How can even a generously proportioned documentary do justice to one of the musical world’s greatest life forces? John Bridcut knows what to do: make sure all your interviewees have a close personal association with your chosen giant in one of his many spheres of influence, then get cellist-disciples from Rostropovich’s Class 19 in the Moscow Conservatoire – here Moray Welsh, Natalia Gutman, Karine Georgian and Elizabeth Wilson - to watch and listen to their mentor talking and playing. The result is a towering model of its kind.

A 50^th birthday is a landmark occasion. One has plenty to look back on, whilst still having much to look forward to. Plus there’s all that life experience to draw on. What’s not to feel positive about? In the case of a gallery that’s built up a remarkable reputation as an innovative space for contemporary art outside London, sheer staying power is surely to be cheered and celebrated – "hear hear" for the next 50 years, and so forth.

Bach: The Well-Tempered Clavier, Books 1 and 2 Roger Woodward - piano (Celestial Harmonies)

It’s not like we’re short of operas. Thousands of works spanning over 400 years make up the western operatic repertoire. Of these maybe 100 get a regular airing in contemporary opera houses, with only about 20 making it into the popular consciousness. For the rest, a trip outside the archives is rare indeed, with many scores still vainly awaiting their “modern premiere”. So why then, with so many works to choose from, do directors persist in returning to Bach – who famously never composed an opera – for inspiration?

A legendary septuagenarian wind player from Switzerland returns to the repertoire with which he made his name 50 years ago, and there's an exciting live reading of a gloomy fin-de-siècle symphony conducted by a contemporary French giant. The same conductor also treats us to a sparkling Stravinsky rarity, and a youthful duo lighten the mood with some Russian fireworks on Merseyside.

This year’s Choral Sundays at the Proms are a wonderfully mixed bag. Mighty choral touchstones are represented by Mendelssohn’s Elijah, both the Verdi and Mozart Requiems and Beethoven Missa solemnis, but there’s also an enticing strand of curiosities. Looming largest among these has of course been Brian’s Gothic Symphony, but emerging now from its sprawling shadow are less obscure but no less interesting works – Britten’s Spring Symphony, and last night Mahler’s folkloric Opus 1 cantata Das klagende lied.

Youth was everywhere to be seen at the Proms last night. Whether in the massed ranks of Britain’s National Youth Orchestra, soloist Ben Grosvenor (even younger than the precocious Benjamin Britten when he debuted his own Piano Concerto in 1938), Prokofiev’s Romeo and Juliet, or DJ-turned-composer Gabriel Prokofiev, it was an evening celebrating the scope of the teenage experience. Even the Late Night Prom joined in the party, coming courtesy of Nigel Kennedy, still surely the oldest and most defiant teenager in classical music.

Nine out of 10 attempts to feed an audience's visual responses to abstract music are doomed to failure; a great communicator will always conjure stronger pictures in the listener's mind. And there's no doubt that young violinist Alina Ibragimova communicates at the highest level. But here she simply held her own to work in shadowplay with both the mysterious spaces of London's most atmospheric venue and the even more intangible visions of twins Timothy and Stephan Quay. Their film around Bartók's Solo Violin Sonata, though defying intellectual analysis and easy correspondence with the musical ideas, is pure choreographic poetry.

The history of maths and music is the history of early Greek philosophy, medieval astronomy, of the Reformation, the Enlightenment and the two World Wars. While mathematics at its purest may be an abstraction, the quest for its proofs is deeply and definingly human, charged with biological, theological and even political motive. Whether through performance or discussions about music, this year’s Cheltenham Music Festival (which begins this week) explores the mathematical processes that have both shaped and echoed the history of Western Europe and its art, tracing musical development from the polyphonic motets of the 14th and 15th centuries to the Minimalist patternings of Steve Reich.

The two-course evening out is made possible by the Wigmore Hall’s late Friday-night concerts, so if you get out of a central-London show - or dinner - by, say, 9.30, you can add a second layer of entertainment at 10. In my case, a ferociously poor hour spent at contemporary dance in Sadler’s Wells was offset by an hour with Joanna MacGregor in a stimulating splicing of Bach and Shostakovich piano music that at least offered something to think about, if not ultimate satisfaction. Evening not entirely wasted, then.