Different Angles on a Musical Object

Josquin, Gestalt, and Aphex Twin

I know how annoying those blog post titles are that try to connect three random things, just to hook you and make you think, “Wait, how is he going to do that?” But just so you know, I had to take things out of this blog title. Boards of Canada and African polyrhythm, for instance.

Ethnomusicologist Simha Arom notes that much of the Central African Republic’s polyphony, amongst the Banda-Linda horn ensembles he researched, is based on a “polyphonic cell,” or a “cyclic rhythmic figure” that constitutes the formal makeup of the music. It’s a result of 16-or-so horn playing a rhythmic pattern that repeats indefinitely. The music varies itself by having individuals come in or out of the texture. But each individual player always repeats the same short groove. When Arom speaks of a “polyphonic cell”, he is speaking of the sound that would occur if they were all playing at once. This polyphonic cell can be presented as a paradigm, in that the whole piece is derived from its pattern, but it may not appear as such at any given time in the performance of a piece. It is, however, the blueprint upon which different realizations and variations are based. Now, what he says next is pretty interesting, quoted at length:


Since the piece is based on the varied reiteration of that combinatory formula, the latter also behaves as paradigm. In consequence, if we were to place on the paradigmatic axis all of the combinatory formulas as they appear during a performance, we would obtain a “meta-paradigm” encompassing the totality of the piece, i.e., the entirety of the individual realizations as well as of the combinations performed therein.

 So, not only is there a polyphonic cell that exists outside of any specific moment in the music—a paradigm of a single iteration of the groove—but there is also a “meta-paradigm” for how that polyphonic cell unfolds, often combinatorially, throughout time.

It’s not a new observation that much of modern electronic music owes its procedures to African and Afrodiasporic music. But in the spirit of what Kofi Agawu calls “contrapuntal readings” between different cultures (he considers this a healthy practice), I’d like to look at several different manifestations of this phenomenon Arom is noting of the “polyphonic cell” and compare it to the music of Josquin. I think this impulse to look at music as a “cell” or “block” or object that can be prismatically understood from several different angles is transhistoric and transcultural.

Gestalt psychology’s principle of invariance
from Wikimedia Commons

In Gestalt psychology, there is a “principle of invariance” whereby humans tend to be able to recognize an object that they’ve never seen before as the same as another object, even if it is rotated, stretched, drawn differently or disproportionately. So, given that Gestalt psychology is the investigation of how the human mind tends to group disparate objects, we tend to group objects on basis of what we assume to be their 3D shape, even if we have never seen or experienced the object from multiple sides. We just guess in our minds what the rest of the object is like. (For more on Gestalt psychology applied to music, see Leonard Meyer below.)

I want to suggest that this approach to the polyphonic cell is a way of treating music like an object, one that demands to be seen from different angles. Polyphony is complex: lots of different actors (or, in electronic music, a single actor’s multiple tracks, “actants” in Bruno Latour’s language) are producing melodies that vie for our aural attention. What do we listen for? It’s probably impossible to really get the complexity of polyphonic music the first try.

This is why electronic music often gives us multiple tries at it. Polyphonic EDM repeats, and repeats, and repeats, and each time it gives us the sound “object”, or Arom’s “polyphonic cell” with a different voice removed or another voice added. This is the akin to the combinatorial aspect that Arom notes in Banda-Linda horn music.

How would we visually represent this? Arom speaks of a “paradigm” and a “meta-paradigm.” I am not positive I have interpreted him correctly, but I am going to assume that this maps onto the categories “synchronic” and “diachronic” (in a particular moment in time of the music vs. across the temporal span of the music). If we combine these, we get the paradigmatic axis that makes up the “totality” of the piece. So, in other words, we might be able to represent the piece analytically in such a way that there would be no information loss in our portrayal of the piece, even though we didn’t do a score-format transcription. Somebody, just looking at our paradigmatic analysis, might be able to reproduce an entire song, if the paradigm + meta-paradigm really did constitute the “totality” of the piece.

