The Symphony of Psalms, which ended the Philharmonia’s Stravinsky series last night, is an indelible masterpiece, silencing the tired but persistent accusation that Stravinsky’s music is clever but cold. Abstract it may be, but suffused with an exile’s deep longing, spritual hope rising in harmonies of heart-stopping consolation until that final, revelatory C major chord. This performance (with three Swedish choirs) was of focused beauty and searing sincerity; I have never heard better.

Stravinsky's music, chameleonic yet always itself, offers so many lines of thought. One struck me immediately with the descending, even harp notes and tender, veiled strings at the start of his 1947 ballet Orpheus last night: the inexorable beat of time is so often pitted against an expressive, human voice. Esa-Pekka Salonen, who started out as a rhythm and textures man, now gets the humanity too.

The last time but one that the Three Choirs Festival was in Gloucester the main offering was Elgar’s oratorio The Kingdom, and there’s a kind of inevitability about the same work turning up again, same place, same occasion, six years later. After all, the Three Choirs has not survived for almost 300 years by a fidgety policy of constant renewal.

I had been looking forward to last night's concert since it was first announced over a year ago. For a Stravinsky nut the chance to hear pieces whose live performances are vanishingly rare was not one to be missed. And it turns out there are enough other fans of austere late Stravinsky to sell out St John’s Smith Square, which proved a very suitable venue for this programme.

“Choleric humour, pathos and kindliness are mingled in conflict," wrote Robert Simpson of Nielsen’s 1928 Clarinet Concerto. The work was written for a player with a complex character, full of contradictions. Last night’s soloist, Mark van de Wiel, the Philharmonia's principal clarinettist, gave a fluent performance of the work convincing on its own terms, portraying the protagonist as an introvert and anti-hero.

Looking past the ballets for Diaghilev, there are still many superb scores by Stravinsky honoured more in scholarship than performance. In Myths and Rituals, the Philharmonia addresses that lack of wider appreciation with five concerts from May to September. The series got off to a promising start last night with the tiny fanfare for three trumpets – Monteverdi with attitude and wrong notes – from 1955, which was one of Stravinsky’s first thoughts for his last ballet, Agon.

Elgar & Walton Cello Concertos Steven Isserlis (cello), Philharmonia Orchestra/Paavo Järvi (Hyperion)

"It’s all very well, but you can’t call it a symphony". So said William Walton of Mahler’s Third, all six movements and a hundred minutes of it. Jakub Hrůša conducted the Philharmonia last night on fine if hardly infallible form in a performance notable for its restraint in a work remarkable for the excess which raised Walton’s eyebrow.

Vaughan Williams’s A Sea Symphony, premiered in 1909, is from perhaps the last era in which pieces readily found favour with both critics and audiences alike. It launched Vaughan Williams’s reputation as a major national figure at the age of 38, and has become a favourite of choral societies ever since. But looking beyond its status as a choral warhorse, how does it hold up more than a century after it was written?

Bernd Alois Zimmermann’s Nobody knows de trouble I see is a popular concerto, but it’s an unlikely hit. Zimmermann maintains a distanced relationship with the spiritual on which the work is based, and, while there are jazz elements too, this is a long way from crossover. Zimmermann maintains his modernist/serialist perspective throughout, and all the jazz ideas – the trombone glissandos, the sax section replacing the French horns, the vaguely improvisatory trumpet writing – are configured within a strict and austere single-movement structure.