Teaching Nested Tuplets: The “Inception” Method

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!

Bass Drum Evolution

The evolution of marching percussion is punctuated: long periods of stasis followed by rapid changes, often brought about by a simple idea that spreads quickly throughout the drumline world. Competitiveness, and now the availability of online videos, are usually the driving forces.

Three popular changes in recent years are:

  • Bass drum playing zones
  • Bass drum tuning
  • Bass drum grip


Bass drum playing zones:

A bass drum has the same basic physics as any other drum – striking it in the centre is louder than if you strike the drumhead near the edge. Velocity and stroke height are often the primary, and only, way that ensembles vary their volume. To broaden the dynamic range of the instrument even further, players can strike the drumhead at the upper edge for a quieter sound with a longer sustain. This is usually done between the manufacturer’s logo and the drum hoop. The addition of playing zones to your bass ensemble will widen the overall dynamic range and textural palette.


Bass Drum Tuning:

There has been a big change in bass drum tuning in recent years. In the past there were relatively even intervals between the five bass drums. The overall pitch of the entire line has moved higher and higher with each decade. With ensembles tuning so high, the bassline started to lose its powerful sound when playing unison impacts. Many American marching bands have used six bass drums, and tuned the largest drum extremely low. This drum was utilized as the drumset’s “kickdrum” of the ensemble. It also plays the unison impacts – giving the bassline a strong sound. However, six basses may not be practical in many situations, and contemporary ensembles have moved to tuning the bottom (fifth) bass as low as possible (with added muffling to decrease sustain), while tuning the upper 4 as high as possible for maximum articulation and clarity. This is an exceptionally effective tuning method for indoor ensembles, and has quickly become the standard.

Bass Drum Grip:

The relationship of the players’ fingers and thumb to a bass mallet is the same as that of the snare and multitenor. The difference lies in the position the hand holds the stick along its shaft. Snare & tenor drummers hold a stick with the fulcrum (thumb and index) at the natural balancing point of the stick – approximately one third from the bottom. This results in a small portion of the stick/mallet protruding out the back of the hand. What is different for a bass drum is that the striking surface is on a vertical plain, and the head of the mallet has significant weight — changing the overall balance of the mallets. Performers should slide their grip down to the bottom of the mallet, with the butt of the stick flush with the back of the hand. This grip provides as a counterweight for the mallet, vastly improving player comfort, speed, and endurance.