In 1947 Friedrich Smend published a study claiming that J. S. Bach used a natural-order alphabet (A = 1 to Z = 24) in his works. He demonstrated that Bach incorporated significant words into his music, and provided himself with a symbolic compositional theme. Here, Dr Tatlow investigates the plausibility of Smend's claims with new evidence, challenging Smend's conclusions.

In the eighteenth century the universal harmony of God's creation and the perfection of the unity (1:1) were philosophically, morally and devotionally significant. Ruth Tatlow employs theoretical evidence and practical demonstrations to explain how and why Bach used numbers in his published compositions.

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.

Subjects covered include bibliographic tools of Bach research and sources of literature; Bach's family; Bach biographies; places Bach lived and worked; Bach's teaching; the liturgy; Bach source studies and the transmission of his music; repertory and editions; genres and individual vocal and instrumental works; performance practice; the reception and analysis of Bach's music; and many others.

The Ashgate Research Companion to Johann Sebastian Bach provides an indispensable introduction to the Bach research of the past thirty-fifty years. It is not a lexicon providing information on all the major aspects of Bach's life and work, such as the Oxford Composer Companion: J. S. Bach. Nor is it an entry-level research tool aimed at those making a beginning of such studies. The valuable essays presented here are designed for the next level of Bach research and are aimed at masters and doctoral students, as well as others interested in coming to terms with the current state of Bach research. Each author covers three aspects within their specific subject area; firstly, to describe the results of research over the past thirty-fifty years, concentrating on the most significant and controversial, such as: the debate over Smend's NBA edition of the B minor Mass; Blume's conclusions with regard to Bach's religion in the wake of the 'new' chronology; Rifkin's one-to-a-vocal-part interpretation; the rediscovery of the Berlin Singakademie manuscripts in Kiev; the discovery of hitherto unknown manuscripts and documents and the re-evaluation of previously known sources. Secondly, each author provides a critical analysis of current research being undertaken that is exploring new aspects, reinterpreting earlier assumptions, and/or opening-up new methodologies. For example, Martin W. B. Jarvis has suggested that Anna Magdalena Bach composed the cello suites and contributed to other works of her husband - another controversial hypothesis, whose newly proposed forensic methodology requires investigation. On the other hand, research into Bach's knowledge of the Lutheran chorale tradition is currently underway, which is likely to shed more light on the composer's choices and usage of this tradition. Thirdly, each author identifies areas that are still in need of investigation and research.

The enigmatic character of The Art of Fugue became apparent as early as in its first edition, printed more than a year after the composer’s death. Carl Philipp Emanuel Bach, who published both the first and the second editions, raised several unsolved questions regarding this opus. Anatoly P Milka presents a consistent and coherent solution to the unresolved questions about the history, structure and appearance of J.S. Bach’s The Art of Fugue, opening new perspectives for further exploration of this musical masterpiece. Milka challenges the present scholarly consensus that there exist two different versions of The Art of Fugue (the Autograph and the Original Edition) and argues that Bach had considered four versions, of which only two are apparent and have been discussed so far. Only Bach’s illness and death prevented him from fulfilling his plan and publishing a fourth, conclusive version of his opus.

For nearly two centuries Johann Sebastian Bach has been regarded as a cornerstone of Western musical culture. His music inspired subsequent generations of composers and philosophers alike, and continues to capture our imaginations in many ways. Bach studies is part of this picture, often seen as providing excellent examples of musicological scholarship. The volume editor has chosen thirty-one published articles which, in his view, not only represent a broad spectrum of the scholarly discussions on Bach's life and works, but will also facilitate the on-going study of Bach's creative genius. The articles have been selected to ensure that this volume will be considered useful for not only those students who are currently engaging in Bach studies at universities but also for more seasoned Bach scholars as they consider the future direction of Bach studies.

This book shows how information theory, probability, statistics, mathematics and personal computers can be applied to the exploration of numbers and proportions in music. It brings the methods of scientific and quantitative thinking to questions like: What are the ways of encoding a message in music and how can we be sure of the correct decoding? How do claims of names hidden in the notes of a score stand up to scientific analysis? How many ways are there of obtaining proportions and are they due to chance? After thoroughly exploring the ways of encoding information in music, the ambiguities of numerical alphabets and the words to be found “hidden” in a score, the book presents a novel way of exploring the proportions in a composition with a purpose-built computer program and gives example results from the application of the techniques. These include information theory, combinatorics, probability, hypothesis testing, Monte Carlo simulation and Bayesian networks, presented in an easily understandable form including their development from ancient history through the life and times of J. S. Bach, making connections between science, philosophy, art, architecture, particle physics, calculating machines and artificial intelligence. For the practitioner the book points out the pitfalls of various psychological fallacies and biases and includes succinct points of guidance for anyone involved in this type of research. This book will be useful to anyone who intends to use a scientific approach to the humanities, particularly music, and will appeal to anyone who is interested in the intersection between the arts and science. With a foreword by Ruth Tatlow (Uppsala University), award winning author of Bach’s Numbers: Compositional Proportion and Significance and Bach and the Riddle of the Number Alphabet. “With this study Alan Shepherd opens a much-needed examination of the wide range of mathematical claims that have been made about J. S. Bach's music, offering both tools and methodological cautions with the potential to help clarify old problems.” Daniel R. Melamed, Professor of Music in Musicology, Indiana University

The collection of essays represents a through and systematic study of Bach's B-minor Mass by leading scholars in the field and includes a range of discussions relating to the Mass's historical background and contexts, structure, sources and editions, and its reception in the late eighteenth and early nineteenth centuries.