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Musical Mathematics is the definitive tome for the adventurous musician. Integrating mathematics, music history, and hands-on experience, this volume serves as a comprehensive guide to the tunings and scales of acoustic instruments from around the world. Author, composer, and builder Cris Forster illuminates the mathematical principles of acoustic music, offering practical information and new discoveries about both traditional and innovative instruments.With this knowledge readers can improve, or begin to build, their own instruments inspired by Forster's creationsshown in 16 color plates. For those ready to step outside musical conventions and those whose curiosity about the science of sound is never satisfied, Musical Mathematics is the map to a new musical world.
- Sales Rank: #476685 in Books
- Brand: Brand: Chronicle Books
- Published on: 2010-07-14
- Original language: English
- Number of items: 1
- Dimensions: 11.25" h x 2.00" w x 9.00" l, 5.40 pounds
- Binding: Hardcover
- 952 pages
- Brand Name: Baker and Taylor Mfg#: 9780811874076
- Shipping Weight: 5.45 lbs
- Manufacturer:
- Genre:
- All music products are properly licensed and guaranteed authentic.
About the Author
Cris Forster is a musical instrument builder, composer, and scholar. He lives in San Francisco.
Most helpful customer reviews
13 of 13 people found the following review helpful.
Essential Reading for Musicians, Makers & Listeners
By John Schneider
Musical Mathematics: On the Art and Science of Acoustic Instruments
by Cris Forster
Sir Thomas Beecham once famously quipped that, "...the British public doesn't really understand music, they just like the noise that it makes." Sadly, the same can be said for most musicians when it comes to their instruments. We all spend untold hours dealing with HOW to play them, but rarely consider WHY these marvelous inventions do what they do. In fact, the simplest concepts of rhythm, pitch, & volume, the basic building blocks of music, are all determined by numbers. But the very nature of instruments themselves - the scales they play, the colors they produce, how well they project their sound...all of these elements are also deeply determined by math. For thousands of years, this has been the realm of the instrument builder, who, more often than not, relied on intuition and received knowledge to practice their craft. Now Cris Forster has cracked the code, and reveals with uncanny scientific accuracy the principles behind instrument design, the vibrations of strings, bars and tubes and the very scales they produce.
This is not the work of some ivory tower theorist, a mathematician with music as an after hours hobby. This author has sawdust in his hair and the strong hands of an artisan, having earned this knowledge the hard way, spending decades creating museum quality instruments of striking originality. He begins with basic principles: how do strings, rods & bars vibrate? We get the mathematics for all of these, and their application on real musical instruments. These formulae are absolutely essential for luthiers & craftsman, who will be amazed that the author has also created a new method for measuring Mass called the Mica mass unit. This revolutionary approach will save builders hours of time when measuring materials by bypassing conversions from the traditional English mass unit to a new inch-based unit. This new discovery is so important that the book begins with it's explanation, which may scare off quite a few non-numerate readers, but for many, it alone will be ample reason to own this groundbreaking volume.
The realm of Music Theory (remember it's antique name: `Musical Science'?) has always promised to explain the magic of music by parsing the mystical alchemies of melody & harmony. But it has really only been in the past generation that we have developed the tools to adequately explain the complex interaction between mechanical vibration and human perception. The mathematics of human hearing are explained (how we really hear), as are the methods and units used to accurately measure pitch. It is now common knowledge that the twelve equal-tempered tones of Western music are but a few of the hundreds available to the musician. How we have arrived at this historic compromise is a fascinating story that the author reveals in exquisite detail, tracing the trajectory from the ancient Greeks (Archytas, Ptolemy, Pythagoras, Aristoxenes et al) through the Renaissance & Baroque eras, to the present day. Happily, Forster is also multilingual, translating many critical primary and secondary texts previously unavailable to the English reading public. Of course the mathematical complexities behind meantone tunings and the numerous evolutionary well-temperaments are explored in great depth before we arrive at modern equal temperament, a tuning so challenging that it's adoption over a century ago created a new profession: the piano tuner. Previously, tunings were simple enough to be done by the instrument's owners, since most included many pure intervals of Just Intonation, another subject discussed at great length and of profound importance to the development of both the language of music and its instruments.
