Canon #93, Meteorite

I’m pleased to share Canon 93, “Meteorite.”

When I listen to this piece I can imagine a collage of scenes where we see, in one moment, a meteor traveling rapidly through space against a backdrop of stars and planets, and in another moment, the meteor ensconced on Earth, where it’s been sitting for hundreds or thousands years, with vegetation growing around it, as a group of humans discovers it and tries in vain to dislodge it and see what’s underneath. This imagery came to me after I had finished composing the piece, while I was trying to choose a name for it. The piece itself is not intentionally programmatic – each passage was not designed to represent a specific moment in a meteor’s journey – but the more I experiment with this imagery after the fact, the more it seems to click.

My canons are named after gems and minerals – is “meteorite” one of those things? Well, people do make cool jewelry from meteorites, and one can find “meteorite” listed in gemstone glossaries, even though the term does not refer to one specific substance. One of my earlier canons – so far my only one to explore an alternate tuning system – is called Chondrite and that’s a specific category of meteorite. One of the little things I go through in naming my pieces is to question whether a new name should be off limits because I’ve already used a related name. But I have a piece named Quartz and a piece named Amethyst and I consider that situation to be fine even though amethyst is a kind of quartz (yet the pieces themselves aren’t closely related). So I decided it’s also fine to name the current piece Meteorite – I really like this name – even though I’ve already used Chondrite and the two pieces aren’t closely related except for the fact that I consider them both to have elements of “weirdness,” the quality of being “far-out,” irregular, or unconventional in relation to my other pieces.

The seeds of this piece were created back at the beginning of May, when I started a long series of experiments with retrograde imitation. I would write a theme, then reverse it and superimpose it upon itself, trying different vertical and horizontal skews until something provocative emerged. In my early experiments, I worked with themes that had some element of disorder: that’s to say, they avoided a clear tonal center and a recognizable pulse. In some cases the melodic contour was jagged, eschewing a sense of line. I became fascinated by the way I could take these short, irregular themes and turn them into canons in a way that either magnified or reduced the sense of disorder. On the one hand, I could make an irregular theme sound even more chaotic and unpredictable by placing it into a canon, and then I could repeat the canon again and again with various adjustments to the vertical and horizontal skews between the parts. I could do this in a way that created sustained mayhem. You could listen to the result and never guess that it had been constructed systematically through the repetition of short unit. You might assume something new was happening at each moment. On the other hand, I could take an irregular theme and turn it into a canon that sounded clearer, more cohesive, more goal-directed than either part by itself. Assuming it was possible to displace the parts rhythmically in a way that avoided shared hits, the result might sound like a single, through-composed line, not like a canon at all. And then by varying the vertical skew between the parts, I could create many different versions of that same line, each with a distinct character, and yet each fundamentally linked to the others.

So, starting this past Spring, I began amassing dozens of retrograde canons that explored these two different extremes, using the canon process to increase the order or magnify the disorder inherent in a theme. At some point in my experiments, I changed course. I moved away from tonally ambiguous themes with unstable rhythms and started to focus on simple ideas using pentatonic scales and regular rhythms. From this later, more tuneful material, I created Canon 92, “Ammolite.” After finishing work on Canon 92 in early August I went back to my earlier non-tonal material and forged it into Canon 93. The two pieces are connected in that they emerged from the same series of experiments, and they’re both large-scale works made of many short retrograde canons woven together. They’re different in the tonal and rhythmic material they use and the aesthetic goals they pursue.

My canons always benefit from interpretation by a skilled performer — the same is true of any music — but I think many of my canons can still be understood – if not fully enjoyed – by listening to how a computer “plays” them. But Canon 93 is one piece where the computer-generated preview leaves much to be desired. That’s because the more chaotic sections in the piece are actually full of short gestures that can be heard as distinct phrases, but the phrase boundaries can be easy to miss if the performance doesn’t emphasize them. In working with this material over several months, I’ve learned to hear these phrases (i.e. my ear has learned to parse them), and so even when I listen to the more wild or disorderly parts of the piece, everything makes “sense” to me, so much so that I’m not sure I’d even call these sections wild or disorderly anymore. Without a performer to elucidate the phrases (or without a lot of MIDI editing on my part) some sections of the computer-generated preview might sound much more chaotic or confusing than I actually intend them to be.

I’ve used the word “chaos” a lot so I should say something about chaos as an aesthetic goal. There is art out there that seeks to challenge the listener by making him or her feel disoriented, overwhelmed, or confused. This has never been my goal for an entire piece though I’m becoming increasingly interested in how this goal can be pursued at the scale of an individual passage, as a way of creating contrast within a piece. In Meteorite, I often use a more chaotic passage as a kind of preparation, a way of leading into a more cohesive or tightly organized passage, so that when the cohesion arrives it can be perceived as such. I’m also interested in the idea of presenting material that sounds chaotic and then repeating the material enough that the listener can become familiar with it and begin to perceive an organizing principle within it. For me, the goal of a “difficult” passage is not to prevent the listener from perceiving a pattern or organizing principle, but simply to delay this perception so that when it arrives it can be experienced as a kind of revelation.

Some miscellaneous notes about the piece:

The ethos is similar to my earlier pieces Thulite and Thorite but those pieces don’t use retrograde imitation. And where Thorite and Thulite used the octatonic scale as a tonal framework, Meteorite makes full use of the chromatic scale without any specific framework in mind. One technical similarity between Meteorite and the earlier pieces is that they all avoid shared hits – the voices are staggered in a such a way that they never play together on the same beat, except for in certain special passages. I find that the consistent avoidance of shared hits is a feature that can add a kind of suspense (as in a tightrope walk), and a sense of order or intentional design to a piece, particularly a piece that doesn’t employ tonal hierarchies to gain these same qualities.

A few of the passages in this piece combine mirror inversion along with retrograde (e.g. the opening and closing passages), but the majority use retrograde only. As with Ammolite, the parts are often placed close together vertically in such a way that they cross, creating emergent themes and/or fusing into a unified line.

Some of the themes in this piece function almost like lego pieces: they may be presented first as discrete units, and later placed side by side in such a way that one flows directly into another, so they “snap together” into a new, longer phrase that is heard as a single unit.

One can view the piece as consisting of three sections with no pauses between them. The first section introduces lots of ideas and sets up contrasts between them. The statements in the first section tend to be shorter and more discrete and they are often arranged in a question-and-answer fashion. Midway through the piece, we enter the second section. This is where lines start to flow in a smother and more extended way. Some of the material here brings to my mind a jazz saxophonist playing long bebop lines, or a Baroque performer riffing on the organ, though of course the musical language of the piece is different from either of those styles. This second section is where we experience the greatest sense of cohesion, fluidity, and rhythmic energy in the piece. Finally the second section gives way to a third section that mostly reprises material from the first. Some of the more chaotic content from the first section is restated with some variations, representing a dissolution or breakdown of the coherence that had come to being in the second section. Only one new theme is introduced here, a plaintive tune that occupies only a few bars in between restatements of earlier material. The piece ends with the same rushing lines that opened the first section (I think of these lines as representing the meteor in flight) but the vertical displacements between the parts are changed and now the lines begin with a prefix — an extra bar of jagged material — that lets us perceive the line as a progression from jagged to smooth, finally ending on a single target note. Although the piece does not aim to establish a tonal center — in fact, it aims to prevent any candidate tonal center from lasting too long — it is hoped that the last note in the piece sounds “right” in a way that any other of the twelve pitches would not, there must be implicit tonal hierarchies at play.

At roughly eleven minutes, Meteorite happens to be my longest piece so far. It forms a trio with its predecessors Birdsong and Ammolite, which are also extended works made from many short canonic passages. Those two pieces are long too, in comparison to my other canons, but for me they move forward in a way that seems almost expeditious, whereas Meteorite demands my attention in a way that makes me feel I’ve spent quite some time in a labyrinth before I find my way or am delivered out. It’s a piece that I’m still learning to hear, and as I come to know it better and better, it doesn’t seem quite as long as it once did; I wouldn’t want it to be shorter.


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.

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Canon #91, Birdsong

My latest canon takes inspiration from birdsong. It’s my first canon that refers to a sound-world outside itself, and at over six minutes, it’s also my longest canon so far. It’s able to be long because it’s not a single continuous canon but rather a montage of over twenty-five canonic episodes, each one attempting to capture something that I’ve heard in the universe of bird vocalizations. Each episode is a strict inversion canon, where the follower moves in the opposite direction from leader, and most episodes are what I might call “rapid-fire” canons where the follower enters very quickly after the leader. The piece doesn’t have an plot per se, but among the canons I’ve written, it’s the one that might be the most suggestive or accommodating of a plot. It was particularly fun to write, and I’m particularly excited to share it:

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Canon #90, Thorite

Announcing Canon #90, “Thorite.”

This piece is a sequel to Canon #89, “Thulite” — I chose the name “Thorite” simply because it’s another mineral beginning with “th.”

Like its predecessor, this piece uses the octatonic or diminished scale. The articulation is staccato, and the voices almost never coincide. Each voice speaks in the pauses and gaps left by the other voice. Sometimes these gaps are between phrases (creating a sense that the voices are “taking turns”) and other times they’re within a phrase (creating a sense that the voices are speaking over one another).

This framework (octatonic scale, staccato articulation, no shared hits) allows for a good amount of freedom in composition. I found that I didn’t need to micromanage the intervallic relationships between voices in the same way that’s necessary with other canons. There’s one exception. I tried to keep the voices from playing the same pitch in direct succession, because the sound of an octave (even if staggered) is distinct enough that the listener might expect it to have some special meaning; if no special meaning is found, the experience is slightly disappointing. Other than avoiding octaves, I could pretty much let the voices flow according to their own whims without having to plan their vertical relationship on a note-by-note basis. This meant that I felt comfortable writing the piece from beginning to end without going through my typical iterative outlining process.

One thing I loved about writing this piece is the way it all grew from the material in the first twelve bars. In writing those first twelve bars, I kept facing the challenge of inventing new material — pulling something out of thin air, so to speak — but once those few bars had been written, the rest of the work was about restating and recombining the opening material — finding new meaning in it — all the way to the end.

On a technical front, the leader is in the bass most (but not all) of the time, and there’s a one-bar lag between leader and follower. The piece is notated in 4/4. It stays mostly in the octatonic scale containing C#-D but occasionally visits the other two octatonic scales (the one containing B-C and the one containing C-C#). It starts with imitation at the major sixth above, but the interval of imitation shifts around throughout the piece.

A rough outline of the piece might go like this. First there’s about ten bars of “conversation” where various key phrases are introduced. The conversation gives way to a passage that I call the “drunken zigzag.” Here, the voices ascend in an up-down-up-down fashion that is highly patterned, but is made to sound chaotic through a jagged, unpredictable rhythm. After the drunken zigzag, there’s a bit more conversation that then leads into the first “stretto,” a passage where the same theme is layered on top of itself multiple times. It’s not exactly akin to a fugal stretto and one could argue that stretto isn’t the right word to use here, but it’s the best one I’ve got at the moment so I’m using it. Next we have a bit more conversation with echoes of themes from earlier conversations, and then we have a restatement of the drunken zigzag, this time with some doubling and a different interval of imitation between the voices. This second drunken zigzag then leads into a new stretto that’s based on the themes from the first two bars of the piece, rearranged so a phrase of the form AB now becomes BA. After this middle stretto we hear more conversation (again, with echoes of the previous ones) and this leads into another drunken zigzag that’s special because it’s at half the speed (e.g. the rhythmic values are doubled). Next there’s some connective material that has the purpose of launching us into the third and final stretto, which uses the same rhythmic structure as the first stretto, but now the theme is descending instead of ascending. This third stretto visits all three transpositions of the octatonic scale, and leads us back to the C#-D scale where the piece began. The piece concludes with a repeated statement of a now-familiar phrase, first introduced in the second bar of the piece, with the voices finally, conspicuously imitating each other at the octave.

I’ve tried to blog about each canon I write, but there’s always much more to say about the piece than I can hope to write down. Reaching my ninetieth canon feels like something of a milestone so I’m planning to try something new. I’ll make a video where I walk through the piece and try to share how it works. Stay tuned for that.


Canon #89, Thulite

Announcing Canon #89, “Thulite.”

Many of my canons pursue an orderly relationship between leader and follower. As much as I want a canon to be interesting and provocative – a goal which sometimes results in musical complexity – I still want the canon’s structure to be clear. It’s not sufficient that the follower echoes the leader; this echoing must also be apparent to the ear. There’s a certain classic sound of contrapuntal imitation that I’m usually going for, regardless of whether the musical language is antique or modern. The leader announces a melody and we hear the follower reproduce it in a way that seems preordained, inexorable, “right” – like the voice of God. The leader sets an expectation and the follower fulfills it.

In writing my latest canon, “Thulite,” I wanted to try for a different aesthetic. I wondered if I could write a canon where the follower didn’t seem to be imitating the leader – where the two voices actually seemed to be antagonizing or contradicting each other – even if in fact, the follower was copying the leader exactly. Perhaps if the leader behaved in a more erratic, jagged, and unpredictable way than I usually seek, the follower too would sound unpredictable, as if it were doing its own thing altogether, even if that “thing” had been heard once before. Perhaps if the voices occasionally became entangled, the leader/follower relationship itself would be obscured.

To achieve this goal of a canon that doesn’t sound canonic, I put aside my typical writing process where I start with a skeletal outline and add detail in a series of iterations. Instead I composed the piece “on the fly,” one measure after another, without knowing anything about what might come next. The piece became a series of brief episodes, some of them having the jerky, erratic quality that I had been going for, and others having more of the classic imitative sound. The piece goes back and forth between chaotic and structured. But even in the latter case, the voices still seem to tug against each other with accents that don’t line up nicely.

The piece reminds me of the jerky, sudden, shifting movements of a cat-and-mouse game.

When I sat down to write, I intended to generate new material from beginning to end, but then I found a way to reuse some of what I had already written. One section from the early in the piece is repeated near the end with the same rhythmic structure but different melodic contours. And then, at the conclusion, we hear the material from the very beginning of the piece repeated in a different “key.” I put the word “key” in quotes because the piece is not conventionally tonal. Most of the material is in the B-C half-whole diminished scale (or octatonic scale). We hear enough material in this scale that its sound becomes familiar – a kind of tonal comfort zone – even though there is no specific center. In the middle of the piece, the leader remains in the established B-C half-whole diminished scale while the follower shakes things up, transposing material to the two other half-whole diminished scales (the A-sharp-B one and the C-D-flat one). As the piece approaches the conclusion it settles back into the pure B-C diminished scale, but then, in a surprise, the final passage is stated with both voices in the foreign C-D-flat diminished scale.

Importantly, the voices never play on the same beat, though they come as close as a 32nd-note away. I wanted the rhythms to seem whimsical and less ordered than my typical style, but I tried to achieve this without anything fancy like changing meters, complex polyrhythms, metric modulation, or the like. The score is notated in 4/4 and looks quite conventional. The imitation is strict: the follower copies the leaders intervals and rhythms exactly.

Some of the challenges in this piece were 1) keeping a sense of variety within the selected tonal material of the half-whole diminished scale, 2) maintaining a sense of gestural discord between the voices and avoiding the classic sound of imitation, 3) disrupting the beat while maintaining enough of sense of meter that the music can be heard as tugging against something, 4) creating episode-to-episode transitions that sound natural on the one hand but unexpected on the other.

My typical writing process usually leaves me with a result that seems final and unchangeable, but Thulite, written in an atypical way for me, opened so many possibilities, and could have gone in so many directions, that I feel the piece is only one of many possible manifestations of the intentions at play. Usually it feels right to name a piece after a gemstone or mineral, but with Thulite, for the first time, I wondered if I should change my naming scheme and use a more descriptive title. To keep things simple, I decided to stick with stones for now. My next steps will be to write a few more canons that explore the stylistic ideas that Thulite brought into focus for me.


Only Twelve Notes

How is it possible that all of music… uh… make that all of Western music… uh… make that much of Western music is formed from only twelve notes? How is it possible that some of the greatest music takes flight with fewer than twelve notes — only seven, or only five? This is a question that often occurs to people taking their very first steps in learning about music theory. If you knew absolutely nothing about the technical side of music, but you only knew of the infinite variety of musical experience – the way music can make you feel ecstatic and depressed and every shade in between, the way music can keep you entertained for hours on end – you might be shocked to learn that all of these diverse and brilliant riches are constructed from at most twelve elements. It seems unbelievable that you’d never get bored of those same twelve elements repeated over and over. But then you get used to the idea. As you learn more about music theory, you may feel that you understand how it all works, but the question “Only twelve?” might still cross your mind from time to time. I myself was thinking about it the other day and imagining how I might respond to a beginning student who insisted that there simply must be more than twelve notes. I imagined several responses I’d give the student, and I’ll record them here.

