A System for Acoustic Chord Transcription and Key Extraction from Audio Using Hidden Markov Models Trained on Synthesized Audio

Kyogu Lee
Stanford University, CA, USA (March, 2008)

ABSTRACT

Extracting high-level information of musical attributes such as melody, harmony, key, or rhythm from the raw waveform is a critical process in Music Information Retrieval (MIR) systems. Using one or more of such features in a front end, one can efficiently and effectively search, retrieve, and navigate through a large collection of musical audio. Among those musical attributes, harmony is a key element in Western tonal music. Harmony can be characterized by a set of rules stating how simultaneously sounding (or inferred) tones create a single entity (commonly known as a chord), how the elements of adjacent chords interact melodically, and how sequences of chords relate to one another in a functional hierarchy. Patterns of chord changes over time allow for the delineation of structural features such as phrases, sections and movements. In addition to structural segmentation, harmony often plays a crucial role in projecting emotion and mood. This dissertation focuses on two aspects of harmony, chord labeling and chord progressions in diatonic functional tonal music. Recognizing the musical chords from the raw audio is a challenging task. In this dissertation, a system that accomplishes this goal using hidden Markov models is described. In order to avoid the enormously time-consuming and laborious process of manual annotation, which must be done in advance to provide the ground-truth to the supervised learning models, symbolic data like MIDI files are used to obtain a large amount of labeled training data. To this end, harmonic analysis is first performed on noise-free symbolic data to obtain chord labels with precise time boundaries. In parallel, a sample-based synthesizer is used to create audio files from the same symbolic files. The feature vectors extracted from synthesized audio are in perfect alignment with the chord labels, and are used to train the models.

Sufficient training data allows for key- or genre-specific models, where each model is trained on music of specific key or genre to estimate key- or genre-dependent model parameters. In other words, music of a certain key or genre reveals its own characteristics reflected by chord progression, which result in the unique model parameters represented by the transition probability matrix. In order to extract key or identify genre, when the observation input sequence is given, the forward-backward or Baum- Welch algorithm is used to efficiently compute the likelihood of the models, and the model with the maximum likelihood gives key or genre information. Then the Viterbi decoder is applied to the corresponding model to extract the optimal state path in a maximum likelihood sense, which is identical to the frame-level chord sequence. The experimental results show that the proposed system not only yields chord recognition performance comparable to or better than other previously published systems, but also provides additional information of key and/or genre without using any other algorithms or feature sets for such tasks. It is also demonstrated that the chord sequence with precise timing information can be successfully used to find cover songs from audio and to detect musical phrase boundaries by recognizing the cadences or harmonic closures.

This dissertation makes a substantial contribution to the music information retrieval community in many aspects. First, it presents a probabilistic framework that combines two closely related musical tasks chord recognition and key extraction from audio and achieves state-of-the-art performance in both applications. Second, it suggests a solution to a bottleneck problem in machine learning approaches by demonstrating the method of automatically generating a large amount of labeled training data from symbolic music documents. This will help free researchers of laborious task of manual annotation. Third, it makes use of more efficient and robust feature vector called tonal centroid and proves, via a thorough quantitative evaluation, that it consistently outperforms the conventional chroma feature, which was almost exclusively used by other algorithms. Fourth, it demonstrates that the basic model can easily be extended to key- or genre-specific models, not only to improve chord recognition but also to estimate key or genre. Lastly, it demonstrates the usefulness of recognized chord sequence in several practical applications such as cover song finding and structural music segmentation.

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