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In the Baroque era improvisation was common, and organists, such as Buxtehude and Bach, were skilled at it. Baroque composers before Bach's time had started to write down their variations and the formal structure which came most readily to them was the Ground Bass.
A Ground Bass is a form of ostinato. In such a piece of music there is a recurring bass line and the variations are written over it. Such pieces are examples of "continuous variation" for, in most works entitled "Theme and Variations", each variation is a distinct section.
There are two names for Ground Bass pieces - chaconne and passacaglia. The distinctions are worth noting and certainly exist in plenty of examples. However, composers have not always used the names correctly, so their meanings have become blurred.
A chaconne is a series of unbroken variations invented on a recurring chord progression. Indeed, the 'theme' is the chord progression itself.
A passacaglia has a more melodic bass line rather than a prescribed series of harmonies. The theme is 'singable'. Passacaglias tend to be in a slow triple meter.
The important thing to remember about a passacaglia is that the ground does not change.
Having said that, In Bach's famous Passacaglia in C minor, however, he uses a borrowed theme as the basis for twenty variations, most of which state the ground literally in the bass. Some of the later variations place the ground in upper parts. In a couple of variations the ground disappears altogether.
In Purcell's "When I am laid in earth" from "Dido and Aeneas" the ground bass repeats exactly with no melodic or rhythmic change whatsoever.
Some passacaglia themes include chromatic phrases, the prime example, again, being Purcell's Ground Bass aria "When I am laid in earth". [Purcell was a real genius when it came to writing the melody over a Ground. He liked to overlap the melody so that the end of a melodic phrase did not match up with the end (and thus, the next statement) of the Bass] Eighteenth-century audiences would have recognised the chromatic descent in Dido's Lament as a formula which, for them, held a meaning. In opera, such music was reserved for the most poignant of scenes, while in church music it was associated with the pathos of Christ's crucifixion.