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We present a new system for the harmonic analysis of popular musical audio. It is focused on chord estimation, although the proposed system additionally estimates the key sequence and bass notes. It is distinct from competing approaches in two main ways. First, it makes use of a new improved chromagram representation of audio that takes the human perception of loudness into account. Furthermore, it is the first system for joint estimation of chords, keys, and bass notes that is fully based on machine learning, requiring no expert knowledge to tune the parameters. This means that it will benefit from future increases in available annotated audio files, broadening its applicability to a wider range of genres. In all of three evaluation scenarios, including a new one that allows evaluation on audio for which no complete ground truth annotation is available, the proposed system is shown to be faster, more memory efficient, and more accurate than the state-of-the-art.