Canon #92, Ammolite

Canon 92 is a major effort of mine that’s been in the works for three months — my summer of 2021. I named it “Ammolite” which is an iridescent rainbow-colored gemstone made from fossils of the extinct ammonite mollusk. For me, Canon 92 is indeed a rainbow of moods and feelings, arranged in a kind of kaleidoscopic pattern such as we might see in an ammolite gem itself:

There are three important technical elements at play in this piece. First, retrograde imitation is used exclusively. This means that the follower always plays a backwards or reversed version of the leader’s material (with a rhythmic skew and vertical displacement that changes from passage to passage). Second, all the themes are made from scales with five or fewer notes. Most of the themes are in the familiar major and minor pentatonic scales, but some themes use scales with as few as three notes. (I should mention that even in these three-note passages, the listener might hear four or more distinct pitches because the two voices may be playing in a different transposition of the three-note scale.) Third, the voices overlap extensively, to the point that they sometimes lose their individual identities and fuse into an emergent or compound melody. This fusion is an intentional aspect of the piece’s design, beginning with the opening passage which sounds like a single voice even though it’s formed from two.

Until I began work on Canon 92, retrograde was not among my favorite concepts to work with, though I think I used it successfully a few times (see my crab canons Zebra Marble and Peridot). I hadn’t been keen on retrograde because it’s often difficult for a listener to perceive or follow this kind of imitation, and I usually favor intelligibility as an aesthetic objective. The reverse version of a melody often sounds nothing like the original, and it’s challenging enough to perceive their relationship when you’re given the best opportunity; that is, when you hear the versions one after another. But when the two are superimposed, you can’t possibly grasp their connection in real-time because you’re hearing the beginning of the backward version before you’ve heard the end of the forward version: you don’t yet have enough information to recognize the link. For this reason, I’ve tended to think of retrograde more as a game or challenge for the composer than a feature for the listener to consciously enjoy.

What dawned on me recently is that retrograde becomes more intelligible when applied on a smaller time scale. I used to think that to write a “canon in retrograde” you’d have to reverse the leader’s line in its entirety, so that the first measure would be played alongside the reverse version of the very last measure. But why not apply retrograde on a measure-by-measure, or phrase-by-phrase basis? Why not accompany the first measure with its own “local” reversal, and then do the same for subsequent measures? For example if my original material is structured as |123|456|789| I could transform it into |987|654|321| but I could also transform it into |321|654|987|, right? So, in Canon 92, retrograde is not applied on the scale of the entire piece; rather, it’s applied to individual themes, and sometimes to individual phrases within a theme. The scope of the reversal – the amount of material that gets treated as a unit to reverse – changes from passage to passage but the basic idea is to keep it small and manageable.

Repetition is another way to make retrograde more intelligible. First you apply retrograde on a local scale to create short retrograde canons, and then you repeat these short canons a couple of times (possibly with transpositions or other kinds of variation). The more times a listener hears the retrograde imitation, the better the chance that they might recognize what’s happening; and certainly, retrograde imitation tends to have enough inherent complexity that repetition does not quickly lead to saturation and boredom. And so Canon 92 uses repetition heavily: almost every nugget of material is repeated at least once.

One thing that can be frustrating about working with retrograde is that it wreaks havoc on the grammar of a musical line, particularly if the line is tonal. Let’s take the gesture of moving from the leading tone to the tonic in a major scale; now reverse this gesture, and you’re going from the tonic to the leading tone. The musical meaning is totally different. A resolution turns into an injection of tension. So it takes a lot of engineering to write a tonal melody that can be played backwards and still make sense. But guess what? It’s a lot easier when you work with a simple scale that doesn’t support leading-tone-to-tonic resolutions that take a different meaning when reversed. What is such a scale? In working on Canon 92, I realized that pentatonic scales and retrograde imitation have an almost magical synergy. If you write a pentatonic tune and play it backwards, there’s a chance it’s going to sound “grammatical” right off the bat, without any tinkering or fine-tuning; the same cannot be said of tunes that use a full major or minor scale. Of course, rhythmic coherence is another issue. A complex rhythm is more likely to turn into nonsense when reversed; but if you restrict your pentatonic themes to simple rhythms, the chances of obtaining something meaningful from the reversal process are greatly increased. The word “chance” is important here and I’ll come back to it.

Pentatonic scales themselves had proved elusive in my canon-writing efforts until the current piece. Early in my canon-composing journey, I made it a goal to explore all different kinds of pitch material, and I did that with great curiosity and joy, but when it came to writing with the familiar major and minor pentatonic scales, arguably the simplest scales of all, I could never make a canon I loved. That changed with Canon 92 and perhaps the reason is that I shifted the balance between engineering and chance in my compositional approach; so now let me come to the topic of chance.

