Are you a musician planning to release an album but struggling to put your tracks into a coherent sequence? Are you planning a live concert but feeling unsure how to organize the program? Here are some tips that might help.
These tips come from my own experience as I put together an album of new music I’ve composed over the past five years. I’ve got 35 tracks with a playing time of 93 minutes. My mastering engineer requires a track order before he’ll begin work on the project. Each track needs to have a number — 1, 2, 3, 4… — and the engineer needs the tracks ASAP. Here’s why the problem is impossible:
There are too many options. If you have 35 items like I do, the number of ways you can organize them is 10,333,147,966,386,144,929,666,651,337,523,200,000,000.
Each option is time-consuming to evaluate. Listening to the material in any particular order takes a 93-minute investment which is emotionally exhausting.
My reactions change each time I listen. I might like a certain transition between two tracks the first time I hear it and not like it the second time.
If I listen to a certain order too many times, I start to memorize it. Then it’s hard to tell whether I like it because it’s effective or just because it’s familiar. Familiarity is confounding.
I’ve dedicated years of my life to creating this material, so the stakes are high. A bad order means that my tracks will compete with each other rather than elevating each other. Some pieces will not have a context in which they can shine.
Each piece was conceived on its own, without thought to how it might fit in a sequence. The pieces all have different styles and moods. I had no plan for how they were supposed to fit together.
But as I write this post, I’m in good shape. My track order is mostly finalized and I’m ready to send it to my mastering engineer next week. An impossible problem became possible for me, thanks to these ideas:
Think of a story that you want to convey with the tracks. I’m grateful to @alexgardner for offering this suggestion when I reached out for help on Twitter. At first, I thought that my tracks were so heterogeneous that they couldn’t fit into any unified narrative. What I realized is that the narrative doesn’t have to be evident to the listener. It can be a “secret” story — one that’s known only to me — one whose only purpose is to help me wrap my mind around the problem.
Make a list of track attributes. I’m grateful to @gahlord for this suggestion, also via Twitter. I created a spreadsheet listing the starting and ending note of each track and a brief description indicating bright/dark, fast/slow, and long/short.
Decide on a goal for the ordering. In my case, the goal is to sustain a sense of variety throughout the album so that each track can be experienced fresh. I decided that variety and contrast are more important to me than grouping tracks by theme or emphasizing similarities between them. My desired shape is “fractal” rather than “linear.”
Pick a middle piece — one to go right in the center of the album. Then go through each of the remaining pieces and ask if it should come before your middle piece, or after your middle piece. This lets you break the problem in half.
Next, choose your first and last pieces. Now you’ve got: Opening -> Middle -> Ending.
Next, distribute your biggest pieces. What are the longest, densest, or most important pieces remaining? Pick the top two and put one in each half of the album. Now you’ve got Opening -> Big Piece #1 -> Middle -> Big Piece #2 -> Ending.
Try to make contrasting pairs — two tracks that are very different, but that also sound good together and flow well, one into the next.
Now try to identify twins — two tracks that are very similar. Experiment with placing twins before and after a contrasting pair, as if to form a ring around it. So if A and B are a contrasting pair, while X and Y are twins, you’d have something like X -> A -> B -> Y.
Make a provisional commitment. Choose an order as quickly as you can, and then rename all your tracks according to that order, using filenames like 01_MySong, 02_MyOtherSong, 03_MyOtherOtherSong. This gives you a reference point to measure future changes against.
Now see if you can improve your provisional order by swapping pieces, so for example, the piece in slot 5 and the piece in slot 11 might trade places.
Make short clips out of all your pieces. Each clip should consist of the opening 3 seconds plus the closing 3 seconds of the piece. Once you’ve made these clips, you can put them in any order you’re considering and listen to the whole playlist in a minute or two. This is a way to quickly preview an order without having to listen to all the material over again.
Once you’ve arrived at an order you feel good about, review each track and use your intuition to determine whether the track is “happy” in its current position. Does the track get along with its neighbors? Does it sound better in their company than it would sound all by itself? If you find any tracks that aren’t “happy” move those ones, but leave everything else where it is.
These ideas worked for me — maybe they’ll work for you too?
If you’re an artist who makes things to please your own eye or your own ear, why would you seek an audience? If you create a piece of art for the satisfaction it brings you, and if that satisfaction is experienced by you, hasn’t the art’s purpose then been fulfilled? Assuming it’s hard work to cultivate a following for your art, why would you invest in that?
