This is a Q&A about canons that I wrote sometime after finishing my forty-fifth canon. It was included in the liner notes of my collection of digitally rendered canon performances, now titled Canon Previews. It applies just as well to the album Canons, featuring harpsichord performances by Matthew McConnell, that we’re now releasing.

Q: What is a canon?

A: You could say it’s a piece of music built on the idea of an echo. In a two-part canon you have one part that leads and another part that lags a little bit behind, echoing everything the leader does.

Q: Isn’t that how the children’s tune Row, Row, Row Your Boat is often sung?

A: Yes, Row Row Row Your Boat is a simple canon. You could start singing Row, Row, Row Your Boat at one moment, and I could start singing the same tune from the top, a few moments later, entering right when you get to the word “gently.” In that case, you’re the leader (or “dux” in Latin) and I’m the follower (or “comes”).

Q: Can any tune be sung that way?

A: Not really. Try this kind of staggered, overlapping presentation with a tune like Happy Birthday and it would sound horrible – our voices would clash – but if we do it with Row, Row, Row Your Boat we harmonize because the tune is constructed to fit on top of itself. We could do it with Frere Jacques, but it probably wouldn’t work with Itsy Bitsy Spider. Of course, canons can range in style and scope from children’s pieces to the marvels of Bach’s work in The Art of the Fugue and The Goldberg Variations.

Q: What were your goals in composing a whole album of canons?

A: I love listening to canons and I wanted to write music that I’d enjoy hearing. As I continued with the project, it became a kind of survey where I tried to explore every type of canon that’s commonly known and tried to devise some of my own variants of the form.

Q: What makes canons interesting to hear?

A: When you listen to a canon you’re always hearing something new mixed with something old – the next idea or gesture is superimposed on the idea you just heard a moment ago. The old material may sound familiar when it resurfaces, but it may also sound different in its new context, with its new accompaniment. When we listen to any kind of music we tend to remember what we heard in the preceding moments, and that memory still rings in our mind as we absorb the current sounds. You could say all listening is canonic, in that there’s always some kind of echo transpiring in our mind’s ear. But in a canon, the echo becomes explicit, and we get to hear a running fusion of the present with the immediate past.

Q: That sounds intriguing, but aren’t canons sometimes confusing?

A: They demand active listening. It helps to be aware that you’re listening to a canon – not just any kind of piece – and to try following the relationship between the parts. Sometimes that’s easier to do once you’ve listened to the piece several times and become familiar with the theme. I find that some music, even very good music, gets boring if you listen too often, while other music only grows in interest the more you listen. Canons often fall in that second category – they can sometimes be hard to approach, but they are also hard to exhaust.

Q: The canon is an old form, tracing back to the Middle Ages – the famous piece Sumer Is Icumen In comes to mind – would you say the canon is outdated?

A: As a form, the canon is really quite simple: you’ve got a leader and a follower – that’s it. There’s nothing like the structural complexity of the classical sonata where you have sections – introduction, exposition, recapitulation – each with its own characteristics and substructures. The simplicity of the canon concept makes it timeless, in my opinion, and that’s borne out by the fact that we have canons by Machaut and canons by Stravinsky. And canons have lots of technical parameters that can be varied – the lag between the parts, the interval that separates them vertically, the style of counterpoint used, the manner of imitation – creating an endless variety of challenges and possible solutions.

Q: You said the canon is simple as a form – does that mean canons are easy to write?

A: No, I mean the concept of a canon is simple to describe, but the execution can be excruciatingly difficult, because the follower places so many restrictions on what the leader can do. Unlike fugues where imitative or canonic writing can be interspersed with free counterpoint, a canon has to sustain its own “echo” from beginning to end. Whatever the leader does in one section must be crafted so it will blend with the previous section that’s being repeated by the follower, and that requirement never lets up.

Q: Why bother with the restrictions of the canon form? If you can incorporate short imitative passages into freer pieces, why confine yourself to writing in canonic fashion from start to finish?

A: From a composer’s perspective, the challenge of a tighter, more restrictive form can be inspiring. One seeks to discover how much is possible under the severest constraints. From a listener’s perspective, the more restrictive form lets you relax in a sense, because you know exactly what you’re getting – when the form is clear, you can focus on the content. And it can be exciting to hear how the composer pulls it off; even if you haven’t tried writing a canon yourself, you might still be aware that you’re witnessing a difficult and uncommon feat, something like a puzzle being stated and cleverly solved in front of you.

