Canons 81 and 82

Announcing two new Canons, #81 “Selenite” and #82 “Kyanite.”

These pieces were written as an exploration of the rhythmic pattern of 8 pulses divided as 3+3+2.

One place where I had encountered this pattern before is the bluegrass guitar crosspicking pattern: down-down-up, down-down-up, down-up. Another place it appears is in the final piece of Bartók’s Mikrokosmos which uses the mixed time signature 3/8+3/8+2/8 — and that’s the choice I made here.

As these pieces came together, I noticed I could feel the pulse in two different ways. It’s possible to count in eight notes “ONE-two-three ONE-two-three ONE-two” which matches where the accents actually fall in the music. But since we have a total of eight eighth notes, everything fits into a 4/4 measure. In fact, it’s possible interpret the pieces as being in 4/4 and count quarter notes “ONE-two-three-four”, in which case you’ll perceive a syncopation where the accented third beat of each 4/4 measure comes early. Here’s the rhythmic figure that occurs at the beginning of both pieces, written two ways:


Selenite and Kyanite are related by more than their rhythmic pattern: they emerged from different versions of the same outline. Selenite is a canon at the second above; Kyanite is a canon at the seventh below. Both pieces have a two-measure delay and are 21 measures long. They are dissonant canons that emphasize minor sevenths, major seconds, and perfect fourths. Instead of aiming for uniform dissonance, however, both pieces have consonances interwoven among the dissonances, aiming for some sense of tension and resolution. In these pieces I was guided by my ear and a certain sound I wanted to achieve, as opposed to any systematic policy for making contrapuntal choices; still, the question of whether something was “admissible” mostly seemed clear to me and I did not feel much uncertainty in deciding whether a particular idea fit into the sound-world I was trying to create. The one point that did cause me some questioning was the treatment of parallel fifths and octaves. Selenite took shape as one of my canons where the sound of parallel fifths is embraced; I assumed Kyanite would be the same but later I found myself editing out the many of the parallels that I had included there. Why did the parallels seem to belong in one piece but not the other that’s so similar? I have no idea.

When I finished writing Selenite I tried to swap the top and bottom lines but the result was not convincing. This surprised me because I had earlier tried inverting the skeleton (the initial outline that I used for the piece) and I liked how it sounded. Sometimes, but not always, when the skeleton for a piece responds well to inversion, the finished piece does too; in this case, it didn’t. I looked for ways to edit the inverted piece to make it work, but didn’t get very far. I felt there was still some material worth exploring, so I decided to write a new piece from the inverted skeleton. I wondered if the new piece might pair well enough with the first piece that they could live together as sections of a larger piece. But the new material turned out to be different enough that I gave it its own name, Kyanite.

I think of these as modal pieces. In Selenite, the leader starts in C Dorian, makes an excursion to C Ionian (with a glimpse of C Lydian) and returns to C Dorian. In Kyanite the leader starts in Bb Dorian, makes an excursion to Bb Lydian to Bb Ionian, and then ends in Bb Mixolydian. In both pieces, the follower uses a different mode that has the same note set as the leader. So in Selenite, for example, while the leader is in C Dorian the follower is in D Phyrgian.


Canon 80, Mellite

Here’s my eightieth canon, Mellite:

This piece continues my exploration of odd meter. It’s in 9/8 but instead of subdividing the bar as 3+3+3, it uses 3+2+2+2.

Uptempo compared to many of my other pieces, Mellite is an invertible canon at the fifth above / fourth below. It’s in a three-section format where the bass is the leader initially, then the material repeats with the soprano as the leader, and then it repeats again with the bass as the leader, now transposed lower while the soprano is higher. The first section has some voice crossings. In between sections there’s a deliberate “fusion” of the voices in parallel octaves for one bar. The lines constantly alternate between simple and compound melody. The tonality is F major with an excursion in each section to the dominant key of C and a return.

Looking through the score note by note, you would see lots of similar motion between the parts but if you look at the skeleton of the piece, it emphasizes contrary motion. This is a tension that interests me.

The audio is different from any of the clips that I’ve included in my “Canon Previews” album so far. Typically, when I release a software-generated preview clip, I use the same basic piano sound and I put minimal effort into tweaking the musical “interpretation” that the software produces. I like it this way. I don’t really want my preview clips to be too refined. That’s because I want each piece to someday fall under the care of a (human) performer, and I want to leave room for them to make their own choices and for me to hear the unexpected in their approach. But in the case of Mellite, I did a little more work on the preview audio than usual. I couldn’t get my notation software, Finale, to play the piece with the accents how I wanted them, so I opened the piece in a MIDI editor and started changing note velocities, and from there I experimented with different virtual instruments.

