Historical Tuning of Keyboard Instruments:
Theory and Practice

Historical Tuning Book

This book clearly and concisely presents essential concepts to provide a historical, theoretical, and practical understanding of tuning systems and a strong foundation for future study.

Contents Include:

• Basic theory of vibrations and relationships of frequencies of musical intervals clearly and simply explained.

• Construction of musical scales using Pythagorean, meantone, equal-temperament, and well-temperament systems.

• All of the mathematical relationships, frequencies, and beat rates for each of the above systems.

• The historical and practical reasons for using each of the above systems.

• Methods of actually achieving each of the above tunings and temperaments on a harpsichord or piano.

• A complete mathematical derivation and explanation of the use and ways of calculating cents of various intervals and commas.

• Many exercises for readers to test and reinforce their understanding. Answers to these exercises are in the back of the book.

• An explanation of why the piano keybord has its conventional pattern.

• A high-precision method of tuning a guitar using beats of harmonics.

74 pages, 8.5" x 11"; soft cover with comb binding that lies flat; and a substantial number of diagrams, tables, and illustrations of tuning schemes. Arranged and indexed for easy reference. ISBN 0-9645919-1-X. Price: $20.00.

Download a PDF file of the chapter on Well Temperament of this book


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About the Author:


Robert Chuckrow at Piano

Robert Chuckrow (born in 1936) has a Ph.D. in experimental physics, which he received from New York University in 1969, and has taught physics at New York University, The Cooper Union, and The Fieldston School in Riverdale, New York. He has taught courses in the physics of sound at both NYU and Fieldston. He has built two harpsichords and a clavichord and has restored a number of old keyboard instruments. He has studied T’ai Chi since 1970 and has taught it extensively. He has written four other books, one on weight-loss and diet, one on Tai Chi Walking, and two others on T’ai Chi. His The Tai Chi Book was an Independent Publisher’s Book Award finalist in health and medicine. His most-recent book, Tai Chi Dynamics, was honored in the martial arts / alternative health category by the Independent Publisher Online Magazine Highlighted Title Program and won the best-book award in health: exercise and fitness from USA Book News.

For Robert Chuckrow’s website on T’ai Chi, which includes thought-provoking, unconventional articles on T’ai Chi and other health-related subjects such as nutrition and natural weight-loss, click: http://www.chuckrowtaichi.com


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