Almaty: Kazak Universiteti, 2013. — 24 p. This paper is specifically designed to study the basic principles of mathematics and music correlation from ancient to modern times. The role of mathematics in the formation of compositional technique has been determined. On their basis, the young author created original music compositions in the modern academic mainstream. This study...
Springer, 2023. — 307 p. This book offers an in-depth analysis of musical variation through a systematic approach, heavily influenced by the principles of Grundgestalt and developed variations, both created by the Austrian composer Arnold Schoenberg (1874-1951). The author introduces a new transformational-derivative model and the theory that supports it, specifically crafted...
Springer, 2002. — 288 p. In Western Civilization Mathematics and Music have a long and interesting history in common, with several interactions, traditionally associated with the name of Pythagoras but also with a significant number of other mathematicians, like Leibniz, for instance. Mathematical models can be found for almost all levels of musical activities from composition...
Dave Benson, 2006. — 520 p.
Since the time of the Ancient Greeks, much has been written about the relation between mathematics and music: from harmony and number theory, to musical patterns and group theory. Benson provides a wealth of information here to enable the teacher, the student, or the interested amateur to understand, at varying levels of technicality, the real...
Aberdeen: Dave Benson, 2008. — 531 p. Waves and harmonics What is sound? The human ear Limitations of the ear Why sine waves? Harmonic motion Vibrating strings Sine waves and frequency spectrum Trigonometric identities and beats Superposition Damped harmonic motion Resonance Fourier theory Fourier coefficients Even and odd functions Conditions for convergence The Gibbs...
Boca Raton: CRC Press LLC, 2000. — без пагинации, 14 файлов в архиве. Книга посвящена приложению математических методов к анализу музыки. Рассмотрено применение разведочного анализа данных, анализа временных рядов, иерархических методов, цепей Маркова, метода главных компонент, дискриминантного и кластерного анализа, многомерного шкалирования и т.п. Предназначена, с одной стороны,...
Chapman&Hall/CRC, 2004. — 285 p. An essential aspect of music is structure. It is therefore not surprising that a connection between music and mathematics was recognized long before our time. Perhaps best known among the ancient “quantitative musicologists” are the Pythagoreans, who found fundamental connections between musical intervals and mathematical ratios. An obvious reason...
Cambridge University Press, 2020. — 184 p. — (Australian Mathematical Society Lecture Series 28). — ISBN: 978-1-108-79445-9. The Mahler measure is a fascinating notion and an exciting topic in contemporary mathematics, interconnecting with subjects as diverse as number theory, analysis, arithmetic geometry, special functions and random walks. This friendly and concise...
Proceedings of the Second International Conference, MCM 2009, John Clough Memorial Conference, New Haven, CT, USA, June 19-22, 2009. — Springer, 2009. — 316 p.
These proceedings comprise 26 refereed research papers that were presented at the Second International Conference on Mathematics and Computation in Music (MCM 2009), which met in conjunction with the John Clough Memorial...
Springer, 1984. — 324 p. Defining the problem situation. The mathematical approach. The experimental approach. The mechanistic approach. Contacts and criticisms. An example from the second generation. Conclusions.
Springer, 1984. — 324 p. Defining the problem situation. The mathematical approach. The experimental approach. The mechanistic approach. Contacts and criticisms. An example from the second generation. Conclusions.
Oxford University Press, 2003. — 200 p. — ISBN 9780199298938, 0199298939 From Ancient Greek times, music has been seen as a mathematical art, and the relationship between mathematics and music has fascinated generations. This collection of wide ranging, comprehensive and fully-illustrated papers, authorized by leading scholars, presents the link between these two subjects in a...
Oxford University Press, 2003. — 200 p. — ISBN: 9780199298938, 0199298939. From Ancient Greek times, music has been seen as a mathematical art, and the relationship between mathematics and music has fascinated generations. This collection of wide ranging, comprehensive and fully-illustrated papers, authorized by leading scholars, presents the link between these two subjects in...
Scientific research. — Philadelphia: Department of Mathematics and Computer Science Saint Joseph’s University, 2008. — 54 p. The Sound of Numbers is a book on the mathematics of music theory—that is, the use of mathematics to describe, analyze, and create musical structures such as rhythms, scales, chords, and melodies. Music theorists have used mathematics to solve musical...
Springer Singapore, 2022. — 257 p. — eBook ISBN 978-981-19-5166-4. 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...
Springer Singapore, 2022. — 257 p. — eBook ISBN 978-981-19-5166-4. 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...
