Music

Nonstandard Contrapuntal Imitation

Imitation in music is when one voice announces a melody or phrase and another voice repeats it. There are lots of ways to “do” imitation. Imitation can be strict, or loose, and it can involve some kind of transformation, like slowing down the material, or speeding it up, or turning it upside down, or playing it backwards. The transformations that I’ve just mentioned all have names — like augmentation, diminution, inversion, and retrograde — and they’ve been used by composers for long enough that they can be considered “standard.” To be sure, their possibilities are boundless, but the concepts themselves have been known to composers for hundreds of years and can be found in any basic counterpoint text. One of the things I’m always looking out for in my own composing efforts is whether there might be uncommon, or perhaps unexplored kinds of imitation that could lead to new musical possibilities. In this post, I want to summarize the non-standard varieties of imitations that I’ve worked with in my canons so far. I don’t know whether any of these are new in the sense that no one’s done them before, but I can say they were all new to me when they first came to mind.

Imitation with Interval Expansion or Contraction

The idea here is that follower expands or contracts the melodic intervals of the leader; not occasionally, but repeatedly and systematically. For example, the leader might employ the whole-tone scale, where every interval has an even number of semitones, and the follower might cut all the leader’s intervals in half. I wrote about this concept in my post on Interval Compression and explored it in Canon 72 “Rhyolite” and Canon 73 “Tellurium.”

Imitation with Insertion or Deletion

The idea here is that follower periodically inserts a new measure that’s not found in the leader’s material — the follower might be extra “talkative.” Alternatively, the follower might skip or ignore one of the leader’s measures — the follower might be “forgetful.” In this way, the lag between leader and follower can change throughout the piece, even though the tempo of the parts is not changing. The important point here is that the insertion or deletion is not a one-time or exceptional occurrence, but a device that is used regularly and systematically throughout the piece. I did this in Canon 67 “Feldspar” and the two pieces that came before it, Canon 65 “Galaxite” and Canon 66 “Rhodonite.”

Imitation with Reordering

The idea here is that follower is allowed to reorder the leader’s material in some way, whether it’s individual measures or entire phrases that get moved around. I wrote about this in a previous post on Reordering Canons and explored it in Canon 94 “Cinnabar.”

Imitation in One Dimension

The idea here is that the follower is required to strictly imitate one dimension or aspect of the leader’s material while being free to alter another aspect. (The freedom to alter another aspect can also be turned into a requirement to do so.) For example, the follower might preserve the directions of the leader’s melodic intervals while freely varying their sizes: if the leader plays A and then goes up to an E, the follower would imitate this by moving upward, but perhaps landing at a D, or perhaps an F. The composer might impose a requirement that the follower must not play the exact same interval as the leader, so E becomes off limits as a landing point if the follower is also starting on A; still, the landing point must be higher than the follower’s initial note, not lower. Another variant of this idea is to say that the follower must copy the leader’s rhythms exactly, but is free to vary (or is required to vary) the leader’s melodic material. In Canon 88 “Carminite,” the follower preserves the leader’s rhythms and melodic directions while varying the leader’s interval sizes in an unpredictable way.

Monophonic Imitation

This idea is not about a transformation that the follower applies to the leader’s material; rather, it’s about the way the two voices are positioned in relationship to each other, and how the result is perceived. If the rhythmic gaps in the two voices are positioned appropriately, it may be possible to superimpose one voice on another so that they never have a shared hit. Furthermore, the voices may be placed in the same melodic range and played using the same timbre, so that it becomes impossible to distinguish them. In this case, there are still two logical voices, and one voice may still be seen on the page as imitating the other, but the listener hears a single line. In this way, a polyphonic process can give rise to a monophonic outcome. You can hear this at the beginnings and ends of Canon 92 “Ammolite” and Canon 93 “Meteorite”. In both cases, the imitation is retrograde.

Imitation with Embellishment

In “traditional” counterpoint, there’s nothing unusual about the idea that one voice might ornament or embellish a phrase as part of the imitation process. But the way we could extend this concept into “nonstandard” territory is if we make the embellishments so numerous or so significant that the phrase seems to become something new altogether. The listener might be prompted to ask whether one voice is really imitating the other, or loosely interpreting the other, or creating new material that’s inspired by the other. Another possibility is that the leader and follower could present two differing developments of the same primary line, the same common ancestor. Perhaps the two lines have a similar contour and hit the same melodic targets, but have different details, different connective tissue. In Canon 42, “Amethyst” I began to explore this idea by writing a bare canon and then repeating it in a way where the two lines were embellished in very different ways.

I’ll follow up with a separate post about non-standard canonic constraints — ways of restricting what’s considered “permissible” in a particular canon — ways that lead to interesting musical outcomes, but ways that don’t involve the style of imitation per se.

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