In this paper, we undertake a critical assessment of a state-of-the-art deep neural network approach for computational rhythm analysis. Our methodology is to deconstruct this approach, analyse its constituent parts, and then reconstruct it. To this end, we devise a novel multi-task approach for the simultaneous estimation of tempo, beat, and downbeat. In particular, we seek to embed more explicit musical knowledge into the design decisions in building the network. We additionally reflect this outlook when training the network, and include a simple data augmentation strategy to increase the network's exposure to a wider range of tempi, and hence beat and downbeat information. Via an in-depth comparative evaluation, we present state-of-the-art results over all three tasks, with performance increases of up to 6% points over existing systems.