Yesterday would have been Leonard Bernstein’s 100th birthday, and who better to help Edinburgh celebrate it than Marin Alsop, Bernstein’s pupil at the Tanglewood Music Center at which he himself studied and which was such an integral part of his life – and with her of course, the Baltimore Symphony Orchestra, of which she has been music director for over a decade?

Alsop kicked the celebrations off by telling us about the eight piece suite A Bernstein Birthday Bouquet written for Lenny’s 70th (at Tanglewood, of course): each short piece (they were supposed to be 90 seconds long) written by a different composer. Alsop believes that they haven’t been played in the UK before, and we heard four of them. Luciano Berio’s contribution was a wittily crafted confection of Beethoven’s Fifth, Die Meistersinger von Nürnberg, The Star-Spangled Banner, and Happy Birthday; John Corigliano somehow contrived to interleave Fanfare for the Common Man with New York, New York, Taru Takemitsu wove intoxicating atmospheres around the rising three notes of Maria, John Williams spliced in bits of America. It was a fun platter of canapés to get us into the mood.

Next up was the more serious part of proceedings: the five movement violin concerto entitled Serenade (after Plato’s Symposium). Bernstein was inspired by many works of literature in his life, one of them being the Symposium, a strange piece which wraps the serious question of the nature of love into the narration of a (fictional) night of drunken revelry shared by Greek philosophers. Nicola Benedetti, who joined the Baltimore Symphony as soloist, is particularly adored by Scottish audiences, but this performance would have been a winner with anyone: her timbre is pure, her manner disarmingly unaffected in a way that well matches Alsop’s style on the podium: crisp, precise and no-nonsense while being completely involved. Serenade starts with a meandering, reflective solo violin line which is picked up in turn by the orchestral violins, violas and then cellos and basses before becoming more playful and thickening out in texture, the performance radiating benevolent good humour. The highlight, though, was the fourth movement, based on Agathon’s paean to the all-embracing power of love. Benedetti bewitched us with her ability to hold a line while the orchestra followed faithfully to fill out the texture.

After the interval, it was time for us to let our hair down and hit Broadway – or, to be precise, the gang-ridden mean streets of the Upper West Side with the Symphonic Dances from West Side Story. Even with the best of source material – and West Side Story is about as good as it gets – adapting Broadway for a classical orchestra is a risky business: showbands and Big Band jazz bands have swing and pizzazz built into their DNA; classical orchestras generally don’t. But Bernstein was a clever and polymathic composer, and the Baltimore Symphony proved that they can swing when they want to. From the off, the excitement generated was palpable, the filmic confrontation between the gangs building the tension to fever pitch.

Every section of a symphony orchestra deserves its day, and the Symphonic Dances make it the day for the percussion section. The back of whole orchestra was surrounded by percussion instruments – marimba, vibraphone, xylophone, glockenspiel and all manner of drums, gongs, bells, cymbals and things to shake. Sharing all these were the Baltimore’s timpanist and five percussionists, who were nothing short of awesome; most prominently, the vibraphone rang through the orchestral wash and commanded attention whenever it intervened. The synchronisation between orchestra and drum kit was also quite superb: the kit is being played at full rock-band pelt, arms flailing and feet pumping; the orchestra is somehow expected to keep perfect time, and the Baltimore Symphony were on the nail every time.

It’s not all tension and thunder: Bernstein artfully weaves schmaltzy tunes like Somewhere and Maria into symphonic form: the strings soar, French horn yearns, the flute introduces the last movement with grace and delicacy. It’s a great suite from a great musical, and Alsop and the Baltimore Symphony did it proud.

Concluded the official programme, Three Dance Episodes from “On the Town” entertained without quite achieving the same level of sparkle – the third dance in particular felt somewhat fragmented. Still, not being quite so taken up by the music allowed one to observe quite how close is the relationship between this conductor and this orchestra, how much they trust each other. Played as an encore, the overture to Candide sent us from Usher Hall into the cool Edinburgh evening with our spirits lifted. Happy Birthday, Lenny; thank you for your cultural omnivorousness and your ability to share it with us through your music.