Girolamo Frescobaldi (1583 - 1643) was an Italian organist, keyboardist and composer whose compositions exerted a great deal of influence on musicians like J.S. Bach. He was the organist at St. Peter's Basilica for over thirty years.
He was one of the first composers of his time to specialize in composing for the keyboard. He did write some music for voice, but the vast majority of his output was for keyboard. In Frescobaldi's time, keyboard music could be played on organ, harpsichord, or clavichord. Unlike many composers of the time, Frescobaldi published many of his works which lead them to be well-known in the musical world of the time. He was an innovator in his composing, his playing and even in the ways he notated his music (which lead to the modern method of notation) and was so acknowledged by his contemporaries.
One of the compositions he printed was also the very first known instance of a set of variations on an original theme, the 'la Frescobalda' variations. Any variations previously were on folk songs or popular melodies. Frescobaldi states his theme (or 'aria' ) at the beginning, and there are four variations on it. In the recording below, the performer follows the practice sometimes done in Frescobaldi's time, of playing a reprise of the original theme after the last variation.
Frescobaldi's Variations On An Original Theme 'la Frescobalda' :