Division
The English term for improvised variations of an upper part over a repeating ground bass, mainly in the 16th and 17th centuries.
What it means
Division is the English term for a technique in which a given melody or bass is "divided" into faster, ornamental note values, hence the name: a long note or a simple melodic outline is broken up into a sequence of shorter notes. It is usually built over a ground, a short bass pattern repeated unchanged, above which the upper part continues in ever more elaborate variants.
The term is closely tied to English musical practice of the sixteenth and seventeenth centuries, though it is occasionally used more broadly for breaking up a note or phrase into faster values.
Musical use
Divisions were written especially for solo and consort music for viol and violin; a well-known treatise of the period, Christopher Simpson's The Division-Viol (1659), describes in detail how to improvise and compose over a ground bass. The principle also appears in vocal music and in ornamentation practices on other instruments.
Division should be distinguished from basso ostinato in the broader sense: basso ostinato refers generally to the repeated bass pattern itself, while division refers to the changing, increasingly ornamented upper part above it. Related but not identical is diminution, in which an existing cantus firmus is elaborated with shorter note values; division usually starts from a bass pattern, diminution more often from a given melody.
Performance practice
Practice divisions first over a simple, slowly played ground bass so you have the harmonic framework securely in your ear before ornamenting it. Increase the rhythmic density from one pass to the next rather than starting straight away with the fastest variant, so the improvisatory build-up remains audible.