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Recent researches on Automatic Chord Extraction (ACE) have focused on theimprovement of models based on machine learning. However, most models stillfail to take into account the prior knowledge underlying the labeling alphabets(chord labels). Furthermore, recent works have shown that ACE performances areconverging towards a glass ceiling. Therefore, this prompts the need to focuson other aspects of the task, such as the introduction of musical knowledge inthe representation, the improvement of the models towards more complex chordalphabets and the development of more adapted evaluation methods.  In this paper, we propose to exploit specific properties and relationshipsbetween chord labels in order to improve the learning of statistical ACEmodels. Hence, we analyze the interdependence of the representations of chordsand their associated distances, the precision of the chord alphabets, and theimpact of the reduction of the alphabet before or after training of the model.Furthermore, we propose new training losses based on musical theory. We showthat these improve the results of ACE systems based on Convolutional NeuralNetworks. By performing an in-depth analysis of our results, we uncover a setof related insights on ACE tasks based on statistical models, and alsoformalize the musical meaning of some classification errors.

Using musical relationships between chord labels in automatic chord extraction tasks