In this paper, we investigate the problem of music classification when training data is distributed throughout a network of interconnected agents (e.g. computers, or mobile devices), and it is available in a sequential stream. Under the considered setting, the task is for all the nodes, after receiving any new chunk of training data, to agree on a single classifier in a decentralized fashion, without reliance on a master node. In particular, in this paper we propose a fully decentralized, sequential learning algorithm for a class of neural networks known as Random Vector Functional-Link nets. The proposed algorithm does not require the presence of a single coordinating agent, and it is formulated exclusively in term of local exchanges between neighboring nodes, thus making it useful in a wide range of realistic situations. Experimental simulations on four music classification benchmarks show that the algorithm has comparable performance with respect to a centralized solution, where a single agent collects all the local data from every node and subsequently updates the model.