Bach's Numbers

Bach's Numbers : Compositional Proportion and Significance

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In eighteenth-century Germany the universal harmony of God's creation and the perfection of its proportions still held philosophical, moral and devotional significance. Reproducing proportions close to the unity (1:1) across compositions could render them beautiful, perfect and even eternal. Using the principles of her groundbreaking theory of proportional parallelism and the latest source study research, Ruth Tatlow reveals how Bach used the number of bars to create numerical perfection across his published collections, and explains why he did so. The first part of the book illustrates the wide-ranging application of belief in the unity, showing how planning a well-proportioned structure was a normal compositional procedure in Bach's time. In the second part Tatlow presents practical demonstrations of this in Bach's works, illustrating the layers of proportion that appear within a movement, a work, between two works in a collection, across a collection and between collections.
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Product details

  • Hardback | 427 pages
  • 180 x 254 x 23mm | 1,010g
  • Cambridge, United Kingdom
  • English
  • 119 Tables, black and white; 8 Halftones, black and white; 1 Line drawings, black and white
  • 1107088607
  • 9781107088603
  • 2,524,468

Table of contents

Part I. Foundations: 1. Bach's numbers; 2. Symmetry, proportion and parallels; 3. Unity, proportions and universal harmony in Bach's world; 4. Bars, compositional planning and proportional parallelism; Part II. Demonstrations: 5. Three collections for strings; 6. Four in two collections for keyboard; 7. Two further collections for keyboard; 8. Two small late collections; 9. Two large late collections; 10. Collections of concertos; 11. Collections of organ works; 12. Great passions and cantatas; 13. Festive cut-and-paste projects: masses and oratorios; 14. Lost blueprints; Appendix 1. Chronological index of musical doctrine.
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Review quote

'[This book] takes in all Bach's major collections and more, including the two Passions, three Oratorios and the B minor Mass. In sheer extent and richness of background, and number of works examined, Tatlow's book is a most original and impressive achievement that will need to be taken into account in future discussions of these fascinating compositions.' David Ledbetter, Early Music 'For anyone who wishes to explore the logical pathways of Bach's genius, Tatlow's analysis gets to the heart of the aesthetic, theological and Pythagorean presuppositions underlying the Bachian concepts of 'Vollkommenheit', perfection through calculation; and 'Harmonie' ... the harmony of proportion, here a mirror of divine order.' Gian Mario Benzing, translated from Corriere della Sera (La Lettura) '... Tatlow's approach to the subject matter is unique, and the vigorousness with which her methodology is applied has uncovered numerous new and unexpected facts. Bach scholarship cannot ignore her voice.' Yo Tomita, Music and Letters ... Bach's Numbers clears the way for some promising new directions in Bach scholarship. Tatlow's work should be valued not only for what it suggests for future study, however, but for what it provides in its own right: a bold historical rendering of Bach's compositional process that forces us to view some of the composer's greatest works in a new light, and with deepened appreciation.' Robert L. Wells, Music Analysis
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About Ruth Tatlow

British-Swedish musicologist Ruth Tatlow is an independent scholar based in Stockholm. Her research into Bach's use of numbers led from her classic monograph Bach and the Riddle of the Number Alphabet (Cambridge, 1991) to its sequel Bach Numbers, through publications on methodology, inventive techniques and the theory of proportional parallelism. In 2004 she co-founded Bach Network UK (BNUK), establishing its open access web-journal Understanding Bach in 2006. She is currently Chair of the BNUK Council, joint editor of Understanding Bach, and a member of the Editorial Board of the American Bach Society. Her research has attracted awards and grants from numerous sources including the Swedish Research Council, the Royal Swedish Academy of Music, the Society of Authors of Great Britain, the British Council, The Hinrichsen Foundation, The Leverhulme Trust and the Royal Swedish Academy of Letters.
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