Rating: 
Summary: Think musical temperament is boring? Think again!
Review: This book did even more than what I hoped it would do.First of all, it grabbed my attention. I didn't even know there was problem with our musical scale, let alone a controversy that lasted hundreds of years and involved the greatest scientific, religious, and musical minds of the day! Then the book explained the subject in an interesting way. So interestingly, in fact, that I found myself wishing for even more of the technical details (imagine that!). I'm not at all convinced (as I was led to believe by other reviewers before I actually read the book) that Mr. Isacoff holds equal temperament to be the only solution and all other temperaments to be inferior. I think he is a realist who sees (and presents) pros and cons in all attempts to solve the fascinating temperament riddle.
Rating: 
Summary: Could have used a lot more math
Review: This book does an adequate job of explaining the troubles inherent in musical tuning to a layperson. However, why does a book about frequencies and the relationships between them avoid the word "hertz"? I would have appreciated knowing HOW far off a modern keyboard's fifth is from a true one, and how big Pythagoras' comma really is. The author seems to be avoiding this kind of exposition in favor of fractions and many, many adjectives, which didn't work for me. At the same time, some concepts pop up in the book unexplained (a fourth is mentioned in passing for the first time on page 143, after we've been dragged through the ratios of octaves, fifths and thirds several times). The book seems to be aimed at people who already know some music theory but can't tolerate math, an audience that probably doesn't exist. While the accompanying history tried hard to entertain, there were too many diversions away from the main topic. Less flavor, please, and more numbers.
Rating:
Summary: Could have used a lot more math
Review: This book does an adequate job of explaining the troubles inherent in musical tuning to a layperson. However, why does a book about frequencies and the relationships between them avoid the word "hertz"? I would have appreciated knowing HOW far off a modern keyboard's fifth is from a true one, and how big Pythagoras' comma really is. The author seems to be avoiding this kind of exposition in favor of fractions and many, many adjectives, which didn't work for me. At the same time, some concepts pop up in the book unexplained (a fourth is mentioned in passing for the first time on page 143, after we've been dragged through the ratios of octaves, fifths and thirds several times). The book seems to be aimed at people who already know some music theory but can't tolerate math, an audience that probably doesn't exist. While the accompanying history tried hard to entertain, there were too many diversions away from the main topic. Less flavor, please, and more numbers.
Rating: 
Summary: No Temperamental Enlightenment Here
Review: This book is a big disappointment. The look and feel of the volume promised much but the content is a complete let down. There is so much irrelevant material here that I gave up reading the book eventually. The author tries to explain a subject which is reasonably complex and which does require a little mathematical know how (not much) and musical (some) knowledge, without using any technical terms whatsoever: in my opinion it is as difficult to do this (if not impossible) as it is explain the word "rainbow" without using the word "colour'. But it is the inclusion of so much padding which makes the book so very hard to read. There is no doubting the author's commitment to his topic but the book fails if its purpose is to enlighten.
Rating:
Summary: A superficial glide
Review: This book is basically a rehash of Isacoff's major source, on which he relies too heavily: J Murray Barbour's 1951/72 "Tuning and Temperament". Barbour's own bias in his otherwise very well-researched book was the assumption that history is a mostly inexorable metamorphosis toward the current scientific triumph (really only a post-Industrial-Revolution conceit): equal temperament, against which all other systems must be measured and found deviant. Musicians didn't always have those same goals, as to quality of the sound they wanted. Barbour and Isacoff don't say that they did, and they dance carefully around it while offering a facade of musical objectivity. But, the historical SWEEP they present still gives that incorrect impression, overall, because of the way they measure value by their own expectations (the modern triumph over supposedly more ignorant methods) instead of the positive expectations of the people who composed tonal music. I found it remarkable that as early as page 6 Isacoff cites equal temperament as "the final solution"...a chillingly accurate assessment, as to the way it eliminates diversity from tonal music, the way somebody else's "final solution" eliminated human beings. Isacoff, to his credit, tries to present various sides of the historical issues; but the effort fails as he consistently errs on the side of embracing scientific triumph (as if equal temperament is the only scientifically plausible solution). He seems bewildered whenever presenting a scientist who never succumbed to the lure of the modern "final solution". More problematic, he tries too hard to sculpt personality profiles around all the major players in the historical record, and his observations