The Hemiola

hemi·o·la Etymology: Late Latin hemiolia, from Greek
hēmiolia ratio of one and a half to one, from hēmi- + holos whole : a musical rhythmic alteration in which six equal notes may be heard
as two groups of three or three groups of two(Merriam-Webster Dictionary)

Early Baroque and Renaissance music sometimes includes a confusing measure – often the next to the last measure at the end of the song (or phrase) as a form of early syncopation.

In modern notation, it seems to be most common with music written in 6/4 time. When using 6/8 or 6/4 time, musicians often do not count all the way to six for each measure. Rather they group them into either two groups
of three or threes of two, with two groups of three probably being more common.

A hemiola is simply switching from two groups of three to three groups of two – while maintaining the same tempo if one were to count the measure in six. If when counting 6 counts, I tap my foot each time I count 1 in 1-2-3, 1-2-3, my tapping would be at a different speed than another person also counting 6 counts, but tapping his/her foot on each 1 of 1-2,1-2,1-2. Yet we would both complete the 6 counts at the same time. Note that one point of frustration is that conductors are often conducting in two threes, and sometimes are able to conduct three twos if all parts have a
hemiola. But some pieces only put a hemiola on some of the parts while the other parts continue with two threes.

Probably the one of the most effective songs for demonstrating this concept is “America” from Westside Story. If you tap with the accents in
the first measure, you would tap twice at the start of each triplet, and then in the next measure, you would tap three times for each quarter note, but at a different speed of tapping so that both measures take the same duration.

http://www.youtube.com/watch?v=Qy6wo2wpT2k&feature=related

You can hear the frequent use of hemiolas starting in the 3rd minute of this 7 minute You Tube video, when she starts singing “I like to be
in America” from America, Westside Story. (If the link doesn’t work, paste the site into the URL.)