The Royal Liverpool Philharmonic has something of a track record when it comes to finding conductors destined for great heights. After all, Sir Simon Rattle was a player in Merseyside Youth Orchestra and started his conducting career in Liverpool. The latest RLPO concert, following that great tradition, included a new face. And what an impact she made.

The concert season’s title may be Rachmaninoff Inside Out. But the work that dominated and got people talking in yesterday’s instalment of Vladimir Jurowski’s London Philharmonic series was by another composer entirely. “Weird, isn’t it?” said the man in the row behind. And that was only after the first movement of George Enescu’s massive Symphony No. 3, one of the most remarkable effusions by the composer and crack violinist chiefly known for his pair of Romanian Rhapsodies, popular picture postcards.

When you’re visiting someone for the first time, it’s probably just as well that you make a good impression – or else you may not be asked back. If that’s what the Carducci String Quartet was trying to do on their début visit to Liverpool, then they did all the right things.  They mesmerised the audience with their performance of the second of Beethoven’s "Razumovsky" quartets, so much so that they were forced to sit down and perform an encore, which turned out to be a little irreverent Shostakovich, in the shape of the Rondo Polka.

If what you wanted to do was go out to the middle of the Mexican desert, invert the Cross and dip it in blood, screaming obscenities all the while, surrounded by a sunburnt band of fellow travellers all off their heads on mescalin, Tutuguri is definitely the music you’d want to do it to.

Ernst Krenek is probably best remembered nowadays as the composer of Jonny Spielt Auf – the quintessential Zeitoper of Weimar Germany and later the archetype of all that was designated “degenerate” in art by the Nazi regime. And perhaps also as – briefly – the husband of Anna Mahler, daughter of Gustav. But Krenek was far more than that. He was a magpie collector of styles and influences whose large corpus of work reflects almost every major 20^th-century trend.

Barbara Hannigan, we all know, is game for anything. This Canadian soprano with the pearliest tones and the dramatic instincts of a Sarah Bernhardt can find beauty and meaning in almost every contemporary composer’s barbed wire. Recently she’s been cavorting on stage as Alban Berg’s Lulu; earlier this month, for a sliver of Ligeti, she paraded herself on the Barbican platform as a gum-chewing schoolgirl in a naughty micro-skirt.

Henry Mancini: The Classic Soundtrack Collection (Sony)

James Dillon calls this major work, premered at the Huddersfield Contemporary Music Festival last November, a “Cubist Stabat Mater”. He sets the hymn, but adds in more recent words, texts on related themes by Picasso, Kristeva and Rilke, among others. The music, too, acknowledges the passage of historical time, with subtle references to musical styles from down the centuries. If this all sounds like a recipe for Postmodern intellectualism and detachment, the results are surprisingly direct – a heartfelt and emphatic response to the image of the grieving mother.

Latvia likes to be different. At least that’s the message they sent out with the cultural programme marking the start of the country’s presidency of the Council of the European Union. Pomp and circumstance were out, and instead we got a Cage-inspired happening, an audio/visual presentation that was many things: part video installation, part performance art. The only thing you couldn’t describe it as was a choral concert.

The mixed grilled school of programme-making is not for the JACK Quartet. Contemporary, contemporary, and contemporary: that was the bill of fare last night at this challenging recital offered by the young American group, graduates of the Eastman School of Music, who derive their capitalised title from the initial letters of the members’ first names. Like the Arditti String Quartet, one of their mentors, you’d never find them playing Schubert. Even someone as gutsy and game-changing as Beethoven appears to be well off the menu.