About the Author
Chalmers is recognized as the "guru" of tuning theory.
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1 of 1 people found the following review helpful:
5.0 out of 5 stars
important point about ratios and cents,
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This review is from: Divisions of the Tetrachord (Paperback)
While the review above is correct in clarifying the 498 vs. 500 cents issue, I thought it important to point out that the call to use the "exact cents value" for a ratio is misguided: the ratio 4/3 does not have an exact cents value, and this is really the crucial point. To 7 decimal places, 4/3 is 498.0449991 cents. This is close enough to 498.045 that we should be OK using that, but any cents value is only an approximation of a ratio, and vice versa. Anyway, Chalmers's book is an encyclopedic account of the multifarious tunings proposed by ancient and medieval authors, and importantly, it also includes proposals from the Islamicate world which found their way into Europe after the Moorish conquest of Spain and the Crusades.
1 of 1 people found the following review helpful:
4.0 out of 5 stars
exhausive, though with a couple irritants,
This review is from: Divisions of the Tetrachord (Paperback)
Chalmers here goes on an extremely comprehensive exploration of a long-forgotten (but highly interesting as a field of study) building block of ancient music: the tetrachord, more commonly known as the fourth. In ancient Greece, the fourth was divided into any number of different types of division, depending on the regional or philosophical or mathematical taste prevalent, and various "flavors" were in fashion from one period to the next.As a tool for the aspiring pure, or just, intonation enthusiast interested in the historiography of ancient tuning systems, this book is a treasure. It does, however, have a couple minor flaws. First, a pure fourth, based on a simple harmonic ratio of 4/3, has a value of about 498 cents, not the even-tempered 500 that he uses throughout the book. This may seem like a completely geeky bit of arcana, but the distinction is more important than mere esotery: if we are to discuss intervals as whole-number ratios, we have to give their exact equivalent in cents, not the nearest approximation in equal temperament. People fought for centuries about how to define certain intervals; we do them injustice if we gloss over that precision. I suppose that should serve as a sort of primer for you: if you're the sort of person who would care (or even know) about the difference between 498 and 500 cents, this book will be invaluable. If you don't care, you should probably spend your time reading something else.
5.0 out of 5 stars
Available free from the publisher!,
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This review is from: Divisions of the Tetrachord (Paperback)
This is an amazingly informative book from a man who never gets bored with the subject. It is encyclopedic, as others have said, but it also has observations on the relevance of the tetrachord, not just a catalog (although it has that too). Many of the ancient Greek theorists had completely different reasonings and systems for tuning the various modes, but they were largely attempting to explain what was already being practiced by musicians; meaning that, for the most part, musicians weren't studying these guys' works to learn how to tune their instruments, they were just tuning them, and these guys came along and wanted to know why they used those notes. So there were plenty of proposed explanations, which together form a great introduction to musical tuning.BUT read it FREE online! The book sold for FAR LESS than $[...] when it was in print! [...]
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