The mineral Mellite is also called honeystone. I was initially attracted to this name for Canon 80 because the upbeat energy of the piece makes me think of the color yellow. While honey moves slowly, and Canon 80 does not, I do like to imaging the bustling activity of bees making honey as I listen to it.





Canon #79, Diaspore

Here’s my Canon #79 – “Diaspore.”

I wrote this piece to explore 11/8 time, divided as 3+3+3+2.

In a recent post, I reflected on why I hadn’t managed to use an odd time signature in any of my first seventy-five canons. The reason is that I’m often seeking rhythmic contrast between the two voices, and I found it difficult to achieve such contrast while still reinforcing the structure of the odd meter. It seemed to me that in order respect the meter, I needed to make the voices more rhythmically similar, but for reasons good or bad, I simply didn’t want to do that. Finally, in Canons 76, 77, and 78 I found an approach I liked. The idea was to have the theme alternate between different subdivisions of the odd meter. So, for example, the theme in Canon 79 alternates between 3+2+2 and 2+2+3 subdivisions of 7/8. When such a theme is layered on itself with a skew, we hear contrasting subdivisions at once. A sense of rhythmic contrast is built into the framework, as is the indisputable fact of being in the odd meter. But now with Canon 79, I think I’ve managed to take the simple, direct approach to writing a canon in an odd meter. In Canon 79, at all times, in both voices, the same subdivision of 11/8 as 3+3+3+2 is operative. And lo and behold, there’s still enough rhythmic variety for my ear.

The piece is harmonically simple, falling squarely in A major with no alterations. It’s an invertible canon at the second, with diatonic imitation, and a lag of one bar. The soprano is the leader in the first half, and the roles are reversed in the second half. The ethos is buoyant.

For whatever reason, I seem to be more at home writing melodies that favor stepwise as opposed to arpeggiated motion; this piece is a rare example where a more arpeggiated style felt natural to me.

I’m happy with how the piece came out, but as I was writing it and listening to some of the early drafts, I wondered if it was just a “toy.” This got me thinking about the differences between “toy” and “miniature” in my own lexicon. To me, a toy is a small disposable piece, a piece that you write to learn something or to demonstrate a point, but that you wouldn’t revisit beyond a few listens because you don’t expect to discover anything new in it. A miniature can be mistaken for a toy because it’s also small and might seem simple, but if you make it your focus, you find enough subtlety and beauty within the piece’s narrow confines to envelop your entire awareness. That’s to say a miniature can become gigantic in your mind, while a toy cannot. As for an etude or technical study, it can be either toy or a miniature.

Of course I’m aiming to write miniatures, not toys, but if one of my pieces seems like a toy should I still give it a name and number and include it in my collection? I suppose so, if I like it well enough. Sometimes what one dismisses as a toy turns out to be a miniature. And sometimes a toy can be made into a miniature with a few small changes. Many of the canons I now consider as miniatures began as toys.




Canon #78, Verdite

Announcing Canon #78 – “Verdite.” Listen to it here:

Canon 78 continues my exploration of odd time signatures – it’s in 7/8 – and it’s a companion piece to Canon 77 which is in 5/4. Like the earlier piece, Canon 78 is an invertible canon at the second, with a lag of one bar. The imitation is diatonic and the sonority emphasizes thirds and sixths. The piece is mostly in G major with some excursions to C. The melody is conceived with an alternating pattern of subdivisions of each 7/8 measure, going like this: 3+2+2 / 2+2+3 / 3+2+2 / 2+3+3. When such a melody is layered on itself with a skew of one bar, we repeatedly hear 3+2+2 against 2+2+3. At least, we hear a sense of 3+2+2 against 2+2+3; we don’t hear exactly that because the melody has been densely elaborated on top of that metrical framework and does stray from the framework or obscure it at times. The bass is the leader in the first half, and the roles are reversed in the second half. The ethos is sprightly and the texture is saturated. The piece came together pretty quickly, which for me means a few days. As with many canons, it was the cadences that caused me the most questioning. In many of my invertible canons I place a full cadence at the end of the first half and often leave a pause before beginning the inverted section. In this case I wanted to keep the motion going across sections, so I tried the make the cadence at the midpoint less conclusive than I normally would. As for the final cadences, they’re often challenging because, while you can always get the motion to stop, it’s not always apparent how to do that in a short space and do it in a way that’s convincing and satisfying. Here the solution involved bringing the lines quickly through an initial deceptive cadence, moving into an extra bar of free counterpoint which leads to the final cadence. A C# in one place hints at D major, which seems to add some freshness to the final return to G.