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Mathematical Music Theory: Algebraic, Geometric, Combinatorial, Topological And Applied Approaches To Understanding Musical Phenomena
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 mathematical content. One example is the application of methods from Algebraic Combinatorics, or Topology and Graph Theory, to the classification of different musical objects. However, these applications of mathematics in the understanding of music have also led to interesting open problems in mathematics itself.The reach and depth of the contributions on mathematical music theory presented in this volume is significant. Each contribution is in a section within these subjects: (i) Algebraic and Combinatorial Approaches; (ii) Geometric, Topological, and Graph-Theoretical Approaches; and (iii) Distance and Similarity Measures in Music.
A Compendium Of Musical Mathematics
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 chapter, we tackle the question of the classification of chords and scales. Chapter 2 is a mathematical presentation of David Lewin's Generalized Interval Systems. Chapter 3 offers a new theory of diatonicity in equal-tempered universes. Chapter 4 presents the Neo-Riemannian theories based on the work of David Lewin, Richard Cohn and Henry Klumpenhouwer. Chapter 5 is devoted to the application of word combinatorics to music. Chapter 6 studies the rhythmic canons and the tessellation of the line. Chapter 7 is devoted to serial knots. Chapter 8 presents combinatorial designs and their applications to music. The last chapter, chapter 9, is dedicated to the study of tuning systems.
Flora Capensis
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Portraying Cicero in Literature, Culture, and Politics
Cicero has played a pivotal role in shaping Western culture. His public persona, his self-portrait as model of Roman prose, philosopher, and statesman, has exerted a durable and profound impact on the educational system and the formation of the ruling class over the centuries. Joining up with recent studies on the reception of Cicero, this volume approaches the figure of Cicero from a ‘biographical’, more than ‘philological’, perspective and considers the multiple ways by which different ages reacted to Cicero and created their ‘Ciceros’. From Cicero’s lifetime to our times, it focuses on how the image of Cicero was revisited and reworked by intellectuals and men of culture, wh...
Developments in Language Theory
This book constitutes the proceedings of the 19th International Conference on Developments in Language Theory, DLT 2015, held in Liverpool, UK. The 31 papers presented together with 5 invited talks were carefully reviewed and selected from 54 submissions. Its scope is very general and includes, among others, the following topics and areas: combinatorial and algebraic properties of words and languages, grammars, acceptors and transducers for strings, trees, graphs, arrays, algebraic theories for automata and languages, codes, efficient text algorithms, symbolic dynamics, decision problems, relationships to complexity theory and logic, picture description and analysis, polyominoes and bidimensional patterns, cryptography, concurrency, cellular automata, bio-inspired computing, and quantum computing.
Algebra
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Harvard Studies in Classical Philology, Volume 89
This volume of thirteen essays includes "Herodotean Cruces," by Robert Renehan; "Wine, Water, and Callimachean Polemics," by Peter Knox; "Vindiciae Horatianae," by D. R. Shackleton Bailey; "The Libri Reconditi," by Jerzy Linderski; and "A Lousy Conjecture: Housman to Phillimore," by Alan Cameron.
