Compound metre (or compound time), is a metre in which each beat of the bar divides naturally into three equal parts. That is, each beat contains a triple pulse. The top number in the time signature will be 6, 9, 12, 15, 18, 24, etc.
Compound metres are written with a time signature that shows the number of divisions of beats in each bar as opposed to the number of beats. For example, compound duple (two beats, each divided into three) is written as a time signature with a numerator of six, for example, 6/8. Contrast this with the time signature 3/4, which also assigns six eighth notes to each measure, but by convention connotes a simple triple time: 3 quarter-note beats.
Duple time - 2 strong beats in a bar dividing into 3 eighth notes
Although 3/4 and 6/8 are not to be confused, they use bars of the same length, so it is easy to "slip" between them just by shifting the location of the accents.
Compound tripple time - 3 strong beats in a bar dividing into 3 eighth notes
Compound quadruple time - 4 strong beats in a bar dividing into 3 eighth notes
Compound metre divided into three parts could theoretically be transcribed into musically equivalent simple metre using triplets. Likewise, simple metre can be shown in compound through duples. In practice, however, this is rarely done because it disrupts conducting patterns when the tempo changes. When conducting in 6/8, conductors typically provide two beats per bar; however, all six beats may be performed when the tempo is very slow.
Compound time is associated with "lilting" and dancelike qualities. Folk dances often use compound time. Many Baroque dances are often in compound time: some gigues, the courante, and sometimes the passepied and the siciliana.