Isorhythmic Rounds

Isorhythm A compositional technique that associates a sequence of musical notes with a repeating rhythmic pattern.
Round A composition in which multiple voices perform the same melody, optionally repeated indefinitely, but with each voice beginning at different times so that different parts of the melody pleasently coincide and fit harmoniously together.
Put simply, the isorhythmic round is a means of activating a harmony or different melodies according to a set of special rules. For example, suppose you have three tunes, the first is three notes long and is composed of Ab, Bb and C. The second is composed of two notes, Db and Eb. Finally a third tune is composed of F, G and F (see figures 1, 2 and 3, respectively).
Figure 1: Ab, Bb and C
Figure 2: Db and Eb
Figure 3: F, G and F
When played simultaneously and each voice is repeated immediately, you get the following (see figure 4). The next chord in the series would by Db F Ab, or a repeat of the entire figure.
Figure 4: Figures 1, 2, and 3 put together.

A Less Simple Isorhythmic Round

What happens when we use more snippets and melodic lines that make the melodic segments more complex, both rhythmically and melodically, as in the following example?
This melodic snippet is long enough to require two lines to show it.
Now, when you juxtapose them, it sounds like:
This pattern is naturally much longer than the simple example. It takes a considerably longer for each snippet to be fully played out in such a way as to arrive once again at the beginning of the juxtaposition. And it is not as easy to distinguish between the individual components. This example just happens to allow the listener to distinguish the shorter segments and discern a relationship. However, when this is absent, something almost magical happens. An emergent quality appears.
Consider for a moment the rhythmic relationship between the five voices. If we were to express the relationship as a simple ratio, it would be 2:2:3:5:7. Put another way, the notes in snippet one are each 2 eighth notes in length, while the notes in snippet 5 are each 7 eighth notes in length. This is a key aspect of the isorhythmic round as we will later discover.

Excerpts of My Compositions that use Isorhythmic Rounds:

BerceuseFrom Idyll #16 for flute and piano.
Beginning of 3rd movement of Symphony of Short Rounds for orchestra.
Middle of 3rd movement of Symphony of Short Rounds for symphony orchestra.
Following the introduction to the 5th movement of Symphony of Short Rounds for symphony orchestra.

From Raw Round to Composition

This is a problem with which I have struggled since I invented the concept of the isorhythmic round. However, some treatments seem to work better than others. For example, in the Berceuse for flute and piano, I through-composed the melodic line over the round, and the round is heard in the piano accompaniment. This is how I have typically approached composing for individual instruments with piano accompaniment. However, in the Symphony of Short Rounds , I didn't have the luxury of a single player. Instead I had to have a means of compressing the round so that it could be scored for the orchestra (i.e., painting with a broad brush). In this case, I condensed many lines into a single line, ensuring to preserve the attack points, but placing less emphasis on the note length that characterizes a melodic segment.
Fortunately, going from a raw isothythmic round to finished music is pretty straight forward because Bang Box can readily export any of its content in a format that is easily understood by most of the heavy-weight music notation software packages, like Finale or Sibelius. I have been a Finale user for many years and while I tried using Sibelius, I found that it was a lot of hard work to learn the newer software -- more than I was willing to invest. So I stayed with Finale and put up with its minor irritations while using it to create broad tapestries of sound as well as simpler solo pieces.
Is all of my music based on isorhythmic rounds? No, it is just one tool in my virtual tool-bag. But, in my humble opinion, its a good one! If you choose to try using the technique, send me a sound clip or the score so that I can see and enjoy how you have solved the problem of moving from the raw round to a completed composition.

Creating the Melodic Snippets

I personally found this task to be both easy and fun. In my millieau, harmony is king. For me, everything proceeds from the harmony. So I spend a little time each week playing chords at the piano, perhaps even progressions of chords. To do this I may use a tone row, and with the first five or six pitches of the row, construct a chord. Then as I progress from one chord to the next, I will substitute the next pitch or two in the row for the same number of pitches that make up my harmony. I have found that this is a good heuristic for building compelling chord progressions that are not overly dissonant or shocking. In my esthetic, the music must always be beautiful so carefully approaching and resolving a dissonance is essential to achieving a balance between avoiding the often simplistic harmony of the common practice period while achieving something dissonant but lovely. I keep my machinations in a notbook so that if I don't find anything good right away, I can return to it later, change it and search again.

Once I have a harmonic progression I like, I will start planning out the piece. For each harmony (again, using the piano) I create a set of six or seven inversions of the original harmony. It is the set of inversions along with the original harmony that form the melodic lines I use to create an isorhythmic round. So the isorhythmic rounds I use generally have many of the same notes but in different octaves. When I'm ready, I enter my chords into bang box and use it to realize the isorhythmic round (it is generally too time consuming to write them out by hand and then try a variety of them on the piano). I rarely use the first permutation I create, but rather, iterate through as many as 100 different permutations before I find one that I think sounds good. Bang Box makes this easy to do, automating many of the tedious and repetitive aspects of finding a good round. If I don't find one on day 1, I'll set it aside and come back to it tomorrow. A good round can jump out rather suddenly and quickly or take many days to shape what I'm working on into something good enough to find its way onto a score.

I also have certain musical expressions that I try to avoid, like the rising perfect fourth, which I regard as a harsh dissonance and will try to avoid at nearly any cost.