Brighton Festival, Various venues, BrightonGiustino, Trinity College of Music, London

In Brighton, 'Giovanna d'Arco' was performed next to Anish Kapoor's sculpture of dismemberment

It must have been a noisy place, the mind of Joan of Arc. All those visions, all those voices, the tinnitus of celestial commands. From Schiller to Shaw, Tchaikovsky to Verdi, Anatole France to Marina Warner, the story of the 19-year-old patriot, visionary and virgin has fascinated artists and historians.

And, on Monday afternoon, while riot police and anti-war protesters fought in the pleasure gardens, two readings of the same legend collided in the crumbling concrete of Brighton's Old Municipal Market as Anna Grevelius and Chamber Domaine performed Rossini's Giovanna d'Arco from among the blood-red body-parts of Anish Kapoor's Dismemberment of Jeanne d'Arc.

Written for mezzo-soprano and piano in 1832, for private performance by the celebrated courtesan Olympia Pélissier (later to be Rossini's second wife), Giovanna d'Arco celebrates the tomboy heroine of France in limpid, moon-bathed whispers and defiant fioritura. The flames invoked are not those of the stake but those in the eyes of the Angel of Death, for this is Joan on the eve of battle, devout but untried, "a lamb among lions". Orchestrated by Salvatore Sciarrino in 1989, in Rossini's favoured rose and violet timbres, the gran scena's pathos is intensified. A dove-like flute (Anna Wolstenholme) answers Giovanna's plangent questions, a jubilant clarinet (Duncan Prescott) cheers her on through the victory cabaletta, while the bassoons and cellos press and push below, warning of retribution.

It is a measure of Rossini's sophistication that the pity of Giovanna d'Arco works independently from the listener's knowledge of the violent end that awaited Giovanna. Youth and bravery are what touches, and Grevelius's faultless performance – first gently insinuated then incendiary – captured these qualities. Singing from a white scaffold, with the players and conductor Thomas Kemp below, the pure-toned ingénue was a startling contrast to Kapoor's five-part installation: two severed limbs, two conical mounds of igneous rubble, a deep, oval void hacked into the floor; brutal centrepiece of Brighton Festival's sculpture trail and the "after" to Rossini's "before". This is Joan the victim of sexual mutilation: her womb eviscerated, her breasts sliced off, the femininity concealed beneath her armour laid bare and bloody. It didn't happen. Though 15th-century executions operated on the more-is-more principle, her body was burned twice to avoid leaving relics, her ashes scattered in the Seine, her story left open to centuries of interpretations.

There was more girlish vulnerability in Kate Royal's lunchtime lieder recital at the Pavilion Theatre, and another violent death. Schumann's Maria Stuart Lieder progresses from the poignancy of the young queen's "Abschied nach Frankenreich", through the urgency of "An die Königen Elisabeth" and on to the resignation of "Abschied von der Welt" and the final, austere playout of "Gebet". In this, as in Brahms's blanched and bitter "Anklänge", in the exuberant birdsong of "Nachtigallen schwingen" and in the wild lovers' metaphors of "Wie die Wolke nach der Sonne", pianist Christopher Glynn's sensitive voicing and nimble articulation were as impressive as Royal's expressivity. Hers is a generous, open, frank voice that sounds as though it could burst into laughter or tears at any second – and she's a persuasive storyteller.

Save for the Takács Quartet's assured and well-contrasted programme of Haydn, Bartók and Schumann at the Brighton Dome, this has been a week dominated by youthful heroics. In the Old Royal Naval College Chapel, Greenwich, there was a double dose: that of Giustino, the bear-battling, monster-murdering shepherd-turned-soldier of Handel's 1737 opera, and that of Trinity College of Music Baroque Orchestra, which made its debut in Olivia Fuchs's production, coached and led by baroque violinist Walter Reiter, and conducted from the harpsichord by Philip Thorby.

Long dogged by its runt-of-the-litter reputation among London's conservatoires, Trinity fielded a stylish ensemble, with vividly varied articulation, tone and phrasing from the violins, a delectable trio of recorders (Emma Williams, Julie Dean and Alice Clarke), and an alert and characterful continuo double-bass (Jan Zahourek). Ellan Parry and Johanna Town's production and lighting designs conjured Constantinople's seashore and imperial palace from little more than scaffolding and a scrunch of plastic sheeting, sending miniature battleships speeding across the nave on pulleys and concocting a sea-monster from two giant lobster claws.

Fuchs mobilised her whooping cast of clowns, cleaners, sailors, princesses and political predators through Wren's handsome aisle and galleries. The lack of surtitles (too expensive) proved advantageous as the singers worked overtime to convey the emotional roller-coaster of military machinations, romantic intrigues and improbable perils in song and gesture. This was an infectiously charming, energetic show, with some notably poised singing from young soprano Zoe Bonner (Arianna) and her mezzo sidekick Georgina Murray (Leocasta). Daniel Roddick's feline Amanzio, Peter Kirk's athletic Vitaliano and Matthew Kellett's Polidarte played for maximum laughter, Helena Daffern worked the boy-girl travesto thing as Anastasio, while Cara Curran's shy, bespectacled, valiant Giustino handled her heavy, glossy contralto voice with the half-excited, half-terrified air of a learner driver at the wheel of a very large car.

Festival to 24 May (01273-709709)