Additive Rhythm

When many classically-trained musicians start to learn rhythm—or at least the theory of rhythm—they often see a diagram that looks something like this:

Each note divides into the next clearly and evenly. This 'divided' concept of rhythm fits nicely with the way most traditional classical music is grouped in measures, which are then subdivided into smaller rhythms.

Additive rhythm flips this idea on its head, by adding together smaller units of rhythm in order to produce larger units or groups (meters). The term “additive rhythm” also usually means that there will be different kinds of rhythmic groups added together—usually 2’s and 3’s:

By creating different combinations of groups of 2 and 3, we can create interesting and unusual rhythmic patterns, patterns which are used by musicians and composers in many styles of music all over the world.

To help us get into the world of additive rhythms, this musical experiment is all about improvising and trying to play with different patterns of 2 and 3. I hope you'll give it a try: for one thing, it's really fun, and for another it will hopefully help you hear how lots of different music uses additive rhythms of 2 and 3 all the time.

Materials

  • Your instrument or voice. A metronome (preferably one with faster speeds).
  • Optional: Paper and pencil

Steps

1. Pick a collection of notes, like a scale, key, mode, or some other pitch collection (e.g. a chord, pitch set, etc.). These should be notes that you like and that you can play well without thinking too hard. I used C Lydian in the video, but you could use just about any group of notes you want (C major is fine!)

2. Put your metronome on a fast tempo. In the way that I’ve written down these examples, each click of the metronome will equal 1 eighth note. So, if you want to start slow to get comfortable, that's perfectly fine, but I probably wouldn't use a tempo below 100 bpm (beats per minute) since this will represent your eighth-note speed.

3. Start to feel the rhythm in groups of two (2 metronome clicks for each beat). You can count, tap your foot, or bob up and down. Once you feel comfortable with that, play the groups of two (quarter notes) on your instrument. Try to feel a solid pulse in groups of two.

        In this example, if each metronome click is eighth = 150 bpm, then the quarters will = 75 bpm

4) Next, try improvising a melody in groups of two using only notes from the scale or pitch collection you've picked. This example of a possible improvisation uses only groups of 2, and is in D minor (natural minor). The rhythms are combinations of eighth, quarter, and half notes, but other duple rhythms would be possible as well:

5) Repeat steps 3) and 4) but now using groups of three (three eighths = one dotted quarter)

         In this example, if each metronome click is eighth = 150 bpm, then the dotted quarters will = 50 bpm

        In this example, if each metronome click is eighth = 150 bpm, then the dotted quarters will = 50 bpm

         An example of a possible improvisation in groups of 3

        An example of a possible improvisation in groups of 3

6) Try to alternate the pulse between groups of 2 and 3 together. You'll notice that if you're tapping or moving to the larger beats (quarters and dotted quarters), the speed of each beat will change from moment to moment (the 2's are quicker than the 3's). If this is new to you, spend a few minutes just feeling this alternation, either just moving with your body, or by playing one note on your instrument. Once that feels comfortable, you can start to improvise.

7) You can also get creative and try many different combinations of 2 and 3. Here the possibilities are endless, since 2 and 3 can be combined in so many different ways, and you can keep adding new groups with no limit. When doing this, it can sometimes be helpful to keep track of the patterns of 2 and 3 by using a shorthand of dashes for 2 and triangles for 3:

As before, play your pattern on a single note and once that feels easy you can start to improvise. Of course, you can also just improvise freely between 2's and 3's without a plan, but if you want to see one example of a really complicated pattern here's an example that uses the combination 2 + 3, 2 + 3, 2 + 2 + 3,  2 + 2 + 2 + 3, 2 + 2 etc. (!!!), as well as showing the dashes and triangles in the music:

Finally, here’s the music for the Messiaen piece I used as an example at the end of the video. Can you figure which groups are in 2 and which are in 3? (N.B. I’ve changed the beaming slightly from Messiaen’s version to make this challenge a little easier)

And lastly, here are some links to music that features different kinds of additive rhythm:

Olivier Messiaen: Quartet for the End of Time
Although almost the entire piece is made of additive rhythms, you can skip to 25:21 to hear the Dance of Fury movement from the video)

Philip Glass: Einstein on the Beach

Can you figure out what they're saying?

Martin Scherzinger: Mask and a Mask

Music inspired by mbira music written by my friend Martin Scherzinger. Can you hear when the rhythmic groups change between 2 and 3?

As always, I hope you keep trying new things and your own experimentation at home. And, if you create something you really like, please share it below!