If you were asked to divide the world's songs into categories, how would you do it? I asked a few friends, who came up with love, loss, sorrow, separation, beauty, praise, wonder, doubt, fear, dreams, anger, work, oppression, loneliness, nostalgia, homesickness and more. Daniel Levitin, however, claims that "music has shaped the world through six kinds of songs: friendship, joy, comfort, knowledge, religion and love." What enduring principle lay behind the selection of just those six? We don't find out, because although this is a cheerfully wide-ranging book, it's certainly not a rigorous one.

Isn't there more to the world's music than songs? It turns out that, for Levitin, song is "a convenient shorthand for music in all its forms, to refer to any music that people make, with or without melody, with or without lyrics". Maybe your iPod thinks so, but for most of us "song" means a melody sung with words. Levitin's careless definition is surprisingly capricious for a scientist, more so when he says things such as: "The evolution of mind and music is easiest to follow in music that involves lyrics, because the meaning of the musical expression is less debatable." That's nonsense, because it supposes that the meaning of words is identical with the meaning of the music they are set to, which is often - sometimes deliberately - not the case. The point is eloquently made by the song lyrics he quotes, which give hardly any clue to what they have sparked off in composers' minds, or to the impact that their musical settings will make on us.

Furthermore, it implies that the meaning of purely instrumental music is unlikely to be crystal clear. But even though abstract music can express things that are difficult to put into words, most music-lovers would argue that the mood is often very clear, and the range almost infinite. In any case, having said he doesn't wish to exclude non-vocal music, Levitin in fact writes mainly about pop songs, the genre he knows and loves best.

Just as "song" is loosely used, so too is "world", for despite references to the music of other eras and places, this study centres on modern America, ignoring vast swaths of folk and art song from elsewhere. How, for example, can anyone write a book about the world's songs without acknowledging the 600 written by Schubert, who is mentioned once as the composer of "Who is Sylvia?" but doesn't even make it into the index?

Levitin is a musician and record producer turned neuroscientist whose successful book, This Is Your Brain on Music, provided a fascinating account of what happens in our minds when we listen. In this follow-up, emanating more from his carefree musician self, he adopts a looser approach, allowing himself to riff on personal anecdotes which often go off at a tangent to his main argument, and sometimes come across as substitutes for serious thought. He can't resist name-dropping his illustrious friends, drafted in as experts on song writing: "Sting confided in me ... While I was dining with Joni Mitchell at an outdoor restaurant once ..."

At his best (the chapter on knowledge songs, for example), he's a genial guide to scientific thinking on why humans create music, and why we respond to it as we do. And he updates us on new evidence about the chemicals released in our brains by music, and about its power to help us work, move and feel in tandem.

However, when it comes to writing about music itself, there's a gulf between his undoubted love and appreciation of it, and his knowledge of what makes it what it is. Far too often, his descriptions of music are clumsy or superficial: "The 'blues' technically refers to a type of chord progression, in its simplest form what musicians call I-IV-V7 (pronounced 'one, four, five-seven') ... typically done in twelve- or sixteen-bar phrases (hence the term 'twelve-bar blues')." This is simply inadequate, and doesn't give any sense of the blues' characteristic shape. One minute he's telling us that blues are "the ultimate comfort song in western society during the last hundred years" and citing as his first example "California Girls" by the Beach Boys, which is light years removed from the heart-rending pain of historic blues. The next, he says that "the lullaby is the classic song of comfort", a poor description in any case of music which throughout the ages has reflected the complex melancholy of maternal feelings.

Evoking the effects of the combination of words and music is a subtle art which is certainly not Levitin's strong point. He deals better with the words themselves, but a song lyric is only part of a song, and doesn't conjure up the music if you don't already know it. Reading this book is, in fact, a bit like reading the lyrics of an unknown song: the music seems to lie tantalisingly out of reach.

 Susan Tomes's A Musician's Alphabet is published by Faber. To order The World in Six Songs for £13.99 with free UK p&p call Guardian book service on 0330 333 6846 or go to guardian.co.uk/bookshop