Interval Compression

In music, “imitation” is what happens when one musical part or “voice” repeats the material stated by another voice. Episodes of imitation occur in many forms and styles of music, but the canon is the one form where imitation is sustained from start to finish.

One of the reasons why I see boundless possibility in the canon form is that the idea of imitation itself can be interpreted in so many ways. Imitation can be direct or it can involve some systematic way of changing or transforming the original material: when the follower repeats what the leader “said,” the follower can state the content verbatim, or say it in a different way.

Some of the most common kinds of transformation that occur in counterpoint are to turn the original material upside down, to change its speed (make it faster or slower), to play it backwards, or to do some combination of these things together. And so we have canons in contrary motion, canons in augmentation or diminution, canons in retrograde, and so on.

Why bother crafting pieces of music with these special technical properties, these “deviant” forms of imitation? Because they can provide a fascinating experience for the listener, where two manifestations of the same idea may be heard together and compared. If we take a melody and turn it upside down does it still bear an audible relationship to the original? Does it carry the same affect? Each time we listen to such a “canon in inversion”, for example, we might notice new connections between the original melody and its mirror image, or we might perceive differences in sound or meaning that hadn’t been apparent before.

As I continue writing canons myself, I’ve been seeking to experiment with other kinds of transformation – other ways of interpreting the idea of “imitation” – that have been less commonly addressed than those mentioned above: inversion, retrograde, augmentation, and diminution. The technique I explored in my two latest canons could be called “interval compression.” The idea is that follower should cut all of the leader’s melodic intervals in half: if the leader makes a jump of an octave (12 semitones) from C to C, for example, the follower would copy this gesture by leaping a tritone (6 semitones) from C to F#. So the follower presents a vertically compressed or “squished” version of everything the leader does.

Is it possible to make meaningful music with this unusual constraint? And why bother doing this? As with many technical constraints that can seem arbitrary at first, it forces you to write music that you probably wouldn’t think of otherwise. But beyond that, it’s an interesting way of addressing the question of what makes two melodies sound similar or different: is it the specific pitches they hit, the specific intervals they use, or is it just their rhythms and basic contours? How similar do the two parts – the leader and its “squished” follower – sound to you as you listen?

Here is Cannon 73 “Tellurium”:

Here is a visualization of the first part of of the canon:


And here’s how it looks if we align the two parts, eliminating the lag between leader and follower so they can be more easily compared:


To make this canon work out cleanly, I confined the original theme to a whole-tone scale so that all melodic intervals would be divisible by 2. The transformed theme, the result of this division, consists largely of chromatic motion as you can see in the images.

Canon 73 was borne from the same outline as its predecessor Canon 72 “Rhyolite,” a piece with a much slower and more brooding demeanor:


Canons on Clavichord

This is a quick note to announce phase II of the canon project I’ve been working on with keyboardist Matthew McConnell.  Following the release of our album Canons, which was performed on harpsichord, we are beginning a work on recording a second set of canons for clavichord. I look forward to keeping listeners up-to-date on this exciting second phase of the project. One of the first pieces we’ve recorded is the canon “Celestine” which I wrote about in my post on Parallel Octaves. I’ve added Matt’s clavichord performance of Celestine to the end of our first album as a teaser, and you can listen to it below. Please help us continue with this recording project. The best way to support us is to download our first release of Canons and/or share the link with someone who might be interested.

Music, Songwriting

Dramatic vs. Deadpan Style in Songwriting

When setting text to music, a composer must choose what kind of relationship the words and music will have: will it be a close relationship where the music reflects every nuance of the text? Or will it be a more distant relationship where the music leaves the text free to “speak” for itself? These different approaches could be called the dramatic style, and the deadpan style of text setting, respectively.

Continue reading


Close Listening

In my efforts to share my new album Canons with listeners who might be unfamiliar with counterpoint, the harpsichord, and so on, I often mention that Canons isn’t background music: the stuff needs concentration. I suggest that listeners find a quiet place and really focus. But every time I say this, I realize that close listening is a thing that I myself have had trouble doing in recent years. I wonder, is close listening even possible now in 2017, the age of distraction?