My need to answer this question is pressing. I’m a musician gearing up to release new work this year. I’ve sworn that I won’t let my music go into a void, not this time. But my energy fades whenever I think of self-promotion. I’m an introvert. Marketing has never been my thing. I hope that knowing my reasons for wanting more listeners will help me stay motivated to connect with them. If you’re an artist facing a similar question, I hope you might gain something from the thinking I’ll share.
But if you’re aiming to earn income from your art, I have nothing to add to what you already know. A larger audience means more income, so it’s obvious why you’d want more viewers or listeners. And if your art carries a social or political message, a larger audience means more impact, a better chance to advance your cause. If your art is meant to communicate something specific to someone specific, it can’t function in an empty room. And if your creative process relies on feedback beyond what your own eyes and ears can provide, a larger audience might help you do better work. And if you’re seeking validation and prestige, a larger audience means more of that. These situations are clear: you need an audience.
But what if you’re making art for art’s sake, what’s your reason then for seeking an audience? What if you’ve been laboring on your own for years – as a “nobody” as Emily Dickinson would put it – to do something that’s really hard but really rewarding? And what if you’re doing this for the joy of it – not to please anyone else, but just yourself? Not to profit from it, not to further a social cause through it, but just to experience the pleasure and fascination that it brings you? What if achieving an aesthetic ideal is more important to you than any practical outcome? What if you do your best work in solitude? And what if you vow to keep pursuing this ideal no matter what – no matter whether there’s a market for it, no matter whether anyone ever praises your product or asks you for more of it? If this is you, why would you care whether your audience consists of one or one million people?
In my case, I compose music in a particular format called canon. I’ve been doing this since 2014. A two-minute canon can take me two months to write. Each piece brings me immeasurable joy to create and behold. I feel blessed that I’ve had the opportunity to study music year after year, starting pretty young, and ultimately to create the kind of music I want to create. I’m further blessed to have a collaborator who has performed and recorded my works. My music has been enjoyed by a handful of people who know me personally, and a tiny few who have somehow discovered me online. Why isn’t that enough for me?
Why do I feel – as I prepare to release ninety minutes of new work this year – that more people must hear it? Why have I vowed that this time, I won’t let it be ignored? I won’t simply put it online and hope that people find it. I won’t just email a dozen reviewers and shrug when no one replies. This time, I’ll do the work necessary to bring my music to those who are poised to enjoy it, and I’ll do the work necessary to expand that circle. But if I wrote the music for myself and experienced the pleasure I was seeking from that act of creation, why does any of this matter?
I used to think of this question in terms of the intrinsic value of the work itself. I believe the work is unique, and exciting, and that it makes a contribution within its particular niche, so the world needs it. If I keep the material to myself by not sufficiently promoting it, then it will go to waste. This would be a disservice to the music and to the world.
I’ve never been happy with this reasoning because it focuses on a negative outcome – the music going to waste – which leads to a burden – I must save the music from oblivion. Furthermore, the world is already full of music. Beautiful music is hard to make, but humanity has been making it for centuries, and it’s not a scarce resource. No one person will ever get to know more than a tiny fraction of the great music that’s available; ditto for visual art and literature. This will be controversial but I’ll say that while humanity needs art, it doesn’t need any particular piece of art – there are no “essential” works – including anything I make or anything you make. The world could benefit from what we make, surely, but the possibility of benefiting from something is different from needing it.
So I’ve tried to identify other motivations for pursuing an audience, motivations that don’t rely on the assumption of need. Let’s suppose that I’m doing something optional and unnecessary. Why might I still want more people to hear and appreciate it, and why would I be willing to put in the hard work to achieve that goal?
My first answer is simply that I want others to experience the same joy that the music has given me. As for why this is so, I believe that joy is expansive: when we find joy in a certain thing, we want others to feel that same joy, from that same thing. And when others feel that joy, our own is magnified. This is just how joy, the emotion, works – it makes us yearn for connection, kinship.
Second, I want to share my knowledge. For me, knowledge is similar to joy in that when I’ve learned something useful I want to convey it to someone else. I’ve had to learn many things to be able to write the music I write. I’ve had to find ways to surmount countless musical challenges, creative challenges, and personal challenges. If someone’s totally new to canons and counterpoint, I want to welcome them into this part of the musical universe. But if someone knows about these things already, I want to see if I can offer them some bit of new insight that may help or inspire them in their own journey.
Third, I want to grow through interaction and collaboration. I know I can write more of the music I’ve been writing, and within that domain there are endless possibilities I want to explore. But I’m ready to branch out. Someone could recommend an album that might change my life. Someone could ask a question that opens a new musical direction for me. Someone could teach me a new technique for composing or a new way of listening. Someone could become a new collaborator and together we could make something great. I want to grow not only in the ways I’ve planned for myself already, but in the ways I can’t predict, haven’t even conceived. But none of this can happen if my music stays with me in a bubble.
