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Polyrhythms (was Re: Meditations on the awful sounds of the Alesis SR-16 drummachine)

Mark Hamburg wrote:

> On the other hand, this same bass player would tend to look at me with a
> sort of "what? are you kidding?" look when I'd program in drum loops 
> a cycle of 2 against a cycle of 3 against a cycle of 5 etc..
> By the way: When people on this list talk polyrhythms, do you generally 
> multiple ways of dividing a single bar of music or multiple bar lengths?

The term "polyrhythm" certainly is a loaded one.  I suppose in its widest 
sense "polyrhythm" can mean any contrasting rhythmic patterns in music.  
So technically, triplets played over a backbeat could be considered to be 
polyrhythmic.  Of course this is such a standard pattern that no one 
thinks twice about using it.  Another standard practice, as Mark 
mentioned, is dividing the accents within a single bar.  For example, 
breaking a bar of 4/4 into three groupings of eighth notes as 3/3/2 or 
2/3/3 or 3/2/3.  Again, an everyday occurrence.

The next level of polyrhythms would be along the line of "compound" 
rhythms like 6/8, where the count is divided into two equal groups of 
three.  Generally you'd tap your foot on the 1 and the 4, which creates a 
nice tension between a feeling of duple and triple meters.  This also 
occurs in 9/8 and 12/8 rhythms when they're evenly divided into groups of 
three.  For instance, Irish "slip jigs" in 9/8 still have very much of a 
waltz-time feeling, being three equal groups of 3.  

Another term that you sometimes see for "polyrhythm" is "cross rhythms."  
This is more what Mark means by the "cycle of 2 against a cycle of three 
against a cycle of 5."  Let's start a little bit simpler, with 4 against 
5.  In this instance, you would have 2 contrasting time signatures 
occurring simultaneously.  Although this can be achieved by a single 
player, it's easier to visualize this polyrhythm as a duet.  Drummer A 
will be playing in 4/4, accenting only the 1.  Drummer B plays in 5/4, 
also accenting only the 1.  What happens is that after the first four 
beats the rhythms go out of phase with each other, so that you're hearing 
each drummers' accents on 1, but they're occurring at different times.  
After 20 beats (four measures of 5/4 and five measures of 4/4) the rhythms 
will again coincide on "1" (the twenty-first beat) and then begin to 
diverge again.  This too creates an interesting tension between the two 
separate time signatures that resolves on beat 21.

My training is in North Indian classical music, where this type of 
polyrhythm (or cross rhythm) is very common.  In Hindi this is called 
"layakari" which literally means "rhythm work."  Part of the reason for 
its popularity is that there is no harmony in Indian music, only rhythm 
and melody, so this is one way to add variety to the music to keep it more 
interesting.  There are many ways to do this.  For instance, in plucked 
stringed instruments like sitar or sarod, there are a set of openly-tuned 
rhythm strings ("chikari") which are used to create various rhythmic 
patterns.  In an extended performance, one would play a long solo section 
before joining together with tabla to play compositions.  In this solo 
section of three movements ("alap-jod-jhalla") the second two movements 
are exclusively rhythmic.  Although there is no set meter in these 
sections, a pulse is present and the rhythms become increasingly more 
dense over time.  Again, in order to keep things interesting, the soloist 
will vary the stoking patterns using cross rhythms.  For instance, a 
typical pattern across 8 counts would be: 3/3/2.  This can get doubled 
into 3/3/2/3/3/2 or further divided into many variations, e.g., 
3/3/3/3/2/2 or 2/2/3/3/3/3 or 3/2/3/2/3/3 etc.  Generally this is done by 
systematically playing through a large number of permutations, usually in 
a logically flowing order.  Using one or two counts of silence within the 
pattern is still another way to create tension and maintain interest.

After playing any number of increasingly dense rhythmic patterns, the solo 
section comes to a frenzied conclusion.  After this, the soloist begins to 
play precomposed material (with continuing improvisations) in a strict 
time signature ("tala") along with the tabla player.  This too leads to 
much polyrhythmic interplay.  Generally what happens is that the tabla 
player maintains a steady stereotypical rhythmic pattern (called "theka") 
over which the soloist plays the precomposed melody and variations.  At a 
certain point the soloist will begin the "layakari" usually starting with 
simple cross rhythms.  In North Indian music the most common rhythmic 
cycle is 16 beats (called "tintal").  The tabla player marks out the 16 
beats (subdivided into four equal groups of 4).  So the soloist may begin 
by playing patterns of 3 against those sixteen beats, similar to the 
"triplets over a backbeat" mentioned above.  The next round of rhythmic 
interplay usually goes to a more complex pattern, such as 5 against 16.  
In actual practice this becomes more like 5 against 4.  However, instead 
of having a perfectly interlocking and meshing rhythm, usually the soloist 
will "tie up" the loose ends by filling in the remaining beats.  For 
example, if the soloist is playing in a 5 against 4 pattern within the 16 
beat cycle, he will play the contrasting pattern up to beat 30, then play 
the remaining two beats normally (to round out to 32 beats, i.e., 2 cycles 
of 16).

