Starting with the ancient Greeks, Western culture has kept up a heated relationship with the ethereal architecture of music, which taunted thinkers drawn to its otherworldly marriage of the intangible and the concrete. Pythagoras, the multidisciplinary genius who mixed math with mysticism, originally formulated what's now known as the octave scale by divining magical ratios between certain notes, fixing the fleeting properties of harmony and melody into a rational system thought to hold the deepest secrets of the cosmos. Musicians of the time were earthly translators of the language of God, recreating "the music of the spheres" while quavering with the fear that playing the wrong notes could send the universe crashing down around them. The story of Pythagoras' musical system lies at the root of Stuart Isacoff's Temperament, an astounding and accessible journey through the culture-defining narrative hidden in arcane music theory. The book traces the trajectory of Western music as it developed, concomitant with larger cross-cultural tides, from ancient Greece through medieval times, the Renaissance, the Age Of Reason, and so forth. The story essentially follows the parallel paths of scientists trying to pull apart the mechanics that make harmony work, and musicians tinkering with Pythagoras' sanctified formula. Scientifically, music exerted a powerful pull on some of history's giants, from Leonardo da Vinci and Filippo Brunelleschi to Galileo, Newton, Descartes, and Rousseau, to name just a few figures who play a prominent role in Temperament. Over time, many of their findings seemed to confirm music's role in the higher order. Newton discovered that the "space" between musical notes corresponds proportionately to the distance between colors in his just-discovered spectrum of light. At the turn of the 17th century, Johannes Kepler posited that planets orbit elliptically, rather than in circles, and found that their relative speeds at different orbital points match with the ratios in Pythagoras' musical scale. Meanwhile, musicians were grappling with mathematical glitches in the system that turned some chords into "wolf sounds," and wouldn't allow for certain combinations of notes that were pleasing to the ear but thought to be impure. Messing with the ages-old formula was heresy of the highest order, particularly considering music's substantial role in religious ceremony. But just as painting changed with the discovery of realistic one-point perspective, music changed to incorporate increasingly secular, earthly concerns, eventually arriving at the modern reconfigured system known as "equal temperament." Isacoff, an editor at Piano Today, does a wondrous job of illuminating such advances to non-musicians. All that's necessary is the simple knowledge that a piano has a finite number of keys, and that their existence is not arbitrary. By tying music together with math, science, art, and philosophy, Temperament brings life to the process by which "number, sound, and virtue wrapped themselves like intertwining vines around the trunk of Western culture."