Oxford University Press, 2022. — 680 p. — (Oxford Studies in Music Theory). — eBook ISBN 978-0190246013. Exploring Musical Spaces is a comprehensive synthesis of mathematical techniques in music theory, written with the aim of making these techniques accessible to music scholars without extensive prior training in mathematics. The book adopts a visual orientation, introducing...
Cambridge University Press, 1961. — 285 p. Sir James Jeans (1877–1946) is regarded as one of the founders of British cosmology, and was the first to suggest (in 1928) the steady state theory, which assumes a continuous creation of matter in the universe. He made many major contributions over a wide area of mathematical physics, but was also well known as an accessible writer...
Singapour: World Scientific, 2024. — 283 p. The purpose of this book is to provide a concise introduction to the mathematical theory of music, opening each chapter to the most recent research. Despite the complexity of some sections, the book can be read by a large audience. Many examples illustrate the concepts introduced. The book is divided into 9 chapters. In the first...
Paris: Delatour, 2006. — 348 p. If you like advanced mathematics and music theory, this is a pretty good book. It is a collection of topics of current applications of mathematics and music theory. The organization of the topics seems a little disjointed, there are some typos and a few poorly worded sentences (presumably because English is not the author's native language), but...
Paris: Delatour France, 2006. — 316 p. If you like advanced mathematics and music theory, this is a pretty good book. It is a collection of topics of current applications of mathematics and music theory. The organization of the topics seems a little disjointed, there are some typos and a few poorly worded sentences (presumably because English is not the author's native language),...
Springer, 2024. — 347 p. This open access book offers a historical context and an overview of the field's current artistic and scientific research. Sonic design includes the construction and performance of acoustic instruments but also recording, editing, mixing, and synthesizing sounds using analog and digital electronic devices. This book explores sonic design from the...
Editor: Robert Peck, Associate Professor and Coordinator of Music Theory. Louisiana State University, School of Music. Contents: (currently available online - for a limited time). Welcome -. Thomas Noll & Robert Peck. Continued fractions, best measurements, and musical scales and intervals - J. Douthett & R. Krantz. The legacy of John Clough in mathematical music theory - David...
Proceedings of the First International Conference on Mathematics and Computation in Music, MCM 2007, held in Berlin, Germany, in May 2007. — Springer, 2007. — 336 p. — ISBN 978-3-642-04579-0.
This book constitutes the refereed proceedings of the First International Conference on Mathematics and Computation in Music, MCM 2007, held in Berlin, Germany, in May 2007.
The 51...
New York: Springer Science & Business Media, 1997. — 528 p. This book presents a coherent state-of-the-art survey on the area of systematic and cognitive musicology which has enjoyed dynamic growth now for many years. It is devoted to exploring the relationships between acoustics, human information processing, and culture as well as to methodological issues raised by the...
New York: Springer, 2016. — 323 p. This textbook is a first introduction to mathematics for music theorists, covering basic topics such as sets and functions, universal properties, numbers and recursion, graphs, groups, rings, matrices and modules, continuity, calculus, and gestures. It approaches these abstract themes in a new way: Every concept or theorem is motivated and...
New York: Springer, 2021. — 1007 p. This book presents comprehensive coverage of the latest advances in research into enabling machines to listen to and compose new music. It includes chapters introducing what we know about human musical intelligence and on how this knowledge can be simulated with AI. The development of interactive musical robots and emerging new approaches to...
World Scientific Publishing Company, 2018. — 325 p. Introduction About the Editors Rhythm and Transformation In the Beginning Was the Beat Metered Time Rhythms Timelines and Groove The Beat Class Circle and Modulus Application of the Modulus: Polyrhythm Application of the Modulus: Tihai Endings Transformations of Rhythms Introduction to Rhythm Class: Classroom Activity...
World Scientific Pub Co Inc, 2018. — 371 p. Questions about variation, similarity, enumeration, and classification of musical structures have long intrigued both musicians and mathematicians. Mathematical models can be found from theoretical analysis to actual composition or sound production. Increasingly in the last few decades, musical scholarship has incorporated modern...
New York: ISTE/Wiley, 2017. — 283 p. This book is built to start from elementary and fundamental bases to the first degrees of harmony. It provides many theoretical and technical bases of music, presenting in detail relations between physics and music (harmonics, frequency and time spectrum, dissonance, etc.), physiological relations with human body and education.
New York: Springer, 2017. — 345 p. In particular the contributed chapters introduce advanced techniques and concepts from modern mathematics and physics, deriving from successes in domains such as Topos theory and physical string theory. The authors include many of the leading researchers in this domain, and the book will be of value to researchers working in computational...
