A typical task in wireless sensor networks (WSNs) is to collect data from sensor nodes towards one or many sinks in a multi-hop convergecast structure. In this paper, we focus on the data gathering problem with differentiated traffic, each addressed to a specific sink in multichannel WSNs. In order to find a collision-free optimized multichannel time slot assignment that minimizes the data gathering cycle, we propose a centralized traffic-aware algorithm called MUSIKA. We formulate the problem as a linear program and compute the optimal time needed for a raw data convergecast in an illustrative example. More generally, we run simulations on various network topologies to evaluate the performance of MUSIKA in terms of cycle length, maximum buffer size and slot reuse ratio for different use cases: redundant functional processing chains, different application functionalities per sink.