degenerate into "ad hominem" dismissals of people he'd rather not have us believe. Isacoff also asserts piano supremacy over the harpsichord, as if the harpsichord is not worth much consideration anymore (and he even introduces the instrument with the unnecessary Beecham quote, biasing his readers against its virtues!); that's anathema to those of us who specialize in harpsichord! Isacoff's treatment of 17th and 18th century irregular systems (asymmetric tunings) is so curt and dismissive as to be almost non-existent; clearly, he doesn't understand them and would rather not deal with them, even though they have been continuously in use since at least the 17th century. His discussions of Do-Re-Mi present a related problem. While his frequent reliance on Do-Re-Mi is probably useful to some modern readers whose only exposure is the movie "The Sound of Music", it whizzes right by the historical teachings of hexachords and mutation (the way solfege really was taught). Most seriously, in all the historically valid irregular systems of keyboard temperament, those steps such as Do to Re, Re to Mi, or Fa to Sol are NOT the same size as one another, and that is an expressive advantage (having more than one size of whole step in the same scale...helping the listener's ability to recognize each tonality as distinct). Isacoff seems not to be aware of this. In his paradigm, that whole middle layer of circulating tunings between regular meantone and "the final solution" is wiped right out; never mind that our favorite composers wrote their best music in such systems, and that the subtle expressivity of that tonal music (the software) is heard to best advantage when the hardware is set up correctly. In short, overall, the human-interest angle of Isacoff here makes it look as if he simply wanted to do a Thomas Cahill spin-off, in a different field. His unscholarly sloppiness is not limited to the mining of Barbour. For example, the big point Isacoff tries to make about Willaert is lifted straight from the book "Lutes, Viols, and Temperaments" by Mark Lindley, but then twisted to Isacoff's own goals and explicated far beyond his own apparent understanding of ensemble singing. And, he really should have consulted Rita Steblin's reprinted dissertation, "A History of Key Characteristics in the 18th and Early 19th Centuries", to see how musicians felt about tuning and the ways in which tonalities interact. Steblin supplies hundreds of historical records that are obviously outside Isacoff's apparent awareness. Anyway, Isacoff's book is entertaining, while dismayingly unscholarly: playing fast and loose with the evidence and not documenting any of his assertions other than listing a short bibliography (far too short for a book of this size, and a topic of this complexity). It's an attempt to boil down a complex field of mathematical and artistic science into a thrilling peep show; and that attempt devalues scholarship itself. His whole argument boils down to the observation that modern pianos are ubiquitous, and the related assumption that pianos now are in an optimal tuning for the music they play, that nothing better is or has ever been available. Well, that's where he's mistaken. A reader completely new to the topic of temperaments would be much better served by simply starting with Lindley's excellent article "Temperaments" in the New Grove Dictionary of Music and Musicians, and then exploring the sources found in that bibliography, with Steblin high on that priority list.
Rating:
Summary: A superficial glide
Review: This book is basically a rehash of Isacoff's major source, on which he relies too heavily: J Murray Barbour's 1951/72 "Tuning and Temperament". Barbour's own bias in his otherwise very well-researched book was the assumption that history is a mostly inexorable metamorphosis toward the current scientific triumph (really only a post-Industrial-Revolution conceit): equal temperament, against which all other systems must be measured and found deviant. Musicians didn't always have those same goals, as to quality of the sound they wanted. Barbour and Isacoff don't say that they did, and they dance carefully around it while offering a facade of musical objectivity. But, the historical SWEEP they present still gives that incorrect impression, overall, because of the way they measure value by their own expectations (the modern triumph over supposedly more ignorant methods) instead of the positive expectations of the people who composed tonal music. I found it remarkable that as early as page 6 Isacoff cites equal temperament as "the final solution"...a chillingly accurate assessment, as to the way it eliminates diversity from tonal music, the way somebody else's "final solution" eliminated human beings. Isacoff, to his credit, tries to present various sides of the historical issues; but the effort fails as he consistently errs on the side of embracing scientific triumph (as if equal temperament is the only scientifically plausible solution). He seems bewildered whenever presenting a scientist who never succumbed to the lure of the modern "final solution". More problematic, he tries too hard to sculpt personality profiles around all the major players in the historical record, and his observations degenerate into "ad hominem" dismissals of people he'd rather not have us believe. Isacoff also asserts piano supremacy over the harpsichord, as if the harpsichord is not worth much consideration anymore (and he