Mota , S. & Igoa, J. M.
Universidad Autónoma de Madrid
Recursion is a highly relevant combinatorial property exhibited by a number of sign systems, such as language and music, which also share another outstanding combinatorial property, namely discrete infinity. Given the close relationship between language and music as cognitive faculties (cf. Igoa, 2010), the aim of this work is to discuss how recursion is used and understood in these two domains of inquiry, and more specifically how it is applied to the structure of language and music. To this end, we first distinguish different notions of recursion, as originating in the formal sciences (mathematical logic), and later applied to the study of language and other domains within biology and psychology, and emphasize the difference between recursion as a property of the structural description of formal objects, and recursion as a kind of formal operation (and eventually a computational process of the human mind). Next, we report a series of syntactic analyses of linguistic and musical materials: a sample of well-formed sentences, whose analysis was based on Chomsky’s (1955/1975, 1965) generative grammar formalisms, and a selected sample of musical excerpts, whose analysis was inspired on Lerdahl and Jackendoff’s (1983) generative theory of tonal music. Our analyses yielded a number of structural commonalities as well as some differences stemming from combinatorial properties particular to each domain. As regards the commonalities, both language and music were found to share a similar form of grammar and syntactic structure that is deployed in the time dimension. In addition to this “horizontal”, time dimension recursion, music also shows recursion in a “vertical”, harmonic dimension.