Let’s take Aphex Twin’s “We Are the Music Makers” from Selected Ambient Works 85-92. The song is an 8-minute process of muting and unmuting various tracks, which, heard together, are our polyphonic cell. Richard James has come up with a pretty complex polyphonic cell, which is the musical material on the left below. You never do end up hearing all the elements simultaneously. The closest you get is something like the “climax” of this song at 6:00, but it is missing the bass. Overall, you end up hearing all sorts of different combinations of tracks (“voices”, as we might call them in the fifteenth century). This allows you a curious insight into the nature of the cell. You hear all sorts of things you wouldn’t otherwise have noticed; for instance, you might have assumed that Richard James’s bass track, if you had just heard it as 3a+3b, was all a single “voice”, but he has cleverly split it up into two separate tracks and effectively gets two melodies out of one. Sometimes you hear 3a, sometimes 3b. (I am sorry my figure doesn’t notate when. I’ll make it better someday.)

This starts to feel a lot like the Gestalt principle of invariance. Although we are hearing something different each iteration of the cell, we can recognize that something is being repeated—even though each constituent part is absent at one point or another. So it’s a bit like looking at a musical object from several different angles, yet recognizing it to be the same object. One obvious caveat is: there has been information loss, since I just put “drum” and didn’t actually notate out the drum (because it was too hard and didn’t repeat as cleanly as the notes). It’s not coincidental that drums are the hardest aspect of EDM to be formally reductive about.

Another example is Boards of Canada, “Roygbiv“, a just really lovely song. (Another one my wife introduced me to.) Here I have analyzed it slightly differently. Since it operates in clear 4-bar phrases (in some ways, it’s strangely Mozartian), I just outlined the “cell” as I would a normal score. This cell gets repeated five times and then fades on the sixth. Here you can really sense how your brain is getting an education in how to listen to this music: you hear the bass first, then some supplementary background lines, then the melody, then just melody and accompaniment, and then everyone altogether. Had you heard it together from the outset, you likely would not have been able to comprehend it. If we treat the polyphonic cell as an object and apply the principle of invariance across the form of the song, it suddenly gets that Boards of Canada magic.

“Roygbiv” polyphonic cell
“Roygbiv” diachronic paradigm

Now the moment you’ve been waiting for: Josquin, this blog’s namesake. His situation is a bit more complicated, because he is going to introduce two variables into the situation. First, unlike Aphex Twin or BoC, Josquin is going to decouple musical material from track. That is, if you equate “track” with “voice”, the superius of Josquin might sing material that the tenor sings and vice versa. However, you can still make a paradigm of the music and track its existence through the tracks/voices. Second, Josquin is also going to allow for minor transformations of his constituent elements, up or down by a fifth usually. (Here I am not speaking historiographically, since Josquin is not responding to EDM. Hoping that’s obvious.) These two changes means that, although there is a similarity in the way you can analyze Josquin’s music, its approach to the “musical object” is more complicated.

Take “Sanctus” from Missa Hercules Dux Ferrarie. Here you have a very few number of musical elements on display. Josquin is reusing and modifying a lot of his material cyclically. I have outlined the constituent parts all at the top of this colorful figure, except for a tiny bit in perfection 14 which doesn’t fit with anything else (noted in gray). Then I’ve put their disposition across time below. This time, I have to use colors, since the equivalent of Josquin’s “tracks” no longer corresponds to the constituent parts one-to-one. There is some information loss, obviously, since I haven’t noted when something has been transposed up or down (although, if I had spent more time in Inkscape, how hard would that have been?). However, the music is operating in a similar way, reducible to this sort of paradigmatic understanding.

“Sanctus”, Missa Hercules Dux Ferrarie

But this raises an interesting question: what is the cell in Josquin’s music? Because he has unmoored the musical motives from specific “tracks”, it is unclear what object it is he is giving us different angles on. It is something like the cantus firmus, the long red lines in alto and then tenor. This is not too far from the historical reality, since one of the central questions in mass repertory of the fifteenth and sixteenth centuries is how composers treat cantus firmi in musical form and how the surrounding voices react (see Sparks and Wegman below). Like the others, Josquin is turning the musical object around, seeing what different angles reveal, but the object has become more internally complex, fluid, reacting to the very act of being examined, like a smartphone’s accelerometer changing its display depending on how you angle it. (Sorry, that metaphor was not poetic, but at least it’s relatable.) Josquin’s music, besides all the surface-level differences, has a similar feel to BoC and Aphex Twin (and, of course, to African polyphonies, although people said so long before me, like Arom and England), owing to Josquin’s love of repetition, his “obsessive compositional personality” (see Rodin).

