How, in 1705, was Thomas Salmon, a parson from Bedfordshire, able to persuade the Royal Society that a musical performance could constitute a scientific experiment? Or that the judgement of a musical audience could provide evidence for a mathematically precise theory of musical tuning? This book presents answers to these questions. It constitutes a general history of quantitative music theory in the late seventeenth century as well as a detailed study of one part of that history: namely the applications of mathematical and mechanical methods of understanding to music that were produced in England between 1653 and 1705, beginning with the responses to Descartes's 1650 Compendium musicand ending with the Philosophical Transactions' account of the appearance of Thomas Salmon at the Royal Society in 1705. The book is organized around four key questions. Do musical pitches form a small set or a continuous spectrum? Is there a single faculty of hearing which can account for musical sensation, or is more than one faculty at work? What is the role of harmony in the mechanical world, and where can its effects be found? And what is the relationship between musical theory and musical practice? These are questions which are raised and discussed in the sources themselves, and they have wide significance for early modern theories of knowledge and sensation more generally, as well as providing a fascinating side light onto the world of the scientific revolution.

The author displays versatile cases of the intersection of music and mathematics, moving from philosophical and aesthetic considerations about «mathesis» to practical studies, discussing the interaction between music and other arts, and providing a practical research of contemporary music compositions.

How, in 1705, was Thomas Salmon, a parson from Bedfordshire, able to persuade the Royal Society that a musical performance could constitute a scientific experiment? Or that the judgement of a musical audience could provide evidence for a mathematically precise theory of musical tuning? This book presents answers to these questions. It constitutes a general history of quantitative music theory in the late seventeenth century as well as a detailed study of one part of that history: namely the applications of mathematical and mechanical methods of understanding to music that were produced in England between 1653 and 1705, beginning with the responses to Descartes's 1650 Compendium music?and ending with the Philosophical Transactions' account of the appearance of Thomas Salmon at the Royal Society in 1705. The book is organized around four key questions. Do musical pitches form a small set or a continuous spectrum? Is there a single faculty of hearing which can account for musical sensation, or is more than one faculty at work? What is the role of harmony in the mechanical world, and where can its effects be found? And what is the relationship between musical theory and musical practice? These are questions which are raised and discussed in the sources themselves, and they have wide significance for early modern theories of knowledge and sensation more generally, as well as providing a fascinating side light onto the world of the scientific revolution.

During the past 40 years, mathematical music theory has grown and developed in both the fields of music and mathematics. In music pedagogy, the need to analyze patterns of modern composition has produced Musical Set Theory, and the use of Group Theory and other modern mathematical structures have become almost as common as the application of mathematics in the fields of engineering or chemistry. Mathematicians have been developing stimulating ideas when exploring mathematical applications to established musical relations. Mathematics students have seen in Music in Mathematics courses, how their accumulated knowledge of abstract ideas can be applied to an important human activity while reinforcing their dexterity in Mathematics. Similarly, new general education courses in Music and Mathematics are being developed and are arising at the university level, as well as for high school and general audiences without requiring a sophisticated background in either music nor mathematics. Mathematical Music Theorists have also been developing exciting, creative courses for high school teachers and students of mathematics. These courses and projects have been implemented in the USA, in China, Ireland, France, Australia, and Spain.The objective of this volume is to share the motivation and content of some of these exciting, new Mathematical Theory and Music in Mathematics courses while contributing concrete materials to interested readers.

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 to sound production by traditional instruments or by digital means. Modern music theory has been incorporating more and more mathematical content during the last decades. This book offers a journey into recent work relating music and mathematics. It contains a large variety of articles, covering the historical aspects, the influence of logic and mathematical thought in composition, perception and understanding of music and the computational aspects of musical sound processing. The authors illustrate the rich and deep interactions that exist between Mathematics and Music.

This volume comprises a selection of papers presented at the first International C- ference on Mathematics and Computation in Music – mcm2007. The conference took place at the Staatliches Institut für Musikforschung PK – National Institute for Music Research in Berlin during May 18–20, 2007 and was jointly organized by the National Institute for Music Research Berlin and the Society of Mathematics and Computation in Music. The papers were selected for the conference by the program committee and classfied into talks and posters. All papers underwent further selection, revision and elaboration for this book publication. The articles cover a research field which is heterogeneous with respect to content, scientific language and methodology. On one hand, this reflects the heterogeneity and richness of the musical subject domain itself. On the other hand, it exemplifies a t- sion which has been explicitly intended by both the organizers and the founders of the society, namely to support the integration of mathematical and computational - proaches to music theory, composition, analysis and performance. The subdivision into three parts reflects the original structure of the program. These parts are opened by invited papers and followed by talks and posters.

Selected Contributed Papers of the Tenth International Congress of Logic, Methodology and Philosophy of Science, Florence, August 1995