This book introduces path-breaking applications of concepts from mathematical topology to music-theory topics including harmony, chord progressions, rhythm, and music classification. Contributions address topics of voice leading, Tonnetze (maps of notes and chords), and automatic music classification.Focusing on some geometrical and topological aspects of the representation and formalisation of musical structures and processes, the book covers topological features of voice...

This book presents original research applying mathematics to musical rhythm, with a focus on computational methods, theoretical approaches, analysis of rhythm in folk and global music traditions, syncopation, and maximal evenness. It honours the legacy of computer scientist and music theorist Godfried Toussaint.In addition to addressing a topic pioneered by Toussaint, application of mathematics to representation of musical rhythms, the volume also builds upon his interest in analys...

Organized Time is the first attempt to unite theories of harmony, rhythm and meter, and form under a common idea of structured time. Building off of recent advances in music theory in essential subfields-rhythmic theory, tonal structure, and the theory of musical form--author Jason Yust demonstrates that tonal music exhibits similar hierarchical organization in each of these dimensions. Yust develops a network model for temporal structure with an application of mathematical graph ...

How is the Beatles' "Help!" similar to Stravinsky's "Dance of the Adolescents?" How does Radiohead's "Just" relate to the improvisations of Bill Evans? And how do Chopin's works exploit the non-Euclidean geometry of musical chords? In this groundbreaking work, author Dmitri Tymoczko describes a new framework for thinking about music that emphasizes the commonalities among styles from medieval polyphony to contemporary rock. Tymoczko identifies five basic musical features that jointly contr...

Electronic music evokes new sensations, feelings, and thoughts in both composers and listeners. Opening the door to an unlimited universe of sound, it engages spatialization as an integral aspect of composition and focuses on sound transformation as a core structural strategy. In this new domain, pitch occurs as a flowing and ephemeral substance that can be bent, modulated, or dissolved into noise. Similarly, time occurs not merely as a fixed duration subdivided by ratios, but as a plastic...

A guided tour of the mathematical principles inherent in music.Taking a "music first" approach, Gareth E. Roberts's From Music to Mathematics will inspire students to learn important, interesting, and at times advanced mathematics. Ranging from a discussion of the geometric sequences and series found in the rhythmic structure of music to the phase-shifting techniques of composer Steve Reich, the musical concepts and examples in the book motivate a deeper s...

Ths Papaer outlines the newly discovered {@ April 2017} double intertwined Wave EQUATION for the Prime Numbers, which precisely explains the Randomness of the Prime and the Prime Gap Distribution. The Equation precisely describes the Primes as an Inter ference Wave Patttern and the reason it has been so difficult to determine is the length; for just the first 7 Prime Numbers the pattern length is >223 million.However, there are smaller patterns embedded into the larger picture, a little li...

This book explores the web of pitch relations that generates the musical language of non-serialized twelve-tone music and supplies both the analytical materials and methods necessary for analyses of a vast proportion of the 20th century musical repertoire. It does so in a simple, clear, and systematic manner to promote an easily accessible and global understanding of this music. Since the chromatic scale is the primary source for the pitch materials of 20th-century music, common sub-collec...

With musical scores and helpful charts, noted jazz educator and featured jazz soloist, Jerry Coker, gives the beginning performer and the curious listener insights into the art of jazz improvisation.Improvising Jazz gives the beginning performer and the curious listener alike insights into the art of jazz improvisation. Jerry Coker, teacher and noted jazz saxophonist, explains the major concepts of jazz, including blues, harmony, swing, and the characteris...

(Berklee Guide). Melody is a subject too often neglected in the teaching of music. This unique resource gives melody that attention it deserves, and proves that melody writing is a skill that can be learned. Through proven tool and techniques, you will learn to write interesting melodies, how melodic rhythm influences rhyme, what makes harmony progress, and the many dynamic relationships between melody and harmony. This clear and comprehensive approach to songwriting unlocks the secrets of...

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 interplay between these two ancient disciplines. The story is long as well as broad and involves physics, biology, psycho acoustics, the history of ...

This open-access textbook's significant contribution is the unified derivation of data-assimilation techniques from a common fundamental and optimal starting point, namely Bayes' theorem. Unique for this book is the "top-down" derivation of the assimilation methods. It starts from Bayes theorem and gradually introduces the assumptions and approximations needed to arrive at today's popular data-assimilation methods. This strategy is the opposite of most textbooks and reviews on data assimil...