While it is nearly uncontroversial that music is subject to some ‘syntactic rules’, it is initially very unclear that music has ‘meaning’ in anything like the usual sense. We sketch a conceptual framework in which music can trigger inferences about a music-external reality, and may even be endowed with (highly underspecified) truth conditions. But their source is very different from that of most truth-conditional phenomena in language: normal auditory cognition and aspects of iconic semantics (used for pictures, gestures, and some aspects of signs) are better models than compositional semantics in language.