Algorithms for melody search and transcription

This thesis studies two problems in music information retrieval: search for a given melody in an audio database, and automatic melody transcription. In both of the problems, the representation of the melody is symbolic, i.e., the melody consists of onset times and pitches of musical notes. In the first part of the thesis we present new algorithms for symbolic melody search. First, we present algorithms that work with a matrix representation of the audio data, that corresponds to the discrete Fourier transform. We formulate the melody search problem as a generalization of the classical maximum subarray problem. After this, we discuss algorithms that operate on a geometric representation of the audio data. In this case, the Fourier transform is converted into a set of points in the two-dimensional plane. The main contributions of the first part of the thesis lie in algorithm design. We present new efficient algorithms, most of which are based on dynamic programming optimization, i.e., calculating dynamic programming values more efficiently using appropriate data structures and algorithm design techniques. Finally, we experiment with the algorithms using real-world audio databases and melody queries, which shows that the algorithms can be successfully used in practice. Compared to previous melody search systems, the novelty in our approach is that the search can be performed directly in the Fourier transform of the audio data.