Music

Nonstandard Contrapuntal Imitation

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

Imitation with Interval Expansion or Contraction

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

Imitation with Insertion or Deletion

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

Imitation with Reordering

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

Imitation in One Dimension

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

Monophonic Imitation

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

Imitation with Embellishment

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

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

Music

Canon #94, Cinnabar

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.

Music

Reordering Canon

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.

Life, Personal Development

10 Keys to Finishing

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.

Life, Personal Development

Finishing Stuff

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.

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Music

Canon #4, Topaz – Revised

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.

Music

Gospel Gifts

Want to hear some fantastic gospel singing? Here are four of my favorite selections that I’ve found in the Internet Archive’s vast catalogue of digitized 78rpm records. Scroll down to read the story of how I first came upon these gems.

Even though I don’t think there’s much point in trying to compare musical styles or in arguing whether one is better than another — they’re all unique and multifaceted and fundamentally incomparable, like people themselves — if you insisted that I name the one musical style that I find the most moving, I mean the most physically and spiritually rousing, I mean the style that most makes a person want to stand up and clap and sing, I mean the stye that most makes a person want to praise “the Lord” in the current moment of listening, no matter the prior depth of the listener’s belief — I would have to say it’s gospel music, especially the gospel music composed and performed by black artists. But even though I’ve held gospel music in high regard for as long as I can remember, it was a genre that I didn’t really collect, back in the CD era when I still collected music.

Fast forward to Sunday September 19, 2021. It’s the streaming era now, and the most common way I encounter new music is by clicking links that are shown to me on YouTube or Twitter, a process of mindless self-subjugation to the whims of an algorithm, a process that leaves me thoroughly uninvested in the music I find. But on this particular Sunday, my partner and I wanted to take a day trip… and because we decided to go ahead and rent a car even though we were getting a late start with noon coming and going and no destination chosen… and because we finally got in the car and turned on the radio and started flipping through FM stations… and because we whimsically kept flipping even after finding a few decent options… only because all those things happened the precise way they did, including the nice weather that prompted the idea of the day trip in the first place, we landed on WZBC 90.3 Newton, “Boston College’s premier student-run radio station!”, at exactly the right time, 12:25pm, when it was playing selections from a compilation titled A Capella Black Gospel on the NarroWay label, and I was rapt.

Later that day I did some sleuthing and found that my favorite selection from the radio broadcast — “In The Garden” by a group called The Masters of Harmony of Detroit — was available online at The Internet Archive. It turns out that archive.org has a treasure trove of digitized 78rpm records that are in the public domain, now freely available to play and download in beautifully scratchy audio. If you were a kid in the 1980s like I was, your parents probably had a collection of LPs and maybe a separate box of 45s stashed away somewhere, and maybe in that special box there were a few stray 78s. Even back in the 1980s, 78s seemed like relics to me. I certainly never imagined that years later, I’d be able to go somewhere called “online” and search for any of those 78s my parents owned, and any 78s my neighbors owned, and in fact any 78s anybody ever owned, and probably find them and be able to hear them without needing a record player.

It looks like “In the garden” is one of the few available recordings by The Masters of Harmony of Detroit even though the group’s remarkable leader, Thomas Kelly, who founded the group in 1953, kept performing with it through 2017 when he was 103 years old. I’m particularly taken by the entry of a strong, cutting bass voice halfway through that track, and it made me realize that strong bass entries — whether vocal or instrumental (e.g. a powerful emergence of the subject in a Bach organ fugue on the pedal) — are pretty much my favorite thing that can happen in music. Anyone else share this preference for those moments when the lowest voice takes the spotlight?

The other three selections are not ones I heard on the radio that fortunate Sunday the 19th, but ones that caught my ear in the subsequent week of digging around the collection of gospel 78s at the Internet Archive. “I’m Alright Now” stands out to me for the way it builds and builds till it reaches a point of near-ecstasy but stops in time to fit neatly on one side of a 78. Who is this amazing soloist? I’m not sure how to find out, but I did follow a link to a scanned issue of The Cash Box magazine from 1955 where the album is reviewed. The reviewer gave “I’m Alright Now” a C+ which meant “Good” according to the magazine’s uninflated grading scheme. Still, I’d say the grade should have been a couple of letters higher — what do you think?

The third selection, “Run on Home and Live with God,” starts with such passion that I imagine the ensemble and soloist had been singing their hearts out for hours, reaching a state of utter joy before the recording was made. For a producer or recordist, it must have been a challenge in those days to try to represent the best of what a group could do, given that you had only two short sides of a 78 to work with. Certainly this track has me hooked on the Soul Satisfiers of Philadelphia — but who were they and how can I hear more? It’s tantalizing that in our current age when so much media is instantly accessible, we can’t access anything by this group except for this one track and the flip side.

As for “Precious Lord” by the Kinds of Harmony of Alabama, well, I find it hypnotic, complex, and totally moving — maybe you do too?

Music

Canon #93, Meteorite

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

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

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

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

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

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

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

Some miscellaneous notes about the piece:

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

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

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

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

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