveals that the applied method is valid, research can be broadened to other music genres, for example Grego- rian chant, pop music or music from non-Western cultures. Finding a Zipfian curve in most types of music will be a strong argument for communication in music and will give us more insight in what elements carry the musical message. Only when we know which elements convey the musical message and how they evoke our emotional responses a signal-emotion matrix will come within our reach. Bibliography Bentley, J. (2000). Programming Pearls. Addison-Wesley, Inc. Best, K.-H. (1996). [...]

[...] Type 2 artificial text in which the order of the letters is preserved, but all punctuation marks and space marks are removed. An arbitrary letter is chosen as delimiter between the 'words'. Letter-level Markov text (Bentley, 2000) After counting how many times every letter in a sample text follows a letter A or follows a letter and so on, each letter in the artificial text can be made a random function of its predecessor (order-1 Markov text) or its n predecessors (order-n Markov text). [...]