So I find myself again thinking that musical repetition in our own time is less about inducing trance, revisiting trauma, or numbing ourselves with consumerist titillation, as I railed about in the last post. It seems more, in these cases, about cultivating a kind of contrapuntal intelligence. Repetition of this kind is almost a discipline, an education in attending to that which would be apparent to none of us on a first hearing.

Things I mentioned:

Simha Arom, “The Music of Banda-Linda Horn Ensembles: Form and Structure” and African Polyrhythm and Polyphony

Kofi Agawu, The African Imagination in Music and Representing Africa

Leonard Meyer, Emotion and Meaning in Music

Edgar Sparks, Cantus Firmus in Mass and Motet 1420-1520

Rob Wegman, Born for the Muses: The Life and Masses of Jacob Obrecht

Nicholas England, “Bushman Counterpoint”

Jesse Rodin, Josquin’s Rome

Big thanks to Victoria Chang for starting me thinking about this.


Moonchild and other thoughts on sampling

When it comes to sampling and remixing, there is more to talk about than just copyright infringement, according to Eduardo Navas. There are profound cultural issues to be reckoned with: “as a form of discourse Remix affects culture in ways that go beyond the basic understanding of recombining material to create something different,” (3). Take “Rapper’s Delight”, for instance, by Sugarhill Gang. The Gang samples “Good Times” by Chic, loops it, and raps atop. Navas argues that this type of sampling is “regressive” because we are using the pleasure of the repeated loop to insulate ourselves from, I guess, the brutality of existence. “The power of sampling is always based on a diversion, one that can be presented, as a state of repressed desire that is completely mediated, showing no solution except to point to itself,” (28). The sample and its repetition is an escape from reality.

Tommy-rot, I say! I am sympathetic to Navas’ desire to move away from mere discussion of copyright when it comes to sampling. And it’s not Navas’ fault that he has pushed my buttons, but it is a pretty old saw by now: cultural critics start applying Freud, Barthes, and Deleuze to musical repetition and we find out that it’s all bad, bad. Escapist (as in Navas’ application of Barthes), craven consumerism (Robert Fink talking about American minimalism), revisiting trauma (Wim Mertens). Can’t we let repetition off the hook a little bit? Maybe, just maybe, we’ve dramatically over-theorized.

Instead, let’s assume sampling has something to tell us and that it’s not that we’re repressing. Take, for instance, “Doors Closing” by Moonchild, available on iTunes, Spotify, Apple Music and so forth, in their 2017 album Voyager. (Thanks to my wife for finding this music. The album is perfect for a stay-in date night or for a dusky summer evening. Or both!) This particular track samples the sound of a public transit vehicle closing its doors.

Jingle Jangle

This electronic jingle-jangle, accompanied by the conversational yet conclusive “doors closing”, is a good fit for the lyrics of the song. On the one hand, the keyboard and bass play underneath the jingle-jangle (yes, I will continue to use this word) and cleverly harmonize it and embed it into the texture of the song on loop. On the other hand, the “doors closing” morphs into a set of lyrics: “You think my love is an open door? \ No, no, you can’t come and go as you please.”

I suppose it would be easy to chalk this up to a clever play on words. The 1:24-long deep cut is hardly a candidate to overthrow much of the existing scholarly criticism on musical repetition and mixing and so forth. But I think there is a lot going on in here that deserves some attention.

