According to legend, Pythagoras, the Greek philosopher and mathematician of the sixth century B.C.E., was passing by a blacksmith's shop one day. Inside the shop, hammers were striking anvils, making a tremendous din. Pythagoras noted that periodically a beautiful harmony was being produced. Intrigued, Pythagoras entered the shop to try and discover what caused this phenomenon. He observed that when the relative size of the striking hammerheads formed certain ratios-2:1, 3:2, etc.-the emerging sounds blended into a concert of pitches which were pleasant to the ear. He hurried home to recreate these same ratios using lengths of string. By applying some method of friction-striking or plucking the strings-he was able to produce musical notes.
Changing the length of the string would vary the number of vibrations. Pythagoras discovered that the concurrent sounds making the most pleasant harmonies were produced from the simplest ratios: by shortening a string by a half (2:1) an octave was formed; the 3:2 ratio produced the musical interval of a perfect fifth; a perfect fourth was heard when the string formed the ratio of 4:3.
In Pythagoras's world, numbers were everything; the cosmos itself could be understood through mathematics. His discovery of the relationship between the concord of elementary ratios and the harmony of music appeared to be a logical extension of his cosmology.
Unfortunately for Pythagoras, there was a fatal flaw to this system, one which has plagued music theorists for thousands of years since. As Pythagoras's play with proportions is taken to its logical extreme-when the scale is divided up into the twelve notes which make up our scale, including sharps and flats-the notes which are produced tend to go hopelessly out of tune and create terrible-sounding disharmonies. The system simply brakes down. Pythagoras, who believed the universe was ordered in accordance with mathematical principles, came to realize this, and found the implications terrifying. He found it impossible to reconcile that a system founded on uniformity could lead to such discord. He swore his followers to secrecy on the matter.
This flaw is the central topic of Temperament: The Idea that Solved Music's Greatest Riddle by Stuart Isacoff. His examination of how this puzzle affected music for more than two thousand years provides a wonderful tale touching on all aspects of culture in the Western world, including art, science, and theology. We meet wise popes, and corrupt musicians, and vice versa; it is a parade of the great and the small, each making his contribution to the development of the musical scale we know today.

"It is a tale that includes temperament' in all its diverse meanings: from the elements that shape the temperament, or character, of pivotal thinkers; to endless efforts to temper-or transform-the material world into something more desirable; to the practice of tempering, or altering, the purest, most beautiful harmonies..."

As we journey though the ages, Isacoff guides us with a sure hand, relaying the beliefs of the time, the misguidedness as well as clearsightedness of each era. This is a book which ventures far and wide. The history of music is at its centre, of course, but it also reaches into the worlds of theology, physics, art, architecture, and philosophy. Isacoff segues almost seamless from one field to the next, providing enough background for each subject, enabling us to follow the developments with ease. A person who loves classical music, but who is unfamiliar with its history or inner workings, will be caught up in all of the different parts of the story as Isacoff carries us through the world of mediaeval Gregorian chant, to the music of the Renaissance, and into the Age of Enlightenment when we run directly into the now unavoidable problems of the Pythagorean laws.
Music by this time was no longer able to cope with the jarring sounds which emerged from an instrument tuned by the old method. The scale ("do-re-mi-fa-sol-la-ti-do") is made up of tones and half tones-half tones only occur between mi and fa, and then again between ti and do, and at the interval between a white note on a keyboard and the black note next to it. A new method was proposed by which each of the whole tones would be evenly spaced. The half tones remained problematic, since the ratio between them forced each to be slightly closer either to the note that followed, or to the one that preceded. There was an unearthly beauty to the sound of certain chords produced by this method, but also utter chaos with others.
This was still a world in which men of science were in search of harmonic proportions in the universe. At this stage of the book, Isacoff introduces us to Kepler, who is convinced that the size of the interval of a major third in music is directly related to the variance in the ellipse of Saturn's orbit, and that the same can be found between other intervals and other planets. We have already passed other scientists and musicians-Newton, Galileo, and Galileo's father the musician and music theorist who has a run-in with his former teacher on the subject of the proportions of the musical scale. Finally, Rameau steps into the fray, and it is he who advocates the adoption of the tuning system which we employ today.
Temperament deftly walks the fine line between scholarly work and entertainment, presenting the reader with the best of both worlds. The research is exhaustive, attested to by the inclusion of a bibliography which is ten pages long. My only quibble on this score is that several times during the reading of the book, I wanted to know the exact source of Isacoff's information about some of the more obscure characters-and there are many of them-but such references were not provided. Perhaps I am asking for too much in the way of scholarship for a work which aims to entertain as much as to inform. Isacoff handles all of his historical figures with respect, but not one of them does he treat with awe or reverence. They are all human and fallible.
Music is the backbone of this work. Throughout his wanderings, Isacoff never strays far from the delight of song and melody. As he describes the proportions of the Florence cathedral, or the discovery of the moons of Jupiter, we are kept constantly aware of the longing for harmony which permeates life. While reading a book which aims to show that there is really no music of the spheres, we find ourselves almost able to hear it all around us.