Music Mathematics And Language
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Music, Mathematics and Language
This book presents a new approach to computational musicology in which music becomes a computational entity based on human cognition, allowing us to calculate music like numbers. Does music have semantics? Can the meaning of music be revealed using symbols and described using language? The authors seek to answer these questions in order to reveal the essence of music. Chapter 1 addresses a very fundamental point, the meaning of music, while referring to semiotics, gestalt, Schenkerian analysis and cognitive reality. Chapter 2 considers why the 12-tone equal temperament came to be prevalent. This chapter serves as an introduction to the mathematical definition of harmony, which concerns the ratios of frequency in tonic waves. Chapter 3, “Music and Language,” explains the fundamentals of grammar theory and the compositionality principle, which states that the semantics of a sentence can be composed in parallel to its syntactic structure. In turn, Chapter 4 explains the most prevalent score notation – the Berklee method, which originated at the Berklee School of Music in Boston – from a different point of view, namely, symbolic computation based on music theory. Chapters 5 and 6 introduce readers to two important theories, the implication-realization model and generative theory of tonal music (GTTM), and explain the essence of these theories, also from a computational standpoint. The authors seek to reinterpret these theories, aiming at their formalization and implementation on a computer. Chapter 7 presents the outcomes of this attempt, describing the framework that the authors have developed, in which music is formalized and becomes computable. Chapters 8 and 9 are devoted to GTTM analyzers and the applications of GTTM. Lastly, Chapter 10 discusses the future of music in connection with computation and artificial intelligence. This book is intended both for general readers who are interested in music, and scientists whose research focuses on music information processing. In order to make the content as accessible as possible, each chapter is self-contained.
Music Math
Music Math explores the surprising and profound connection between science and music, revealing the mathematical structures underpinning harmony, rhythm, and musical form. It demonstrates that musical composition isn't solely driven by emotion but is also a structured system governed by mathematical rules, dating back to Pythagoras and evident in Bach's intricate works. The book delves into how mathematical principles govern musical intervals and scales, offering an objective framework for analyzing and creating music. Readers will discover the role of numerical sequences like the Fibonacci sequence in melodic construction, providing a deeper understanding beyond subjective appreciation. This unique book progresses logically, starting with fundamental concepts such as ratios and scales before advancing to complex topics like counterpoint, harmony, and algorithmic composition. It highlights how the physics of sound waves, insights from computer science, and cognitive psychology enrich our understanding of music. By balancing technical precision with accessible explanations and visual aids, Music Math welcomes musicians, scientists, and anyone curious about the intersection of these seemingly disparate fields.
Language, Music and Computing
This book constitutes the proceedings of the First International Workshop on Language, Music and Computing, LMAC 2017, held in St. Petersburg, Russia, in April 2017. The 18 papers presented in this volume were carefully reviewed and selected from 52 submissions. They were organized in topical sections on the universal grammar of music, the surface of music and singing, language as music, music computing, formalization of the informality.