Inspiration for a composition can come in many forms; a letter from Clara Schumann, the brutality of Stalin's police, growing deaf or hearing birdsong. The final concert of John Adams’ short residency at the Barbican focused on a more reverent strain of influence, however: the peculiar tendency for living composers to want to reference dead ones.

In the introduction to the UK première of his Absolute Jest, Adams delivered a short overview of musician-inspired music, and it would appear that for him the genre is about honouring genius, and repaying debt to preceding innovators. Written for string quartet and orchestra, Absolute Jest is laced with excerpts from Beethoven’s “late” quartets and a few more bombastic references for ballast. But there is more to the work than simply reference-spotting. True, there is a certain pleasure to be had in recognising one scherzo or another, hidden away in a second trombone part, but Adams has treated the raw material in such a way as to make it unsettlingly new. For example, repetition of material from the Presto of Op. 131 quite deliberately avoided the familiar vibrancy of its original setting, and as such, a cherished motif was subverted in its relegation to a lesser figure. The orchestra excelled in calmly registering these cool inventions, almost always to a definite pulse. With harmonic development arriving in a conspicuously piecemeal fashion, interest came largely from overlapping and tricky rhythmic lines, woven together by all-woodwind and string subsections. Surrounded by the LSO, the St Lawrence String Quartet played these rehabilitated fragments with a straight face – a rather humorous juxtaposition.

The most obvious characteristic one would attribute to the piece is cleverness – the idea, its conception, and its humour were all noticeably intellectual – and so one wonders if that’s a quality that’s valuable on its own. Fortunately, in this performance at least, the gathering momentum and devastating percussive effects created gripping entertainment that allayed any fears relating to cleverness. This has been well summed up in the LA Times, and it seems only appropriate to quote Mark Swed here: “It’s a great entertainment, as long as you don’t think too hard about it”.

The same cannot be said of Carter’s Variations for Orchestra, which requires the absolute attention of the listener and the orchestra. The LSO worked through the early passages with moments of relative serenity, while stacked triplets were tossed around, giving the piece momentum without fuss. But following a short fugue section, the theme became much clearer, forcing succeeding variations into the open. From this point on, the LSO achieved a glorious sense of drama which could not be ignored. They grew out of fortissimos and instilled more and more interest in each new timbre. Each fresh swell seemed to have the resonance and magnitude required for an explosive final bar, but on it continued, until finally a muscular timpani entry blotted out the drama.

Theoretically at least, the Variations were written with the intent of re-energising the classical form within the European academic vocabulary of atonality and the series. The challenge there is not small and one imagines Adams, among others, would not take it up on the grounds of exclusivity.

The contrast of Carter’s rather learned complexity with the easier charm of Charles Ives and Aaron Copland made for a varied first half. In Ives’ Country Band March, where most phrases can be traced back to anonymous American folk material, there was more jest, as the LSO sent up the image of a misfiring amateur band with precise imprecision. But still, there were moments of beauty; when the over-loud drums stopped and the exposed brass lines fell away, a more precious and intonated duet of clarinets and violins was presented as the heart of the piece. This, as well as Copland’s Appalachian Spring, would be tempting to perform as folksy patriotism (particularly now that Copland’s white-note harmonic style has defined the sound of the US military and presidency on TV and film), but Adams and the LSO played the borrowed hymns, songs and nursery rhymes with a quiet dignity, emphasising instead disjointed orchestration and lilting rhythms.

It is rare that such musical variety fits an overarching theme so well, but this concert succeeded where many others failed. Adams’ short stay at the Barbican ended with a concert whose performance was dedicated and respectful, and whose programme was as good humoured, intelligent and entertaining as one could reasonably expect.