Last year I had the incredible fortune of taking John Riley's rhythmic analysis class at the Manhattan School of Music. John is an incredible player and educator, with an immense knowledge of rhythm. One lesson that resonated with me was his explanation as to how to mathematically figure out exactly where to place the subdivisions in complex polyrhythms; such as “9 over 2”, “7 over 3”, or “5 over 4”.
While I am not encouraging to be consciously thinking about this in the moment while you are performing, it is helpful to process this in the practice room to truly get an honest sense of polyrhythms and superimposing rhythms.
Check out this 3-step process, where I use the polyrhythm “5 over 4” as an example:
1) Step 1: Using the bottom number, notate 4 note values in the bottom staff
2) Step 2: Using the top number, fit 5 note values in each bottom value
3) Step 3: Using the bottom number, pick every 4th note on the top staff.
a. The 1st, 5th, 9th, 13th, &17th triplet become the "5" in the "5 over 4" subdivision.
This is what a "5 over 4" polyrhythm will look like on paper, but now you know and understand where each subdivision lies.
Hope this can inspire further creativity improvisationally or compositionally, or just further your awareness of polyrhythms.
Bijan Taghavi is a pianist, composer, and educator currently based in New York, NY. For more information visit http://www.BijanJazz.com.