A Data-Driven Model of Tonal Chord Sequence Complexity

We present a compound language model of tonal chord sequences, and evaluate its capability to estimate perceived harmonic complexity. In order to build the compound model, we trained three different models: prediction by partial matching, a hidden Markov model and a deep recurrent neural network on a novel large dataset containing half a million annotated chord sequences. We describe the training process and propose an interpretation of the harmonic patterns that are learned by the hidden states of these models. We use the compound model to generate new chord sequences and estimate their probability, which we then relate to perceived harmonic complexity. In order to collect subjective ratings of complexity, we devised a listening test comprising two different experiments. In the first, subjects choose the more complex chord sequence between two. In the second, subjects rate with a continuous scale the complexity of a single chord sequence. The results of both experiments show a strong relation between negative log probability, given by our language model, and the perceived complexity ratings. The relation is stronger for subjects with high musical sophistication index, acquired through the GoldMSI standard questionnaire. The analysis of the results also includes the preference ratings that have been collected along with the complexity ratings; a weak negative correlation emerged between preference and log probability.