The Wagner Clan, by Jonathan Carr

Richard Wagner's most famous exhortation, Kinder! Schaff' Neues! (Children, make something new!) can hardly have been more assiduously followed than by his great-granddaughter Katharina at her Bayreuth debut this month. On the stage that Wagner built, the 29-year-old Katharina mounted a setting of Meistersinger that depicted Wagner himself disco-dancing in his underpants and concluded with a scene in which a bunch of musicians are tossed in a skip and set alight by a crowd offering quasi-fascist salutes. These innovations earnt the youngest scion of the Wagner dynasty a riot of boos at curtain down, which she blithely dismissed as "part of a director's job".

Controversy like this may be just what she needs to convince the Richard Wagner Foundation Bayreuth, which funds and controls the Festival, to appoint her to the post of director. The job is occupied by her father, Wolfgang, a canny octogenarian who organised a lifetime directorship for himself in the 1970s. Having weathered acrimonious challenges from other, more qualified, members of the family, Wolfgang has let it be understood that he will only step down if the trustees appoint his daughter in his stead.

As Jonathan Carr's splendidly readable and intelligent history of the Wagner family makes clear, such soap-operatic heights of histrionic infighting are no less a part of Bayreuth tradition than the music itself: almost from the instant that Richard Wagner died, his descendants' history has been one of plots, counterplots, backstabbings, lies, manoeuvres and double-dealings. It is a story that makes the name Wagner gave to his house in Bayreuth – Wahnfried, meaning "peace from delusion" or even "rest from madness" – seem profoundly ironic.

Carr's dry and unseduced account begins with a portrait of Wagner's musical and intellectual development, a task traditionally confounded for historians by the Master's persistent and wilful ambivalence. Wagner was a financial incompetent who periodically bankrupted himself on lining his residences with silk; he went into print as an anti-Semite while keeping a circle of Jewish friends; he was an urbane philanderer and a notorious charmer who would emit a "piercing scream" if guests dared to talk amongst themselves at dinner. He resists easy explication.

Carr's consideration of his life gives way to a rigorous discussion of the questions that have dominated most studies of Wagner and Wagneriana since the Second World War. These are: first, can Wagner's opinions, views or music really be said to have influenced the development of Nazism? Secondly, given the peculiarly close association between the Nazis and Bayreuth, is the Wagner legacy an ineradicably tarnished one and has the festival any place in a modern Germany?

Bayreuth's unique circumstances render such questions perennially relevant. They begin with Wagner's wife, Cosima, who nurtured the composer's legacy and his festival with fierce pride through 43 years of widowhood. As Carr shows, her brand of anti-Semitism was already considerably less reflective than her husband's: it became even more implacable after she welcomed into her circle Houston Stewart Chamberlain, author of the international bestseller The Foundations of the Nineteenth Century. This foul but silver-tongued book set forth the ideas of Aryan supremacy and of the hierarchy of races that would later be adopted by the Nazis: Chamberlain married a Wagner daughter and later settled at Bayreuth, where Goebbels, on his death, described him as "our spiritual father, trailblazer, pioneer".

From 1920, Siegfried Wagner (the composer's son) and his wife, Winifred, played host at Bayreuth to Adolf Hitler himself. The friendship between the Führer and Winifred – already tackled this year in A N Wilson's dubious, Man Booker-longlisted confection Winnie and Wolf – ensured that, exempt from the control of Goebbels' propaganda ministry, Bayreuth became a Hitler fiefdom during the Nazi years and the Wagners themselves a uniquely privileged clique.

Some argue that it has never recovered from the stigma. One such is Gottfried Wagner, Wolfgang's son, who now lectures internationally on his family's history of anti-Semitism. Another was Friedelind, Winifred's daughter, who fled to America and mounted a campaign in the press against the Nazi regime. But Carr's resolutely unsensational history will surprise those who think of Wagner's music as the soundtrack to Nazi Germany. He shows that not only did performances of the operas decline during the period of Nazi power, but that most of Hitler's top brass were bored stiff by Wagner's work.

Carr follows the family's history up to the most recent bids for power, taking in the various reparations and equivocations that the Wagners have made – or failed to make – towards their troubled heritage. The account draws on a number of German sources that are unavailable in English, and the information this makes available is occasionally shattering: for instance, it only became apparent recently that Wieland Wagner, the festival's director between 1951 and 1966, spent the war working in a laboratory staffed by concentration-camp labour designing guidance systems for the V2.

Carr has been a Bayreuth visitor for more than three decades, and his sincere enthusiasm for the festival shows in the prescription he offers for when Wolfgang finally steps down. He argues that, in contemporary Germany, the air of Bayreuth can only satisfactorily be cleared by the Wagner family backing "the preparation and publication of a scholarly history, in which independent judgment is backed by full documentation". This is surely a legitimate request, and it can only be aided by the publication of a book as good as this. In its depth of research, its wealth of anecdotal interest and in the refreshing sanity of its judgments, it offers both a fascinating introduction to laymen and a wealth of new information to the most dedicated Wagnerians. Before making their next decision, the trustees at Bayreuth might do well to take note.