New Archiving, Fingering, and Assessing Techniques for Sheet Music Using Advanced Signal Processing Approaches

In this thesis, advanced signal processing techniques are proposed to archive the musical scores, guide the novice pianists to play piano with appropriate fingerings, and assess the harmonization for musical composition. The mathematical frameworks for these three applications are established and the corresponding optimization problems are formulated. The optimal solutions are also provided. First, the hard- and soft-archiving approaches for storing and distributing musical scores are investigated. By use of the popular musical scripting language, LilyPond, as the intermediate data format, we propose to encode the LilyPond script, which is converted from the original musical score, to the two-dimensional quick-response (QR) code(s). Instead of using the intuitive conventional image recognition software to recover the original musical score, we propose to benefit from the error-resilient QR codes since they have the inherent error-correction capability. Our proposed hard-archiving scheme based on the LilyPond script and QR codes leads to 100% of musical-score reconstruction accuracy while the conventional method using image recognition can only result in 0% to 80%. Thus, our proposed new scheme is very promising for proving a new robust musical-score archiving method. Second, the comparative study on the automatic fingering, i.e., the computer generated fingering-index sequences for novice pianists, is carried out in this work. Two major approaches, namely rules-based and probabilistic approaches, are investigated. The genetic algorithm as a solution using the rules-based approach and the Viterbi algorithm subject to the hidden Markov models using the probabilistic approach are studied for the automatic fingering optimization. Twelve ergonomic rules are adopted to benchmark the ergonomic compliance of each fingering index sequence. According to the experiments we conduct, the genetic algorithm leads to slightly better performance than the probabilistic approach in terms of ergonomic compliance. On the other hand, the genetic algorithm requires much larger time complexity than the probabilistic approach as the trade-off. Third, the procedure of generating four-part harmonization is investigated. By use of an exhaustive search, we propose a new new algorithm known as the ``Whac-a-Mole\u27\u27 algorithm. The basic idea is that we tackle the chord with the lowest degree of harmonization with an exhaustive search for each iteration. Our purposed algorithm leads to 16% better efficiency than the method which is to randomly choose a chord to implement exhaustive search