This lesson will serve as an introduction to polymeters and polymetric ideas.  A polymeter is exactly what the name implies, two or more meters or time
feels occuring simultaneously.  In order to effectively practice these concepts, you'll need a metronome and your guitar (or whatever instrument you
play) or you can play the upper rhythms with your hands by clapping, patting your leg, etc..  When I would practice ideas like these, I would just play the
lowest power chord available on my guitar (E5 before I got my hands on a 7-string) and tap my foot against a hard surface so that the sound of my
tapping was loud enough to be heard with the sound of my instrument.  Now that you have your metronome and are set up, let's go at it.  The first
rhythm is a painfully simple 4/4 time feel where you are tapping and playing quarter notes together.  The second rhythm below shows how you can take
the same rhythm as the first rhythm and shift it to another part of the beat (the second 16h note in this example).  The thing to focus on when playing
this rhythm is trying to hear the two rhythms an two separate entities, not one composite rhythm; this is VERY important.
The next two rhythms take the same idea as seen in the first two and shift the placement of the upper rhythm to the second 8th note and 4th
16th note.  When I say that the upper rhythm is the same, I'm referring to the way the distance in time between the upper notes remains the
same in these first four examples.  Make sure that these ideas are pretty much second nature.  Remember all the examples at varying tempos
so you have a true awareness of the concept and aren't relying on any kind of muscle memory.
The next two example take a pattern of constant 8th notes in displace them a 16 note in the second example below.  If
you can do the first four examples, this one should come pretty easily to you.  Try it out/
Now, lets take the above concepts of shifting a rhythm to different parts of the beat using a pattern of two 16th notes.  First,
they are played on the first and second 16th note, then shifted to the second and third, then to the third and fourth and,
finally, to the first and fourth 16h notes.  Remember, try to hear the tapping of the foot and the playing of the upper rhythm
as two separate entities, not a composite rhythm; I can't stress that enough.
So, by now you get the idea of how to derive all the variations.  Try to do a similar thing to the examples above
with groupings of three 16th notes.  Once you have those down, you're ready to get into an actual polymetric
example like the one below.  Here, we're taking a rhythm in 3/4 and playing it "against" a 4/4 time feel.  You
can also look at the example below as if it were a 3/16 rhythm (where you're only playing the first of the three
16th notes) against a 4/4 feel.  Remember to hear the two distinct rhythms.  If it's difficult, take it slow and
break it down into a composite rhythm at first.  Then, when you're pretty comfortable, you can play it at a more
flowing tempo and focus on hearing the two time feels distinctly.
Now, we have idea below that is similar to the one above, except there are more notes being played.  
One way to view this is as a 3/16 rhythm were the first and third of every three 16ths are being
played while you rest on the 2nd 16th.
So, now you're ready to try polymetric ideas involving grouping of fives.  Below is one thing that I
used to practice when first learning a new grouping.  The basic idea is to play constant 16th notes
while accenting the first of every group of five 16ths.  In other words, in the first measure below, you
would accent on the first 16th of beat one, the second 16th of beat two, the third 16th of beat three
and the fourth 16th of beat four.  In the second measure, you wouldn't accent at all in beat one, then
you would accent the first 16th of beat two, and so on...  Also, while you're accenting this way on your
instrument/hands, with your foot tapping, you're going to accent on the first beat of every measure of
4/4.  This will make sure you're feeling the two rhythms as separate entities.  Try it out.
Next, after getting the 5/16 "against" 4/4 feel down, let's make the rhythm more jagged.  This
time, we'll be playing the first, third and fifth 16th notes of every grouping of 5/16.  Continue
to accent on the first 16th of every 5/16 grouping and accent with your foot on the first beat
of every measure of 4/4.  Take it slow and focus on hearing the two distinct rhythms.
As a final example, let's take a grouping of 7/16 "against" 4/4.  Use what you've learned to build
a feel for 7/16 "against" 4/4 then try the example below.  This one involves playing only the first,
fifth and sixth 16th notes of every grouping of 7/16.  When you can do this one, you have a
good grasp on the basic concept of polymetric thought.
As always, I encourage you to come up with your own variations and ways of doing things.  There
are a multitude of exercises and ways to practice polymetric ideas; I've presented one way that
worked for me.  I hope that you've been able to gain something from this lesson, and, most
importantly, that you apply it in your own craft.  These kind of ideas are very unique and can widen
the scope of a musical idea significantly when applied in the right context.  Good luck and stay
tuned....
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