While Friday night’s triptych of solo Bach began and ended in a sombre, contemplative place, the arc created for the second sequence by pairing the final sonata for solo violin with the second and third partitas is altogether more dramatic. In Ibragimova’s ordering we opened with the monolithic D minor Partita, warming through the C major Sonata before ending joyfully with the E major Partita.

I can’t be alone in often leaving a Proms violin concerto convinced that the Bach encore was the best bit. The Royal Albert Hall is a chameleon space, capable of dwarfing the largest orchestra and muting the weightiest of Wagnerian singers, but also of amplifying solo performances, lending them a clarity, an intimacy, unique to this unlikely venue. It’s a well-documented phenomenon, which makes it all the more surprising that so many of Bach’s solo works for violin are receiving their complete Proms premiere this weekend.

Roger Wright may be gone from the BBC Proms, replaced for now by a committee, but his legacy lives on. His zeal to recover areas of English musical culture that may be considered the festival’s birthright resulted last night in a first Proms performance of Sancta Civitas, which Vaughan Williams late in life accounted the favourite of his choral works.

After years of pussyfooting around pop, hoping the Pet Shop Boys will write something in a passable classical idiom, the Proms has embraced the most euphoric popular genre of all - dance - to its bosom. Pete Tong, long-standing Radio 1 presenter and DJ, is probably the high priest of this music, and under his guidance last night, Radio 1 and the Heritage Orchestra, conducted by Jules Buckley, brought a near-capacity Proms crowd to a booming climax in way that's quite possibly never happened before.

Gergiev’s programme for this concert raised eyebrows when the Proms were announced: all five Prokofiev piano concertos, presented in chronological order, over the course of a long evening. As it turned out, he had some good reasons for his plan. The three Russian pianists he lined up – Daniil Trifonov (Concertos 1 and 3), Sergei Babayan (2 and 5), and Alexei Volodin (4) – had between them the talent to carry any programme.

A packed Albert Hall told an instructive story: programme Holst’s The Planets at the Proms and you can dare to do anything in the first half. Besides, though it will be a red letter day when we don’t have to put “women” in front of “conductors”, the Marin Alsop Last Night effect may have kindled interest in Susanna Mälkki, top of a still too-small list from the two concerts I’ve heard her give with the BBC Symphony Orchestra.

After four years, 55 cities in 22 countries and an award-winning recording, Leif Ove Andsnes’s Beethoven journey came to an end last night in an emotionally charged evening at the Royal Albert Hall. And in a delightful light-hearted moment after all the serious music making was done, Andsnes finished the concert vigorously playing the tambourine in an orchestral encore.

Stop miking Bryn Terfel. Stop over-miking musicals; the show voices in a hybrid cast don’t need much. Too much ruined English National Opera’s recent Sweeney Todd, and in this Proms adaptation of Grange Park Opera’s summer crowd-pleaser it sent the voices ricocheting around the Albert Hall, making mush of the words and stridency of the few belt-it-out moments.

So to the second leg of Leif Ove Andsnes's journey through the Beethoven concertos, and a distressingly underpopulated Royal Albert Hall. Perhaps the punters were put off by the wintry weather, or perhaps by the dread names of Schoenberg and Stravinsky on the bill. Either way, it is shocking that Andsnes’s wonderful playing should have been to anything other than a full house.

Beethoven’s piano concertos have been no strangers to any Proms season. Only five years ago our own Paul Lewis embarked on a cycle not so very far, in terms of elegance and stylishness, from that of the present pianist-in-residence, Leif Ove Andsnes. Where Lewis proved a phenomenal trill-master, Andsnes’ runs and flights make his own approach especially rich and rare.