Triplets and hemiola are compound entities in simple time. They say, play 3 notes in the time of 2.
Tailed notes like quavers and semiquavers can be beamed in a group of three with the numeral 3 written above. Three beamed notes to be played in the time of 2 are called triplets. A quaver triplet plays for the time of a crotchet.
Crotchets and minims cannot be beamed. To write three crotchets or minims in the time of two write the three notes under a square bracket with the number 3 above. In common time three crotchets or minims in the time of two are called hemiola.
A tripplet plays 3 within the time of the beat or for the time of the beat. A hemiola plays 3 over the time of the beat.
In simple time you are used to counting by 2 and 4. Triplets are counted by 3. Think of time in the form of a clock. In duple time the clock strikes 12 and 6. Triplets strike at 12, 4 and 8.
Hemiola are very difficult to count because they don't show the beat. Think of them this way. A crotchet is equivalent to two tied quavers. A crotchet hemiola is equivalent to two quaver triplets with every second note tied. The quaver triplets give you the beat. In a crotchet hemiola the second beat is halfway between the second and third crotchets. You play the second crotchet a triplet quaver before the beat and the third crotchet a triplet quaver after the beat.
On the beat, triplets and hemiola group naturally to the entities of simple time.
A minim hemiola covers an entire 4 - 4 bar. A crotchet hemiola covers the first or second half of a 4 - 4 bar. Hemi is a Greek prefix meaning half. A quaver triplet equates to a crotchet. A semiquaver triplet equates to half a crotchet.
If a hemiola or triplet begins off the beat such that it crosses the simple time x4 groupings then it must still be written to be correct in simple time. A simple technique is used. It is based on the fact that a minim hemiola can if necessary be written as two crotchet hemiola. A crotchet hemiola can if necessary be written as two quaver triplets and so on.
Here are some hemiola and triplets which begin off the beat or cross over the bar's half way mark. Here is what we do with them. We break the crotchet hemiola into two quaver triplets so we can slice the bar in half. We divide the quaver triplet into two semiquaver triplets so we can see the beat and adhere to simple time rules.