The beauty of Forster's presentation is not only the length and depth to which he goes to explain the history and detail of these fascinating European tunings, which have all but determined the very repertoire that we hold so dear, but that is only the beginning: the section on World Tunings is alone worth the price of admission. The author admits:
"Long before I began writing this book, I envisioned discussing Chinese, Indonesian, Indian, and Arabian tuning theory in the same breath as Greek and Renaissance tuning theory. Why not? Music is a universal language not only because human beings have ears and a desire to make music, but also because people all over the world cultivate and investigate the subject of musical mathematics."
What follows is over 300 pages of superb detail devoted to the notes of the ch'in, fretting of Arabic `ud (Al Farabi, Ibn-Sina, Al-Kindi et al), various pelog & slendro scales of Indonesia, the Turkish tunbur, Indian vina, sarangi & sitar and more.
If you have ever pondered the intricate diversities of the Arabic maqam or Persian dastgah you will find them not only beautifully diagrammed and explained, but also compared and contrasted, a clearly 21st century approach that embraces our increasingly global musical resources. How do the ancient Greek modes compare with the ragas of India? Look no further. And these are not simply diagrams of the results of research - in most cases the scores of tuning tables include the musician's original descriptions of their tunings, not just the results. In other words, we benefit from the exact description of ancient modes in modern terminology (ratios & cents), but also get specific instructions as to how they were achieved in contemporary practice, regardless of century. The result? A truly three dimensional view of our shared musical heritage.
Musical Mathematics culminates in the tunings and instruments that Forster knows best: his own. Though his credo is simple: "I build because the tunings and timbres I want to hear do not exist on store shelves", the results are anything but. From the extraordinary double-sided spinning Chrysalis to the elegant choreography of the Glassdance, Forster's instruments glisten with originality. Of course the canons and marimbas immediately recall the instruments of Harry Partch (1901-1974), and the connection is not casual, since the author spent several years as the curator for the Harry Partch Foundation, eventually rebuilding the entire `orchestra' of original instruments. Forster's versions, however, transcend the originals in both skill & scope, expanding the tonal resources to include pitches based on the 13th harmonic of the overtone series (Partch's stopped at the 11th), and reaching a stunning level of craftsmanship that one can only described as first-class.
What's missing? The most obvious thing of all: sound. A compact disc or two would have gone a long way towards making these numbers live. If ears could salivate, yours will be drooling at the chance to actually taste these vibrational delicacies, having read about them in such detail. Luckily, Forster's own music can be heard in over a dozen mp3 excerpts found on the website [...] Or, if seeing is believing, look no further than the Chryalis Foundation's recent DVD A Voyage in Music to see the instruments in action and meet the man that made them, as well as the people that play them.
There are also several compositions from various traditions that have been painstakingly transcribed from recordings. Sadly, several of these musical jewels are long since out-of-print, and though the author helpfully includes all references to those still available, it would be both costly and time-consuming to recreate his extraordinary listening library. Clearly, a compilation disc would be an excellent supplement to the book. As for the pages & pages of scales, modes, dastgah, raga, etc., it would surely have taken another few years to actually record all of the material, let alone on the appropriate instruments. Perhaps the answer as to why this was not done can be found in Chapter 13: "Building a Little Canon" - it seems as if the author is challenging the reader to make a little sawdust themselves if they want taste the fruits of all of this hard-earned knowledge!
Musical Mathematics is essential reading for anyone interested in music, innumerate or not. For the builder, it's details are simply indispensable. For the musician, the historical and practical perspective on the materials of music should be basic reading. This is surely the guidebook for 21st century musicmaking, and as such, belongs in every library. Where Partch's Genesis of a Music is in uequal parts a manifesto, autobiography, intonation history & cookbook (yes, you really can recreate the instruments with those recipes), it's author once admitted that the pioneering work was written for the rebellious young man that he was back in the 1920's. Forster's Musical Mathematics is clearly the next step: it goes deeper and farther than Genesis, keeps the editorializing to a minimum (though when it comes, it is no less piquant & provocative), and offers sophisticated & exactly practical answers to anyone daring to pick up a piece of wood or wire and ask those materials to make music. Whereas Partch was a self-proclaimed "Philosophic music man seduced into carpentry", Forster is surely a craftsman of the highest order, seduced into mathematics to answer his own burning questions as to how physical and musical materials behave, in order to bring them to the highest level of perfection. We will be thankful for generations to come that he took a decade of his own productive life to write down the conclusions.
