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(2018) Computational models of rhythm and meter, Dordrecht, Springer.

Christoffel rhythms

Georg Boenn

pp. 65-81

Christoffel words have been known to the field of mathematics since Jean Bernoulli in the late 18th century. Today, they have gained specific interest in the area of combinatorics on words (Berstel, Combinatorics on words: Christoffel words and repetitions in words. American Mathematical Society, Providence, 2009; Glen, Combinatorics of Lyndon words, 2012; Lothaire, Applied combinatorics on words. Cambridge University Press, Cambridge, 2005). This chapter will show that they are also useful for music analysis and composition. Remember that a word is an ordered, finite or infinite sequence of symbols taken from a finite alphabet that is the non-empty set A.Transcribing a Christoffel word into a rhythmic pattern is very simple. It only involves a mapping of the letters of the word to note onsets and silences. An analysis of the resulting rhythmic patterns indicates that they are strongly related to archetypical classical rhythms and to world music rhythms. When working with Christoffel words, one discovers similarities to African and Latin-American music, Minimalism, and other musical styles that feature non-symmetric meters and rhythms. The links with rhythms and meters of many different cultures provide a fertile ground for musical exploration and discovery. We also show that there exists a unique Christoffel word, or one of its conjugates, for every Euclidean rhythm. We will present a structural comparison between Christoffel words and Euclidean rhythms.

Publication details

DOI: 10.1007/978-3-319-76285-2_6

Full citation:

Boenn, G. (2018). Christoffel rhythms, in Computational models of rhythm and meter, Dordrecht, Springer, pp. 65-81.

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