Towards the end of his life, Morton Feldman began to explore the effects of extreme duration on the listener and performers. In a work that spans nearly 90 minutes (which pales in comparison to the 5-hour String Quartet no. 2), the player needs to break a piece into manageable sections to rehearse. Usually, a composer gives us a helping hand by delineating one section of material from another by way of a musical form. In “formless” or “indeterminate” music, however, the player has to do that work for themselves.
In any piece of music, the player is tasked with counting, often to the same number over and over again. It’s a perfectly logical system of dividing up a time-based artform into smaller, more conceptually digestible units. For example, it’s a much simpler task to count to 4 over and again for the duration of a piece that has 300 measures in it than it would be to count straight through to 1,200. You’d lose track of your place somewhere in that 1,200. A piece of music will also have some melodic landmarks to help orient the listener’s memory as a piece continues for some time. It’s not that we can’t handle sitting through a 90-minute work, it’s that we need some sonic hand-holding, or form.
In this practice excerpt, Brendan is meticulously building about 10 measures of music (out of 1,100). Each measure is divided into two triads, or groupings of three pitches. Those pitches are traded among the three different lines of music (and not always in the same order) as Brendan reads each group of three systems (5-lined staff) in the score from top to bottom, then left to right. He has to decide, depending on proximity, which hand plays which note since Brendan woefully only has two hands. Let’s not make him feel bad about this, it isn’t his fault.
THEN, if that weren’t enough to frustrate the player (or maybe it titillates the player?), Feldman also divides each measure into units of 3 and units of 4. This type of rhythmic figure is known as a polyrhythm. In the first measure of this example, the top two lines are divided into four eighth-note units (further subdivided into sixteenth notes), and the bottom line is divided into three eighth-notes (also further subdivided into sixteenth notes). The player not only has to manage accurate time keeping, but also has to play notes that aren’t aligned correctly (meaning, sometimes a note that needs to happen earlier in the measure, visually appears later). Which results in a lot of fraction division. You know, the stuff you were probably mad about learning in third grade. If you’re curious about more of the mathematics, let us know! We’re happy to lend a helping hand!
Think of it like when you’re in the left turn lane at a traffic light. Your blinker is clicking away at its own speed while the car in front of yours is blinking at a slightly different rate. Occasionally your blinkers line up, but then they fall out of sync. If you want to try a polyrhythm for yourself, try tapping to the same speed of the car in front of you with one hand while tapping your car’s blinker with the other! Go on, try it. You know you want to.
Now start tapping your foot to the speed of the car blinker behind you.*
I’m sure you’re asking yourself, “Why anyone would put themselves through this type of process?” This is something that players of new music regularly grapple with: is it all worth it? Brendan and I certainly think so. We were drawn to this type of music because it challenged our perception of what music could (or should) be. When a listener takes a step back from the minutiae of the work and stops trying to hear musical conventions (melodic line, harmonic progression, form, etc.), they will begin to hear other things: a butterfly flapping its wings as the tones trickle through the fingers of the pianist, for example. Or maybe you might hear something more cosmic. Do you hear raindrops, maybe? Does it sound like a slowly crawling glacier? Do you hear a place, a temperature, a color? Did you know those things could even be possibilities? When you let go of any notion of form or structure, your mind is capable of constructing its own narrative, unique to you and your own lived experiences.
I can only hope that no two experiences are the same.
-- Dr. Leslie Ann Leytham, Co-Artistic Director, Project [BLANK]
*Note: Before all the percussionists come for me, I know full well that the blinker example is technically phasing…..but it’s the best real-world example I’ve ever found to explain polyrhythmic ratios. :)
“This is a rough visual breakdown of the various elements in the piece - a color-coded and symbolic way of looking at the whole of the piece as a way to better understand its structure. This gives me a sense of where each section is headed, and if there are even any sections at all. As a performer, knowing how these larger structures relate to one another informs how each passage is interpreted, how to direct direct energy to and from key moments. It's a way of making sure I don't miss the forest for the trees, so to speak.”
-- Brendan Nguyen
FROM THE COMPOSER’S NOTE IN THE SCORE
“As a composer I am involved with the contradiction in not having the sum of the parts equal the whole. The scale of what is actually being represented, whether it be of the whole or of the part, is a phenomenon unto itself. The reciprocity inherent in scale, in fact, has made me realize that musical forms and related processes are essentially only methods of arranging material and serve no other function than to aid one's memory.
What Western forms have become is a paraphrase of memory. But memory could operate otherwise as well. In Triadic Memories, there is a section of different types of chords where each chord is slowly repeated. One chord might be repeated three times, another, seven or eight – depending on how long I felt it should go on. Quite soon into a new chord I would forget the reiterated chord before it. I then reconstructed the entire section: rearranging its earlier progression and changing the number of times a particular chord was repeated.
This way of working was a conscious attempt at formalizing a disorientation of memory. Chords are heard repeated without any discernible pattern. In this regularity (though there are slight gradations of tempo) there is a suggestion that what we hear is functional and directional, but we soon realize that this is an illusion: a bit like walking the streets of Berlin – where all the buildings look alike, even if they're not.”
— Morton Feldman