Back in the 1990s, when I was in my teens and early twenties, I didn’t have the tools I needed to write the music I wanted to write – I was frustrated – but I did have something wonderful going for me: I was a passionate and dedicated listener with a very active listening practice. I’d spend hours listening to CDs, doing nothing but that, and it was bliss.

Now I’m in my early forties and I’ve finally gained the tools to create my own music. While I spend a lot of time listening to my own pieces as I’m working on them, my broader listening habits have lost their vigor and focus. Instead of sitting down to immerse myself in a full album with total concentration, I’m more likely to skip between clips on YouTube while checking my email or reading news, clicking “like” occasionally as a way of reminding myself to return – someday – to a piece of music that deserves more attention.

This decline of my listening routine is due in part, paradoxically, to my stride in writing music. My own compositions take much of my attention now, and they satisfy some of the craving that used to make me search outward. Another part of it probably has to do with growing older. Having spent my youth exploring every musical style and category I could find, I’m less likely to stumble upon a completely unvisited frontier that holds me rapt. And a big part of it has to do with the demise of CDs and all of the rituals that went along with collecting them, rituals that helped prepare me for, and build my investment in the listening experience.

I spent the summer of 2014 meticulously transferring my collection of over two-thousand CDs to hard drive, hoping that easy digital access to all my music would revitalize my listening life, but it seemed to have the opposite effect: without the physical process of searching for a CD on a shelf, putting it in the player, flipping though the printed liner notes, and so on, I found myself listening less often, and with a diminished commitment to any particular album.

Some years earlier I’d had a similar experience, where obtaining easy access to a trove of music proved strangely anticlimactic. I found out that as a cardholder at the Boston Public Library, I could log on to the library’s online catalog from anywhere and play a vast collection of streaming music in all genres, for free — stuff that wasn’t yet available elsewhere online. All this free music was a greater boon than I could ever have imagined in my teens when I used to spend weeks saving every available penny so I could buy just one coveted CD. And yet after browsing my library’s online collection and remarking on how impressive it was, I promptly forgot about it.  How could that be? How could I discover, and then simply ignore, the very sort of musical treasure trove I had spent my youth wishing for?

I’m tempted to blame my scattered listening attention on the Zeitgeist, to say that in the age of Spotify and YouTube — in the age of tweets and cat videos — it’s growing harder and harder to be a focused listener who shuts out the world and finds deep communion with an album-length creation. And without vinyl records or CDs to anchor the process of collecting and playing music in physical reality, the experience loses some of its significance. But I’m open to the possibility that my problems with listening today are incidental as opposed to fundamental, that they could be “solved” by some simple changes in my life. Maybe close listening is no more difficult now in 2017 than it ever was, as long as you set yourself up right.

I think that what I’ve been missing for some time has just been a good place to listen – I’ve almost had it, but not quite. While I’m reluctant to attribute my listening habits to material circumstances, it’s true that a person’s living environment – how it’s arranged – affects their routine behaviors. In recent years, my environment hasn’t been fully conducive to close listening. You could say I haven’t had the best listening feng shui.

I spent months in 2014 consolidating my music collection, but my overall listening setup became less convenient than it had been in some of my previous apartments, where there was always a beckoning shelf of CDs and a CD player that was completely disconnected from the internet and a chair where I could sit and listen without the distraction of a nearby computer screen. All those things mattered.

When I moved into my current home, I couldn’t find a good way to situate my “nice” stereo system (pair of bookshelf speakers, amplifier, etc.) in the office where I’d have the most privacy, so I put it in the living room, a place of interruption. At some point, the remote control for my amplifier died and I never replaced it, so turning it on and adjusting the volume meant walking across the room – a “first-world” problem that seems almost laughable in its triviality, and yet constitutes the subtle “friction” that influences the statistical mechanics of one’s daily behaviors. I never took the time to set up a dedicated computer for playing music, or a home file-sharing system to store it, so whenever I wanted to play my digitized collection through my nice stereo, I had to bring my laptop to a table in the living room, attach an external drive containing my FLAC files and also attach a DAC transmitter that would communicate with a receiver connected to the stereo, and then fidget with some software to get things to play.

