Interval Compression

In music, “imitation” is what happens when one musical part or “voice” repeats the material stated by another voice. Episodes of imitation occur in many forms and styles of music, but the canon is the one form where imitation is sustained from start to finish.

One of the reasons why I see boundless possibility in the canon form is that the idea of imitation itself can be interpreted in so many ways. Imitation can be direct or it can involve some systematic way of changing or transforming the original material: when the follower repeats what the leader “said,” the follower can state the content verbatim, or say it in a different way.

Some of the most common kinds of transformation that occur in counterpoint are to turn the original material upside down, to change its speed (make it faster or slower), to play it backwards, or to do some combination of these things together. And so we have canons in contrary motion, canons in augmentation or diminution, canons in retrograde, and so on.

Why bother crafting pieces of music with these special technical properties, these “deviant” forms of imitation? Because they can provide a fascinating experience for the listener, where two manifestations of the same idea may be heard together and compared. If we take a melody and turn it upside down does it still bear an audible relationship to the original? Does it carry the same affect? Each time we listen to such a “canon in inversion”, for example, we might notice new connections between the original melody and its mirror image, or we might perceive differences in sound or meaning that hadn’t been apparent before.

As I continue writing canons myself, I’ve been seeking to experiment with other kinds of transformation – other ways of interpreting the idea of “imitation” – that have been less commonly addressed than those mentioned above: inversion, retrograde, augmentation, and diminution. The technique I explored in my two latest canons could be called “interval compression.” The idea is that follower should cut all of the leader’s melodic intervals in half: if the leader makes a jump of an octave (12 semitones) from C to C, for example, the follower would copy this gesture by leaping a tritone (6 semitones) from C to F#. So the follower presents a vertically compressed or “squished” version of everything the leader does.

Is it possible to make meaningful music with this unusual constraint? And why bother doing this? As with many technical constraints that can seem arbitrary at first, it forces you to write music that you probably wouldn’t think of otherwise. But beyond that, it’s an interesting way of addressing the question of what makes two melodies sound similar or different: is it the specific pitches they hit, the specific intervals they use, or is it just their rhythms and basic contours? How similar do the two parts – the leader and its “squished” follower – sound to you as you listen?

Here is Cannon 73 “Tellurium”:

Here is a visualization of the first part of of the canon:


And here’s how it looks if we align the two parts, eliminating the lag between leader and follower so they can be more easily compared:


To make this canon work out cleanly, I confined the original theme to a whole-tone scale so that all melodic intervals would be divisible by 2. The transformed theme, the result of this division, consists largely of chromatic motion as you can see in the images.

Canon 73 was borne from the same outline as its predecessor Canon 72 “Rhyolite,” a piece with a much slower and more brooding demeanor: