Polyrhythms: An analytic approach

        A polyrhythm is basically a way to notate a rhythm, usually with a ratio, that doesn’t fall into the common denomination of duple-based (8th, 16th, 32nd, etc...) rhythms. The most common sort is the triplet but there are many more applications.

       One popular way of explaining them is to picture two people taking two different step sizes to get from on point to another.  The distance traveled is the same, but the people only make perfectly overlapping steps once that set distance has been covered.

       Seeing as this subject has a very mathematical nature, the best way to break it down is with all-encompassing variables.

        For polyrhythm X:Y, in general terms, first solve the product XY. Then write out that many notes marcating every X number of notes w/ an accent (>) and every Y notes w/ a hat accent (^).  (I use accents only to mark the notes and not to indicate a specific dynamic level)

example- 3:2                                

(I usually use a duple notation since this step is just to establish a relative rhythm between the hands)

     Next, remove the taps, or the unaccented notes, while maintaining the same sticking for the remaining accented notes, including a double stop, to indicate the starting point of both sub-divisions, on the first note:

-3:2 after removing extraneous notes        

    This gives you two separate rhythms superimposed over each other with one hand dividing the allotted space into X pieces and the other into Y pieces.  Playing each hand on a separate surface provides further clarification as to how this process divides the limbs into different meters.

-3:2 on separate surfaces (snare & hi-hat)        

     Now, repeating the pattern, first count X notes along with the right hand and Y for the left noting that either time, "one" occurs on the double stop.  Repeat for "Y" on the opposite hand. 

     This is only the first part of the process of playing a polyrhythm since most of the time, only the X part is played, while the "Y" merely serves as a reference point to the length of the rhythm.  It's kind of like the inverse of a time signature in that the second number is length and the first determines how that lenght is pulsed, istead of the other way around.

     To notate the "X" part of a polyrythm, first understand that X:Y can be read as "X notes in the place of Y of the same kind of note."  A simple example of this would be eighth note triplets.  These basically fit three eighth notes into the space of two.

---6/17/97