Resolution: I’m going to spend $1000 buying albums made by independent musicians.

There’s been a lot of talk about the injustices of the streaming economy, and a lot of hand-wringing about Spotify recently, but if every listener committed to investing a non-trivial amount of money on independent artists and albums each year, the whole world of music-making would be better off. Back in the CD era, I used to spend all my spare cash on albums, why not now?

The twist in this project is that I’d like to build my new record collection from your suggestions. Instead of collecting music the way I did in the past, carefully selecting what I thought would please my very particular taste, I’d like to listen to whatever my network suggests I listen to. That means friends, acquaintances, readers, you.

I’ll do my best to promote each album I buy by favorably reviewing it in person, on Twitter, through this blog, and possibly elsewhere. And while this project lasts, I’ll be listening to my new purchases exclusively, staying away from any “free” content online and any music I had collected in the past.

To anyone who knows of an interesting new album created by an independent musician, tell me about it in a comment here on this blog post, or contact me on Twitter, and I will strongly consider it for purchase. Artists, please don’t be shy about suggesting your own work — I do want to hear from you directly. Wondering what kind of music I like? Read below…

FAQ:

What’s the timeframe?

I’m planning on a six-month timeframe, officially starting March 2022 and ending Aug 2022, though I’ve already bought three albums earlier in 2022 that I’ll be including in the project. I want to have time to get to know each album I buy, so I’d like to cap my purchasing at five albums per week and have it be lower than that most weeks.

How are you tracking your purchases?

I’ll be recording them in this spreadsheet.

What styles of music are you looking for?

I’m hoping for a mix of classical, folk, singer/songwriter, jazz, and world music. I’m also hoping to broaden my horizons and get to know new styles that I wouldn’t typically seek out.

How picky are you?

I’m interested in hearing any albums that were labors of love for their creators, whether the album was made in a bathroom or a professional studio, by a novice singer/songwriter who only plays three chords or by a virtuoso classical musician. In any case where I don’t immediately connect with the music itself, I will try to learn more about the performer and their story of creating the album, and as long as there’s passion and commitment in the story, I will feel happy to have made the investment and included them in this project.

Why are you doing this?

I’m planning to release an album myself (90 minutes of intricate counterpoint performed on clavichord) but I don’t currently have a sizeable audience to release it to. In thinking about how to build an audience for my own work, I began thinking about what I’d love other people to do for me: I’d love them to “tune in” to what I’m trying to achieve, buy my music, take the time to listen to it closely, and tell others about it. This raises the question: am I doing that same thing for other musicians? The answer is: so far no, not really. I’ve been consuming a lot of “free” music online but not buying or promoting many albums or artists. But that “no” leads to a further question: would I like to do it for other musicians? Would I feel excited and proud to support other creators who are taking the bold step of bringing new music into this world? And here the answer is most definitely yes! So I’ve set myself a goal: spend $1000 on independent music and try my best to promote it. Why not do this?

What do you mean by only giving favorable reviews?

I’m of the opinion that if I don’t enjoy a piece of music, this might mean that I’m not the best person to appreciate and comment on it. I might not understand the work, or the work might not be crafted for ears that function like mine. In such a case, describing my lack of pleasure in the work provides no value to anyone. But if I do enjoy a piece of music, this definitely means that I’m a good person to comment on it. And it puts me in a position to provide value to another listener who doesn’t yet know about the work but stands to enjoy it. I want to provide value where I can and stay out of the picture where I can’t. Generally, I will try to buy albums that I think I have a good chance of coming to love; if there are few that I don’t learn to love, I might not say much about them, but I’ll try to keep listening.

What formats will you be purchasing?

I’m generally looking to purchase digital downloads of albums. If a particular album is available only on CD, I’ll still consider it. I’m not currently set up to play vinyl. I’m not looking for streaming offerings. And while I love Patreon, I’m not currently looking to become a Patreon supporter of each artist I listen to. I’m really just hoping to be able to buy an album and download it as WAV, FLAC, MP3, whatever. Best-case scenario is the artist/album is on Bandcamp.

Will you be tipping?

I’m going to keep my purchasing decisions as simple and frictionless as possible by paying the base price that artists request for their album, hoping that artists have set a reasonable base price that does justice to their work.

If I’m a musician and you haven’t bought my album yet, does that mean you don’t want to?

I’m connected to a number of wonderful musicians I haven’t purchased from yet. That’s not because I don’t want to — I do! I’m just getting started with this project and might need a reminder or nudge.

If I’m a musician and you’ve bought my album, how can I help you promote it?

Funny you should ask. What you can do is make sure I know or can find your story of creating the album and your larger story of coming to make music. What obstacles did you overcome to bring this album into the world? What does the album mean to you? When I’m recommending a piece of music, it’s very hard for me to speak engagingly about the technical details of the music. But it’s easy for me to speak engagingly about the artist’s story… if I know it. Tell me.

