Answer: That's a really interesting question.

For the sake of those who just walked in, let us say that a round is a type of canon (i.e. a composition based on some kind of rule or puzzle); it's a melody written in such a way that it can provide counterpoint (melodic accompaniment) for itself if different singers or instruments begin it at different times. And a "round" is a "circular canon," because its last part also works with its first part, so that performers can just repeat when they get to the end and it will go around forever or until someone drops of exhaustion.

Most people in the United States are familiar with "Row, Row, Row your boat," a famous if not really terrific round, and "Are you sleeping, brother John," better known across the sea and in Cajun country as "Frère Jacques." These are very short and simple and easier to illustrate here than some of their fancier cousins: Here's the first part of "Frère Jacques."

The separation here is two measures. A second and then a third singer can enter after the previous singer has performed two measures. Each repeats when reaching the end.

Mahler used a minor version of this in his Symphony No. 1, so it has the famous-composer-seal-of-approval. You can hear the original Frère Jacques round in the online library of Songworks files.

Now, as to writing your own:

Writing a round that works is not as hard as you might think, though greatness is as hard to obtain as ever. The basic principle is that you do not write the whole melody at once. You write it one segment at a time, all voices together. The computer makes this a lot easier: I'll use Songworks for this example, though I could use Counterpointer or one of Practica Musica's writing activities.

I'll show some of that in a moment, but you might already be asking, how do I write the other parts so that they agree with the first? This is the question of counterpoint: counterpoint is the art of writing two or more simultaneous melodies so that they work together in a meaningful way. We have a program, Counterpointer, whose entire purpose is to teach the art of counterpoint, following principles developed centuries ago in which you do something simple first and then add more complexity bit by bit. Mozart studied those traditional principles, so did Bach, Haydn, Beethoven, Brahms, basically all famous composers. There are lots of books on the subject, too.

To do this right you would really need to know something about counterpoint. But for a start you could try just writing additional parts so that they "sound good." It's easier to write something that sounds good once you understand counterpoint, but for a simple piece you might find you can do pretty well just working by ear. Try when you can to have new voices enter at a the interval of a third or fifth with another voice, try to create full triads when possible, and try to avoid unisons and parallel movement by 5ths or octaves. However, many rounds are a bit loose with their counterpoint, and ours probably will be too. Let's make a round.

First, as with brother John above, we start by inventing the first part of a melody. Let's say this one's for instruments and has no words. The length of each segment will be two measures, though it could be just one. It's easiest if the tune is "diatonic," that is, using just the notes of the major or minor scale. Here's a start:

Now we write counterpoint - a countermelody - that agrees with those first two measures. To begin, copy the first part into the second staff, letting it start a couple of measures later:

Now write accompaniment in the first staff. Be sure to give some variety to the rhythm:

Now we copy the two new measures into the second staff, and since it's now time for the third voice to enter we copy that in too; that's just a repeat of the initial two measures:

And then we write two more measures in the upper staff that will agree with both the lower parts. Since I want to finish this lesson before dinner I'm going to make this last segment the final one. And here we encounter the trick of creating a round: the last segment I write needs to lead back to the first segment, while harmonizing with both the first and second segments:

That's really all the music there is in this simple example of a three part round with three segments of two measures each. If we were printing this to give to players all that would be necessary would be the top line, with an asterisk at the third measure to indicate the entry point of the other players.

But since I live in the 21st century and can easily hear my work on the computer I'll copy and paste these voices, and put in some repeats so that the computer can play the whole thing just as it would sound. Here's the result: