After three days' motoring and clambering around the most awesome natural landscapes I've ever seen, how could a mere concert hall in a city the size of Cambridge begin to compare?

Some things just don’t seem to belong in a pairing. The flute and the French horn both have their distinct sonic personality. It wouldn’t be going out on a limb to suggest that the average listener tends to lean towards one or the other. Even Mozart wrote for the horn out of love but trotted out his flute compositions for money. But opposites can and do attract and so it once more proves in a new recording featuring the horn and the flute and, discreetly chaperoning the pair of them, the piano.

I’m standing with my feet on peaks and my head in clouds, looking down steep Alps at the tiny chocolate-brown chalets of little Verbier way below on the green slopes. It’s ravishing up here on the top of Fontanet, and I tarry, gloating over the botanical riches around me of milky-blue gentians, royal-blue harebells, glistening edelweiss, dark little orchids and garnet-bright sedum, watching the trickling water of a brook, and replaying last night’s music in my head. And if you move quick you can do this yourself before next Sunday.

Getting to Mull is an improbably romantic journey to classical music-making. One can easily understand why Mendelssohn was so affected by his experiences in Scotland – and Mull. On the three-hour train journey from Glasgow one sheds the habits of everyday life: the train winds through thickets of Forestry Commission plantations, which suddenly open out into wild panoramas of mountains and lochs, or a dramatic ruined castle against the skyline.

For so many days a year, Cheltenham's Regency symmetry and conservative values totter and buckle as they veer dangerously towards relative festive liberalism. As I sliced into one of the four annual beanfeasts, the Cheltenham Music Festival, it struck me how well lopsided, sometimes painful bendings of a classical framework by Schumann and Brahms sat with a battery of volatile percussion celebrating Steve Reich's 75th birthday. Even the adventure served up by trebles over in Norman and medieval Tewkesbury glimpsed a beast in the jungle.

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.

When Alfred Brendel first mentioned Kit Armstrong to me, in early 2008, I knew there was a film there. He was brimming with excitement: Kit had come to him with an interpretation of a Chopin Nocturne that displayed a command and maturity that was baffling considering Kit was 13 at the time of the recording. Alfred led me into his inner sanctum, a practice room filled to bursting with two Steinways, a large carved idol from New Guinea, Liszt’s death mask and a rich and varied collection of paintings and images, some of them revealing the pianist’s wicked Dadaist sense of humour.

Cambridge University, cradle of Newton, Keynes and Wittgenstein, of Wordsworth, Turing and Tennyson, has produced 15 prime ministers and more Nobel Prize-winners than most nations. In its 200-year history, the university’s debating society has hosted princes, politicians and leaders in every field: the Dalai Lama, Winston Churchill, Nelson Mandela, and last week a 25-year-old east-London DJ, Kissy Sell Out.

It’s Holy Wednesday in Cuenca, and going round the corner into Cathedral Square I’m surrounded by hordes of guys in multicoloured mufti who look like the Ku Klux Klan, with unnecessarily pointy hoods. Twenty of them are carrying a heavy float with a large statue of Jesus on it. In Cuenca things are fairly austere, compared to other places where there’s a lot of self-whipping, or where, if you have sin on your conscience, you may end up banging nails into your hands, as in Mexico. Still there are alternative amusements – the Copa Del Rey final of Real Madrid v Barcelona is blaring out of bars – and it’s the 50th edition of Cuenca’s Religious Music Festival.

In the later 19th century, violinist and composer Joseph Joachim was hailed as the most brilliant fiddler of his day, but today his name lives on via the great works that he helped to bring into the classical repertoire. Brahms dedicated his Violin Concerto to Joachim, while Bruch's First Violin Concerto was substantially revised by Joachim and became closely identified with him. Both the Schumann and Dvořák concertos were written for him, though Joachim never performed the latter.