Essentially, the best way to explain it to someone who doesn't already know what they are is this:
Think of common factors in math. (Yes, there is math involved. This is why Music Theory replaces a math course =) )
Multiples of two (broken into threes): 0 2 4,6 . 8 . 10,12...
Multiples of three (broken into twos): 0 3,6 9,12 15,18...
The common factors in both multiples represent the "beats" where the accents of the rhythms are felt. The least amount of measures to compare one full overlapping cycle of these "common beat denominators" is two. Every time the cycles overlap, is where the downbeat of the measure is. If you subdivide the multiples of 3, you get sets of two (duples), and if you subdivide the multiples of 2, you get sets of three (triples). Also, the time signature of a piece is important in determining the type of hemiola. For example, playing music that is in triple time, a hemiola within the music would make you feel three duple rhythms over an elongated period in two measures, as opposed to two "normal" triple rhythms in two measures of triple time.
This 3-against-2 hemiola is very common, but there are certainly ridiculous ones that could potentially go 3-against-4, or 5-against-3. There is a contemporary piano etude written by Gyorgy Ligeti, which is essentially an unpredictably changing hemiola. The right hand barline is offset by one beat every single measure, so the downbeat for both hands never matches until the end.
Confused yet? Subdivision, music theory, analysis, scrutiny? Is music supposed to be this complicated?
And this is only one concept out of dozens that you have to pick out in two measures, of a piece that could be hundreds and hundreds of measures long. Plus, it doesn't include control of touch, technical execution, control of dynamics, observance of tone color, articulation, and the two measures' place in the structure of the piece as a whole. Now you know why pianists spend hours in the practice room!!! It isn't just to play our music through hundreds of times until we are bored out of our mind, it's to work on small details like this...
And as my former piano teacher would agree, yes complicated, but mechanical, definitely not!!
"Play it like music, not a hemiola. I don't like labeling!"
-Joe Zins
As musicians, what is the extent of our music analysis? One can argue that no knowledge and all "heart" will make you lose the structure of the music you are trying to convey. On the other hand, one could argue that too much knowledge could lead to mechanical "heartless" playing that seems more "computer" than human.
Where's the balance?
Hmm... I'm not sure. I'll let you know when I get to that point.
KKZ