While I had a library of glorious music within pretty easy reach, the slight inconvenience of accessing it made me more inclined to take the lazier route: fulfilling my listening appetite through those many music videos that came my way through Facebook and YouTube while I was surfing online, listening to them through my computer’s built-in speakers or a cheap pair of headphones that I inexplicably refused to upgrade. Of course, there’s nothing inherently wrong with listening to music through Facebook or YouTube, except that when we encounter music through these online channels, we’re usually already in the state of distraction and impatience that web browsing perpetuates, and music can’t cure us of that, no matter how good it is.

What I’ve needed has been a quiet place, dedicated entirely to listening, free from interruptions, with an inviting chair, a good pair of speakers, easy access to my digitized collection, and no computer screen glaring in my face as I listen. With some time, some money, and some rearranging of my home office, I finally achieved that — just a few days ago.

Despite being an audiophile at heart, I’ve tended to skimp on audio equipment, fearing that if I let myself become too enamored of high-end stuff, I’d bankrupt myself, with audio nirvana remaining forever elusive. My view has shifted as I’ve launched my composing efforts and have come to see audio equipment not as an indulgence but as a tool of work that’s well worth the investment. So I recently invested in a great pair of studio monitors that let me hear things in my music collection that were simply never audible before. I control them from an audio interface sitting at the main computer workstation in my office. The interface has an analog volume knob that makes it easy, and pleasant, to adjust levels. I cleared out a corner in my office for the speakers and put my computer workstation facing at an angle away from them, so I can swivel in my chair away from the workstation and face the speakers directly with the computer screen out of my main line of sight. When I want to focus, I can turn away from the computer and toward the little “chapel” of music that I’ve set up in the corner of my office.

I may still be in a honeymoon period with this new equipment and new office configuration, but I do have preliminary conclusion. Close listening is still possible. I still have the desire, and the ability to immerse myself listening for hours on end. I can still study a recording, still commune with an album like I used to do in my teens. I can still find that same ecstasy in listening that I remember from my CD-collecting heyday in the 90’s. The internet has not ruined my attention span or my ability to engage with what I love the most. The internet has simply made it easier to become distracted, meaning that my fortifications against distraction must be proportionally stronger today.

In 2017, when we’re trying to concentrate on music, we need to give ourselves all the help we can, and that means carving out the right environment for concentration, which means solving a bunch of practical problems about how to arrange your space, how to gain some distance from your computer screen or mobile devices as you listen, how to make your collection easily accessible, and so on. In the days of records and CDs I think people used to spend more time on building their listening rooms, while today we’re more inclined to listen in random places, from our connected devices, as we attempt to multitask. But it’s still possible to set up a great dedicated room — or corner — for close listening today, and it’s worth doing. Forget all the angst about our distracted, Internet-addicted age where concentration is supposed to be impossible, and invest the time in creating a place where you can concentrate. I wish I had done that a while ago; I’m glad that I did it just now. Long live close listening!

My new “listening chapel” in my home office. My computer workstation is nearby, and it controls the speakers, but importantly, I’m able to face the speakers without the computer screen in my direct line of sight.  These speakers or “nearfield studio monitors” are designed for listening up close.  Arguably they’re a bit too close together in this nook, but they still sound fantastic.  The painting above them is by my father and is dated 3/8/1986.

Some Listening Tips for Canon Newcomers

When I began work on my album Canons I expected that its main audience would consist of three groups of experienced classical listeners:

  • those with a particular interest in counterpoint (folks who own multiple recordings of Bach’s Well-Tempered Clavier, Bach’s Art of The Fugue, Shostakovich’s Preludes and Fugues, Hindemith’s Ludus Tonalis, and so on)
  • those with a particular interest in the harpsichord, and in new repertoire for early keyboard instruments (folks who own a recording of Lambert’s Clavichord by Herbert Howells, for example)
  • those with a particular interest in math-music connections (folks who own the book Gödel, Escher, Bach by Douglas Hofstadter)

At the same time, I hoped that I could turn some new listeners on to counterpoint, including those who don’t consider themselves classical music buffs and who might not know what a harpsichord is.

On the evening of April 3, 2017 I had my first success towards that latter goal. Continue reading


Counterpoint as conversation

I’ve been thinking about what advice I’d give to a listener who wants to explore musical counterpoint. What is the best way to understand a composition where several musical parts (or lines, or voices) are moving independently, in a way that seems fascinating but sometimes overwhelming and difficult to follow?

The best way I can explain counterpoint is to liken it to a spoken conversation. To understand a contrapuntal piece of music, you can apply the same listening strategies that you would use in understanding a conversation between people.

Continue reading


CDs were

CDs were expensive. In the late 90’s a new Hyperion import from the UK could cost $18.99.

CDs took up limited space on your shelf. If you bought a CD you had to figure out where to put it.

CDs couldn’t be had instantly: you had to go to a store and look for them. You had to find the right section of the store (Classical, Folk, World) and flip through rows and rows of discs which might be separated by letter (A, B, C) or major composer (Bach, Mozart, Schubert) or performer or band (Glenn Gould, Bob Dylan, The Doors) or generic category (Vocalists, Historical). Sometimes there was a “Miscellaneous” section for albums that the staff didn’t know what to do with. Sometimes CDs were just miscategorized and you’d only find them by flipping through everything in the aisle. If you wanted more than one CD you’d walk around the store clutching your possible buys and keeping a mental tally of the likely cost.

CDs could be hard to find. You could mail order them but that could take weeks or months.

CDs made you plan your acquisition process. You had to think about which CDs you wanted to get, ask around, read reviews, try to get the person in the store to play you a track or two if they were willing, and then you’d have to be ready for everyone in the store to hear what you were thinking of buying, and what if you hated it? Maybe you could borrow a CD from a friend and listen for a while. Maybe you could trade. Some stores had listening stations where you could hear a few staff selections, and a few stores had a system that could play an arbitrary disc. But many CDs were not available to preview at all — you had to take a chance.

CDs could be duds. You’d think you were going to love a CD but it turned out to be lame, and in buying it you’d lost your chance to buy another CD that you really wanted, but now that this lame CD was sitting around you’d keep trying to listen to it, seeing if maybe you could get yourself to like it — and every once in a while, that worked.

CDs could be great deals. When you spotted a rare or expensive CD on the rack at a used record shop, marked at $7 or $8 you felt lucky, you grabbed it.

CDs always had to pass through a salesperson. You had to take your CDs up to some man or woman at the sales counter, hand the CDs to the person, wait while the person looked over your selections, scanned them, maybe made a passing comment, computed the total, took your cash or your credit card, put the discs in a bag, gave you a receipt and a parting glance.

CDs were possessions. When you bought a CD it became a part of your life. It lived in your bedroom, or your kitchen, or your office. It joined a chorus of CD spines asking to be pulled out. You came to recognize the lettering and color of that spine. You could quickly find your favorite CDs on the shelf using only your peripheral vision and your intuition about where you had probably placed it. There were some spines that you had seen in record shops year after year – the same spine – and one day maybe you’d finally take a chance on that album and bring it home and now that familiar spine would finally join your collection.

CDs could get messed up. Maybe the disc got scratched if you dropped it one day, maybe the jewel case cracked. Every once in a while you might have to clean a CD with a rag or, if you thought it was necessary, a microfiber cloth; and water, or, if you believed in it, that special fluid that came in those little bottles.

CDs reminded you how old they were and where you got them. If you had owned a CD for ten years its case was probably old and worn. If you had bought it used, without plastic wrap, its case probably still held the price tag that had been stamped on it, and that tag probably had the name of the store like Academy Records or Cutler’s or Soundtracks or Colony Music or may be some store in another town or city or country you had visited once on a trip.

CDs came with liner notes and you were more likely to read them in full than, say, a PDF on your computer screen today, competing with thirty browser tabs. Sometimes you’d expect to see lyrics and translations in the notes and you’d find only a blank page. But sometimes the booklet was so thick you’d have trouble squeezing it back into the jewel box and it would all frayed.

CDs had covers that you got to know. Sometimes you’d go to a record shop looking for a certain cover even though you couldn’t remember the title of the album you wanted, and maybe if the salesperson was nice they’d humor you and let you describe the cover and they’d see if they could figure out what album you might talking about and whether it was in stock.

