One man. Four strings. Thirty-six dance movements. Five thousand listeners, perfectly hushed, many of them having queued for hours and rushed to fill the promenade space of the Royal Albert Hall as soon as the ushers let them out of their starting blocks. Yo-Yo Ma's late night Prom – a performance of all six of Bach's unaccompanied cello suites – was an eagerly anticipated event and a giant undertaking. Many of the audience were cellists (two and half hours of unaccompanied cello is a tall order for anyone else) and the atmosphere in the hall was electric.

The six suites form a regular, mathematical pattern: six suites of six movements each, all following the form of Prelude, Allemande, Courante, Sarabande, a pair of dances (Minuets, Bourrées or Gavottes) and Gigue. But within that apparently rigid form, Bach is utterly unpredictable, both in mood – from contemplative to impish to joyful – and in his use of harmony and rhythm. The genius of the music lies in the way Bach grabs you and takes you on a journey into unknown territory: your ears have no way of predicting which turn will come next, but you always feel in safe hands and deeply satisfied by the outcome.

However great the level of that genius, to maintain that variety and the sense of progression over all six suites, played from memory at a single sitting, is a huge challenge. But if anyone is equipped to meet the challenge, Yo Yo Ma is that person: it's over 30 years since he won a Grammy for his recording of the suites, and his performance showed a freshness and vitality undimmed by those years.

It would be pointless for me to attempt to run through every movement of every suite, so I will describe generalities. Firstly, Ma consistently produces a beautiful timbre. He made only sparse use of the more attacking, buzzy sounds that the cello can make, revelling instead in purity of tone, especially in the middle of the register. Time and again, sheer beauty of phrasing took one's breath away: it was like listening to a Lieder singer's perfect control of line and balance. Ma was particularly effective in those passages where Bach persuades your ear that you are listening to multiple voices in counterpoint, when in fact, there is only limited use of multiple stopping. His technique was unimpeachable: runs of notes were utterly sure-footed, with never a hint of timing slightly off, in spite of Ma pulling that timing and rhythm in all sorts of directions. Dynamic variation always felt natural, never forced. Most of all, Ma continuously gave you that feeling that Bach's latest bizarre change of harmony or rhythmic shift was simply inevitable and that the music could not possibly have proceeded any other way.

Ma was a master of infinite moods. There are passages like the first Prelude and the last three Sarabandes that displayed infinite calm, music to salve a troubled mind. There were moments of delight in the intricate filigree of notes. There was pervasive good humour. And on just a few occasions, like the Gigue of Suite no. 3 and the Gavottes of Suite no. 6, the music really let rip with the hurdy-gurdy based dance feel that is familiar to practitioners of French folk dance to this day. I could name a dozen others.

Playing all six suites in a row is a big ask, and I confess that as a non-cellist, my attention had started to wander by the time Suite no. 6 began. But I have to take my hat off to Yo-Yo Ma, who showed complete mastery of this music of infinite variety, achieved with minimal resources and which provided the audience of 5000 with an unforgettable evening's music.