A pair of auspicious debuts marked the City of Birmingham Symphony Orchestra's Prom: Mirga Gražinytė-Tyla was making her London debut, just a day after her first concert as its new music director; plus it was the first time that Hans Abrahamsen's song cycle let me tell you, based on text manipulating Ophelia's words in Hamlet, was to be heard in the capital. Both made remarkable impressions, from the faintest footprint in Abrahamsen's aural snowscape to fate hammering at the door in Tchaikovsky's Fourth.

The concert's opening chords also knocked at the door – in this case, at the Masonic temple – in Mozart's overture to The Magic Flute. It immediately offered an insight into Gražinyte-Tyla's dynamic style, whiplash baton flicks coupled with sharp left-hand jabs packing plenty of punch into her speedy Mozart.

let me tell you is the second work this week at the Proms to draw inspiration from Hamlet. But where Tchaikovsky's fantasy overture paints a doom-laden portrait of the troubled “sweet prince” in rich oils, Hans Abrahamsen turns to Ophelia instead in a ravishing “snow landscape”. His song cycle draws its text from Paul Griffiths' oulipian novella, where he restricts himself to the 481 words Shakespeare allows Ophelia in his play. I find the book maddening, the author voluntarily donning a lexical strait-jacket. However, Abrahamsen's word painting and his dappled orchestral score draw poetry from the seven selected texts.

Soprano Barbara Hannigan, as much a muse as Ophelia (having instigated the commission), gave a bewitching performance, willowy arms sculpting the air. She negotiated the score's ululating vocal line, with its repeated syllable flutters and jagged leaps with ease, colouring high notes differently each time. Ophelia's descent into madness echoes Hamlet's feigned insanity and the soprano is instructed in the score to sing “with broken voice”. Hannigan's Ophelia is both fragile and fierce. In the play, Ophelia drowns herself in the brook. Here she wanders off into the snow, merging into the wintry landscape, gliding and fluttering to the ground like a drifting snowflake. And what a landscape Abrahamsen paints, clusters of microtones over the soft tread of xylophone ostinatos, silvery piccolo shards of glass and spectral high violins. Glockenspiel, celesta and harp daub their icy tintinnabulations, while paper is grazed over the skin of the bass drum. Even if Hannigan's words did not always carry across the Royal Albert Hall's difficult acoustic, under Gražinytė-Tyla's hypnotic beat, the music entranced.

The interpretation of Tchaikovsky's Symphony no. 4 in F minor was full of thought and incident. The fateful opening fanfares were crisply delivered – with meticulous care over dynamics – and the development section was lovingly caressed, although momentum sagged once or twice. Gražinytė-Tyla's energetic conducting clearly signals what she wants, from the flick of the wrist to a left-hand 'claw', a hip wiggle to a slowly raised hand giving the lower brass free rein. She wields a baton with dramatic flair, but in the pizzicato Scherzo she led with an inviting hand and a graceful smile. A couple of pregnant pauses displayed bags of personality and only the symphony's coda, the percussion leading off a tad too fast, threatened to derail her, but a quick recovery led to a triumphant finale.

Clambering to the back of the platform to retrieve a percussionist's music stand, Gražinytė-Tyla brought it – and him – to just behind the second violins, his triangle launching the Diamond Fairy's sparkling variation and coda from the final act of The Sleeping Beauty. “See you in Birmingham!” she piped while its final note still resounded. No doubt about that.