I often find myself explaining the concept of subdividing on allexperts.com, and while it's easy to demonstrate in person, it's always harder to explain over the web. Since I haven't found any Internet resources that illustrate exactly what I'm talking about, I threw this page together as a visual guide.
In a nutshell, subdividing is the concept of filling the notes you play with even notes of smaller value. By thinking of the smaller note values that fit into the rhythms you have, you "fill out" the length of your notes with ones of lesser value, thus ensuring that you play each rhythm correctly.
At this point in a lesson, I would demonstrate on the flute. Since that doesn't help any Internet readers, here are some examples. (Excuse the weird treble notation... I didn't have a good music notation program at the time, but plan to replace these images with something better... eventually.)
Yes, I like Star Wars. :) Now, this rhythm isn't difficult, but just pretend you were having trouble with the dotted eighth and sixteenth notes. You know that the Gs come at the very end of the beat, but pretend you weren't sure exactly when to play them.
This is where your friendly neighborhood subdivider comes in. Instead of guestimating, you subdivide. Since a dotted eighth equals three sixteenths, all you have to do is fill the Cs with sixteenth notes in order to determine exactly how long to hold them.
Make sense? Let's try another example.
This is the spunky little theme from The Great Escape. Sorry about the image quality... hopefully it's readable.
So, we've got more dotted notes, plus some syncopations, too. The best way to subdivide this would be to have underlying sixteenths the whole way.
I ran out of room, but I think you get the idea...
In this example, I filled each note and the rests with sixteenths. During the rests, you'll see that I just repeat the last note before the rests. This is important, because often it's the rests that make a passage tricky, especially when there's offbeat rhythms. This way, by subdividing the rests as well, you know exactly when to come back in.
So the duration of each pitch is still the same, just divided into smaller parts. Which means that when you know you've got to play X number of sixteenths on a certain note, it's impossible to leave that note early or hold it too long, because the subdivision tells you exactly how long it should be.
Now, both of these examples used sixteenth notes as the subdivision. That's not always the case. If you have very long notes, you can use a quarter note to subdivide. Or, if you're in a triple time signature like 6/8, you can use eighth notes as the base. As long as the note can be divided equally by the note value you choose, it doesn't matter what that value is.
Now that the concept of subdivision is clearer (hopefully!), when to use it?
Subdivision can be done either in your head, where you think the smaller values as you play what's written, or you can actually do it, like the examples here, in your practice. I find the actual, tongued subdivision works best on new or tricky rhythmic passages, just so my fingers get used to how long they have to stay on each note. Then, once it starts feeling comfortable, all you have to do is think the subdivision in your head while you play.
Bottom line, subdivision proves that there never has to be any guesswork about rhythm. Rhythm is based on math and subdivision helps you figure out exactly what length each note should be played.