Johann Sebastian Bach

MBBachEXJ S Bach wrote a collection of music which is probably the most instantly recognisable in the classical world. His work covered orchestral, choral, chamber and solo instruments. He wrote "mathematical" music, in that it is possible to break a piece down into progressions which are both predictable and pleasing. That said, he was a phenomenal at improvisation, especially at the keyboard.

The scores he wrote would almost certainly have been embellished in the playing. For example, the second movement of the Brandenburg Concerto No. 3 consists of only two chords in the score. The musicians would have been expected to improvise a complete movement which ended with the two chords written.