So I want a larger audience because I want to share my joy, I want to share my knowledge, and I want to grow. To be clear, this is not my argument for why anyone should listen to my music; this is not where I say what’s in it for them. This article is about me; it’s my explanation of why having an audience is important to me. It’s a “note to self” that I’ll return to when I must choose how to spend my time: composing new work or reaching out to new listeners.
If you’re an artist facing a similar choice, maybe some of these reasons apply to you too?
I don’t mean to diminish music by posing this question.
To call music a tool of pleasure does not lessen music’s importance, because pleasure itself is important and good.
It’s true that the pursuit of pleasure can take a greedy, destructive form, but just as much, it can be a path to connection, even enlightenment. The experience of pleasure can put us in tune with ourselves and with one another. Among the varieties of pleasure, there is physical pleasure, there is spiritual pleasure, and music offers both.
If music can make us sad, it does this in a way that brings us pleasure. We are happy to be moved to cry, when it’s music that’s doing the moving. If music can make us disoriented or confused, it does this in a way that brings refreshment, expands our field of view, and so delivers the pleasure of growth.
Of course, music is a business. Music is pursued for money, fame, and influence. Music is an academic discipline. Music is a way to glorify God. Music can have a mission: it can tell a story, advertise a product, raise awareness for a cause, spark a revolution.
Sheer pleasure is not the only reason to sing, or play an instrument, or write a note on staff paper. But if you look at the essence of music, if you consider why we’re addicted to music – it’s about pleasure.
Take away people’s willingness to pay for music, and we’d still make it. Take away music’s academic prestige and we’d still want to learn about it. Take away the large concert venues, the rock stars, the virtuosos — take away music’s connection with fame, and we’d still sing in the shower. But if music didn’t bring us pleasure, then the other reasons for making it would lose their support. If it didn’t make us feel good, then music would no longer be a way for anyone to make money or get famous or achieve any other goal.
Why is it necessary to remind oneself that music is about pleasure?
Musicians might need such a reminder because our work is difficult, and that difficulty can be so intense as to consume us and makes us forget what we’re really after.
I am a musician. That means, in some sense, that I’ve dedicated my life to pleasure… to seeking out a certain form of pleasure, and sharing that pleasure with others.
But what did I learn in my first music lessons as a kid? That I’d have to practice before I could play what I wanted to play.
The study of music is all about delayed gratification. In my own path as a musician:
I’ve wanted to sing a note but couldn’t reach it or hold it in tune, so I needed to practice more and/or give up on reaching that note for the time.
I’ve wanted to play a passage on guitar that I had spent dozens of hours preparing but I couldn’t pull it off, so I needed to practice more and/or try an easier piece.
I’ve wanted to sight-read a piece but constantly got stuck, so I needed to go slower and try an easier piece.
I’ve wanted to compose a piece of my own but didn’t know how to start so I had to muddle around for years looking for an entry point.
I’ve wanted to improvise a solo but couldn’t get my bearings or synchronize with a group so I had to go back to the woodshed.
I’ve wanted to make a recording to share but couldn’t press “record” without promptly making a dozen errors.
I’ve wanted to receive a response to music that I had labored for months to create but I heard only silence in response and didn’t know how to connect with those who might appreciate what I’d done.
I’ve wanted to delight someone with my music but found that it didn’t speak to them.
This is just a way of saying that the effort to experience pleasure and offer it to others through music can come upon obstacles that cause stress, distraction, insecurity, and doubt.
When music frustrates me, I’ve taken to reminding myself that music is about pleasure, and my capacity for pleasure is intact, no matter what pitfalls arise. I can laugh. I can love. I can delight in things. I already have everything that music can give me, or that I might seek to achieve through it.
In those moments when I am skeptical of my own abilities or path forward in music, I remind myself that we – all musicians – are seeking the same result, the spreading of pleasure. I can work towards that end no matter what, through efforts musical and non-musical alike.
I sometimes do a little experiment. I take the densest, driest music theory textbook I can find on my shelf, I flip through the pages and look at the squiggles – dense squiggles I have poured over many a time before – and I remind myself that all of this is just a recipe to give someone a good time. That’s why we’re arranging notes in various combinations and laboring to follow precise instructions about how those notes should be performed… it’s all to give someone a good time. Really, that’s all it’s about – pleasure – but that is important.
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.
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.
I’m pleased to announce Canon #94, Cinnabar, written this past December and completed on Jan 1, 2022.
When I started working on Cinnabar, my aim was to explore the idea of a reordering canon. I wrote an outline and spent many days developing it, only to find that I had arrived at a dead end. My efforts at development — so diligent, so persistent — had only made the outline worse! This creative disappointment transpired in a span of several days when I was already in low spirits, for no particular reason, just generally feeling crumby. In an effort to lift my own mood, I went back to an earlier version of my outline and thought “Let me try doing something silly with this.” The idea was to decorate my carefully-planned outline in a totally preposterous way, entirely for my own amusement, writing nonsensical themes and absurdly discordant counterpoint with no plan anymore to turn it into a finished piece. But once I got going, the “silliness” began to acquire its own internal grammar, and the composition process turned quite serious again, but now it was unstuck.
I chose the name Cinnabar for two reasons. First of all, the interval palette and melodic style of the piece reminds me somewhat of my Canon 74, Ruby, and both substances are bright red. Second, I wanted a name that contained some element of humor. The names of gems and minerals aren’t all that funny in general, but cinnabar stood out to me because when I say cinnabar I think of “cinnamon bar” or “cinnamon bun” or “Cinnabon,” and this thought leaves me mildly amused, what can I say?
Let’s talk about the structure of the piece. The soprano plays a series of six-measure phrases, with some space left at the end of each phrase. We can label those phrases as 1, 2, 3, 4, 5, up to 14. The bass plays the same phrases as the soprano, but in a different order. That’s what I mean when I call Cinnabar a “reordering canon.” In this piece, the bass order happens to be 3, 1, 5, 2, 7, 4, 9, 6, 11, 8, 13, 10, X, 12. (“X” represents a bass-only phrase that’s not stated by the soprano). When the two parts are executed simultaneously, we hear a series of phrasal pairings or contrapuntal episodes separated by brief pauses. At the beginning, we hear phrase 1 over phrase 3; next, we hear phrase 2 over phrase 1; then phrase 3 over phrase 5, and so on. For the most part, each phrase is restated two episodes after we first hear it, which is to say the restatements are close together but usually not consecutive. Some phrases are heard for the first time in the soprano, while others are heard for the first time in the bass (i.e. if we think of the bass as reordering the soprano’s phrases, it might place some phrases in an earlier position). The piece ends with a mirror inversion of the opening episode, where we hear phrase 3’s inversion over phrase 1’s inversion.
Most phrases undergo a chromatic transposition when they are restated; so phrase 1 begins on a C# when we first hear it in the soprano, but it gains a pickup gesture leading to an F# when we hear it in the bass. One of the challenges of writing the piece was finding the right transpositions for each episode (I say episode here because each phrase has a planned intervalic relationship with its companion phrase, so the two must be transposed together). The goal is to maintain a sense of variety throughout. Since the episodes are tonally ambiguous and the piece has no specific key, it is possible to transpose the episodes arbitrarily, but experimentation reveals that the options are not equivalent. Care is taken to avoid starting too often on the same note or in the same range, and also to avoid having the phrases start or end too squarely on the beat, and also to avoid reusing the same pickup and ending gestures, so that each episode begins and ends in its own distinctive way.
The relationship between the two voices in this piece is what I might describe as “choreographed chaos.” The voices may sound at times like they are contradicting each other, or tripping over each other, or going off in their own directions obliviously, but they still give each other enough space that their own individual features can shine through the discord. Whatever “destructive interference” occurs between the parts is meant to be occasional and not constant — that’s to say, the clamor is full of deliberately positioned gaps that allow us to peek inside and see each protagonist clearly. As we hear the parts interact, we might think “This can’t go on much longer — it’s unsustainable!” But they always reach a discernible cadence or stopping point after each six-measure span, as if they had been rescued just in time — saved by the bell. These evenly timed cadences are one giveaway that the seemingly chaotic relationship between the parts has been carefully planned.
A dissonant interval palette is used throughout, and great attention is paid to maintaining this palette, so that if a prominent consonance were to occur, it might sound “wrong” in contrast to all of the staged clashes and pratfalls that come to sound “right.” Tonal centers are never maintained for long, but they are allowed to develop just long enough that we can feel pulled towards certain notes and can experience others as unexpected or out of place.
The penultimate passage is marked lacrimoso and may be the closest I’ve come in any of my canons to writing a passage that sounds vaguely Chopinesque. The sorrowful ethos of this one passage is an unanticipated break from the scherzando quality of the piece, and an intensifier of the return to scherzando in the final passage.
I mentioned that Cinnabar reminds me of Canon 74, Ruby, but Ruby has a severe demeanor, not a comical one; the resemblance is in the musical materials used, not the overall tone. If I try to think of another canon that has a comical element, #49, Gallium comes to mind. In that piece, the two voices start out with a harmonious, tonal relationship, then progress towards increasing discord and tonal ambiguity, and then suddenly spring back to clarity and alignment. I think that many of my other canons have bits of humor here and there, if you know where to look — but the current #94 and the earlier #49 are two I’ve written so far that actually strive to maintain it across the span of the piece.
My upcoming composition, Canon 94, has an unusual structure. I call it a “reordering canon.” There are two ways to frame this concept. To start out, we need to subdivide our melodic material somehow. We might focus on individual measures, or sections containing some fixed number of measures, or phrases occupying a variable number of measures. Once we’ve chosen a way to subdivide our melodic material, we can describe a reordering canon in either of the following ways:
It’s a canon that has a leader and a follower, like any typical canon has, except the follower is allowed to rearrange the leader’s material — playing the leader’s melodic subdivisions (measures, or sections, or phrases) in a new order. In this case, the leader’s order is considered to be the original or primary one. We would label the leader’s melodic subdivisions as 1, 2, 3, 4, etc. The follower’s order would then appear as a scrambling of that sequence, like 3, 1, 4, 2.
It’s a canon where we dispense with the roles of leader and follower. Instead we begin with an unordered set of melodic fragments. Each of the voices is responsible for playing some permutation of the set. That’s to say, each voice must play all of the fragments in the set, but each voice may play them in its own unique order. So one voice might play 4, 1, 3, 2 while another plays 3, 4, 2 1.
The only difference between these two descriptions is that in the first case, we assume that the material has an “original” order (maybe we are working with a pre-written tune). This lets us identify a leader that plays the original tune and a follower that rearranges it. In the second case, the material does not come with any specific order so it’s not meaningful to assign the roles of leader and follower.
To see what possibilities this idea opens up, and what new challenges it creates, let’s first review how a standard canon works. In a standard canon, the leader and follower play the same material in the same order, but the follower begins after a delay. We hear the follower constantly echoing the leader, always a few measures behind, never catching up.
Here’s a diagram of a standard canon consisting of four sections. I’m using the term “section” to refer to some number of measures — the same number of measures in the canon’s lag or delay. In this case, the bottom line is the leader; the top is the follower.
Look at the arrows. The blue arrows show transitions: section 1 flows into section 2, which flows into section 3, and so on. The red arrows show contrapuntal pairings: section 1 is heard above section 2, section 2 is heard above section 3, and so on. Together, the arrows represent the constraints that make canons interesting, and that make canons hard to design.
Examining the arrows in this diagram, we can see that the inner sections (all but the first and last) have four distinct responsibilities:
Each section has to make sense coming after the previous section — it functions as a successor.
Each section has to make sense coming before the next section — it functions as a predecessor.
Each section has to sound good below the previous section — it functions as a bass line that accompanies its predecessor.
Each section has to sound good above the next section — it functions as a soprano line that accompanies its successor.
If you understand this, you understand the basic challenge of canon writing.
But not all canons work like this.
It might seem that an echo — the unmistakable experience of hearing the follower repeat what the leader announced a few moments earlier — is the defining aspect of a canon, but in fact the term “canon” has long included pieces that have no discernible echo. In a retrograde canon, the two lines may start at the same time, with one line playing a reversed or backwards version of the other line’s material. Here’s how that might look:
As we listen to such a piece, we don’t hear a follower echoing the material that the leader had played a moment ago. Instead we hear two contrapuntal parts that may seem to be doing totally different things. In the diagram above, we see that soprano begins with section 1 while the bass begins at the same time, with a reversed version of section 4. We have to wait till the end of the piece to hear section 1 restated in the bass, but it occurs there in a backwards form, which may sound nothing like the forwards form.
If retrograde canons lack an echo, why do we call them canons at all? We call them canons because one voice can still be seen as imitating the other voice. Imitation is key. Imitation is what makes it a canon. The follower’s material is wholly and systematically derived from the leader’s material. It’s just that the imitation here is a complex kind — the imitation involves a transformation, namely reversal.
If we’re going to allow “imitation” to include a transformation as extreme as reversal, and still call the piece a canon, we might ask what other kinds of imitation could be employed to good musical effect. Along with reversal, the standard ones are inversion (turning the material upside down), augmentation or diminution (playing the material faster or slower), and of course transposition (playing the material higher or lower). Those are the ones you’ll find in a textbook, but what else is possible?
I’ve been pursuing this question in many of my compositional efforts. In a separate post, I will summarize the other nonstandard forms of imitation that I’ve explored. Here, let’s delve deeper into the reordering concept, where the follower must imitate each of the leader’s sections, but the follower is free to change their order. A reordering canon, as I’m calling it, can be visualized like this:
As you can see, where the top line plays sections 1, 2, 3, 4, the bottom line scrambles that order and plays 3, 1, 4, 2. Both parts start at the same time, similar to what happens in a retrograde canon, but this diagram does not show a retrograde canon. Even if the bottom line played 4, 3, 2, 1, it still wouldn’t be a retrograde canon. That’s because a retrograde canon does more than reverse the order of the sections; it reverses all the notes inside each section. We’re not doing that here. The contents of each section are still being played in their regular, forward-moving direction. It’s just that the order of the sections has changed.
Does a reordering canon have an echo? Yes it does, but it’s a more complex kind of echo than we hear in a standard canon. In a standard canon, the echo comes from one part: the follower echoes the leader. In a reordering canon, the echo comes from both parts. That’s to say, some of the sections will be announced first by the bass and imitated later by the soprano; while other sections will be announced first by the soprano and imitated later by the bass. And the delay — the length of time between a section’s initial statement and the onset of its echo — may vary from section to section. In the diagram above, we can see that section 1 is imitated by the bass immediately after it is stated by the soprano; section 3, on the other hand, is only imitated by the soprano after a delay of one section has passed since the bass first announces it.
Is a reordering canon easier or harder to write than a standard canon? In one sense, there are more constraints at play. In a standard canon, any section has only one horizontal context: for example, section 3 would always occur between sections 2 and 4, whether we’re considering the top line or the bottom line. But in a reordering canon, each section has two horizontal contexts. In the diagram above, we see that section 3 occurs between 2 and 4 in the top line; but in the bottom line it serves an opening role and then leads into section 1. Furthermore, each section still serves in two vertical capacities: in this case, section 3 is the bass that we hear below section 1 at the beginning of the piece, and the soprano that we hear above section 4 later on.
By the looks of it, you might think that a reordering canon should be harder to construct than a standard canon, because there are more constraints at play. But there’s one difference that allows a great deal of freedom in how a reordering canon can be composed. In a reordering canon, each section still serves in two vertical roles, but no longer has to serve as the bass to its predecessor specifically and the soprano to its successor specifically; instead, it might be paired with distant sections. For example Section 3 might not have to sound good below section 2 and above section 4; instead, its companions might be Sections 22 and 36! This opens up a lot of compositional options that just aren’t available in a standard canon.
And while it might be challenging to write a sequence of sections that can be played in two different orders (e.g. 1, 2, 3, 4 and 3, 1, 4, 2) there are ways make it work. In my first exploration of reordering canons, I’ve found it helpful to work at the phrase level rather than the measure level. In Canon 94, each section is a self-contained six-measure phrase, there are pauses between the phrases, and I allow for any phrase to be freely vertically transposed. It’s still challenging to write a set of phrases that can sound good in two different orders, but I feel there’s more leeway in how phrases can be rearranged than in how the fragments or gestures inside a phrase can be rearranged. Of course, that depends on the style, phrase structure, and musical materials in use.
We might observe that the traditional contrapuntal operations like retrograde and inversion produce one specific “output” for any given “input” whereas reordering gives the composer many permutations to choose from. Is this too much freedom to still call reordering a kind of imitation, and the resulting piece a kind of canon? The whole reason I’m interested in the reordering concept is because it’s a way to introduce more freedom into canon writing, but I don’t personally think it’s so much freedom that the piece ceases to be a canon. As we’ve seen, there are still many constraints to work with, and one line is still responsible for repeating the other line’s material. If we compare reordering with retrograde imitation, we see that retrograde imitation can completely change the sound and character of a line, including each of its sections, while reordering preserves the sound of each section. Arguably, reordering is less of a drastic transformation that note-by-note reversal, even though there are more ways to do it.
I was asked to restructure my last post on Finishing Stuff as a numbered list:
1. It goes without saying that if you want to finish a project, you should commit to finishing it, and you should make this commitment as early as possible. But it’s easy to promise yourself you’re going to achieve a certain outcome and then find, weeks or months later, that the promise was unrealistic: “Oh well.” Instead of an empty commitment, what you want to make is an actionable commitment. Make a promise about how you’ll behave throughout the project. Promise yourself that you’re going to do something – a little something – towards finishing the project every day: not busywork, but work that specifically moves you closer to the end. For every moment you spend envisioning a brilliant outcome, also spend a moment picturing the daily choices that will help you get there. Imagine yourself struggling with a task that’s boring and tedious, but imagine that you’re feeling good about this task because you know it’ll move the project forward. Think of finishing as a mantra, not as a goal that you set once and forget.
