Want to learn more about 20^th century music in action? Starting tomorrow, you could lose yourself in the labyrinth of the Southbank’s year-long The Rest is Noise festival, and plough your way through Alex Ross’s monumental but partisan study of that name. Or you could learn a lot in a short space of time from John Adams’s mini-residency with the LSO at the Barbican.

Once upon a time, Gyorgy Ligeti heard a rehearsal performance of a piece of music he wrote soon after graduating from the Franz Liszt Academy of Music in Budapest. Just once. Then it was banned by the Hungarian apparatchiks responsible for the arts and he had to wait another 20 years to hear it played in public. It was the Concert Romanesc (Romanian Concerto), written in 1951 and drawing from his memories of, and research into, the folk music of the Romanian Transylvania of his boyhood.

It was the kind of programme that great pianist Vladimir Horowitz used to pioneer, with the simple balm of Scarlatti offset by Scriabin’s flights of fancy, and a dash of virtuoso fireworks to conclude. Though he is an admirer of the master, and even featured Horowitz’s hyperintensification of an already extravagant Liszt transcription in this recital, Yevgeny Sudbin is very much his own man: a thinker verging on the visionary who always seems to know exactly where the more extreme fantasists among his chosen composers are heading.

Elgar declared a “massive hope in the future” as the human programme behind his epic First Symphony’s final exultant sprint. That hope was sprinkled like gold dust around the featured artists of this all-English concert. There are good reasons to be optimistic about the effective, colourful scores of 32-year-old Anna Clyne; we know that Benjamin Grosvenor, her junior by 12 years, is already a pianist of mercurial assurance, a real front-runner.

Bartók, Eötvös, Ligeti – Violin Concertos Patricia Kopatchinskaja (violin), Frankfurt Radio Symphony Orchestra, Ensemble Modern/Peter Eötvös (Naïve)

Holst? Yes. Britten? Maybe. But John Adams? Programming Adams’ Guide to Strange Places as the extended opener in this National Youth Orchestra of Great Britain concert made complete sense after a few minutes; conductor John Wilson’s strengths as an interpreter of Hollywood film scores and British light music made him ideally suited to unpick the thornier metrical complexities of the Adams work. Wilson’s beat is disarmingly precise, every gear change spelt out with refreshing precision.

Faced with yet another world premiere from his friends in the Borodin Quartet, Shostakovich severely asked them whether they’d yet played all of Haydn’s quartets (they hadn’t). As a listener, I feel the same about Bach’s cantatas. Whether or not a lifetime will be enough to catch each of these varied and ever surprising little miracles in the flesh, Kings Place’s Bach Unwrapped series includes a chance to hear nearly 30 of the 200 from seven different ensembles in less than a year. Unfortunately it looks as if I drew the short straw at the end of the first four concerts.

The Mayan calendar recently suggested it was all over. It is now, almost. 2012 was, by anyone’s lights, an annus mirabilis for culture on these shores. The world came to the United Kingdom, and the kingdom was indeed more or less united by a genuine aura of inclusion. Clumps of funding were hurled in the general direction of the Cultural Olympiad, which became known as the London 2012 Festival, and all sorts leapt aboard. Just for a start, those opera companies who had been burning to perform a version of Vivaldi's L'Olimpiade could now finally proceed.

Messiahs of all kinds multiply at this time of year: the meek and the threadbare as well as the proud and polished. On the Sunday before Christmas, it was hard to choose between two potential archangels who could hardly fail given their respective pedigrees. It may have initially come down to a choice between single star soloists, soprano of the year Sophie Bevan at the Wigmore or flawless countertenor Iestyn Davies (pictured below by Marco Borggreve) at St John’s.

Valery Gergiev’s exploration of the music of Karol Szymanowski is one of the most vitalising series mounted at the Barbican in recent years - to compare, say, with Sir Colin Davis’s Sibelius and Berlioz, Michael Tilson Thomas’s tributes to Leonard Bernstein, or Gergiev’s own Shostakovich and (increasingly) Prokofiev.