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.