Cham: Springer, 2021. — 372 p. This book shows how information theory, probability, statistics, mathematics and personal computers can be applied to the exploration of numbers and proportions in music. It brings the methods of scientific and quantitative thinking to questions like: What are the ways of encoding a message in music and how can we be sure of the correct decoding?...
New York: Columbia University Press, 2021. — 304 p. Why does a clarinet play at lower pitches than a flute? What does it mean for sounds to be in or out of tune? How are emotions carried by music? Do other animals perceive sound like we do? How might a musician use math to come up with new ideas? This book offers a lively exploration of the mathematics, physics, and...
Boston: MIT Press, 2007. — 257 p. In Music and Probability, David Temperley explores issues in music perception and cognition from a probabilistic perspective. The application of probabilistic ideas to music has been pursued only sporadically over the past four decades, but the time is ripe, Temperley argues, for a reconsideration of how probabilities shape music perception and...
Boca Raton: CRC Press, 2013. — 357 p. The Geometry of Musical Rhythm: What Makes a "Good" Rhythm Good? is the first book to provide a systematic and accessible computational geometric analysis of the musical rhythms of the world. It explains how the study of the mathematical properties of musical rhythm generates common mathematical problems that arise in a variety of seemingly...
NY: CRC Press, 2013. — 342 p. At first glance, mathematics and music seem to be from separate worlds—one from science, one from art. But in fact, the connections between the two go back thousands of years, such as Pythagoras’s ideas about how to quantify changes of pitch for musical tones (musical intervals). Mathematics and Music: Composition, Perception, and Performance explores...
New York: Chapman&Hall/CRC, 2016. — 694 p.
This book provides a comprehensive overview of music data analysis, from introductory material to advanced concepts. It covers various applications including transcription and segmentation as well as chord and harmony, instrument and tempo recognition. It also discusses the implementation aspects of music data analysis such as...
Unpublished. — 2009. — 176 p. Basic Concepts. Horizontal Structure. Harmony and Related Numerology. Ratios and Musical Intervals. Logarithms and Musical Intervals. Chromatic Scales. Octave Identification. Properties of Integers. The Integers as Intervals. Timbre and Periodic Functions. Rational Numbers As Intervals. Rational Tuning.
СПб. : Bodlib, 2006. — 91 с. : ил. — ISBN: 5-902882-43-5. В истории музыки известно большое число различных звуковых систем — звукорядов. С древнейших времен их возникновение объяснялось математическими соотношениями между музыкальными звуками. В этой книге на популярном уровне излагается история развития теоретических представлений о строении звукорядов, в сопоставлении с...
М.; Ижевск: Институт компьютерных исследований, 2013. — 432 с. — ISBN: 978-5-4344-0132-6. Математика — признанная царица наук — вовлечена практически во все исследования, известные человечеству. Ее применение будет обязательным повсюду, где требуется установить взаимосвязь между пространством, временем и мыслью. Не стала исключением из этого правила и музыка, представляющая...
Монография. — Москва; Санкт-Петербург: Нестор-История, 2018. — 68 с. В книге рассмотрены вопросы построения музыкальных звукорядов в тесной связи с объективными математическими закономерностями — свойствами цепных дробей и рациональных приближений. Введение Предварительные замечания Квинтовая цепь Погрешность и интервал Цепные дроби Цепочка медиант Свойства интервалов Конечные...
Публикация, перевод с латыни, комментарии, указатели Р. Поспеловой. — Москва: Музыка, 2009. — 712 с. Книга представляет собой первое на русском языке научное исследование музыкально-теоретической системы Иоанна Тинкториса (ок. 1435 – 1511), знаменитого нидерландского музыкального теоретика, автора первого в истории музыки напечатанного музыкального словаря («Terminorum musicae...
Пер. с латин. Н.А. Алмазова. — СПб.: РАН, С.-Петерб. науч. центр, изд-во Нестор-История, 2007. — 273 с. — ISBN 978-598187-202-0. 15 апреля 2007 г. исполнилось 300 лет со дня рождения одного из величайших ученых всех времен, математика, механика, астронома, физика Леонарда Эйлера. Деятельность Л. Эйлера на протяжении более полувека была тесно связана с Петербургской академией...
Пер. с латин. Н.А. Алмазова. — СПб.: РАН, С.-Петерб. науч. центр; Нестор-История, 2007. — 273 с. — ISBN 978-598187-202-0. 15 апреля 2007 г. исполнилось 300 лет со дня рождения одного из величайших ученых всех времен, математика, механика, астронома, физика Леонарда Эйлера. Деятельность Л. Эйлера на протяжении более полувека была тесно связана с Петербургской академией наук....
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