It has been, we can safely agree, a truly terrible week. Art, culture, call it what you will, is unequal to the task of diagnosing a nation’s ills, let alone curing them. But on a night such as the inaugural Comedy Prom, it comes equipped with healing balm. This evening was maybe not perfect. There were wrinkles, little bits here and there that didn’t quite work. But the Saturday night that the BBC Proms gave over to the business of laughter could not have been more opportune. This is going to sound hokey, but comedy on this occasion brought its audience close to a state of grace.

Several Prommers fainted, possibly out of boredom, in a longer than ever first movement of the Brahms Violin Concerto. The boredom, palpable around me, came not from pianist Dejan Lazić transcribing the fiddle part for his own pleasure - a communicative musician might have made us forget the original - but from the failure of Brahms's song to soar. Dyspeptic by half-time, I found everything awry: several obscure concert overtures would have worked better than Frank Bridge's Rebus, I'd have preferred many short cello-and-orchestra pieces to Holst's Invocation and thought any conductor might suit Elgar's Enigma Variations better than Vassily Sinaisky. Wrong, fortunately, on the last two counts.

What a difference a change of scene makes. During Sakari Oramo’s 10 years at the helm of the City of Birmingham Symphony Orchestra he wasn’t exactly diffident; but you felt you could invite him to tea without any crockery getting broken. Now, I’m not so sure. Last night at the Proms, conducting one of his three current babies, the Royal Stockholm Philharmonic Orchestra, his arms spun like windmills. His torso lunged to the left, then to the right. With energetic facial expressions he made love, picked a fight, grinned like a clown - whatever was needed to propel the emotional dramas of his all-Scandinavian programme. And the orchestra seemed wired to his every move. I’ve never heard such an exciting or compelling performance of Nielsen’s Symphony No 4, The Inextinguishable – the symphony with the duelling timpani, and certainly inextinguishable on Monday night.

This year’s Choral Sundays at the Proms are a wonderfully mixed bag. Mighty choral touchstones are represented by Mendelssohn’s Elijah, both the Verdi and Mozart Requiems and Beethoven Missa solemnis, but there’s also an enticing strand of curiosities. Looming largest among these has of course been Brian’s Gothic Symphony, but emerging now from its sprawling shadow are less obscure but no less interesting works – Britten’s Spring Symphony, and last night Mahler’s folkloric Opus 1 cantata Das klagende lied.

Tim Minchin, the Australian minstrel comedian, is known by his catweazel hair, thickly kohled eyes and dazzlingly witty songs bashed out at a grand piano about, among other things, the debatable existence of the Almighty. Lately his repertoire of tricks has been expanding. He has toured his show with a full orchestra, he wrote the songs for the RSC's rapturously received stage adaptation of Roald Dahl's Matilda (which comes to the West End this autumn) and on Saturday he is hosting the first ever Comedy Prom.

Youth was everywhere to be seen at the Proms last night. Whether in the massed ranks of Britain’s National Youth Orchestra, soloist Ben Grosvenor (even younger than the precocious Benjamin Britten when he debuted his own Piano Concerto in 1938), Prokofiev’s Romeo and Juliet, or DJ-turned-composer Gabriel Prokofiev, it was an evening celebrating the scope of the teenage experience. Even the Late Night Prom joined in the party, coming courtesy of Nigel Kennedy, still surely the oldest and most defiant teenager in classical music.

Marley & Me: that’s the film about living with a neurotic dog, out now on DVD. And Mahler & Me? It could be the Gustavo Dudamel story. Conducting Mahler was what first brought everyone’s favourite Venezuelan to world attention, when he won the 2004 Mahler Competition in Bamberg. Given the turbo-charged excitement always stirred by his Simon Bolívar players – no Youth Orchestra now, mark you, but a Symphony Orchestra, grown-up, professional – this Prom visit would have been sold out long ago even if they were playing Glazunov.

Leonard Tanner, my old choirmaster, used to say that Brahms was a composer with his feet in three different camps: the Baroque period, the Classical period, and the Romantic. Possibly he had a fourth leg too, poking into the music of the future. Composers adept at these multiple postures filled Thursday’s sometimes lustrous orchestral Prom given by the BBC Scottish Symphony Orchestra and their chief conductor Donald Runnicles. Brahms was represented of course (the Second Symphony); also the great nostalgist Richard Strauss, watering his old age and the wasteland of defeated Germany with his Four Last Songs.

According to Classic FM’s managing director Darren Henley there are many people who find the term “chamber music” offputting, if not downright intimidating. Perhaps the best explanation of the genre comes from a musicologist who has termed it “the music of friends”. It’s a lovely description and one that, for the very best ensembles, can extend beyond the confines of quartets or duos to even the largest of symphony orchestras.

Jealousy of people who live in Birmingham is not (I venture to hazard) so widespread a phenomenon as to merit a name all its own. After last night’s Prom from the CBSO and music director Andris Nelsons however, a term may well have to be coined for all of us Londoners whose green-eared envy seems unlikely to abate any time soon. We’ve heard the recordings and the rumours of greatness trickling down from the West Midlands, but the opportunity to see this partnership in action further south is rare. Conquering the Royal Albert Hall with an evening of generous, emotive music-making, the CBSO have issued quite the challenge to their London rivals.