Q: So would you say canons are all about technique and cleverness?

A: No. Writing a canon sometimes feels like working through a puzzle, but I think a good canon must transcend its puzzle aspect and communicate something as a piece of music. And that’s why I’m not entirely opposed to “cheating” in some cases.

Q: What do you mean by cheating? Isn’t the canon a strict form?

A: There are many canons where the leader and follower indeed play identical music. Strict canons are great from the standpoint of a music copyist: you don’t need to write the tune out twice, you can just write it once and indicate when the players should enter. But sometimes you find you’ve explored all the “legal” options – perhaps you’ve arrived at something satisfactory – but you realize you can make the music come alive if you allow a few subtle details to vary between the leader and the follower. Perhaps one voice plays a certain note sharp while the other plays it natural, perhaps one voice uses an ornament while the other remains plain. There’s also a choice to be made at the end: you can let each voice finish on its own schedule, or you can bring them to a unified cadence, in which case you often have to stop the canonic imitation and write some free counterpoint for the conclusion.

Q: I understand the point about freedom at the cadence, but what’s so difficult in canon writing that it would push you to bend the rules in the middle of the piece?

A: Maybe the crux of the challenge is that solid bass lines don’t always make the most interesting melodies, and interesting melodies are sometimes not harmonically forceful enough to make strong bass lines, but anything you write in a canon must function both as a bass line and as a melody line. Sustaining a sense of harmonic clarity and forward motion along with melodic interest can be very challenging. In freer forms of music, you can move from one harmony to another by having the bass line “announce” the change while the upper parts flesh it out. But in a canon, if the bass line is the leader, any gesture it makes is going to be parroted later in the top voice. This creates situations where the harmonic movement sounds redundant, or else you’re locked into one harmony for longer than you want to be there. Most of the time you can work around this by relying on musical double meanings – on the fact that notes, even entire gestures, have multiple interpretations and can belong to more than one harmony. But in some cases you can get great musical value by allowing one or two subtle alterations in the line depending on whether it’s serving in a bass or melodic capacity.

Q: How often do you break the rules in the album?

A: Roughly half of the pieces are strict and the other half include some exceptions here and there. In the pieces where I bend the rules, I always try to do it subtly – you want to stay true enough to the canon form that the listener can maintain their bearings, can be confident that their effort in “matching” the lines in their ear will not be frustrated by lots of superfluous deviations. The ideal exception is one that makes the music sound better without even being apparent as an exception.

Q: If rule-bending is musically advantageous in some places, why did you keep any of the canons strict? Why not bend the rules in every place where doing so might be fruitful?

A: One motivator was laziness, actually. You spend thirty hours working on a canon and in the end you’re left with 30 seconds of music – I was always looking for ways to get a little more length out of these pieces, and when you make a canon “invertible” you can basically double its length with no extra work. But for a canon to be easily invertible you’ve got stay away from alterations that need to be adjusted after you perform the inversion – strictness is your friend in this case.

Q: Let’s back up – what’s an invertible canon?

A: It’s a canon where the positions of the voices can be swapped. That’s to say, if the bass voice is the leader and the soprano is the follower, you can repeat the canon with soprano as the leader and the bass as the follower and it still sounds good. This shouldn’t be confused with writing a “canon in inversion” which means that the follower doesn’t directly copy the leader, but instead presents an upside-down version of what the leader does.

Q: But what makes some canons invertible – where the leader and follower can be swapped – while others canons don’t allow for this?

A: To talk about invertibility means we’re assuming a systematic treatment of dissonance and consonance where certain intervals are considered acceptable on strong beats while other intervals must be avoided or properly prepared and resolved. In some of the canons in the album I follow a traditional approach that treats a perfect fourth between the bottom and top voice as a dissonance while the perfect fifth is a consonance. When you take the bottom voice and transpose it up by some number of octaves to the top position, you find that perfect fifths become perfect fourths, meaning that an interval that was legal on strong beats has now become illegal. However, if you avoid perfect fifths on strong beats and allow only thirds, sixths, and octaves, you never run into this problem. Thirds become sixths through the process of inversion, and vice versa; and octaves remain as octaves. You write the canon once following these special restrictions, and then almost as if by magic, you’ve got a second section of the piece that arises by swapping the parts – it’s clearly related to the original canon, and it’s “legal,” but it sounds different enough to engage the ear as new material.