First, let’s take a minute to laud these three great musicians, Amber Navran, Max Bryk, and Andris Mattson. What they did here is pretty smart. And you’ll have to forgive me if I wax a little nerdy here. Scroll down more hastily if this ceases to be interesting. This is the jingle-jangle, notated musically:


It’s got a nice sound; I can see why these guys were attracted to it. It’s an A-flat chord next to an F9 chord, and so you get a pleasant, Debussy-style enharmonicism. Now, how an alternative R&B group would approach these chords is another question. They make the overall song happen in F, so that deals with the F9 chord and gives the sound a bluesy feel. But this A-flat chord is a tricky one. They treat it in two ways.

One interpretation of the Jingle-Jangle

This first way is to envelop the A-flat triad, enharmonically, into a F#13(11+) sonority, the favorite sonority of jazz since Art Tatum. This works really well, since F#-dominant is a tritone-substituted V7 into F. Great!

But what worked for a substitute chord should work for its original, right?

Another interpretation of the Jingle-Jangle

This is the second way. It’s a little darker in its sonority—C9(13-/9+)—but the payoff is great. What’s even better is that we now have two different “interpretations” of this jingle-jangle, two different ways of understanding its harmonic content. More importantly, it has become musical. See, there’s a reason I keep calling it a jingle-jangle—is it really music at all, when it’s just a little sound that tells people to stand clear of the doors? But Moonchild has bestowed upon it the dignity of Being Music. Now, bets are, if you commute on some random LA subway and you have heard this song, you’re going to feel strangely moved by this jingle-jangle.

So sampling is a way of dignifying things that are too mundane to be perceived aesthetically. But there is even more to this, I think.

The sample itself (jingle-jangle + “doors closing”) is a fascinating semiotic unit. The sample, heard in its original context on the subway, signifies that the doors are about to close. How does it do that? The unit operates externally as an index, to borrow Charles Peirce’s term, that is, “our interpretation comes in virtue of some brute, existential fact, causal connections” between the sign and signified. (This and the following come from the Stanford Encyclopedia of Philosophy.) The doors will close when we hear the sound; we can expect them not to close if we don’t hear the sound just as much as we expect them to if we do. But within the unit, there is another signified-signifier relationship, between the jingle-jangle and “doors closing”, the music and the words. This is what Peirce might call a symbol, that is, “if we generate an interpretant in virtue of some observed general or conventional connection between sign and object, then the sign is a symbol.” There is no causal or necessary connection between the jingle-jangle and the man speaking. They merely go together to reinforce the aggregate semiotic content: the music serves, maybe, to grab our attention and, if we’re used to it, to remind us of what’s about to happen, whereas the words make it unambiguous to first-time users of the subway.

Moonchild in “Doors Closing” bifurcates this semiotic unit right down the middle. They take advantage of the fact that the relationship between the symbolic sign and signified is more or less arbitrary. On the one hand, they take the words and use their ambiguity to equivocate and make a clever song about love and commitment. On the other, they take the jingle-jangle and make it into some jazzy music. But there are even further layers of metaphor here. Because “Doors closing” is not just a metaphor for “Commit to this relationship or get out” but it is a metaphor for: “I am like a house (or a subway or whatever); I have a life, a schedule, other priorities besides you. You can’t just access me whenever you’d like.” In other words, “Doors closing” is a metaphor for a metaphor.

This ties back into our musical analysis above. Not only have Amber Navran’s lyrics taken advantage of the ambiguity of “Doors closing” to multiply possible meanings, but the keyboardists have taken advantage of the ambiguity of the jingle-jangle to enumerate different possible musical meanings. Both of these aspects of the original sample are getting disassembled and reassembled in similar creative ways.

Hand-drawn diagram for the visually-minded

At the end all of this, we have sampling and looping that has operated constructively. It is a bit like reading a metaphysical poet: from the mental gymnastics of the poetry, our ears and eyes are trained to face the world itself as a poetic object, where mundane things (a compass, a flea, yes, even a subway jingle-jangle) can be heard aesthetically, with the aid of a little irony and playfulness. Armed with weapons such as these, no human should be afraid of pessimistic psychoanalysts, or so I say.

Things I mentioned:

Eduardo Navas, Remix Theory: The Aesthetics of Sampling

Robert Fink, Repeating Ourselves: American Minimal Music as Cultural Practice

Wim Mertens, American Minimal Music