For once the chandeliers were literally that: as six dozen flickering candles went up, so a figure in white floated down from the rafters in the semi-darkness. Her gown may have been virginal, but the word "Music" scrawled across her chest in punkish scarlet warned of lively diversion. It was an arresting opening to an inaugural union: the Jacobean-style Sam Wanamaker Playhouse at Shakespeare's Globe was about to witness a musical performance for the first time, in a collaboration with the Royal Opera House.

This exuberant start set the mood for an evening of high-class, high-camp, high-art pleasure. Baroque opera, for all the current insatiable hunger to explore the form, remains full of untapped repertoire. L'Ormindo, Francesco Cavalli's 1644 opera, would be new terrain for most of those present in the immaculate, pale-wood 340-seat theatre. Of the Venetian composer's more than 40 operas, only two-thirds have survived and but a handful are performed, with La Calisto the best known.

L'Ormindo proved an excellent choice. The music is lavish and bursting with variety, while the plot proves – for the most part – shameless and saucy. A young wife, tiring of her elderly husband, swoons over two youthful lovers only to find that her preferred choice – Prince Ormindo – is her husband's long-lost son. This turns out to be more convenient than it sounds, and all ends happily. Nine singers, several making their Royal Opera debut, share the roles of human lovers and supernatural forces: Lady Luck, Love, Wind, Destiny and so forth. There is disguise and cross-dressing, false magic and a trick sleeping draft. They also do a top job of relighting candelabras and chandeliers. In Kasper Holten's graceful staging, wholly audible in Christopher Cowell's English translation and with gorgeous Venetian-Oriental costumes by Anja Vang Kragh, the opera came to sparkling life.

Yet Cavalli (1602-76) was never content to entertain. This is far more than a romp. His hallmark is a gift of dark-light contrast, ever slipping from comedy to near tragedy in a quest to reflect human emotion. In this three-act work, tears and laughter alternate in the recognition scene in which the unfaithful but irresistible Amidas (Ed Lyon) is reunited with his first love, Sicle (Joélle Harvey, whose purity and lightness of tone were a joy).

The opera's climax is a prison scene, when the other pair of loves, Ormindo and Erisbe, think their end is near. The harmonies squeeze downward in torment, a ground bass (as used to similar effect by Purcell in Dido's lament) drives the music to grief. The tenor Samuel Boden in the title role and Susanna Hurrell's Erisbe rose to the occasion, intense but never exaggerated. Two ROH Jette Parker Young Artists, mezzo Rachel Kelly and baritone Ashley Riches, made strong impressions as Mirinda and Osman, with Graeme Broadbent, Harry Nicoll and James Laing completing a sterling cast.

Given the intimacy of the space, the audience is nearly part of the action, which is all to the good: no chance for passive watching here. From where I sat, I could hear (perfectly) but not see the small orchestra, hidden up in their gallery. But it was clear, not least from the virtuosic guitar/theorbo playing, this was a crack ensemble. Checking the eight names later, I was not surprised to find it was Elizabeth Kenny, one of Europe's leading baroque musicians.

Her imagination and esprit were matched, if necessarily less prominently, by all. Christian Curnyn, a master of this repertoire, directed from the harpsichord with energy, flair and control. Last week the Royal Opera announced another new collaboration, with the Roundhouse in January 2015, for Monteverdi's L'Orfeo, directed by Michael Boyd and again conducted by Curnyn. This is an exciting way forward for the ROH to perform early repertoire with young voices.

The journey from chamber baroque opera to small-scale contemporary music is less arduous than might appear. Just as Curnyn's conducting illuminated the textures of Cavalli's scoring, so the Nash Ensemble's talent is to give equal voice to chamber music in any variety of instrumental combinations. Their concert on Wednesday combined works by Elliott Carter and Harrison Birtwistle with John Adams' Shaker Loops (1978).

This last, a seminal American minimalist classic, felt odd man out in the context, though the seven string players required did a fine job. Its emphasis on repetition and oscillation, creating what Adams calls a "rippling, shimmering complex of patterns", is a polar opposite to the sparks and shards of Carter's Mosaic (2004). Two recent Birtwistle works, Fantasia upon all the notes and The Moth Requiem, formed the centrepiece, in celebration of his 80th birthday this year. This music seems both to implode and explode; glittering, igneous rock to Adams' rippling surface.

Both pieces make percussive and vigorous use of the harp, Birtwistle's favourite instrument. The requiem, set to a poem by Robin Blaser and an inventory of extinct moths, employs three, together with 12 female voices and alto flute. First heard at the Proms last year, it sounded more anguished, more bleak and yet more luminous, the alto flute (played by the matchless Philippa Davies) weaving a ceaseless dark lament through the whole. The fantasia is also elegiac, dedicated to the composer's friend and publisher – "for Tony Fell in sorrow and anger".

The harp changes constantly between modes – the harpist's feet on the pedals performed their own dance – with the rest of the ensemble pairing and separating in swiftly shifting variety. Single notes, now clarinet or flute, now one of the quartet of strings, cut lines through the fragmentary entity. It brought to mind – of all unlikely composers – Beethoven, specifically the Scherzo from his Op. 59 No 1 (Razumovsky), heard at a Wigmore Hall lunchtime concert by the Belcea Quartet earlier in the week.

In that startling second movement, it's as if Beethoven had jumped forward two centuries, his preoccupations astonishingly close to both Carter and Birtwistle. Each bar is a surprise. If you have some idea that string quartets are comfortable and refined, try this. Tiny musical ideas are wedged hard up against each other, in kaleidoscopic contrast, bursting out into wild harmonies and remote invention that leave you gasping and puzzled. No music is more unsettling, particularly when played with the clean-lined clarity of the Belcea Quartet.

You can listen to it on Radio 3 iPlayer until Monday lunchtime. For that, warm thanks to Roger Wright, who announced last week that he will stop running BBC Radio 3 and the Proms to become chief executive of Aldeburgh Music. Who might take over at the BBC and how they should shape these totems of British musical life are issues for another day.

Star ratings (out of 5)
L'Ormindo *****
Nash Ensemble ****
Belcea Quartet ****