Finding Unique Concepts in Unlikely Places

In his book Effortless Mastery, jazz pianist, composer, and author Kenny Werner wrote, “Don’t forget: Music is something we just made up. It doesn’t actually exist as anything but a game for us.” If you haven’t checked out Effortless Mastery, I highly recommend it. In the meantime, and in the spirit of exploring the “game” of music for exploring’s sake, let’s work our way through a few misfit rhythmic ideas that combine some of the concepts I’ve written about previously. But first, a few thoughts.

Recently I was downstairs in my home tapping through a palindromic Fibonacci beat (see last month’s Rock Perspectives) with a rogue layer of three that weaves its way through different subdivisions. Upstairs I could hear new flooring being installed and the pop punk band Simple Plan playing in the background. The contrasting sounds of my quiet mathematical tapping, the floor installation, and the radio had me thinking about how most people have difficulty connecting with rhythms that are more complex than simple 4/4 grooves.

Good music evokes emotions in the listener. We all react to certain songs that make us feel happy, sad, nostalgic, and so on. Often those emotions are conveyed by the chords, lyrics, and melodies of the music. Rhythm also tugs at different areas of the emotional spectrum, eliciting in the listener feelings of excitement, lethargy, playfulness, and my personal favorite, tension and release. The further you explore the realms of tension, the more that the results can make people physically uncomfortable. I find this fascinating and take great pleasure in pushing that boundary.

From my perspective, even the most alien-sounding rhythms can eventually feel like interesting syncopations of the underlying pulse. But what’s joyous for one can be unbearable to another. This tends to be the case when people experience an initial knee-jerk reaction to the feeling of tension but refuse to explore it further. If you’re able to get past the initial reaction, however, there’s a world of rhythmic possibility available to explore, even if that exploration is only for the fun of experiencing what rhythms can feel like beyond the edges of your current understanding.

Pushing the Boundaries

Now let’s dig into some musical concepts. Exercises 1–3 build us up to a two-bar palindromic Fibonacci groove in 4/4. Let’s take a look again at the first few numerals in a Fibonacci sequence.

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, etc.

The double-bass subdivisions ascend the Fibonacci sequence starting at the fourth position: two 8th notes (2), one 8th-note triplet (3), one quintuplet (5), and eight 32nd notes (8) before cycling backward through those groupings. Shed this until you can feel and execute each subdivision comfortably without sliding into each grouping.

Music as a Game 1

The next example adds 8th notes on top instead of quarter notes, creating three-over-two and five-over-two polyrhythms over our triplets and quintuplets, respectively. Go slowly, and make sure both your bass drum subdivisions and 8th-note hi-hat beats feel clean and even.

Music as a Game 2

Next we’ll apply another Fibonacci number (3) to our hi-hat rhythm by playing every third note, regardless of the subdivision.

Music as a Game 3

To be clear, these exercises aren’t meant for developing speed, and they’re not for application within a typical musical setting—although I’d love to hear that! Rather, they’re purely for experiencing what subdivision and spacing can do when you’re focused on your pulse.

In Exercise 1, each beat will feel like it has its own elasticity within the pulse. In Exercise 2, you should feel time splitting apart in your polyrhythms. And in Exercise 3, you’ll experience that three-layer syncopating all around the pulse before lining up only on beat 1 of each bar. Within these types of ideas I often find little rhythmic gems—things I’ve never heard or felt before. These are the types of concepts that drive me.

Exploring More Math

You can apply other mathematical concepts to music with unique results. Let’s see what happens if we convert some of the Fibonacci sequence into binary, which is a base-2 numeral system used in computer coding that consists of the numbers 1 and 0.

In our base-10 numeral system (the decimal system), the four-digit number 4,321, for instance, has a 4 in the thousands column, a 3 in the hundreds column, a 2 in the tens column, and a 1 in the ones column. In base-2 (binary), each column’s represented numeral is twice the previous column. This is easier to grasp if you read the binary columns from the right to left. Let’s take a look at the numeral 89 as a binary number.

89 = 01011001

To understand this, try thinking of each 1 as a “yes” and each 0 as “no.” Take a look at 89 above, which is an 8-digit binary number. The far-right column represents the number 1. There’s a 1 (“yes”) in it, so we’ve got 1. The next two columns represent 2 and 4, respectively. Both of these columns have a 0 (“no”) in them, so we’re still at 1 total. Following that we have the columns that represent 8 and 16. Each has a 1 in those columns, so we’ll add 8 and 16 to get 24, plus 1 from the first column, to get 25. There’s a 0 in the 32 column, but a 1 in the 64 column. So by adding 64 to 25, we get 89.

The first handful of Fibonacci numbers translate to binary as demonstrated in the following example.

Music as a Game 4

If we think of each 1 in the binary sequence as a note we’d play (“yes”) and each 0 as a note we don’t play (“no”), we can interpret this rhythmically. The entire sequence above is 52 binary numbers, which fit evenly as 32nd notes in 13/8. Let’s apply this onto the kit with our binary Fibonacci pattern applied to the bass drum and the occasional snare. Playing 16th notes on the hi-hat will hold this pattern together nicely.

Music as a Game 5

I’m not suggesting that everyone attempts to be as strange as possible. But sometimes when people start to take music seriously, they forget that it’s okay to explore something simply because it fascinates them. Don’t let anyone tell you that you always need an application at hand for a concept you’re interested in exploring.

There will always be an overwhelming majority of people who live to play within all the rules of this game we call music. But as an art form, music needs people who want to explore the realms of the unknown—those who don’t care what fits within the norms, and who take direction openly from their deepest fascinations. As you dig and explore your own interests, you can legitimately find yourself through music. It’s what happened to me, and there’s no reason to think it can’t happen to you as well.


Aaron Edgar plays with the Canadian prog-metal band Third Ion and is a session drummer, clinician, and author. His latest book, Progressive Drumming Essentials, is available through Modern Drummer Publications.