Titlebook: Mathematical and Computational Modeling of Tonality; Theory and Applicati Elaine Chew Book 2014 Springer Science+Business Media New York 20

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MuSA.RTf tonal induction and tracking algorithms. In this chapter we describe the mapping strategies for transforming a MIDI stream into tonal structures in 3D space, and our solution for overcoming the challenge of real-time concurrent processing of data streams; we will also give examples and present cas

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Sensitivity Analysisby period shows that pieces from the romantic period may be the most challenging for key-finding. We next propose three extensions to the basic key-finding system—the modified Spiral Array approach, fundamental frequency identification, and post-weight balancing—to improve the performance at differe

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Book 2014nd is written for a broad audience, ranging from the layperson interested in music, mathematics, and computing to the music scientist-engineer interested in computational approaches to music representation and analysis, from the music-mathematical and computational sciences student interested in lea

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Argus Segmentation Methody point in the interior of the Spiral Array, segmentation boundaries map to peaks in the distances between the CEs of adjacent segments of music. The best-case computed boundaries are, on average, within 0.94 % (for Regard IV) and 0.11 % (for Regard XVI) of their targets.

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An Abbreviated Surveypiration from interior point methods in linear optimization. The second part of the chapter describes the von Neumann Center of Gravity algorithm and Dantzig’s bracketing technique to speed convergence, and then draws analogies between the algorithm and the CEG method.

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The CEG Algorithm (Part I) a graph showing the evolution of the closest keys accompany the tabular results. A MATLAB version of the CEG code appears in Appendix B. An evaluation of the CEG algorithm follows in Chap. .; the CEG method is applied to polyphonic music in MIDI (Musical Instrument Digital Interface) format in Chap. ., and adapted to music audio in Chap. ..