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Chapter 1

Ay me! what warbles yields mine instrument!
The basses shriek as though they were amiss!

-William Percy, "Coelia" (1594)

The piano is perhaps the most generous instrument ever invented. Its range, from bass to treble, is as large as an orchestra's. It allows ten tones-sometimes even more-to be struck simultaneously, and holds them in the air at a pianist's will. The piano can growl and sing and beat time. It can render arid fugues and impressionist waterfalls with equal naturalness. And, unlike the ungrateful French horn or the finicky oboe, if you keep it in tune, it will be an obedient servant. But the principle that truly underlies the piano's versatility is hidden beneath the geometry of its white and black keys.

Clusters of two blacks, then three, then two, and so on, form a repeating pattern above a solid row of whites. When one's eye has become accustomed to the terrain, the alternating groupings signal the names of each note on the keyboard. There are only twelve different ones (each tied to a letter of the alphabet), and in our modern tuning they are built in equidistant steps, like a well-made ladder.

This arrangement produces wondrous results: Through it, a Chopin prelude can gently weep across the keys; Debussy's perfumed phrases can swirl in gentle clouds; Webern can set in motion intricate strings of melody, like threads of glistening pearls.

All of this is possible only because the modern keyboard is a design in perfect symmetry-each pitch is reliably, unequivocally equidistant from the ones that precede and follow it. This tuning allows a musical pattern begun on one note to be duplicated when starting on any other; it creates a musical universe in which the relationships between musical tones are reliably, uniformly consistent. Playing a piano for which this was not true would be like playing a game of chess in which the rules changed from moment to moment.

Yet, that is precisely what many European musicians practicing before the nineteenth century demanded of their instruments. In fact, for hundreds of years, suggestions that our modern system be used were taken as a call to battle: Musicians, craftsmen, church officials, heads of state, and philosophers fought heatedly against the introduction of this equal-temperament tuning as something both unnatural and ugly. When Galileo's father, Vincenzo Galilei, supported it as an ideal as early as 1581, he promptly became embroiled in a feud with Gioseffo Zarlino, one of the most influential music theorists of the day. (Sensing a good thing, Chu Tsai-yü, a prince of the Ming dynasty, soon after attributed the concept to the work of Huai Nan Tzu in 122 b.c.e.)

The seventeenth-century instrument-maker Jean Denis-an advisor to Father Marin Mersenne, philosopher René Descartes's most trusted authority on science and math-rejected today's approach as "quite wretched." Denis's Treatise on Harpsichord Tuning was published in 1643, the year that a pupil of Galileo's, Evangelista Torricelli, conducted world-shaking experiments in atmospheric pressure, overturning essential elements of medieval cosmology. Though radical changes in worldview were erupting all around him, Denis remained steadfastly loyal to an old tuning system in which the musical distances between notes were determinedly inconsistent, forming a minefield of "wolf sounds" on his keyboard-notes so dissonant they reminded listeners of the howling of wolves.

Harpsichords and organs (precursors of the piano) thus tuned were capable of producing harmonies of magical, uncorrupted sweetness in one moment and-as musicians attempted to duplicate them while navigating the spans of their keyboards-of earsplitting clashes the next. Composers were prisoners of these torturous practicalities, as were vocalists and instrumentalists who tried to join in. Yet the resistance to a remedy that we find perfectly acceptable today-the tuning of equal temperament-was so powerful, the idea was for generations almost unspeakable.

The crux of the problem can be traced to the ancient Greeks, who defined music's most beautiful sounds as arising from inviolable mathematical relationships-the fingerprints of the gods. These were the proportions through which two separate tones could entwine to form a delightful union. Centuries after Pythagoras conceived of the notion, the great astronomer and music theorist Johannes Kepler restated the idea eloquently: "Geometry existed before the creation, is coeternal with the mind of God, is God himself. . . ." Musical harmony was that geometry made sensual, and was not to be toyed with. And yet . . .

As the art of music evolved, a startling paradox arose that threatened to undermine the entire arrangement. When harpsichords or organs were tuned so that they could consistently produce sounds corresponding to one of the venerable formulas, they were rendered incapable of playing the others. No instrument with fixed, unbending notes such as a piano can accommodate them all. Thus, certain combinations of tones that should have sounded sweet and placid could, on an early keyboard instrument, become sour and ragged. In search of a solution, musicians began to temper, or alter, their instrument's tunings away from the ancient ideals. The final solution-today's equal temperament-abandoned most of the revered musical proportions altogether.

Acceptance did not come easily. Critics claimed the resulting music had been robbed of its beauty and emotional impact; supporters countered that since all things are subjective, human ears and minds would learn to adapt. The arguments, however, went well beyond musical aesthetics. Equal temperament represented an assault on an idea that had gripped thinkers in nearly every field as a powerful metaphor for a universe ruled by mathematical law.

Saint Augustine found in music's magical proportions God's revealed plan for the building of his churches. Renaissance philosophers sought in them the secrets of obtaining life from the heavens; composers yearned for the power they had bestowed on ancient musicians to tame wild beasts, seduce the celestial spirits, even lure trees to the surface from beneath the sheltering earth. Kepler found in music's time-honored proportions the rules governing the motion of planets in the sky. And Isaac Newton matched the relationships these proportions established between pitches in a musical scale to the arrangement of colors formed by sunlight passing through a prism.

Music's prized proportions permeated not only the inner sanctums of the church, but the workshops of great artists like Filippo Brunelleschi and Leonardo da Vinci. They became entangled in the world of scientific inquiry-engaging the imaginations of such luminaries as Galileo, Kepler, Descartes, Newton, and Christiaan Huygens. They fed debates between the French encyclopedists, challenging the rhetorical skills of Denis Diderot, Jean-Jacques Rousseau, Jean d'Alembert, and Jean-Philippe Rameau on questions such as "What is 'art'?" "What is 'truth'?" and "What is 'natural'?"

They spurred strange musical inventions from remarkable figures like the sixteenth-century avant-garde composer Nicola Vicentino, Mersenne, and Juan Caramuel y Lobkowitz, a Spanish mathematician, professor of theology, and military engineer at the court of Ferdinand III in Prague. And they instigated the creation of countless tuning systems in an incessant negotiation between the old ways and the forces of change. Along the way, they pointed up the conceits and follies of generations of theologians, musicians, philosophers, and scholars who insisted that the proportions in the mind of God must fit in the mind of man.

The general acceptance of equal temperament led to some of the most exquisite music ever written. Why the resistance to it lasted so long, and how it was gradually overcome, is a story that encompasses the most crucial elements of Western culture-social history, religion, philosophy, art, science, economics, and musical evolution-during a period when Europe was struggling to give birth to the modern age. This book tells that story.

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, following the startling revelation that in certain situations they must be reshaped or they will transform music, Jekyll-and-Hyde-like, into something grotesque.

This last definition, though arcane sounding, marks a profound moment in cultural history. Temperaments, settling like tracks along the winding path of Western civilization, unfettered the engine of musical progress. Once freed, and fueled by the sparks of those most human of qualities-imagination and passion-musical art, with religion, politics, and science in tow, chugged its way inescapably toward our own era.