The first response is a cheeky one: asking more questions. So you’re surprised that there are only twelve notes? Then how is it possible that everything we taste is built from five basic flavor sensations: bitter, salty, sweet, sour, and umami? How is it possible that everything we see is based on three primary colors: red, blue, yellow? How is it possible that all of Shakespeare, no, all of English literature – everything we’ve ever read or written, and everything we will ever read or write – is formed from 26 letters and some punctuation marks? How is it possible that all of the content we’ve ever seen on the Internet – every video, every news article, every comment, every social media post – is represented using only two elements: ones and zeroes?

The second response is to dispute the premise. Yes, Western music has twelve named note but each named note may occur in many different ranges. The note A0 at the bottom of the piano’s range is a very different sonic experience from A7 near the top of its range, but they are both called A. A piano actually has 88 keys, not 12, and each of those 88 sounds different. If someone endeavors to sing the note A at 440hz, their voice may wobble slightly, or they may deliberately employ vibrato, in which case we hear a range of frequencies hovering around the 440hz mark. And in fact, a piano can be tuned in different ways – equal temperament is only one option. The use of twelve named notes is a simplification that conceals a much wider variety of sonic material that music can and does exploit. Music has cymbal crashes and washboard scratches and whispered words and other sounds that don’t have a specific pitch. And there is some Western microtonal music that uses 19 named notes, or 22, or 48….

A third response is to point out that twelve notes actually give rise to a very wide variety of permutations and combinations, which each have their own distinctive qualities. Lets say I want to make a sound combining four of the twelve named notes, and I want to pick one note to be the lowest, another (possibly the same) note to go above it, a third note to go above that, and finally a fourth note to go on top. I can do this in 12^4 = 20736 different ways. Now what if I want to create sequences of note combinations? The possibilities explode.

A fourth response is that notes can be delivered in an infinite variety of ways. A note can be loud or soft. It can be long or short. It can be played by a piccolo or a tuba or a guitar… or an entire ensemble. You can attack a note directly or you can slide up to it, or down to it. On each instrument there are countless articulations. There may be only one named note A, but that A can take countless forms.

A fifth response, perhaps the most interesting to me, is that notes can give different meanings to each other and can renew themselves in our perception. A sequence of notes can put a listener in a certain state of mind, and that state of mind then determines how the listener hears further notes in the sequence. If I play the note C a few times, it may come to sound familiar to you. If I play a C chord, followed by a G7 chord, followed by a C chord again, then the note C will sound like “home.” Even though you may have heard the F# chord millions of times in your life before, the F# chord would sound strange and unexpected if you heard it at this particular moment. Your perception of a note or a chord is not governed as much by your history of hearing it over your lifetime as it is by the context that’s been created by the notes and chords you’ve heard just moments ago. If I had played a different chord sequence – F# followed by C#7 and then F# again – it would be the note F# that you’d experience as “home” while the note C and its chord would sound alien and unexpected.

Music uses gesture and pattern to make certain notes and chords sound familiar while others sound foreign. Once a perceptual frame is established, music can shift it around, making the now-foreign sound familiar and the now-familiar sound foreign. In this way, you can listen to a four-hour concert that uses only twelve named notes, never getting bored with any of those twelve, because the context in which you’re hearing those notes – and thus the meaning those notes acquire – is constantly changing. A C that you hear at the beginning of the concert may not sound the same to you, may not mean the same thing to you, as a C that you hear in the middle or at the end. That C and in fact all of the twelve named notes are only vessels that assume different meanings and affects according to the infinite variety of contexts that they create for each other and the infinite variety of moods or perceptual frames that they put us in. Music uses notes to give meaning to other notes, and as the music continues, the meanings change. While the meaning of C can change over the course of a concert, it can also change from one moment to the next: C might serve as the root or anchor of the chord you’re hearing now — it might be a stable note in this instant — but it might become the tension-giving seventh of the chord you’ll hear next.

A sixth response is that we don’t only hear notes — and the melodies and harmonies they create — when we listen to music. We hear rhythm too, of course. (Another question: How is it possible that most of the rhythms in Western music are made from whole notes, half notes, quarter notes, sixteenth notes, thirty-second notes and their dotted and triplet varieties?) Beyond that, we hear texture. We hear performers, we hear composers, we hear the people the music is about, or the people it’s for; we hear something of the history of when it was written or performed; we hear the memory of when we heard it first or heard it last; we hear the way we feel right now as it relates to the sounds that confront us. We may be something of a different person each time we listen, and listen again, to the same piece. There’s that.