The Discovery of Musical Equal Temperament in China and Europe in the Sixteenth Century

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This study provides little-known mathematical, musicological and scientific facts regarding the discovery of musical equal temperament, and narrates the circumstances of the discovery in the historical and cultural contexts of the period (mid 16th to early 17th centuries) which, in turn, is placed in the intellectual chronology of the Eastern and Western worlds. By offering documentary evidence and information not found in Western publications, the book invites the reader to see the mathematics of the equal temperament and its discovery in an entirely new light.


“The author is fully conversant and equally at home with both the Eastern and Western cultural and scholastic environments. He therefore possesses a unique qualification as an objective scholar to address and assess the issues by drawing from his wide ranging knowledge in cultural history and scientific philosophy of both hemispheres…. Without doubt, the present work is one of the most thorough, convincing, and absorbing of the documents this writer has read in recent years on the topic….demonstrates his tenacity of research, the credence of finding, and his sound discernment.” – Dai Nianzu, Senior Fellow, The Chinese Academy of Sciences

Table of Contents

Table of contents:
Preface by Professor Dai Nianzu
Foreword; Introduction
Part One: Music and Cosmology in Ancient Civilizations
1. Music and Man
2. Knowledge and Learning in Early Civilization
3. The Rise of the Caste of Lunarians
4. Numerology and Geometria (Gematria)
5. The Quadrivium and Scholasticism
Part Two: The Meeting of the Eastern and Western Minds
6. From Empiricism to Experimentation
7. The Wise Men from the West
8. The Saga of Matteo Ricci and the Early Jesuits in China
Part Three: The Quest, the East and the West
9. Chinese Experiments (Synopsis of Tonal Theory in China; Zhu Zaiyu, Philosophical Mathematician)
10. Western Experiments (Synopsis of Tonal Theory in Europe; Simon Stevin, Pragmatic Mathematician)
11. The Reception of Theory of Equal Temperament (Stevin’s Theory; Zhu’s Theory)
12. A Coalescence of Eastern and Western Minds, and the Question of the Transmission of Zhu’s Theory
Postscript: the Cosmology and Ecumenism of Equal Temperament
Appendices: Chronological Listing of Zhu Zaiyu’s Published Works; Chronology of Notable Scientific and Cultural Events in Europe and China from 1500-1600, as Related to the Present Study; Selected Authors and Treatises in Alphabetical Order, with Chinese Ideogram

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