This book constitutes the thoroughly refereed proceedings of the 8th International Conference on Mathematics and Computation in Music, MCM 2022, held in Atlanta, GA, USA, in June 2022. The 29 full papers and 8 short papers presented were carefully reviewed and selected from 45 submissions. The papers feature research that combines mathematics or computation with music theory, music analysis, composition, and performance. They are organized in Mathematical Scale and Rhythm Theory: Combinatorial, Graph Theoretic, Group Theoretic and Transformational Approaches; Categorical and Algebraic Approaches to Music; Algorithms and Modeling for Music and Music-Related Phenomena; Applications of Mathematics to Musical Analysis; Mathematical Techniques and Microtonality
This study demonstrates how smooth voice leading in music can be effectively modeled using concepts from abstract algebra. Minute voice-leading displacements are explained as iterations of the basic operation, the single-semitone transformation (SST). The SST is a type of transformation in which only a single voice in a chord is transposed by a semitone. Unlike previous music theoretic studies, the SST model does not rely on twelve-tone operations on sets to determine voice-leading paths. SST-succession classes can then be defined; they allow SSTs to be generalized as parsimonious voice-leading relations between pair-ordered set classes. Voice leading between chords of different “sizes” can be obtained through split and fuse operations. Once a mathematical basis for smooth voice-leading is formalized, 3D graphical representations in the form of lattices of parsimoniously related chord types can be developed. The study compares the single-voice transformational model to transformational theories of atonal voice leading and to recent work in the emergent field of neo-Riemannian theory. The final chapter examines music from tonal, atonal, and “post-atonal” stylistic periods by Chopin, Scriabin, Webern, Paul Lansky, and John Adams, showing the new voice-leading model’s versatility as an analytical tool.
Anton Webern: A Research and Information Guide offers carefully selected and annotated sources regarding Webern from 1975 to present day, including sources on Webern’s life, his music, and the interpretation and reception of his music. Along with this comprehensive annotated listing of print and online sources, the book discusses the history of research on Webern and includes a brief chronology of his life. It is a major reference tool for those interested in Webern and his music and valuable for researchers of 20th century music and the Second Viennese School.
Tonality and Transformation is a groundbreaking study in the analysis of tonal music. Focusing on the listener's experience, author Steven Rings employs transformational music theory to illuminate diverse aspects of tonal hearing - from the infusion of sounding pitches with familiar tonal qualities to sensations of directedness and attraction. In the process, Rings introduces a host of new analytical techniques for the study of the tonal repertory, demonstrating their application in vivid interpretive set pieces on music from Bach to Mahler. The analyses place the book's novel techniques in dialogue with existing tonal methodologies, such as Schenkerian theory, avoiding partisan debate in favor of a methodologically careful, pluralistic approach. Rings also engages neo-Riemannian theory-a popular branch of transformational thought focused on chromatic harmony-reanimating its basic operations with tonal dynamism and bringing them into closer rapprochement with traditional tonal concepts.Written in a direct and engaging style, with lively prose and plain-English descriptions of all technical ideas, Tonality and Transformation balances theoretical substance with accessibility: it will appeal to both specialists and non-specialists. It is a particularly attractive volume for those new to transformational theory: in addition to its original theoretical content, the book offers an excellent introduction to transformational thought, including a chapter that outlines the theory's conceptual foundations and formal apparatus, as well as a glossary of common technical terms. A contribution to our understanding of tonal phenomenology and a landmark in the analytical application of transformational techniques, Tonality and Transformation is an indispensible work of music theory.
David Lewin's Generalized Musical Intervals and Transformations is recognized as the seminal work paving the way for current studies in mathematical and systematic approaches to music analysis. Lewin, one of the 20th century's most prominent figures in music theory, pushes the boundaries of the study of pitch-structure beyond its conception as a static system for classifying and inter-relating chords and sets. Known by most music theorists as "GMIT", the book is by far the most significant contribution to the field of systematic music theory in the last half-century, generating the framework for the "transformational theory" movement. Appearing almost twenty years after GMIT's initial publication, this Oxford University Press edition features a previously unpublished preface by David Lewin, as well as a foreword by Edward Gollin contextualizing the work's significance for the current field of music theory.
Generalized Musical Intervals and Transformations is by far the most significant contribution to the field of systematic music theory in the last half-century, generating the framework for the "transformational theory" movement.
Reconstructing historical conceptions of harmonic distance, Audacious Euphony advances a geometric model appropriate to understanding triadic progressions characteristic of 19th-century music. Author Rick Cohn uncovers the source of the indeterminacy and uncanniness of romantic music, as he focuses on the slippage between chromatic and diatonic progressions and the systematic principles under which each operate.
'Transformational analysis in practice' is a Must-Have for everyone working in the field or aspiring to develop their music-analytical and theoretical skills in transformational theory. This co-authored book puts together a plethora of analytical studies, diverse both in the repertoires covered and the methodologies employed. It is a much-needed anthology in this sub-field of music analysis, which has been developing and growing in recent years, reaching ever wider outlets in English-speaking countries and beyond, from dedicated conference panels to YouTube videos. The book is divided into four parts based on the repertoires under discussion. Part I encompasses four analytical studies on familiar composers from the European Romanticism of the nineteenth century. Part II analyzes the music of less familiar composers from Brazil and Turkey. Part III offers four contrasting ways to adapt the analytical capabilities of neo-Riemannian theory to the post-tonal music of the twentieth century. Catering to the interests of jazz performers and researchers, as well as those into popular music production, Part IV offers transformational analytical approaches to both notated and improvised jazz, emphasizing John Coltrane’s performance. Providing an invaluable synthesis of a wide range of analytical studies, this book will be an essential companion for many musicology students, as well as for performers and composers.