Q: So does the concept of invertibility only apply to traditional canons?

A: The distinction between invertible and non-invertible is clearest in the context of traditional counterpoint, but even if the canon is “modern” in approach and makes free use of dissonance, it may not sound good when inverted. The distinction between invertible and non-invertible is still relevant. The composer may need to design for invertibility even if the canon uses dissonance in an unconstrained way – it’s just that the criteria for when it has been achieved are more subjective.

Q: You said you used traditional contrapuntal practices in some places, but not all – where did you break with tradition, so to speak?

A: In some cases I used melodic resources that would be considered modern – like the whole tone scale (Obsidian, Moonstone) and the octatonic or diminished scale (Jet) – while still adhering to a traditional treatment of dissonance. Flint and Zebra Marble use lots of chromatic motion on top of a consonant whole-tone framework. In canons like Fluorite and Mica I flipped the rules, emphasizing dissonances instead of consonances on strong beats. That said, I try to not think of musical resources “traditional” and “modern” since it’s not the most telling distinction; sometimes “modern” music can sound stale and “traditional” music can sound fresh, and it’s really freshness that matters.

Q: Some of the canons are labeled as being “at the fifth” or “at the third” – what does that mean?

A: The most common kind of canon is where the follower enters an octave above or below the leader, playing the same notes as the leader, but transposed up or down in register. There are also canons where the follower might enter at another interval, like a third, or a fifth. In these cases, when the interval of imitation is anything other than an octave multiple, the composer has a choice to make. If the follower is to stay in the same key as the leader, the follower will need to adjust some of the leader’s melodic intervals (for example, in C major with imitation at the third, the interval of a major third from C to E would be imitated as a minor third from E to G). If the follower is to proceed in its own key, then it may copy the leader’s intervals exactly (a major third from C to E could be imitated as a major third from E to G#). I wrote some canons of the first kind, where the leader and follower remain in the same key, including Pearl at the third, Coral at the fifth, Tourmaline at the second, and Mica at the fourth, and Moldavite at unison. I also wrote a set of six bitonal canons, named after metals Platinum, Gold, Silver, Nickel, Copper, Zinc, where the follower strictly imitates the leader in a different key: each canon in that group is invertible, and together they explore all 12 possible key distances between leader and follower.

Q: How did you go about composing those bitonal canons?

A: You have a choice of whether to emphasize or conceal the clash between keys; I pursued both objectives in different ways. One the hand, I tried to write lines with clear cadences and a very strong sense of key. When such a firmly tonal line is played in canon, there’s an inevitable tug-of-war between the two key centers. But I wanted this contest to be graceful instead of messy, so I used only consonances on strong beats, crafting the lines so they would mesh smoothly from the standpoint of vertical sonority. Even when the keys are as far apart as C major and F# major, it’s always possible to build a consonant framework using intervals that are enharmonically equivalent to thirds and sixths. The combination of each line pulling towards its own key center while at the same time blending smoothly with the other line makes the six bitonal pieces my favorite works in the album.

Q: What other special types of canons did you explore in the album?

A: In a canon in inversion (also called a canon in contrary motion), the follower plays an upside down version of the leader’s melody (Amber, Carnelian, Graphite, Sugilite). In a retrograde canon, also called a crab canon or a canon cancrizans, the follower starts at the same time as the leader and plays leader’s line backwards; if the canon is invertible, the entire thing may be “rewound” when it reaches its end (Peridot, Zebra Marble). In a prolation canon (also called a mensuration canon, or a canon by augmentation and diminution) the follower copies the leader at a different speed (Lodestone). A spiral canon ends higher or lower than it started and can be repeated in a continuously rising or descending fashion (Alexandrite). An accompanied canon includes one or more lines – often a bass line – that move freely and don’t participate in the canonic imitation (Diamond). A variation canon allows one line to be ornamented and developed differently from the other (Amethyst). Many canons are invertible at the octave but less commonly a canon may be invertible at the tenth (Citrine) or the twelfth (Iolite). A rhythmic tiling canon is a composition in which each player repeats the same pattern, with each player beginning at a different time. The pattern and entry points are crafted so that once all the players have begun to play, there will be exactly one player striking every beat. That’s to say, every beat is covered by one of the players but no two players ever coincide on the same beat. My piece Escher’s Drum is an exploration of this rhythmic concept.

