Polymorphism 1.01

pdf score

:rhythm discussion:

This entire song can be "felt" or "heard" in 3. I wrote the score in 9/8 (except for one passage*) to avoid a sloppy/confusing barrage of tuplets. Much of the song also does emphasize an unenven 9/8 organization as well (such as 2+2+2+3). In any case, "The 3" is the lifeblood of the song, even though those beats are rarely stated. Practicing this song to a metronome set in 3 was the only way that I could precisely transition between all of the sections (even though different metronome settings would have been more useful on particular sections).

*I explain this exception below.

This bass theme is the foundation of this piece: 2+2+2+3. Counting in "The 3", this means a triplet over the first 2 beats and then the last beat.

The right hand enters with a rhythm in 5/8 against the 9/8 in the left hand. They meet again after 9 cycles of the right/5 cycles of the left. This is an example of polyrhythm by displacement (or phasing).

The right hand stops cycling through the 5 and enters a rut (on the 2nd iteration of 9). The left hand juggles around the position of the lone group of 3 beats in the original 2+2+2+3.

The right hands begins resumes its cycles of 5/8 as the left hand continues juggling.

Both hands finally break free of their harmonic and rhythmic stasis as the left hand plays an even 4 beats against "The 3
", which is omnipresent. The right hand teases "The 3", but only explicitly states it in mm.24.

I wish I could remember what inspired me to write this madness. I blame possession by Zuul. The theme in this section appears twice - the next time at mm.95. I originally wrote it out in 9/8 (as it is written the second time), but changed to (12+3+12)/8 because it was easier for me to visualize and think about. To avoid getting unnecessarily bogged down in number and the specifics/shortcomings of notation, I will first describe the rhythmic relationships between the lines.

The lowest note in the left hand preserves "The 3".
The higher note in the left hand places 3 beats over every 2 below. This alone creates generates some interesting complexity in that it takes 2 groups of "The 3" before it repeats. Another way of thinking of the higher part is as 2 groups of the 9/8 from before that connect in the middle to make 18/8: (2+2+2+2+1<>1+2+2+2+2)

To add to this mind-twister, the bass line moves to different pitches after every 4 of "The 3" beats. So even though the rhythm resolves after 2 groups of "The 3", the pitch doesn't allow resolution until 4 groups of "The 3".

If you're still with me, read on (not to be bossy). If not, do what you will. There's only one more layer left to discuss. The right hand part is related to the top of the left hand part, meaning playing off of the 3 over 2 (of "The 3"). The right hand concentrates on every 9 of these beats (the 9 even beats of the 18/8 described above). It breaks these beats down into 4+1+4 (preserving the pattern of the shared beat in each pair of 9/8 bars). Over each group of 4, the right hand plays in the grid of 3 or 6 beats to that 4.

***The choice of 12/8, 3/8, 12/8***
Necessity (not pretension) spurred me to pick this metric scheme. In the original 9/8, the right hand part in this section requires half note and quarter note triplets. While practicing it written this way, I had difficulty knowing if my right hand part correctly locked in with the two rhythms in the left hand. Picking this new meter allowed me to approach the rhythm both by "counting" as well as by "feeling." This choice made my life easier, but that isn't to say it will make yours. Here is the section written in 9/8.

Now, this all might seem like a steamy pile of BS, but the music was intelligible to my ear when I heard the computer obediently play it back to me. Initially, I thought that the computer was as far as it would go. Then I tried to play it, breaking it down and practicing various aspects of one rhythm against another. After my breakthrough of correctly executing 3 over 4 of 3 over 2, I happily realized that I would conquer this passage with some perseverance.

Reenter the world of (relative) rhythmic and harmonic stability: 3 against 2.

I toy around with the bass line not being contained in "The 3". It follows 4 + 5 of "The 3" twice.

The first theme with the 5/8 over 9/8. I embellished the original bass line with the addition of an eighth note at the end.

The 5/8 figure in the right hand is now augmented by a 9/8 appended to it. This makes for 14/8 juxtaposed with the left hand's 9/8 figure. This creates a phasing pattern where each group of 5/8 displaces the two hands and each group of 9/8 preserves that displacement. All the while, the hands go in and out of rhythmic consonance. It takes 14 bars of the 9/8 for the parts to rejoin.

The left hand continues playing the original bass theme in (2+2+2+3)/8. We can count this as 4 and a half beats. The right hand plays 4 beats against the first 3 of those beats and 2 against the last 1 and a half. Thinking in terms of the "The 3" of the song, the right hand simply plays "1-&-2-&-3-&." The right hand continues playing in this grid while generating further syncopation by skipping occasional beats.

The sixteenth note line in the right hand is 3 quarter notes long, so it takes two measures of the bass line before they rejoin. The right hand then plays a new line with the same rhythmic correspondence. Now both hands play the sixteenth note counterpoint in rhythmic unison.

The demonic right hand line from mm.31 returns. The left hand continues to machine gun fire sixteenth notes, which somewhat obscures the polyrhythms. The sixteenth notes follow the division of 9/8 in pairs of measures as (2+2+2+2+1)/8 and (1+2+2+2+2)/8. I approached playing the rhythm in this section by approximation more so than other section in the piece. In practicing, I made sure to keep the sixteenth notes steady against the metronome and then worked at getting the right hand triplets between (or on) the correct sixteenth notes.

Personally, the speed at which I can play the left hand passage here determines how fast I can play the entire song (at the moment, significantly slower than the marked tempo).

The left hand sixteenths continue with emphasis shifted to 2 groups of 9. The right hand also emphasizes these 2 beats.

The original 9/8 with sixteenth note offsets between the hands coming and going.

If any section of this piece is guilty of being born out of emotionless mathematics more than others, this one certainly is. One rationalization I can offer for its existence is that it serves the piece aesthetically in terms of its deconstruction. The most incessant theme of the piece (the bass line) gets stretched out elastically as the right hand plays a rambling line through every permutation.

The left hand begins with the bass line playing all 9 beats for two measures. A measure of 2+2+2+2+1 follows this. After this point the bass line settles into a distorted form of the original with 3+3+3+3+1. As this line is 13 beats long, it takes 13 measures of the 9/8 for it to complete one cycle (which it does before moving on).

The right hand plays against the 2+2+2+3 subdivision of the bass line. The line places 3 beats over each of the 2 and 4 beats over the last group of 3. This structure continues independent of the left hand's meanderings.

The entire section lasts for 16 bars of the 9/8. The line in the right hand is 4 bars long with each bar being a distinct unit. If those units are labeled "a, b, c, d", then the following permutation takes us through 4 cycles: [a-b, b-d, c-a, d-c], [abcd] becomes [cadb] becomes [dcba] becomes [bdac]. It would return to [abcd] in the following iteration if I allowed this nonsense to continue.

The bass line stretches once more into 4+4+4+4+2 (18). The right hand strictly plays on every 4 beats.

See mm.93-94.

Some fanfare in rhythmic unison. Although not difficult to execute tapping along to 9/8 time, this passage presents some difficulty against "The 3" of the metronome. I learned this passage by first practicing it against the 18/8 that isn't stated 
(2+2+2+2+1<>1+2+2+2+2). Once I felt this syncopation ingrained, I worked on tapping my foot to this 18/8 against the metronome's 3.

Return of the 9/8 with 16 note offset between the hands.

Here's "The 3".

Back to R.E.C.ordings

Back to Rob-Cohen.com