Our capacity to express emotional content in music, and how it relates to linguistic prosody, has been the subject of impassioned psychology and neuroscience research in the past two decades. While the musical expression of basic emotions is now understood to rely much on the same acoustical characteristics as speech prosody, the picture is less clear when music is considered a medium not only for basic emotions, but also for social attitudes. The present study aims to test the capacity of musical communication to encode, and be decoded as, a series of 5 attitudes: being domineering (DOM), insolent (INS), disdainful (DIS), caring (CAR) or conciliatory (CON). We recorded a series of 100 improvised duets, in which one musician was tasked to express one attitude and the other to recognize it. First, we found that the encoded attitudes could be reliably decoded from musical interactions, both by the participants of the interactions and by external listeners. Second, using computational audio analysis, we showed that this capacity to decode social intents from music relied on temporal and harmonic coordination cues that did not suggests similarity with language. These results show that musical interactions can be used as a means to directly communicate social attitudes so far believed to be germane to verbal interactions, and that this capacity is not an exaptation from language. In evolutionary terms, this suggests that a lot more social communication would have been possible with music as the sole pre-linguistic "technology" than previously believed.