Q: Do you have a tune in mind when you start writing a canon?

A: Usually not. The theme emerges in many little steps as I write. In fact, many of the melodic ideas in the album would probably never have occurred to me if I had tried to “write a tune” from scratch. The tune only comes together through the continuous cobbling and tinkering that the canon form requires. It’s good not to have too many preconceptions about the theme when you start because you’ll inevitably have to change and adjust your ideas again and again to get them to fit in the canon form.

Q: Do you have a specific process for writing canons?

A: Well, one of the most perilous approaches is to write a really interesting, florid melody lasting a couple of bars, then copy it to the other voice and try to write a counterpoint above it, then copy and repeat. That process can easily lead to canons that drift or that simply can’t be continued. Measure by measure they sound good but on a larger scale they fall flat, and they’re hard to revise since you’ve already elaborated each line and committed to so many little details up front.

Q: So how do you proceed, if not linearly?

A: The most valuable practice I follow is to start with an outline, then elaborate it in stages. The initial outline is usually in whole notes, like a first-species counterpoint exercise. I spend a lot of time on the outline, just listening to really simple arrangements of whole notes – I might spend hours and hours on that. I try to apply the “beer test,” which is to ask whether you’d want to hear that particular whole-note sequence while kicking back with a beer. Is that simple sequence of notes compelling enough that you’d listen to it on your own time, when you’re not trying to “write a canon,” but when you’re just relaxing and looking for a bit of enjoyment? Once you have a good sketch, only then do you begin developing it.

Q: What happens as you develop the sketch?

A: You try various ways of connecting pillars in the outline, adding passing tones, runs, suspensions, experimenting with different rhythms, and so on. You listen to each line separately – you sing it over and over – and then you play the lines together. You try adding detail, then stripping it away, adding, then stripping again. This process is nothing new; in fact, it’s akin to what Thomas Morley described in his Plaine and Easie Introduction to Practicall Musicke from 1597, where he shows how a “divided” passage may be developed from a “plaine” outline.

Q: How do you know when you’ve got it right?

A: I’m always looking for a balance of clarity and interest. Sometimes you can add detail in a way that makes one line more beautiful on its own, but the detail blots out or overwhelms the other line: one part of the canon becomes more “interesting” but the whole becomes more “confusing.” I’m always looking for those details that add to the beauty of each line and also improve the balance and separation between lines. I know a canon is done when it holds my interest from start to finish (there are no “dead” spaces where my attention fades) and when I can hear the lines clearly (there are no “blurry” spots where the parts seem to interfere with each other) and when I can sing one line on its own and enjoy it as a tune.

Q: Do you try to keep the lines equally active at all times, or do you let one line recede as the other comes to the fore?

A: For the most part, I strive to maintain simultaneous interest in the parts, so that the ear’s focal points are not prescribed, but rather the ear will discover something engaging wherever it chooses to focus. I don’t think there should often be a single best or most rewarding place to put your attention: good counterpoint is immersive – something to bathe in. That said, a piece has to breathe – phrases must begin and end, not continue indefinitely, and there should be occasions when one line gives way to the other.

Q: How long does it take to finish a canon?

A: Some of them come together in a day or so; many of them take several days. Usually I’ll spend a day on an outline, then another day or two on elaboration, then another day on corrections and refinements. A couple of the pieces took considerably longer, and some were multi-week efforts.

Q: Why do some of the canons use lots of ornaments like trills?

A: In some cases I used ornaments just because I liked how they sounded, but in other cases I had an additional motivation. I think ornaments can serve as “markers” that help you follow the canon. When you hear an ornament in one line, it stands out, it calls your attention. Then when you hear that ornament come up again in the second line, you recognize a correspondence between those two points in time.

Q: Why didn’t you assign each part to a different instrument to help the listener hear the parts separately?