One could say that a good canon is not an accident. Canons would probably prevail in any ranking of the most tightly designed or heavily engineered of musical objects. I take pride in the careful planning that goes into most of my canons, a process that often begins with a skeletal outline and proceeds in phases of successive elaboration. And yet I’ve long known that it’s possible to create canons in a totally different way, one which eschews planning and design altogether. You can simply write a tune, then layer it on top of itself, and see how the damn thing sounds! You can try out different vertical and horizontal displacements until you find a combination that clicks. If there are aspects of the unplanned canon that don’t sound good, you can tinker until you’ve got something that works. As mentioned above, if you stick with simple rhythms and simple pitch material, and if you’re writing in a style that’s not heavily rule-bound (e.g. a style that doesn’t require formal preparation and resolution of dissonance, a style that doesn’t avoid parallel perfect consonances, etc.), you have a better chance of getting something usable out such experiments. Maybe you write 100 themes, and 99 of them don’t work as canons, but miraculously there’s one that does… and what’s more, it sounds as though it were carefully designed to function as a canon.

This is something that fascinates me about art: if you perform enough experiments with chance, and if you carefully sift through the outcomes of those experiments and collect your favorites, treating yourself more as curator than author, the overall result may seem to manifest intent although it originates in chaos. In my case, the “chance” I took was to write a tune (and another, and another) without knowing whether it would make a good canon. I wrote hundreds of simple pentatonic tunes over a period of three months. Subsequent chances were to arrange each tune in retrograde against itself with a particular vertical and horizontal displacement. My favorite outcomes — the ones I preserved — were the canons that miraculously sounded as though they had been tightly engineered.

I’m reminded of the idea of using a ouija board to ascertain or expose one’s innermost thoughts. To generate the material for this piece, I did something akin to moving my hands around a ouija board for a really long time, collecting lots and lots of words and phrases, discarding the ones that made no sense and keeping the few that did. In the end, I realized that these phrases are what I had been wanting to say for a long time without knowing how.

There’s an exaggeration in this analogy, in that my work was not nearly as haphazard as moving my hands on ouija board. I tried to write the tunes more-or-less freely, without designing them to behave as canons, but I can’t say that I wrote them with total abandon either, because as I worked through this long process I surely gained intuitions about what kinds of pentatonic tunes might turn into good retrograde canons, and my tune-writing choices were guided by those intuitions. Also at play here was my editorial instinct, built up over years of work on my previous 91 canons, an instinct that allowed me to quickly select the very best material from a mountain alluring possibilities.

If I discovered that retrograde and pentatonic scales work well together, I also discovered that retrograde and overlap work well together. As mentioned earlier, a major idea in this piece is to place the lines close enough vertically that they frequently cross. When this crossing or near-crossing occurs, new, emergent melodies are sometimes created. This happens when a bit of one line is followed by a bit of another line: if the two bits are close enough in range, the listener will hear them as a unit rather than assigning them to their respective (separate) voices. This unit takes on an identity of its own that is not contained in either line by itself. I first started exploring this territory in Crossings and have been revisiting it in some of my more recent canons, including Ammolite. Now, if the goal is to create emergent melodies, retrograde is helpful as a source of variety: that’s to say, you get a wider range of emergent melodies than would be possible if you only superimposed the forward version of a theme on another copy of the forward version, like we do in most canons. When you mix in the backwards version, it’s like adding a totally new ingredient.

Once I had created hundreds of short retrograde canons and selected about two dozen of them to keep, I was faced with the question of what to do with all of them. I was afraid that I might have created a lot of good material that was simply too heterogeneous to fit into a coherent piece. I didn’t doubt that I could make a loose collage or medley from the material which might sound interesting in the way a mixtape sounds interesting, but I wanted more. A mixtape can convene lots of good music and can express the tastes of the person who assembled it but, it’s probably fair to say that a mixtape isn’t a first-order work of art in its own right (maybe that’s a debatable point, let’s not go into it). What I’m saying is that I wanted to create more than a loose collage of interesting passages, I wanted to create a unified piece with its own personality and narrative arc. As I listened to the raw material over and over again, two things happened. First, I realized that all the passages are unified by their use of similar musical materials: pentatonic scales, retrograde imitation, contrapuntal overlap, and recurring rhythmic patterns. Since I had been so specific and restrained in the materials I used for my experiments, the outcomes had a kind of implicit unity (like legos that can be snapped together) even though I hadn’t written them with any particular use or context in mind or any sense that they should be made to connect. Second, I found that certain passages gained a personality, almost a “function” in my mind, as I heard them over and over, as though they were volunteering to fill the very roles that would need to be filled to create a satisfying piece. I needed connective material, and certain passages sounded to me like connectors or transitions. I wanted a bright, rousing climax, and one particular passage presented itself as the obvious choice. I needed material that would serve as a kind of cleansing agent, refreshing the listener’s auditory palate, and some passages “raised their hands” for this position. I wanted some brooding, intense, dark material that would carry the listener on a journey before the climax, and some passages stepped forward to do just this.

