You know what they say about men with big hands. Christian Thielemann has them, that’s for sure. Massive, meat-cleaving clappers, carving through the air. They give a pretty heavy upbeat too, and a generalissimo’s point and jab for a cue. If you’re a back-desk violinist in the Dresden Staatskapelle, you know when you’ve been Thielemanned.

Soft power in the shape of cultural ambassadors can go a long way. With a little help from its big guns in banking and industry, Germany has given this year's Proms no less than four of its major orchestras – from Leipzig, two from Berlin, and now from Dresden: all the more reason to wave those EU flags on a typically international Last Night in three days' time.

Daniel Barenboim is as distinctive as he is unpredictable. His considerable strengths – dynamism, passion, keen intellectual engagement – are balanced by some notable weaknesses – clunky tempo changes, lack of detail – but all configure differently in each performance. This Prom was a success largely for the fresh perspectives he brought to Mozart and Bruckner, both composers prone to stiffness and formality from less adventurous performers.

Gone, it seems, is the era of epic three-part Proms. Sunday afternoon's programme, partly billed as a children's hour, might have pleased pianist and pundit Stephen Hough, whose recent broadsheet plea for shorter concerts somewhat overdid the need (lunchtime events already cater to concertgoers in a hurry very well, and the Proms has its late-nighters too). But it left many of us wanting more, not just of Ravel in the second half but also of the distinctive Simón Bolívar earthiness, which was given free rein only in one spirited encore.

Between the Berlin Philharmonic, Leipzig Gewandhaus Orchestra and Simón Bolivar Symphony Orchestra it has been a big week at the Proms, in every sense. Scope and scale have been the watchwords for the orchestral tectonics that have taken place, the sonic landscapes that have been formed and reformed. But concert-goers on Sunday night were hit with an operatic aftershock of overwhelming force, bringing this penultimate Proms week to a close next weekend’s patriotic spectacular will struggle to match.

The BBC Proms is perhaps the only music festival in the world that would (or could) have programmed performances of Steve Reich in a Peckham car-park and Brahms by the Berlin Philharmonic within a few hours of each other. The audacity of it is glorious, the breadth exhilarating, and the fact that both sold out intensely heartening.

What do Boulez's Éclat, for 15 instruments, and Mahler's Seventh Symphony, for over 100, have in common? Most obviously, guitar and mandolin, symbols of a wider interest in unusual sonorities. But while Boulez aims, as often, for needle point precision, Mahler uses selective groups, at least up to his finale when he exuberantly exchanges night for day, to create peculiar and unsettling grades of chiaroscuro.

The BBC Proms is the largest classical music festival in the world – an event whose ambition, accessibility and breadth wouldn’t be possible without the Royal Albert Hall and its capacity of well over 5,000 people. But the building that makes this festival possible, that provides the space for the hundreds of Prommers who fill the arena each evening, is also its biggest curse. Its unwieldy, awkward acoustic is a problem that must be faced and resolved every night, and when it comes to Early Music, it’s a resolution that’s partial at best.

Californian saxophone phenomenon Kamasi Washington is never knowingly understated. He rocked up for his Proms debut on Tuesday night having led a vast musical entourage on tour across Europe all summer, and delivered an ecstatic, if occasionally verbose, statement of intent. There were problems with both the performance and one or two of the compositions. But as a live experience, it was, in places, euphoric. Only a determined curmudgeon could leave without a grin.

Branding, as any marketing manager will tell you, is everything when it comes to selling, and when it comes to selling, classical music is no different from cars, cornflakes or shampoo. It explains why a Mahler orchestral song-cycle would fill the Royal Albert Hall while a similar work by his love-rival and near-contemporary Alexander von Zemlinsky last night left it half empty.