even introduces the instrument with the unnecessary Beecham quote, biasing his readers against its virtues!); that's anathema to those of us who specialize in harpsichord! Isacoff's treatment of 17th and 18th century irregular systems (asymmetric tunings) is so curt and dismissive as to be almost non-existent; clearly, he doesn't understand them and would rather not deal with them, even though they have been continuously in use since at least the 17th century. His discussions of Do-Re-Mi present a related problem. While his frequent reliance on Do-Re-Mi is probably useful to some modern readers whose only exposure is the movie "The Sound of Music", it whizzes right by the historical teachings of hexachords and mutation (the way solfege really was taught). Most seriously, in all the historically valid irregular systems of keyboard temperament, those steps such as Do to Re, Re to Mi, or Fa to Sol are NOT the same size as one another, and that is an expressive advantage (having more than one size of whole step in the same scale...helping the listener's ability to recognize each tonality as distinct). Isacoff seems not to be aware of this. In his paradigm, that whole middle layer of circulating tunings between regular meantone and "the final solution" is wiped right out; never mind that our favorite composers wrote their best music in such systems, and that the subtle expressivity of that tonal music (the software) is heard to best advantage when the hardware is set up correctly. In short, overall, the human-interest angle of Isacoff here makes it look as if he simply wanted to do a Thomas Cahill spin-off, in a different field. His unscholarly sloppiness is not limited to the mining of Barbour. For example, the big point Isacoff tries to make about Willaert is lifted straight from the book "Lutes, Viols, and Temperaments" by Mark Lindley, but then twisted to Isacoff's own goals and explicated far beyond his own apparent understanding of ensemble singing. And, he really should have consulted Rita Steblin's reprinted dissertation, "A History of Key Characteristics in the 18th and Early 19th Centuries", to see how musicians felt about tuning and the ways in which tonalities interact. Steblin supplies hundreds of historical records that are obviously outside Isacoff's apparent awareness. Anyway, Isacoff's book is entertaining, while dismayingly unscholarly: playing fast and loose with the evidence and not documenting any of his assertions other than listing a short bibliography (far too short for a book of this size, and a topic of this complexity). It's an attempt to boil down a complex field of mathematical and artistic science into a thrilling peep show; and that attempt devalues scholarship itself. His whole argument boils down to the observation that modern pianos are ubiquitous, and the related assumption that pianos now are in an optimal tuning for the music they play, that nothing better is or has ever been available. Well, that's where he's mistaken. A reader completely new to the topic of temperaments would be much better served by simply starting with Lindley's excellent article "Temperaments" in the New Grove Dictionary of Music and Musicians, and then exploring the sources found in that bibliography, with Steblin high on that priority list.
Rating:
Summary: Uncertainty and Temperament
Review: This book was interesting to me.But there is another story.
In quantum physics, the Heisenberg Uncertainty Principle expresses a limitation on accuracy of simultaneous measurement of observables such as the position and the momentum of a particle. (1927)
Kurt Godel's Incompleteness Theorem says that ...."any precise mathematical system must contain some statementsthat are neither provable nor disprovable by the means allowed within the system". (1931)
In 1916 Einstein published his general theory of relativity. In it he proposed that gravity is not a force but a curved field in the space-time continuum that is created by the presence of mass. People were astonished by the fact that space and time are under relativity. Even though, the world could stay ease within the determinism where there was a general algorithmic procedure for resolving all mathematical questions.
But since Heisenberg's discovery, Isaac Newton's laws of motion has not been used to predict accurately the behavior of single subatomic particles. The world was then suffered from this uncertainty. Godel gave an additional blow to the people's mental world with the incompleteness.
Roger Penrose, Professor of Mathematics at Oxford University and a physicist, now happily says, "We cannot create any kind of new artistic sensitivity however we may accumulate many times of calculations. Art is a non-computable physics."
I would like to say, "Music is a non-computable physics, too".
But over the centuries musicians, mathematicians, theorists, thinkers, experts and amateurs have been suffered from the comma which is the difference between a perfectly tuned octave and the octave resulting from a tuned circle of fifths. Many great people have been trying to create the perfect scale in vain. Mathematics easily proves that perfection is not possible. Any solution does not exist. Musicians, especially pianists, have been accused of using the Equal Temperament for thier pianos because the Equal Temperament is said to be an anti-musical compromise which leaves each key equally damaged and none perfectly in tune.This comma has put a curse on music.