A: There’s nothing stopping the canons from being played on multiple instruments and I’d be curious to hear it. However, I do feel that using the same timbre for both voices presents a challenge for the composer that, if tackled, results in a better composition. It’s true that when two timbres are very different – as are flute and harpsichord, for example – it becomes possible to “eavesdrop” on the music at any time, even if you haven’t followed it closely since the beginning, and quickly discern which voice is which. But my aim was to write lines that would stand apart on their own, without requiring the aid of diverse instrumentation.

Q: But even the most well-written canon can be challenging for the listener to parse. Why not give the listener a little extra help?

A: A line that’s written with one sonority in mind might not sound good when the sonority is changed. You’ve got to find two instruments that each work well for the given melody, and that combine in a way that preserves the clarity and resonance of the intervals between the parts. I find certain intervals lose their substance when the timbres are too far apart: consider the ringing sound of perfect fifth announced by two trumpets, or even by two mandolins, versus the same interval announced by a trumpet and a mandolin together. The “mixed fifth” will still sound like a fifth but it might not ring in the same way when spread across such different voices. I want to be able to hear the intervallic relationships between parts as clearly as possible – as if the two parts were two gears directly interlocking – and not as if they were slippery wheels, loosely touching. Yet another consideration is that when the timbres are too distinct I find the process of identifying analogous gestures is slowed down. I can still recognize that a melodic fragment played by the flute is identical to one played moments ago by the harpsichord, but the identity may be less apparent or may take a moment longer to perceive. And so I have sometimes found myself listening to canons with disparate timbres and having an easier time separating the voices but a harder time perceiving their relationships moment-by-moment.

Q: What kind of canon did you find to be the hardest to write?

A: Canons with special restrictions like crab canons and canons in contrary motion present special problems: you have to write lines that sound good in reverse, or upside down, and that’s not a very “natural” thing to do. There’s usually a way to pull it off, though, and the reduced set of options means that these canons sometimes seem to write themselves. For me, the hardest form turned out to be the prolation canon, where one voice goes at a different speed than the other. As such a canon progresses, the lines don’t maintain a fixed relationship – the distance between the two parts is constantly narrowing or expanding. It makes the whole thing harder to work with. When I worked on Lodestone, I assigned each note a number and wrote the numbers in the two staves as a way of keeping track of the changing leader/follower relationship. And then there’s a situation where the two lines might come together at one point and begin to diverge, and it’s nearly impossible to avoid parallel octaves at that point.

Q: What is the easiest kind of canon to write?

A: I wouldn’t say it’s “easy,” but the accompanied canon introduces flexibility that doesn’t exist otherwise: the free bass line can be used to clarify the harmony and diversify the texture.

Q: How did you first learn about canons?

A: I first got interested in canons when I was a teenager reading Douglas Hofstadter’s book, Godel, Escher, Bach; if not for Hofstadter’s inspiration I don’t know if I’d be writing canons today. I was also inspired to undertake a lifelong study of counterpoint by a composer I studied with at that same formative time, Stephen Siegel.

Q: What canons by other composers do you like listening to the most?

A: My favorite canons are Contrapuntus XII through XV from Bach’s Art of the Fugue. Those are the works I think of when I think “greatest examples of the canon form.” But there have been a number of pieces I’ve gravitated to over the years without considering at first that they were canons. I had probably listened to Bach’s Goldberg Variations a few hundred times, letting the music wash over me, before really focusing on the nine canonic variations and trying to follow their structure as such. And I fell in love with Ockeghem’s Missa Prolationem before I understood what a prolation canon is, or how Ockeghem’s piece is constructed entirely from such canons. On a lighter note, I should say life would incomplete without Henry Purcell’s boisterous rounds on, shall we say “secular” themes.

Q: The canons in the album have nicknames referring to gems and minerals – how did those names come about?

A: I wanted to make the album easier to navigate. When I got past 25 canons or so I couldn’t really remember which number belonged with which canon. I thought about using bugs as nicknames but I felt bugs had a bit too much personality to impose on these largely abstract pieces; gems and minerals seemed more neutral. I like the image of sound vibrating the stones or reflecting off the stones. In some cases there’s a very loose connection between the nicknames I chose and the content of the pieces (darker stones for some of the darker or more mysterious sounding pieces) but elsewhere it’s arbitrary. ■

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