Most chord recognition systems share a common architecture comprising two main stages: feature extraction and pattern matching, and two optional sub stages: pre-filtering and post-filtering. Understanding the interaction between these basic components is very important not only for achieving optimal performance, but also for assessing the potential and limitations of the system. Unfortunately, there are no studies that sufficiently evaluate the effects of the different approaches to each processing step and the interactions between these steps. In this paper we attempt to remedy this deficiency by performing a systematic evaluation encompassing a wide variety of techniques used for each processing step. In our study we find that filtering has a significant impact on performance, but providing musical context information in the transition matrix is rendered moot by the need to enforce continuity in the estimations. We discovered that the benefits of using complex chord models can be largely offset by an appropriate choice of features. In addition, the initial performance gap between different features were not fully compensated by any subsequent processing stages.

Temporal pitch class profiles - commonly referred to as a chromagrams - are the de facto standard signal representation for content-based methods of musical harmonic analysis, despite exhibiting a set of practical difficulties. Here, we present a novel, data-driven approach to learning a robust function that projects audio data into Tonnetz-space, a geometric representation of equal-tempered pitch intervals grounded in music theory. We apply this representation to automatic chord recognition and show that our approach out-performs the classification accuracy of previous chroma representations, while providing a mid-level feature space that circumvents challenges inherent to chroma.

Hidden Markov models (HMM) have been widely studied and applied over decades. The standard supervised learning method for HMM is maximum likelihood estimation (MLE) which maximizes the joint probability of training data. However, the most natural way of training would be finding the parameters that directly minimize the error rate of a given training set. In this article, we propose a novel learning method that minimizes the number of incorrectly decoded labels frame-wise. To do this, we construct a smooth function that is arbitrarily close to the exact frame error rate and minimize it directly using a gradient-based optimization algorithm. The proposed approach is intuitive and simple. We applied our method to the task of chord recognition in music, and the results show that it performs better than Maximum Likelihood Estimation and Minimum Classification Error.