2. Strip away any exceptions that might be attached to finishing. Don’t say “I’ll finish if…” but rather “I’ll finish by any means.” Ask yourself if you’re willing to prize completion more than you prize quality. This can be difficult because often it’s the dream of a high quality result that motivates you to undertake a project in the first place. You figure that if the outcome is going to be mediocre you might as well not produce it at all. Realize that this thinking is a trap: it sets you up to never finish. Try to flip the relationship in your mind: it’s not the achievement of a particular standard that should allow you to finish; rather, it’s your commitment to finishing that will propel you to achieve your standards.
3. Consider it your job as a creator or a doer to get past the obstacles of the mind that stand in your way: your own doubts, anxieties, and self-criticisms. Just as you might step around a boulder in your path, remember that you can step around your doubts, then look back at them from a distance: you don’t have to tackle each one head-on. As for whether you should succumb to any particularly convincing doubt: maybe someone else would do that, but you can call yourself a creator because you’re willing to prioritize creation over fear and indecision. Discovering ways to stay motivated — to tap into available sources of optimism — is part of the duty you accept. The people who focus on worrying about stuff instead of making stuff are the ones who aren’t making stuff, but you’re different.
4. Spend more time thinking of what you can do with what you have rather than what you can’t do because of what you don’t have. If you’re not well prepared for the project and the conditions aren’t ideal, then this point is especially important: accept it as your mission to find the hidden potential in your current self, in your existing tools, in your present circumstances. If your shovel’s broken, of course, you’ll need to fix it, or get a new one, but what if you’ve got an ugly shovel that works fine? Use it with pride. You’ve heard of a fancier one that could make you 20% more efficient — should you upgrade? There are no rules, but try to decide as quickly as you can and move on, rather than making a new project of weighing the pros and cons.
5. Identify a consumer or beneficiary of your efforts – whether it’s a large audience, or a single person, or you yourself in the future – and place their interests above your current comfort. Say “It’s more important that they receive the product I’m making than it is for me to feel comfortable right now as I’m making it.” Focus on what you want to do for them and how you want them to feel, rather than on the discomforts you’re experiencing as you work. Think of what they’ll gain if you finish, and what they’ll miss out on if you don’t. Imagine that they crave the thing you’re laboring to offer.
6. Always try to make things easier for yourself. Ask “How can I set myself up for success?” rather than “How can I find obstacles that will provide a good justification for why I didn’t succeed?” When you hit a roadblock, don’t slow down; either keep trying to overcome the roadblock or shift to working on some other part of the project that’s not blocked. Try to get simple things out of the way as early as possible, inching closer to the finish line in any way you can. For example, if you need a title and you can choose it now, choose it now.
7. Try to make the project itself simpler, cutting things out, reducing scope where possible. If it’ll budge, bring the finish line closer to you. For example, if you don’t need a title, don’t worry about choosing one. If you don’t need to write an extra paragraph, don’t worry about what it was going to say. Stay open to the possibility that you’ve already finished. Make a habit of asking whether you can release your work right now, just as it is. If you can’t release it right now, then what can you do right now so that if you had to release it tomorrow, it would be releasable?
8. Be open to executing inelegant hacks that get you to the next step. Take pride in these hacks; don’t feel embarrassed about them. Know that every project requires duct tape somewhere. Your methods of work might be very important to you and to your creation, but don’t let an attachment to any particular method of work stop you from finishing the work.
9. OK, you’re serious about finishing, but see if you can keep a sense of humor and lightheartedness at the same time. Is there anything about your situation that’s a little funny? Is there anything that’s a little fortunate? If you’ve made mistakes earlier in the project, and you’re inclined to lament those mistakes, do the opposite. If you failed at something it means you must have taken a risk, which means you must have had some courage, which you should feel proud about; obviously you survived, so now you have the chance to learn and move on – great!
10. Think of the current project not as your final statement but as part of a sequence of projects that you’ll work on as you manifest your creative vision. If this project isn’t shaping up as wonderfully as you hoped, think of finishing it as a down-payment towards achieving something more wonderful the next time around. Also remember that you won’t actually know how good it is until you finish it and step away from it for a while.
In thinking about all the projects I’ve started over the years – anything from essays, to musical compositions, to house cleaning efforts, to travel plans – I wonder if there’s a common reason why some of them got done and others didn’t.
The projects I have in mind are my own solo projects – efforts that I undertook by myself – but to understand why these projects succeeded or failed, it’s helpful to consider why a group project might succeed or fail.
