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Throughout history, the best minds have struggled to define what music is for. To Pythagoras, it was the sound of mathematical, cosmic harmony reverberating in the human soul; to Darwin, a function of sexual selection; to psychologist Steven Pinker, it is a kind of "auditory cheesecake ... crafted to tickle the sensitive spots of at least six of our mental faculties." Like life itself, music is universally experienced yet ultimately eludes explanation.

Author and neurologist Oliver Sacks knows all this — and too much else besides, to attempt any glib definitions. On the first page of Musicophilia: Tales of Music and the Brain, he writes that music "has no concepts, makes no propositions; it lacks images, symbols, the stuff of language. It has no power of representation. It has no necessary relation to the world." His book is ostensibly just a survey of research and case histories of patients whose inner lives have been fundamentally changed by music. Yet in revealing the exquisite complexity of the ways in which our minds are attuned to music, Sacks sharpens our desire to understand its enigma.

In Musicophilia, as in the books that made his literary name, Awakenings and The Man Who Mistook His Wife for a Hat, Sacks dives into the crevices of the human mind in search of a cure and surfaces with enlightenment for us all. We are irritatedly familiar, for example, with the phenomenon of earworms — catchy tunes that loop in our heads, even when we detest them. This "defenseless engraving of music on the brain," Sacks suggests, is a result of the precision with which most of us can replay music internally; built to seek stimuli, the brain rewards itself for its fidelity with perfect repeats of songs. But for the patients in Sacks' book who suffer musical hallucinations — a related and not uncommon condition in which imaginary music seems to come from an outside source that can't be turned off — the results are often debilitating. One patient, June B., has been subjected to a short, repeating playlist that includes Amazing Grace, the drinking song from La Traviata and "a really dreary version" of We Three Kings of Orient Are, for over 10 years.

Sacks' neurological interest in music dates back to the 1960s, when he noted that the parkinsonian patients he was treating could often inexplicably be roused from their catatonia by music. The leaps in brain science since then, particularly in magnetic resonance imaging scans, mean that neurologists can now actually see what happens when we hear or even compose music. Scans show that, neurally, the experience of imagining music is much the same as listening to it. Also, that the corpus callosum, the mass of nerve fibers that wire the two hemispheres of the brain together, is enlarged in professional musicians. "Anatomists today would be hard put to identify the brain of a visual artist, a writer or a mathematician," Sacks writes, "but they could recognize the brain of a professional musician without a moment's hesitation." Yet he worries that by reducing music to a set of neurological functions, "the simple art of observation may be lost ... clinical description may become perfunctory and the richness of the human context ignored."

The fact that absolute pitch — the ability to name any isolated musical tone — shows up on the scanner as an exaggerated asymmetry between the size of certain structures in the right and left sides of the brain falls far short of explaining how it's acquired. What gets closer are the observations that 50% of people born blind or blind from a young age have absolute pitch, and that it's four times more common among first-year music students in Beijing than those in New York — a reflection of the fact that the Chinese are more attuned to pitch, having had to master the precise tones used in spoken Mandarin.

The son of a musical family who still plays his father's Bechstein, Sacks has a strong empathy for the loss suffered by the many neurally damaged musicians who have found their way to him. Most touching of all is his tale of Clive Wearing, an English musician stricken in 1985 with a post-brain-infection amnesia so devastating that from one minute to the next he does not know who, where or what he is. At 69, just two things are unscathed in his inner life: a profound love for his wife and the ability to sing or play on the piano any piece of music set in front of him. Sacks describes Wearing's music as a rope let down from heaven: "Without performance, the thread is broken, and he is thrown back once again into the abyss."

Love for music is a simple joy of life, but even that can be overwhelming, as Sacks found with Tony Cicoria, a surgeon who survived being struck by lightning only to find himself possessed by an all-consuming, life-disrupting passion for listening to, playing and composing piano music. After grappling with Cicoria's musicophilia for 12 years, Sacks decided to let things be — to acknowledge that some of music's eternal riddles are better left unsolved. "His was a lucky strike," writes Sacks, "and the music, however it had come, was a blessing, a grace — not to be questioned."

• MICHAEL BRUNTON
• Neurologist Oliver Sacks explores the exquisite complexity of music's effect on the human mind