Right Hand Rhythm Studies - 3 over 2
by Lucas Michailidis
When considering the meters of 3/4 and 6/8, we will notice that both consist of six eighth notes in total. The difference between the two lies in the way in which they are grouped.
Ex. 1
As we can see, the 3/4 time signature finds eighth notes grouped in three lots of two (resulting in three strong pulses) while the 6/8 - meter consists of eighth notes grouped in two lots of three (resulting in two strong pulses). Alternating between these two meters is known as hemiola and is a common practice found in African and South American music.
Having played these back to back, lets take the strong pulses of each meter and lay them on top of one another. The result is a polyrhythm known as 3 over 2.
Ex. 2
The way in which to master this combination of two simultaneous rhythms is by nominating one to each hand and tapping on knees, or different surfaces. Once the interplay of each rhythm is established, transfer your awareness to each hand, counting aloud the pulses. You should aim at alternating your count so as to reflect the separate rhythm of each hand without skipping or missing a beat. Walking is another excellent way of consolidating this exercise. Study of polyrhythm creates rhythmic acuity that will inform and deepen one's general musicianship immensely.
When applied to the solo guitar arena, polyrhythm offers a unique and under-explored way to create the illusion of separate voices.
Ex. 3
In Ex. 3a, we have assigned notes to each rhythm - the three is found on the top voice and is played with the index, middle and ring fingers (i, m, r) while the two is found in the lowest voice and is played with the thumb (p). Ex. 3b makes this more prominent by assigning a group of three separate notes to the top position while Ex. 3c goes one step further with the addition of two separate notes in the lowest voice.
Ex. 4
Examples 4 illustrate the same concept with a swapping of positions of each rhythm. The three is now situated in the lowest voice while the two is on the top.
You will notice that treating a simple arpeggiated chord in such a polyrhythmic manner results in a sweet, lilting sound that offers great scope for musical application. These exercises also make excellent studies for the right hand (although some right hand fingerings are marked, there are numerous possibilities available).
Be sure to explore the 3 over 2 polyrhythm fully, constructing further exercises, comping patterns and ideas for composition. Also be sure to vary the tempos alongside a metronome.
Now that we have acquired an understanding and mastery of the workings of this polyrhythm, let's take a look at how we can introduce another element into the mix- grouping. With the addition of note grouping, a deeper level of complexity arises, which opens up to some intriguing musical vistas!
Ex. 5
Again, we have the two located in the lowest voice, while the three remains on top. The interesting thing about this example is that while the top voice consists of three pulses, the actual pitches are grouped in two! (i.e., the pitches repeat their sequence after every two). As a consequence, it takes two bars for the cycle to complete itself.
Ex. 6
As seen previously, both the two and three is situated in the same position, but while the lowest voice consists of two pulses, the actual pitches are grouped in three. As a consequence, this cycle now takes three bars to complete.
Ex. 7
Again, both two and three are similarly situated but while the top voice consists of three pulses, the actual pitches are this time grouped in four. This cycle takes four bars to complete.
Let's reciprocate the voices so that the two is situated on top while the three is on the bottom. This creates a subtle difference worth our attention. We can now adopt exactly the same approach with grouping as previously:
Ex. 8
The pitches of the lowest voice are grouped in two resulting in a two-bar cycle.
Ex. 9
The pitches of the top voice are grouped in three resulting in a three-bar cycle.
Ex. 10
The pitches of the lowest voice are grouped in four resulting in- guess what?- a four-bar cycle.
Some closing thoughts…
Grouping a polyrhythm in such a manner can yield fascinating results. The constant, unexpected shifting of note groups tends to create an ambiguity that makes the 3 over 2 less obvious. This is under-explored terrain that can prove fertile ground in numerous musical areas such as composition and improvisation.
A cautionary note when dealing with music on such a mathematical level - be sure to let this material inform your music rather than making it your object desire. Numbers devoid of expression don't tend to count for much (pardon the pun). Our aim here is to relish the interplay of two simultaneous rhythms, while treating them as a springboard for further creative and musical sojourns.
By the way, don't forget to use your metronome.
Until next time,
Lucas
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