Division in music refers to a type of ornamentation

Ornament (music)

In music, ornaments or embellishments are musical flourishes that are not necessary to carry the overall line of the melody , but serve instead to decorate or "ornament" that line. Many ornaments are performed as "fast notes" around a central note...

 or variation common in 16th and 17th century music in which each note of a melodic line is "divided" into several shorter, faster-moving notes, often by a rhythmic repetition of a simple musical device such as the trill

Trill (music)

The trill is a musical ornament consisting of a rapid alternation between two adjacent notes, usually a semitone or tone apart, which can be identified with the context of the trill....

, turn or cambiata

Cambiata

Cambiata, or nota cambiata , has a number of different and related meanings. Generally it refers to a pattern in a homophonic or polyphonic setting where a note is skipped from in one direction and this is followed by motion in the opposite direction, and where either the note skipped from is...

 on each note in turn, or by the introduction of nonchord tone

Nonchord tone

A nonchord tone, nonharmonic tone, or non-harmony note is a note in a piece of music which is not a part of the implied harmony that is described by the other notes sounding at the time...

s or arpeggio

Arpeggio

An arpeggio is a musical technique where notes in a chord are played or sung in sequence, one after the other, rather than ringing out simultaneously...

 figures.

The word was used in this sense to describe improvised coloratura ornamentation as used by opera singers of the day, but it made a ready way of devising variations upon a theme, and was particularly cultivated in the form of the "division on a ground" - the building of successively higher and faster parts onto a repeating bass-line. Examples of "divisions on a ground

Passacaglia

The passacaglia is a musical form that originated in early seventeenth-century Spain and is still used by contemporary composers. It is usually of a serious character and is often, but not always, based on a bass-ostinato and written in triple metre....

" were written by, among others, John Jenkins

John Jenkins (composer)

John Jenkins , English composer, was born in Maidstone, Kent, and died at Kimberley, Norfolk.Little is known of his early life. The son of Henry Jenkins, a carpenter who occasionally made musical instruments, he may have been the "Jack Jenkins" employed in the household of Anne, Countess of Warwick...

 and Christopher Simpson

Christopher Simpson

Christopher Simpson was an English musician and composer, particularly associated with music for the viola da gamba.-Life:Simpson was born between 1602 and 1606, probably at Egton, Yorkshire...

. Simpson gives a lengthy explanation of the art of free improvisation over an ostinato

Ostinato

In music, an ostinato is a motif or phrase, which is persistently repeated in the same musical voice. An ostinato is always a succession of equal sounds, wherein each note always has the same weight or stress. The repeating idea may be a rhythmic pattern, part of a tune, or a complete melody in...

bass-line in his book The Division Viol.