March 10 Update: I was interviewed by Kevin Alexander for his substack “On Repeat,” just published this morning. I have just received a slew of great recommendations today! I’ve spent $93.44 of the budget so far. Taking stock of the project overall: I’m doing very well in discovering great music. Word is starting to spread. Am sensing that folks who hear about this are curious and want to support it. My challenges so far: creating enough uninterrupted time for listening; also, breaking my old habit of just privately enjoying something — being sure to tell someone else about it!

Music is something we do for pleasure, right?

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.

Every piece of music tells a story, and has a story behind its creation — here’s the story of Canon 85, Tin:

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

Imitation with Interval Expansion or Contraction

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

Imitation with Insertion or Deletion

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

Imitation with Reordering

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

Imitation in One Dimension

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

Monophonic Imitation

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

Imitation with Embellishment

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

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

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:

1. 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.
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:

1. Each section has to make sense coming after the previous section — it functions as a successor.
2. Each section has to make sense coming before the next section — it functions as a predecessor.
3. Each section has to sound good below the previous section — it functions as a bass line that accompanies its predecessor.
4. 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.

Here is a major revision of my Canon #4, Topaz, a piece I had initially finished on December 20, 2014:

What is the piece about?

On a technical front, the piece explores what you can do with a long descending chromatic line in the context of a canon. Ever since 2014, I’ve thought of Canon 4 as my “Descending Chromatic Line Piece” because it has continued to be my only canon that features such a line — a sequence of quarter notes descending in half steps — so prominently. On a stylistic front, the piece reminds me of a Bach canon more than many of my other efforts, though it makes no claim of being in the authentic style of Bach, and I’m sure it contains much that deviates from the master’s style. I don’t ever set out to “write like Bach.” I do set out to write music that gives me a hint of the same pleasure that I experience when I listen to Bach. This is one case where I felt I had been successful in creating for myself a pathway to experiencing that pleasure. On an emotive front, I’ve always liked the sense of forward drive in this piece, the propulsion.

What did I do to the piece and why?

I found myself wishing that the original piece from 2014 were a little longer and that the ending were less abrupt. My approach to writing canons has been that I only “say” what I’m ready to say at the time. I try to keep it short and sweet. But sometimes, in retrospect, what seemed appropriately short now seems too short.

Over the years, I had made a few attempts to add material and write a longer ending, but I couldn’t come up with anything that matched what was already there, so I left the piece alone. But recently it occurred to me that a natural way to extend a canon that features a descending chromatic line would be to introduce a new section that features an ascending one. So now the piece has an ABA structure, with the A section featuring a descending line and the B section featuring an ascending one. There’s also a new ending.

How did I do it?

To create the new B section of this piece, I wondered if I would have to write it completely from scratch. The answer was, mercifully, no! I decided to try an experiment which usually doesn’t work for a tonal piece — I made a chromatic mirror inversion of the whole A section. That basically means reflecting all the notes across a horizontal axis so the whole piece is turned upside down, with all of the note-to-note distances preserved exactly. (It’s a laborious process to do this by hand, but software helps out.) This often gives usable results for non-tonal music, especially music that uses symmetric scales like the whole-tone scale or the octatonic/diminished scale — see my piece Birdsong, which uses chromatic mirror inversion everywhere — but for tonal music employing standard major/minor scales it often produces something incoherent. In this particular case though, the result made sense. The long descending chromatic line turned into a long ascending chromatic line, as expected. What surprised me was that the rest of the material accompanying and surrounding the chromatic line also remained intelligible, though not fully “ready to go.” I spent some time revising it, allowing myself to deviate more extensively from strict imitation than I would have done back in 2014, when strictness was more of a priority for me.

As for the ending, the perennial challenge is how to bring the motion of the canon to a stop in a way that is in character with the rest of the piece, but different enough that it can be recognized as an ending, not a continuation; terse enough that it doesn’t sound like fluff in contrast to the tight counterpoint that preceded it, but long enough that it lets you down gently, with some preparation and grace. It’s probably one of the hardest parts of writing canons or any music that’s intricate and dense. To make it harder, I find that endings are an area where my opinions or reactions occasionally lack the stability that I can depend on elsewhere. Generally, what sounded like good counterpoint in 2014 still sounds like good counterpoint to me today in 2021, but what felt like a satisfying ending may not still feel that way; often it does, but sometimes I’m inspired to undertake a revision like the current one, looking for a new ending that hopefully combines logic with some pleasing whimsicality.

How can I hear the new and old versions side by side?

The new version of Canon 4 is here (or use the player at the top of this post); the old version is here. You can also read about my other recent adventures in revision, including my efforts on Canon 18 and Canon 22.