Evening in the Palace of Reason, by James Gaines

Frederick the Great of Prussia took a delight in puncturing men's egos. As a warrior, he humiliated his own knights in battle: "Hunde, wollt ihr ewig leben?" (Dogs, do you wish to live forever?). As a musician - he played the flute - he humiliated Johann Sebastian Bach by summoning him to his court, presenting him with a long and complex piece of music and challenging him to make it into a fugue for six voices, clearly hoping the task was beyond him.

Frederick the Great of Prussia took a delight in puncturing men's egos. As a warrior, he humiliated his own knights in battle: "Hunde, wollt ihr ewig leben?" (Dogs, do you wish to live forever?). As a musician - he played the flute - he humiliated Johann Sebastian Bach by summoning him to his court, presenting him with a long and complex piece of music and challenging him to make it into a fugue for six voices, clearly hoping the task was beyond him.

Instead of inviting the young king to fugue off, the old Kapellmeister took the theme home and finished the job within a fortnight, much (one imagines) to the king's chagrin. Bach, as the author of this wonderfully engaging tale, reminds us, "was a father of the late Baroque, and Frederick was a son of the early Enlightenment". He is as famous for having helped consolidate the foundation of the classical repertoire as he is revered for his cantatas and for his Art of Fugue, composed in an empty Leipzig church in the year of his death (1750). He was a traditionalist. Frederick, on the other hand, regarded himself as a modernist, who had curled his hair and worn clothes of a French cut in his youth, and fancied himself as a musical authority on the new "natural and delightful" galant style which denigrated the "learned counterpoint" of canon and fugue as being worn out.

In bringing these two men together at what Gaines calls the musical "intersection of... a horizontal-vertical crossroads", not to mention "the tipping point between ancient and modern culture," the author presents us with a piece of theatre that is witty, instructive and often bizarre. Frederick's character was influenced by his father, Frederick William, a manic-depressive who for much of his life was either boiling with rage or raging with boils (he suffered from porphyria) and who not only liked to cane the Crown Prince in front of his courtiers, but who ordered young Frederick to watch as the lad's best friend was beheaded.

The old boy thought his son effeminate and blamed his attachment to music, powdered wigs and other French influences for this perceived condition. Bach, too, ingested a lot from French music, but probably shared some of Frederick William's dismay over the narcissism of Versailles and the behaviour of Louis XIV's personal composer, Jean-Baptiste Lully, as shameless a sycophant as could be found in the Sun King's circle.

Gaines relates some hilarious incidents involving Lully, including his allowing members of the audience to copulate in the upper galleries of the opera and for being "outrageously gay" in public (for which Louis upbraided him). Finally, Lully gratified his detractors, among them Molière and Boileau, "by impaling himself in the foot with his baton and dying of gangrene".

Some anecdotes seem to spring from the Brothers Grimm. Because Frederick the Great liked to be guarded by uniformed giants, his spies would kidnap the tallest men they could find. One spy approached a tall young carpenter in his shop and ordered a stout, lockable chest in excess of 6ft long. He pronounced the chest too short, and when the carpenter lay down in it to prove him wrong, the spy slammed down the lid and three accomplices carried him off. When the chest was opened the latest giant "recruit" was found to have suffocated.

As well as giving us glimpses of George I, Pachelbel, Descartes, Newton, Handel, his friend Mattheson and others in an extensive litany of renown, Gaines provides an intelligent analysis of the music then competing for fashionability. At one point, in his discussion of Bach's "almost unspeakably beautiful Actus tragicus," he suggests that we "put down this book, get out the score, put on the music, read the words and the music together; and after playing it through several times, consider the power of inspired (as well as rigorously educated and deployed) genius."

It is, however, a book that is almost impossible to put down when one is dancing, swerving, stumbling through the extraordinary brilliance, blood-thirst, cruelty, fecundity and religious and other feuds of the society that helped to inspire Bach and sustain Frederick. Bach lived for three years after his meeting with Frederick the Great. Great? Gaines repeats part of a valedictory poem for the Kapellmeister written by way of epitaph: "Departed Bach! Long ago thy splendid organ playing / Alone brought you the noble title 'Great'."