One of the most remarkable performers of this style of playing is the 
great santur (hammered dulcimer) player, Pandit Shivkumar Sharma.  Pandit 
Sharma had extensive training as a tabla player before choosing the santur 
as his preferred instrument, and this certainly shows in his elegant, 
precise, mathematical layakari.  I've seen him perform brilliant 
variations of 4, 5, 6, 7 and 9 beats against a rhythmic cycle of 11 beats 
(itself subdivided into four/four/one and a half/one and a half !) as well 
as all of these against a cycle of 15 beats.  Needless to say, he 
routinely plays such cross rhythms against the more common (for Indian 
music) cycles of 7, 10, 12, 14, etc.  I think what impressed me most about 
all of this was that he was playing melodically as well -- following the 
rules of the raga, while coming up with these dazzling crossrhythms.

The tabla player gets his turn too.  (Or as James Brown would say, "Give 
the drummer some!").  The soloist will cue the tabla player to perform a 
solo by playing the precomposed melody repeatedly.  What happens now is 
that the roles are reversed -- the melody keeps basic time for the drummer 
to improvise.  Often at this point the tabla player will play precomposed 
material from the solo tabla repertoire.  However, a sensitive tabla 
player might want to reinforce the idea of layakari, and so will begin to 
perform his variations on the rhythmic interplay.  Sometimes he will 
amplify on what the soloist has just played, at other times he may begin a 
new cross rhythm.  In a spirited performance, one might see a very taut 
back-and-forth exchange of polyrhythmic soli between the main 
instrumentalist and tabla player.

In solo tabla performance there is also a large degree of polyrhythmic 
play.  Usually there will be an accompanying melody ("lehera") which 
serves to keep time.  The tabla player will display various cross rhythms 
against the main cycle, in the same manner as noted above.  Some tabla 
players have also developed more "isometric" polyrhythms.  That is, they 
will play 2 contrasting meters simultaneously -- but not crossing bar 
lines.  In other words, the duration of time for the 2 meters is the same. 
 I've seen one phenomenal tabla player perform a solo simultaneously in 
"jhaptal" (10 beats) and rupak tal (7 beats).  What was most amazing about 
this was that the 10 beats fit perfectly into the same amount of time as 
the 7 beats.  This obviously depends on compressing the larger time 
signature slightly to occupy the same amount of time as the smaller.  It 
was mind-boggling to hear this kind of manual time-stretching.

Getting back to what Mark mentioned about having three or more contrasting 
time cycles:  I've been working on this type of polyrhythm for some time, 
for instance playing 3 against 4 against 5.  The same "falling out of 
phase" occurs here as well, except that it gets compounded by one 
additional factor, so that it will take longer for all the cycles to meet 
at "1."  This occurs at the "least common denominator" for all of the 
cycles.  For example, in 3 vs 4 vs 5, the rhythms come together after 60 
beats to resolve at beat 61, which will be the "1" for all three cycles (3 
x 4 x 5 = 60).  My earliest attempts at this sort of polyrhythm were 
miserable and unlistenable, due to trying to cram too much information 
into the rhythms.  It's much better to leave some space in each one, so 
that you can hear the contrasting patterns that arise from the 
juxtaposition, rather than a jumbled mess.

The EDP (to get back on topic) is a wonderful tool for this type of 
polyrhythm.  For instance, Record one measure of 4 beats, then Multiply by 
three.  Overdub a 3-beat pattern against the three measures of 4.  Now 
Multiply again to 60 (easier than ever to do in Loop IV -- thanks Kim, 
Matthias et al. for this godsend!) and Overdub a pattern of 5 beats 
against the existing polyrhythm.  It takes a bit of getting used to.  I 
personally like the off-kilter patterns that arise from this type of 
polyrhythm, as well as the feeling of "Where the hell is '1' !?!"

I don't have any experience with polyrhythms from African, Afro-Cuban, or 
Brazilian drumming traditions.  I'm wondering if some of the 
percussionists on the list like Dennis, Jon or Rick could share some 
insight on how rhythms are crossed in these traditions and/or any personal 
tips and tricks they have on polyrhythms?