CDs could end up in the wrong cases. CDs could be temporarily misplaced, mistakenly left behind, sometimes permanently lost. CDs could turn up in unexpected places after you had searched for them for days or months. You could end up with duplicate CDs if you bought one you forgot you already owned, or if you bought one you thought you had lost when you really hadn’t. And sometimes two CDs with totally different covers actually contained the same recording.

CDs had to be played through a sequence of steps. Open the jewel box. Press that thingy to release the disc. Hear a little bit of a squeaking sound. Then walk the disc over to the CD player, yes, walk it over there. Eject whatever was inside. Hear the tray open. Take the other disc out and put it aside – wonder where its case had gone. Put in the new disc, press a button to make the tray to retract: a bzzzz followed by a kind of mechanical gurgling sound as the player registered the new disc. Look at the LED light show the total number of tracks. Then press “play” and hear some more mechanical gurgling as the player got started. Then go back to your chair and listen as the music starts.

CDs came with a specific track order. You could program your player to use a different order but that was enough of a hassle that you rarely ever did it. If you liked a CD and listened to it a lot, you got to know the track order so well that at the end of one song your mind would automatically start playing the next song before the CD player actually got to it.

CDs forced you to be patient. Once a CD started playing you’d probably let it keep going for a while because in order to change it you’d have to go through that whole sequence of steps again.

CDs could encounter tragedy. Sometimes a CD player would eat a CD and refuse to give it back and you’d have to plead with it.

CDs could be stacked. You could have all your rap in one stack and all your Renaissance choral music in another stack. Or you could make a stack of new CDs that you had been meaning to listen to, or old favorites that you wanted to revisit. You could merge two stacks or break a stack apart; you could pick up a whole stack and move it to another room.

CDs could be seen all together, in aggregate. You could see how big your collection was – whether it was neatly organized or a mess. You could see when it needed attention, when it was getting shaggy, when it needed to be sorted or pruned. You could see your collection getting bigger and taking more space as you bought more CDs and you could see it getting smaller as you sold CDs or gave them away. People who came to your home could see what music you had.

CDs could be taken on trips, but not too many. When you went on a trip you had to decide which CDs you wanted to take with you. Your backpack had room for five, maybe ten. Could you survive a week away from home with only five albums to listen to? Maybe if you ditched a book or two, or a bag of granola, you could make room for more CDs.

CDs came with a little story that you held in the back of your mind. The music was on the CD. When you bought a CD and took it home you felt like you were carrying the music itself.  That bag from the record shop actually contained Bach’s St. Matthew Passion or Coltrane’s Giant Steps – what a miracle that you could have those things! When you put the CD in the player, the player would read the CD. If the CD had been scratched it might be unreadable, but sometimes you’d see used CDs in the store marked as “scratched, plays fine.”

CDs had players and those players had their own personalities. You could buy a fancy CD player or a generic one. Some people said they were all basically the same but others swore that having multiple lasers and a boutique digital-to-analog converter would make all the difference, would make you happier and more satisfied.

CDs had stores dedicated to them, and you could dedicate days to going to those stores. You got to know where the record shops were, the ones that sold only new discs and those that had a used section. If you lived in a city and had the time and some cash, you could spend a whole Saturday walking from shop to shop. Lots of shops would make you check your bag so you didn’t steal a CD. These things were valuable.

CDs helped you enjoy music. They did this not just by holding the music but by giving structure to your experience as a listener. CDs slowed you down. If you wanted to play a CD you’d have to find it first, then set it up in the player, and by the time the music actually started, you were ready to pay attention.

Your pride in owning a CD – in having tracked down something rare and wonderful – made you more likely to actually listen to it. Your stacks of CDs helped you remember what you wanted to hear. The mild inconvenience of changing a CD made you give more attention to whatever was playing now.

The fact that there were CDs “out there” – amazing, unusual CDs on the shelves of some shop, somewhere – CDs that would blow your mind if only you could get a hold of them – it made life seem like a musical treasure hunt. And when you found a treasure you gave it a special place on the shelf, a special place in your life, and when you listened to it, your awareness of its rarity, of its value as a thing, made you more attentive to the actual music it contained, more ready to receive the real gift.