Music is organised by socio-semiotic systems (music theory), represented by socio-semiotic systems (music notation), expanded by socio-semiotic systems (lyrics), and produced by socio-semiotic beings (humans), but music is not a socio-semiotic system. This is because, unlike genuine socio-semiotic systems, systems of content (meanings) cannot be systematically assigned to systems of expression (musical sounds).
On the model of Halliday's Systemic Functional Linguistic Theory, music can be understood as a perceptual phenomenon that activates mental processes that range over emotions, desires and thoughts.
The counterparts of music in other species include whalesong, birdsong, and the exchange of pheromones in eusocial insects. (That is, whalesong and birdsong are distinct from the protolanguages of whales and birds.) However, music differs from these in activating the meanings of language, whereas whalesong and birdsong activate the meanings of protolanguage, and the pheromones of eusocial insect primarily activate the meanings of perceptual (sensorimotor) systems.
In terms of Halliday's linear taxonomy of physical—biological—social—(socio-)semiotic systems, music is social, but not socio-semiotic.