By John Max McFarland
Each year, the art of marching percussion evolves exponentially. The skill level of today’s students as well as the visual and musical demand on them is drastically higher than it was several decades ago. What was considered college level literature and musical vocabulary at that time is now becoming common place in high schools and even junior high schools. This evolution and expansion of the musical palette has given way to the inclusion of advanced rhythmic patterns, on top of the standard 40 rudiments. One recent musical development in this idiom has been the use of the “nested tuplet” or, in other words, borrowed division within borrowed division.
The most common use of nested tuplets is the non-tuplet, (fig.1) which is essentially nine notes spread evenly over two beats. The non-tuplet can be grouped in many ways, but the most common occurs in three groupings of three. This particular grouping, or feel, can be reimagined as 8th note triplets within quarter-note triplets (fig. 2). To many younger students, the idea of rhythmically executing nested tuplets while maintaining the quarter note pulse with their feet can be a bit overwhelming. I’ve tried many ways to attempt to explain these advanced concepts to students and the most affective and accessible explanation I’ve coined “The Inception Method”.
Inception refers to the 2010 film starring Leonardo DiCaprio. In this film, DiCaprio’s character develops dream-sharing technology, in which he uses this technology to sneak into people’s dreams and steal their classified information. In one attempt, the characters go deeper by sneaking into someone’s dream followed by sneaking into the dream of someone within that first dream realm. As the characters sneak further into each dream realm time moves relatively much slower. This concept of time’s relatively as it relates to each dream realm became the catalyst of “The Inception Method”. (Fig. 3)
Using the non-tuplet (triplet within a triplet) as an example, one must start with the original pulse or “beat”. The original pulse follows as normal; in this case the quarter note gets the “pulse”. (fig. 4) Coincidentally, this will also be the pulse in which your feet move or mark time to. The original pulse would be analogous to someone existing in the natural world, prior to moving into the dream realm. Once that pulse is established, the next step is taking a look at the first instance of borrowed division, or the first dream realm.
The first instance of borrowed division occurs with the 3:2q. Under normal circumstances this borrowed division would relate to the original pulse simply as a quarter-note triplet (fig. 5). It’s important to review this 3 against 2 pattern with your students before moving ahead. An effective method would include marking time and clapping the quarter-note triplet pattern to get comfortable with the relationship of the hands and feet. However, in order to properly interpret the next level of borrowed division in the nested tuplet we have to go deeper and dive into the first “dream realm”. Within this new dream realm the quarter-note triplet now becomes our “pulse”. You can equate this to a 3/4 bar in which the quarter notes are now going in the same speed as the quarter note triplets (fig. 6). As a demonstration, try counting the quarter-note triplets in a normal fashion (trip-o-let) and then try counting them as the pulse (1, 2, 3). Once that quarter-note triplet grouping is firmly established as the pulse, then we can focus on the second instance of borrowed division.
The second instance of borrowed division indicates that you are playing triplets within the quarter-note triplet pulse. Simply put, these would be like playing 8th note triplets in the dream realm (Fig 7). When students get familiar with the pattern within the dream realm pulse, you can then start to work backward and work the coordination of the feet with the now completed nested tuplet (Fig 8). A really good strategy to help practice this with your students is to have everyone start by clapping the quarter-note triplet while marking time to the quarter-note. After that pattern is comfortable, have one person play the full pattern while everyone else is playing the quarter-note triplet. Eventually, with enough repetitions, the student should be able to feel this pattern and, thus, keep a connection with the natural world while simultaneously dipping into the dream realm.
Once a student is familiar with this concept they can explore other combinations of nested tuplets. If your students are taking that plunge, it would be advised to make the first instance of borrowed division something they are more familiar with (in our case, the quarter-note triplet) and then add different tuplets or subdivisions within that pulse (Fig. 9). The combination possibilities are only limited by your imagination. It’s a great way to get your students to rhythmically think outside the box and it will offer more options for vocabulary when arranging/composing music for your student ensembles. Have fun!