So someone who was in love with hemiola would be a "hemiolaphiliac". Or something.
Hermiola is a very interesting rhythmic effect that comes from changing the grouping of beats. We first start seeing it in Spanish music in the 16th century. It usually occurs in triple time as follows. This is from a Baxa de contrapunto by Luys de Narvaez published in 1538:
Very nice. Do you hear how that third measure throws us forward? The unusual rhythmic patterns of flamenco underlie a lot of Spanish music. The history of flamenco is somewhat obscure, but undoubtedly some of its unusual handling of rhythm and timbre, by European standards, comes from the long occupation of Spain--some 700 years--by the Moors. One hemiola-related pattern in flamenco is this one: UPDATE: I fixed a misprint in the flamenco example. Hmm, well now I can't get the example to show at all. I'll have to leave it out until I can figure out what the problem is...
UPPERDATE: I finally got around to redoing this example. This is a flamenco rhythmic pattern, called a compas, that has twelve beats. I have notated it in 6/8. Here are two iterations:
The two layers are often clapped. As you can see the one player keeps a steady pattern that is in 6/8 while the other plays alternating measures of 6/8 and 3/4. The effect is quite remarkable. It does not quite work written in ordinary notation because the downbeats aren't downbeats, but I don't know of another way of writing it down. We find this kind of pattern in, for example, the bulerias:
This is Sabicas, a real master of the bulerias. He is not actually playing the pattern I have shown above, except in bits, but you will find that you can clap it along with him.
So, that's the hemiola.