I is for Improvisation
In Bach's time improvisation - making it up as you went along - played a far greater role in classical musicmaking than it does today. Solo singers and instrumentalists routinely devised melodic ornaments on the spot; the keyboard-players who accompanied them were expected to invent their own parts using just a bass-line and a set of coded instructions for the harmonies (the so-called 'figured bass'); and no virtuoso performer was worthy of the name unless he could extemporise at length with not a note of written music in front of him.
Yet even in this climate Bach's powers of improvisation were legendary. As an organist he was in the profession in which it counted most - organists were required to invent fantasias and fugues on hymn tunes as part of the church service - but there was no doubt that he was the master. There are reports of him making improvisations last half an hour, while in recitals he was apt to devise an entire sequence of pieces on a single theme, capping them all with a fugue.
His most famous feat of improvisation, however, came near the end of his life, when he visited the court of Frederick the Great and was given a 'royal theme' on which to extemporise a ricercar (or fugue) in three parts on the harpsichord. The theme was calculated to make his task as difficult as possible, but he managed it. When asked for a six-part fugue even Bach had to decline, but later, when he had written the original improvisation down, he made it the opening salvo in the sustained contrapuntal onslaught that is the Musical Offering .