Music Experiment And Mathematics In England 1653 1705

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.

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.

This handbook explores the history of mathematics, addressing what mathematics has been and what it has meant to practise it. 36 self-contained chapters provide a fascinating overview of 5000 years of mathematics and its key cultures for academics in mathematics, historians of science, and general historians.

What is the relationship between Eros and music? How does the intersection of love and music contribute to define the perimeter of Early Modern love? The Early Moderns hold parallel discourses on the metaphysical doctrines of love and music as theories of harmony. Statements of love as music, of music as love, and of both as harmonic ideals, are found across a wide range of cultural contexts, highlighting the understanding of love as a cultural construct. The book assesses the complexity of cultural discourses on this linkage of Eros and music. The ambivalence of music as an erotic agent is enacted in the controversy over dancing and reflected in the ubiquitous symbolism of music instruments. Likewise, the trivialization of musical imagery in madrigal lyrics and love poetry highlights a sense of degradation and places the love-music relationship at the meeting point of two epistemes. The book also shows the symbolic deployment of the intertwined ideas of love and music in the English epyllion, and offers close readings of Shakespeare’s poems The Rape of Lucrece and Venus and Adonis. The book is the first to propose an overview of the theoretical, cultural and poetical intersections of Eros and music in Early Modern England. It discusses the connections in a richly interdisciplinary manner, drawing on a wealth of primary material which includes rhetoric, natural philosophy, educational literature, medicine, music theory and musical performance, dance books, performance politics, Protestant pamphlets and sermons, and emblem books.

This is a book guaranteed to make waves. It skilfully weaves the story of one key musical figure into the story of one key institution, which it then weaves into the general story of music in eighteenth-century England. Anyone reading it will come away with fresh knowledge and perceptions - plus a great urge to hear Cooke's music.' Michael Talbot, Emeritus Professor of Music at the University of Liverpool and Fellow of the British Academy. Amidst the cosmopolitan, fashion obsessed concert life of later eighteenth century London there existed a discrete musical counterculture centred round a club known as the Academy of Ancient Music. Now largely forgotten, this enlightened school of musical thinkers sought to further music by proffering an alternative vision based on a high minded intellectual curiosity. Perceiving only ear-tickling ostentation in the showy styles that delighted London audiences, they aspired to raise the status of music as an art of profound expression, informed by its past and founded on universal harmonic principles. Central to this group of musical thinkers was the modest yet highly accomplished musician-scholar Benjamin Cooke, who both embodied and reflected this counterculture. As organist of Westminster Abbey and conductor of the Academy of Ancient Music for much of the second half of the eighteenth century, Cooke enjoyed prominence in his day as a composer, organist, teacher, and theorist. This book shows how, through his creativity, historicism and theorising, Cooke was instrumental in proffering an Enlightenment-inspired reassessment of musical composition and thinking at the Academy. The picture portrayed counters the current tendency to dismiss eighteenth-century English musicians as conservative and provincial. Casting new and valuable light on English musical history and on Enlightenment culture more generally, this book reveals how the agenda for musical advancement shared by Cooke and his Academy associates foreshadowed key developments that would mould European music of the nineteenth century and after. It includes an extensive bibliography, a detailed overview of the Cooke Collection at the Royal College of Music and a complete list of Cooke's works. TIM EGGINGTON is College Librarian at Queens' College, Cambridge.

John Birchensha (c.1605-?1681) is chiefly remembered for the impression that his theories about music made on the mathematicians, natural philosophers and virtuosi of the Royal Society in the 1660s and 1670s, and for inventing a system that he claimed would enable even those without practical experience of music to learn to compose in a short time by means of 'a few easy, certain, and perfect Rules'-his most famous composition pupil being Samuel Pepys in 1662. His great aim was to publish a treatise on music in its philosophical, mathematical and practical aspects (which would have included a definitive summary of his rules of composition), entitled Syntagma music Subscriptions for this book were invited in 1672-3, and it was due to be published by March 1675; but it never appeared, and no final manuscript of it survives. Consequently knowledge about his work has hitherto remained extremely sketchy. Recent research, however, has brought to light a number of manuscripts which allow us at last to form a more complete view of Birchensha's ideas. Almost none of this material has been previously published. The new items include an autograph treatise of c.1664 ('A Compendious Discourse of the Principles of the Practicall & Mathematicall Partes of Musick') which Birchensha presented to the natural philosopher Robert Boyle, and which covers concisely much of the ground that he intended to cover in Syntagma musica detailed synopsis for Syntagma musichich he prepared for a meeting of the Royal Society in February 1676; and an autograph notebook (now in Brussels) containing his six rules of composition with music examples, presumably written for a pupil. Bringing all this material together in a single volume will allow scholars to see how Birchensha's rules and theories developed over a period of fifteen years, and to gain at least a flavour of the lost Syntagma music

This is the second volume in a two-part set on the writings of Thomas Salmon. Salmon (1647-1706) is remembered today for the fury with which Matthew Locke greeted his first foray into musical writing, the Essay to the Advancement of Musick (1672), and the near-farcical level to which the subsequent pamphlet dispute quickly descended. Salmon proposed a radical reform of musical notation, involving a new set of clefs which he claimed, and Locke denied, would make learning and performing music much easier (these writings are the subject of Volume I). Later in his life Salmon devoted his attention to an exploration of the possible reform of musical pitch. He made or renewed contact with instrument-makers and performers in London, with the mathematician John Wallis, with Isaac Newton and with the Royal Society of London through its Secretary Hans Sloane. A series of manuscript treatises and a published Proposal to Perform Musick, in Perfect and Mathematical Proportions (1688) paved the way for an appearance by Salmon at the Royal Society in 1705, when he provided a demonstration performance by professional musicians using instruments specially modified to his designs. This created an explicit overlap between the spaces of musical performance and of experimental performance, as well as raising questions about the meaning and the source of musical knowledge similar to those raised in his work on notation. Benjamin Wardhaugh presents the first published scholarly edition of Salmon's writings on pitch, previously only available mostly in manuscript.

During a period of tumultuous change in English political, religious and cultural life, music signified the unspeakable presence of the divine in the world for many. What was the role of music in the early modern subject's sensory experience of divinity? While the English intellectuals Peter Sterry (1613-72), Richard Roach (1662-1730), William Stukeley (1687-1765) and David Hartley (1705-57), have not been remembered for their 'musicking', this book explores how the musical reflections of these individuals expressed alternative and often uncustomary conceptions of God, the world, and the human psyche. Music is always potentially present in their discourse, emerging as a crucial form of mediation between states: exoteric and esoteric, material and spiritual, outer and inner, public and private, rational and mystical. Dixon shows how Sterry, Roach, Stukeley and Hartley's shared belief in truly universal salvation was articulated through a language of music, implying a feminising influence that set these male individuals apart from contemporaries who often strictly emphasised the rational-i.e. the supposedly masculine-aspects of religion. Musical discourse, instead, provided a link to a spiritual plane that brought these intellectuals closer to 'ultimate reality'. Theirs was a discourse firmly rooted in the real existence of contemporary musical practices, both in terms of the forms and styles implied in the writings under discussion and the physical circumstances in which these musical genres were created and performed. Through exploring ways in which the idea of music was employed in written transmission of elite ideas, this book challenges conventional classifications of a seventeenth-century 'Scientific Revolution' and an eighteenth-century 'Enlightenment', defending an alternative narrative of continuity and change across a number of scholarly disciplines, from seventeenth-century English intellectual history and theology, to musicology and the social history of music.