Senegalese drummers often recite improvised texts while playing, considering the texts to reflect the rhythms’ meanings. Unlike in other African traditions, drums are rarely used as a speech surrogate. It is shown here that Senegalese rhythms involve language-like grammar rules, which are partly independent of the grammar of the players’ spoken language. The rhythms do not acoustically mimic speech, and the speech-drum matching is based on a lexicon of rhythms and their meanings. Players use this lexicon to produce an unlimited number of meaningful rhythms. The analysis of complex rhythms shows nonlinear alignments with spoken sentences containing plurals, definites, and negation. It is concluded that rhythms are generated by drum-specific grammatical rules. The musical functions of the drum grammar make it especially relevant to current work on language and music, and to ongoing debates between functionalist and formalist approaches to grammar.*