Under the compound time beam the beat is a dotted crotchet. Most usually you will want to group the notes by 3. After all, a feel by 3 is what compound time is all about.
Sometimes you will want to feel compound time by 2. Your writing should reflect the feel. Compound time allows you to group by 2 or 3 according to your discretion: what the backbeat is doing and what the musician will find most legible.
Lets start with the natural compound time feel, x3.
x3
In simple time there are 8 patterns of 4. In compound time there are 4 patterns of 3.
Each quaver of the compound time beat can be subdivided into two semiquavers or four demisemiquavers.
x2
Remember how half a crotchet is a quaver. Well half a dotted crotchet is a dotted quaver. Twice a dotted crotchet is a dotted minim. Twice a dotted minim is a dotted semibreve.
Technically we can halve dotted notes at infinitum. Though many small dotted notes do not constitute good writing. In compound time when a beat has a complicated duple (simple time) rhythm it is best to write the beat as a duplet A duplet is a simple time beat written in compound time. You will learn more about duplets a few pages from now.
x2 or x3?
A big part of writing compound time is in knowing how to exercise good judgement. By 2 or by 3? Which is most legible. Here are some examples. Would you rather read the clear rhythmic notation on the first stave or the messy notation underneath? The messy and clear notations spell the same sound and are both technically correct, but which would you rather read?
Rests
Compound time leans itself to dotted rests. Dotted minims and dotted crotchets, foreign to simple time, are perfectly at home in compound time.
Remember to use your rests to show the beat. Show the divisions under the beam.