The Heisenberg Uncertainty Principle;
The position and momentum of a wave in space have been changed in form to the time and frequency of a wave. Here is a sound wave as a time-varying signal. Now we have found out the fact that it is impossible for us to know the exact frequencies in our sound wave at an exact moment in time. When frequency is 0.1Hz, delta t should be more than 1 /(4*pai*0.1) sec which is about 0.80 sec.
Middle C of the equal temperament is calculated approximately as 261.6256Hz. If you want to determine C with this precision 0.0001Hz, you need delta-t of 800 sec, or 13 min 20 sec. If you want to get the exact Middle C, you need an infinite time and a continuous wave of C.
In other words, theoretically we cannot get the perfect fifth tone with a frequency from a root tone with a frequency f0 by calculating f = f0 * (3/2).
In another treatment, the "uncertainty" of a variable is taken to be the smallest width of a range which contains 50% of the values, which, also in the case of normally distributed variables, leads to a lower bound of
delta f * delta t =< 1/( 2*pai ) for the product of the uncertainties. For different types of wave packets and for other treatments, the uncertainty can be set to a much lower bound.
In this physical world there can exist no temperament based on the ratios of whole numbers. Even harmony must live with this "uncertainty".
The Fourier Transform Theory:
You may say again that it is only for the subatomic world. But the Fourier Transform Theory reveals that the sound wave cannot get rid of the Uncertainty of Time and Frequency. A physical signal, such as sound pressure can be represented as a continuous function of time. This is the time domain representation of the sound. There is an equally valid frequency domain representation.
The uncertainty clouds cover the differentials of pitches which depend on various temperaments. And this uncertainty might be able to break the historic curse over the music.
Music of Sacred Temperament (the Well Tempered Clavier)
Rating:
Summary: Why is the piano the most complete instrument?
Review: This is an absolutely beautiful book. It is a pleasure to read and very informative. The book's focus is to show how a single concept originating with the mathematical and musical studies of Pythagoras, later Greek philosophers, the Middle Ages, the Renaissance through to the invention of the piano and the music of the great masters of Classical music has shaped music itself. Isacoff explains the mathematical relationship of thirds, fifths and octaves in a clearer and more interesting manner than any piano teacher I ever had, which makes Temperament (the title of the book referring to the taming and organization of vibrations into notes) a good primer on music theory. Apart from the lucid explanations of musical theory and its relationaship to mathematics, this book is also rich in historical detail, philosphy and of course music. It is well organized and is so well written that it can be read in a weekend. The book is not intended for the musical theorist, who might demand more specific texts; however, the music lover, the lover of ideas and their evolution will find this book almost indespensable. When you read this book you'll rediscover the very pleasure of reading and it will make you hungry for more. One of the best books of 2001 and one of the best I ever read.
Rating: 
Summary: Nice Beginner Read
Review: This is one of the most readable books on the history of temperment I have ever encountered! If you have ever wanted to know a little something about European music history, or the theory behind European music - definitely pick this up. It's a comfortable read, full of short anecdotes, and a non-technical style that is fresh and uninitimidating. Unfortunately, it sacrifices well-roundedness, and limits itself in the interest of a reader-friendly view. This is certainly not a comprehensive view on the subject and includes nothing of non-European music systems. I don't see this as a failing, merely different target. I would encourage the interested reader to take the basis provided with this book to further research and form one's own opinion
Rating:
Summary: Great fun!
Review: This was a fantastic read! Remember that this book is a LAY book! So certain 'scientific' expectations should be a bit relaxed. Isacoff is a great writer with an amazing ability to conjure vivid imagery. If you are a history, or music history, buff, you'll find this a fun read. I like to compare this book to Norman Cantor's "In the Wake of the Plague". Like Cantor, Isacoff's writing style can meander a bit and enter unnecessary information - but the critical difference is that Isacoff always comes back to the main point (i.e. has a point at all), and as a result, the distractions are not distractions, but really interesting tidbits about the movers and shakers in the history of keyboard temperament. This is a great summer, light read that will keep you fascinated. I know so much more now about the modern day piano than I ever did! Highly recommended!
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