# Difference of positions based on basic stoke breakdown of rudiments

### Published papers on the data:

For the study of snare drumming via motion capture, there are scaffoldings to anchor one's understanding of how mathematics could be used to decipher movement in a vector space. While some remediation may be needed (see remediation document here (paper), the application of mathematics and more specifically kinematic data to snare drumming can lead to some discoveries not easily proven through the eyes of a master. Although the eyes of the master are still relevant and important, motion capture supports the ideas practiced by those same masters. In other words, this motion capture study is not meant to replace the pedagogical practices; instead, the study is meant to enhance the practices of those masters.

While this particular combination of mathematics and snare drumming is novel, what is not new is the use of technology to enhance the understanding of technique. Sanford Moeller was one of the first to use the modern film of the time to share the practices of Civil War drummers (1). Even Jojo Mayer used film to expressed the lineage of Moeller (2).

The difference between these three drummers is minimal and mathematics helps in that analysis on the anatomical level. The goal for this exercise in analysis is to produce a reductive model of snare drumming. At this point, there is a linear model based on the positions over time; however, the more accurate reduction would be sine, or cosine, wave reduction of movement for every basic stroke and rudiment. While this may seem difficult, the data from the motion capture study supports the reduction to a certain point.

## Overall analysis through triangulation of movement

The triangulation of movement for the 3 drummers are based on the sequencing of positions over time. To review, the positions are as follows (The positions are synonimous to the five number summary used for statistical analysis: mode, median, maximum, minimum, and standard deviation):

1. Tap position: this position refers to the the placement of the shoulder, elbow, and wrist at the time where the stick contacts the drum. This can be analyzed through the relative minimum value of the wrist in the resultant vector.

2. Up position: this position refers to the placement of the shoulder, elbow, and wrist at the time where the wrist is at its relative maximum value in the resultant vector.

3. Rest position: this position refers to the placement of the shoulder, elbow, and wrist at the time where the wrist shows at least two consecutive frames of the same position. In other words, the rest position refers to the mode, or repeating number in a data set.

4. All trials are transformed to have a zero as their median value. In other words, all anatomical markers and vectors are calculated with a zero for the median value. This algebraic transformation allows for the analysis of the anatomical markers to be analyzed in terms of intersections.

5. The standard deviation for each trial, anatomical marker, and vector allows for the analysis of consistency of movement. All anatomical markers in their vectors have a value for standard deviation for the entire trial and for each position listed above.

### Basic Strokes

The first phenomenon to be explored is the set basic strokes. To review, the basic strokes are composed of positions: rest position, up position, and tap position. Each basic stroke orchestrates around the positions for snare drumming. In terms of logic, it can be said the the positions are a set of elements of the set of basic strokes. Furthermore, the rudiments are composed of basic strokes; so, it can be said that the rudiments are a subset of the basic strokes. To summarize, the basic strokes are a superset of the positions and basic strokes.

The following are the arrangement of basic strokes via positions:

Basic Stroke Types: Full, Up, Down, Tap, Buzz

Full Stroke: Rest->Up->Tap->Rest

Up Stroke: Rest->Tap->Up->Rest

Down Stroke: Rest->Up->Tap->Rest

Tap Stroke: Rest->Tap->Rest

Buzz Stroke: Rest->Up->Tap(n)->Rest

The Full Stroke

Full Stroke: Rest->Up->Tap->Rest

The full stroke has many variations among drummers. For the 3 drummers in this experiment, the full stroke starts at the up position, travels to the tap positions, and finally returns to the up position.

Alternative Full Stroke Sequence: Up->Tap->Up

Here are videos for each of the drummers in this trail:

For all videos and data for M_Drummer, see the links below:

(No Trial Present for N_Drummer)

Note: M_Drummer does not have data for the full stroke. However, M_Drummer does 'flash' his rest up position. This could be used for data, but this position can be analyzed through the other trials.

As seen above, each drummer (except M_Drummer) has an average of positions and a standard deviation. As a method of analysis, the data will be reduced to a triangulation; meaning, the positions in time are used to construct a linear approximation. Time will be represented by frame count and position will be represented through the transformation matrix where the median of each anatomical marker and vector is equal or approaching zero.

As seen in the triangulation of the full stroke trial for N_Drummer, the analysis is based on the following values:

a. The average of positions in respect to time

b. The intersection of linear equations based on the position values

This process can be performed for each vector and anatomical marker.

B_Drummer Triangulation

As seen in the triangulation, B_Drummer does not return to the up position for the z-vector.

Each basic stroke will be analyzed in this manner. After this initial analysis, the rudiments will undergo a similar analysis based on positions.

Social Media

IG: RudKnowMusic

Book: Rudimental Coordination

1. Moeller, S. A. (1950). The art of snare drumming. Leedy & Ludwig.

2. Mayer, J. (Director). (2007). Secret Weapons for the Modern Drummer: A Guide to Hand Technique. [Film]. S.l.: Hudson Ltd.