I then followed the same “overnight cooking” process that I had used with my previous canon, #91. I forced myself to arrange all these passages into a preliminary order, and then I let the amalgam sit overnight. My fear was that I might wake up, listen to the piece, and feel totally confused about what to do next, but mercifully the opposite happened. My reactions to various transitions from one passage to the next were strong and unambiguous. I loved some of the transitions; I hated others. Now the challenge was to keep rearranging the material until I could listen from start to finish and love all the transitions. I wanted each individual passage to shine in its new home. I had come to love these various passages as individuals, but I found that if a passage is placed in the wrong context, it loses its thrust. The question was: could I find an arrangement where each passage seemed “right” in its particular place and sounded at least as engaging as it had when I’d heard it earlier in isolation? Each individual component should only gain, and not lose anything, by joining the larger whole: that was the hope.

As I kept listening to my work-in-progress again and again, I started mentally hearing the beginning of the next passage as the end of the previous one approached… in the same way that happens when you’ve listened to a favorite album so many times that the ending of one track automatically triggers in your mind the sound of the next one. I took this as a good sign: if my ear was latching onto the order of the passages, then the order must have some sense to it, otherwise my ear would have rejected or fought against it by refusing to internalize it. (And indeed, this refusal did happen in some specific places that I later changed.) In editing the piece, I would cut out certain passages to make the piece leaner, and then I’d go back and add them in again, or add different ones in to see what might happen. The piece kept moving back and forth across the threshold from unified to disjoint. To finally land on the unified side of the threshold, cutting out the excess was key, but cutting wasn’t the only key: there were two or three short passages that got added in later stages of the editing process and which turned out to be essential, I think. Kill your darlings but revive the ones that didn’t really deserve to die.

As for the dramatic arc of the piece, I’d describe it like this. There are several “acts” that are connected by transitional material. The transitional material has an open-ended, atmospheric quality that allows you to imagine what you might be looking for, as with a Rorschach ink blot. The piece opens and concludes with this ink-blot material and such material occurs between each of the proper acts. Act I is about energy, curiosity, and invention. Act II begins with a sense of refreshment and/or renewal, and continues with the qualities of Act I but with a slightly darker tone, and an increased sense of severity. (I really consider Acts I and II as part of a larger unit, but because there’s transitional material in between them, I’ve numbered them separately.) Act III is the “workhorse” section, where curiosity is replaced with purpose and direction; play is replaced with effortful work. I think of a nighttime journey, an urgent search. The ethos is darker and more intense than before. Act IV takes a turn into brightness. The connective material leading into this final Act gives way to new pulse. Tentative at first, the music blossoms into a full celebration – almost like a country dance – perhaps a dance on the day following a successful journey or search. The heroine has been found safe, reunited with the hero, everyone’s happy. This merry country dance turns out not to be the conclusion of the piece; rather, it gives way via a short transition into the true climax, a bustling tangle of melody which is more animated than the dance itself and more abstract. The climax finally yields back to the open-ended “ink blot” material, similar to the material that opened the piece, but now with a distinctly brighter tint. And so the piece is ultimately a progression from darker to lighter… with an ammolite-like range of colors exposed along the way.

As I generated the initial material for this piece, I certainly felt like I was writing the tunes, but I wondered if I was really “writing” the canons that came from them. The process of finding the right vertical and horizontal displacement felt more like discovering a canon inside a tune, not like composing a canon step-by-step as I’m used to doing. I would sometimes listen to these “discoveries” and think to myself, “That’s a nice canon — I wish I had written it!” But as I collected more and more material, a sense of authorship came eventually — I felt that I myself was somehow reflected within the many tunes I had written and the canons I had found inside them. Arranging these canons into an arc was a deeply personal process where I followed my instinct at every step. Perhaps it’s because I relinquished some conscious control throughout the composition process that an aspect of my soul found room to manifest in this piece in a way that had not quite happened before. If I could materialize any music at this moment to share with you — if I could pull any new, finished composition out of thin air — it’s Ammolite I’d pull.

Ammolite image credit: James St. John, CC BY 2.0, via Wikimedia Commons

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