  Recent researches on Automatic Chord Extraction (ACE) have focused on the
improvement of models based on machine learning. However, most models still
fail to take into account the prior knowledge underlying the labeling alphabets
(chord labels). Furthermore, recent works have shown that ACE performances are
converging towards a glass ceiling. Therefore, this prompts the need to focus
on other aspects of the task, such as the introduction of musical knowledge in
the representation, the improvement of the models towards more complex chord
alphabets and the development of more adapted evaluation methods.
  In this paper, we propose to exploit specific properties and relationships
between chord labels in order to improve the learning of statistical ACE
models. Hence, we analyze the interdependence of the representations of chords
and their associated distances, the precision of the chord alphabets, and the
impact of the reduction of the alphabet before or after training of the model.
Furthermore, we propose new training losses based on musical theory. We show
that these improve the results of ACE systems based on Convolutional Neural
Networks. By performing an in-depth analysis of our results, we uncover a set
of related insights on ACE tasks based on statistical models, and also
formalize the musical meaning of some classification errors.