When a whole team of people succeeds or fails at achieving a goal and you want to figure out why, you can look at how well they got along, how motivated they were, how clearly they understood their mission, and so on, but perhaps the first question to ask is whether they had a good leader or project manager. Was there someone on the team who took it as their primary responsibility to steer the project to completion? And how skillful was this person in a managerial capacity, whether they called themselves a manager or not?
When you undertake a solo project, of course, you play many roles at once: you’re the person who comes up with the ideas, you’re the person who edits and refines the ideas, you’re the person who executes the ideas, and you’re the person who makes sure that all of these things happen within the time and resource constraints at hand. But you might not put the same effort into each of these roles.
What I realize in considering the history of my solo projects is that there have been some where I accepted the responsibility of “project manager” from the get-go and others where I avoided it. Some projects literally started with my thinking “I’ve got to get this done – how can I get it done?” and others started with my thinking “Let’s explore some possibilities and see how it all turns out.” I’m going to venture to say that the projects where I took on the responsibility of “project manager” are the ones that succeeded, and the ones where I avoided that responsibility… you guessed it. But all of this can be phrased in a way that doesn’t use the term “project manager” at all.
The projects that got finished are the ones where I made finishing a priority from the outset. They’re the ones where I started thinking about how to finish from the very moment I began work. They’re the ones where I constantly returned to the goal of finishing at each step, weighing any choice I might make according to whether it would move me closer to finishing, or further away.
The projects that got abandoned are the ones where I didn’t make an early commitment to finishing. They’re the ones where I started out with a goal like exploring or experimenting or testing the waters, but not necessarily finishing. They’re the ones where I assumed that if I just spent enough time and put in enough effort and gathered enough material, finishing would happen naturally. They’re the ones where I didn’t become concerned with finishing until late in the game, and even then, my commitment was conditional, not absolute: “I’ll finish this if…”
The difference boils down to an active versus a passive view of finishing.
The active view is that you’ve got to work at finishing all the time. Finishing is part of the project, it’s one of the things you grapple with, just like you grapple with the project’s content – the sentences in the essay, the notes in the musical composition. If you’re making art, then finishing is part of the art. A way to finish is part of what you’re creating.
The passive view is that finishing comes about naturally once you’ve put in sufficient time and effort. Finishing isn’t something that you consider or worry about per se; rather, it’s the end state that you reach as a matter of course. If you simply work hard enough on the content of the project, eventually you’ll finish.
Here are some thought patterns and behaviors that typically arise when you take an active view of finishing:
You remain open to the possibility that you’ve already finished. You periodically ask “Can I release this right now, just as it is?” If you can’t release it right now, then what can you do right now so that if you had to release it tomorrow, it would be releasable?
You try to get simple things out of the way as early as possible. For example, if you need a title and you can choose it now, you choose it now.
When you hit a roadblock, you don’t stop or use this as an excuse to slow down; either you keep trying to overcome the roadblock or you shift to working on some other part of the project that’s not blocked.
You always try to make things easier for yourself. You constantly ask “How can I set myself up for success?” rather than asking “How can I identify obstacles that will provide a good justification for why I couldn’t succeed?”
You make the most of the tools you have at hand, rather than wishing you had a fancier shovel. If your shovel’s broken, of course, you fix it, or get a new one, but what if your shovel works fine? You’ve heard of another one that could make you 20% more efficient — do you upgrade? When finishing is a priority, you find a way to decide quickly and move on, with a bias to keeping what already works; when finishing is not a priority, then weighing the pros and cons of any potential upgrade becomes a new project of its own.
When you experience doubt or anxiety, you take it as your job as a creator or a doer to move past the anxiety. If you’re worried about your abilities or about the project’s worthiness, you realize that this worry is an obstacle to finishing, just like any other obstacle, and it’s your mission to get past whatever obstacles come up, including those of the mind. Finding ways to diffuse or defang your anxieties, rather than giving them more airtime and a chance to grow, is part of what you signed up for when you signed up to finish. Finding ways to stay motivated — to tap into available sources of optimism — is part of the duty you assumed.
It can seem mystifying how the same person can be so effective in completing one project but so ineffective in completing another. But the mystery recedes if you look at the strength of that person’s commitment to finishing. If they were committed to finishing from the very beginning, then they probably spent time throughout the project managing themselves: taking stock of their progress and re-calibrating their efforts to give themselves the best chance of reaching the goal. If they weren’t really committed to finishing from the very beginning, then they probably didn’t do any of that until the project had already gone on for a while, maybe spiraling out of control. In both cases, they may have worked very, very hard — it might have felt to them that they were doing their absolute best, working as hard they possibly could. It’s just that in one case, the work was aimed at finishing and in the other case, it wasn’t.