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Deep Learning (DL) is now commonly used in music processing such as Automatic Chord Recognition (ACR), with Convolutional Neural Networks (CNN) being popular in such tasks. Compression of CNNs has become a research topic of interest, focussed on post-pruning of learnt networks and development of less expensive network elements. CNNs assemble high level structure in data from small simple patterns. Music signals are often processed in the spectral domain where much known structure is present. We propose the FifthNet, a neural network for chroma-based ACR that incorporates known structures in its design through data manipulation and parallel processing. We find that FifthNet is competitive with popular ACR networks while using only a small fraction of their network parameters