- John Schneider, KPFK, Los Angeles
Director of MicroFest [...]
5 of 5 people found the following review helpful.
Kraig Grady's review of Musical Mathematics
By Terumi Narushima
Musical Mathematics by Cris Forster is a rigorous and highly organized book that deals with the construction and tuning of acoustic instruments. In a clear and graspable way, the book first tackles the physics of instruments, a subject that is often the greatest stumbling block for readers interested in building instruments of their own design. After a detailed examination of the subject of mass, Forster guides us through his knowledge of strings, which includes their physical properties and different usages on musical instruments. Only in retrospect does one realize what a careful choice as a starting point this is because it easily leads us to a more complex study of bars, rods, and tubes. Resonators follow, with thematic connections that reach back to earlier chapters and forward to air columns and flutes. A chapter on geometric progressions, logarithms, and cents concludes the first part of the book, and at the same time acts as a bridge to the study of tunings. The second part presents the reader with a strong foundation of the history of tuning in Western civilization and throughout the world, and the methods employed to realize these tunings. The book ends with an examination of Forster's own instruments, which are extremely beautiful in both design and sound. He remains one of the greatest practitioners among instrument builders.
Although I have spent many years in the field, I discovered in Musical Mathematics a fresh and above all generous presentation of knowledge both with regard to acoustics and the history of scales. For example, the chapter on Chinese music discusses an approach to string tuning that I have never encountered in any other sources. Because of his own translations from other languages, Forster's research is not limited to English texts; for this reason, his book is filled with many new sources that provide fresh perspectives of the historical record. The subjects of Indonesian, Indian, Arabian, Persian, and Turkish tunings are likewise treated with much care and depth. Perhaps the book might be compared to Harry Partch's Genesis of a Music, but there are marked differences. The latter was written to explain Partch's music and instruments, and only secondarily to help others build their own unique instruments. Musical Mathematics, on the other hand, focuses more on the needs of creative individuals; it encourages musicians to discover and explore aspects that are most useful and fruitful to their own work. It is toward this goal that Forster shares the benefit of his knowledge and experience.
Yes, here is a book I surely wish I would have had 30 years ago when I first started out as a just-intonation composer and instrument builder. Musical Mathematics is truly as useful to the beginner as to the most accomplished expert in the field; both will find much value in this book. Also, it is obvious from his thoroughness and practical insights that Cris is an authority who has actually worked with the materials -- an important aspect that sets this publication apart. This is a work of depth and breadth written in a spirit of sharing and helpfulness for those interested in the subject. Musical Mathematics is a watershed book that will, without doubt, change acoustic instrument building for the better, and change many of our views on the history of mankind's intonational practices.
2 of 2 people found the following review helpful.
The Absolute Landmark for the 21st Century!
By Cameron Powers
Cris has written THE English language book for our times! I have been a student of Arabic music for 35 years and have listened deeply to the harmonies of this ancient musical form. I have known for many years that there is a magic in the ancient tunings and have written a couple of books about this myself. And I have of course heard references to the wisdom of the ancient teachers. But nowhere until Cris published this book have I been able to find the true translations of meanings of these ancient sources! I am in complete awe of Cris' work as he brings first-of-a-kind scholarship to so many ancient world music traditions. This book might have been created by a team of ten scholars it is so comprehensive. But ten scholars would have had difficulty bringing a single-minded focus to these subjects in the way Cris has. Cris elaborates these subjects with exquisitely detailed mathematical exposition but never strays from addressing the central points for which we are collectively driven to find answers. No matter which angle you approach you will find more than what you could imagine. Thanks Cris! Cameron Powers
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