For example, over a square (literally) European measure of four quarter notes,

ONE two THREE four, a Cuban percussionist layers a series of eighth notes, grouping them in threes, ONE and two AND three and FOUR and . . . . The resulting integration of African and European rhythm is a cell called the tresillo. Sublette's desire to show the pervasiveness of the Cuban influence leads him to stress the similarities among its various progeny, including early boogie-woogie, tango and rock'n'roll, but he neglects their subtle variations.

As I remember my old Jimmy Yancey piano-blues records, the accented "and" was really the last third of a triplet. When Piazzola uses the pattern he calls it a milonga and you can feel a rock-steady eighth-note pulse underneath it.

When Stevie Wonder uses it, it's still an eighth-note pulse, but a more relaxed one, somewhere between rock and bossa nova in feel. In music notation these rhythms all look the same, but to our ears they sound distinct -a sign that our notation is not designed for capturing rhythms.

There is nothing so difficult as explaining the obvious, because the obvious shouldn't require an explanation; it should be plain as the nose on your face.

I admire Sublette for his good humour and geniality in guiding us through this history, although there is one point at which he seems to lose patience. After an exposition of the Yoruba pantheon, he remarks that "If anyone reading this thinks this is all so much mumbo-jumbo, perhaps Cuban music is not for you".

Which is not just bad-tempered, but wrong. No one much believes in universal languages any more, or in music as a universal language, but surely there is no doubt that it can be a transcendent language. At this very moment an eleven-year-old girl somewhere in Seoul is practising Schumann with perfect understanding, even though German Romanticism, Clara Wieck, Eusebius and Florestan are so much mumbo-jumbo to her.

Nevertheless, Sublette's basic point is well taken: polyrhythms make sense in a religious context. Polyphony, rhythmic or melodic, is appropriate for religious music because of the sense it gives of mystical unity. Our minds take in that there are independent voices speaking, though they may not be agile enough to disentangle the threads of the conversation; the fact that the voices at some level unite to make a whole is a matter of mystery. We cannot perceive the unity of a Bach fugue or of a Yoruba drum ensemble by concentrating hard on figuring out the individual parts; we can only relax and let the unity overwhelm us.

Once Sublette locates us solidly in Cuba he intertwines the history of classical and popular music with the country's political and cultural development, giving American readers plenty of reason to squirm. At times, one feels overwhelmed by the quantity of information, as the latter part of the book becomes more and more encyclopedic, and the niggling freshman thought "How much of this am I going to have to know for the exam?"

begins to intrude. But how fortunate a freshman would be to have a music history text written with such clarity and grace and sense of narrative flow, grounded so firmly in the realities of the working musician's life! We learn not just that movie theatres were important performing venues in the early 1900s, with musical acts before the film, during the intermission, and after, but that the entire evening could be enjoyed for the price of a working-class meal. And that Gonzalo Roig, future founder of the Orquestra Sinfonica de la Habana, worked as a pianist at a movie house that showed silent pornographic films (in 1909!) with "variety shows that included live onstage sex acts between the films. One wonders what his accompaniments might have sounded like . . .".