Math

There are a few projects under development. One project consist of motion capture analysis of percussion; another deals with a mapping of western harmony to a cartesian plane. These projects were developed through a daily geometric practice I started in 2015 and tapered off in 2023. Most of these works can be found here.

Select Journals are available for some of the experiments.

For the motion capture experiment, the current focus is on analyzing a few projects relating to snare drumming. One project deals with 3 different drummers compared via basic strokes and selected rudiments. The other project is one drummer over a course of about a year (3 experiment dates total). Both projects are analyzed in a similar manner; where the positions for each snare drummer is taken into account. Positions for snare drumming, as it relates to this experiment, detail aspects of the five number summary found in high school pre-calculus classes. These statistical occurrences are minimum value, maximum value, mode, median, and mean with standard deviation.  For the minimum value, the displacement data displays two positions within this portion of the 5 number summary. Both the tap position and the rest position, are represented by this minimum value in relation to displacement within a certain vector. For the maximum value, the wrist is analyzed to have range of values for the up position. These two values, maximum and minimum, provide insight into the displacement of the positions: up, tap, and rest. 

The basic strokes can be analyzed as different arrangements of the positions; while the rudiments can be seen as different arrangement of basic strokes. 

Project Outline

1. Motion Capture Studies

   1. Comparative Study of Three Drummers

   2. Comparative Study of One Drummer Over One Year

   3. Drumset and the Application of Snare Drumming Data Analysis

   4. Guitar as a Percussion Instrument

   5. Dancing as Technical Development

2. Cartesian Mapping of Chords and Scales

   1. Theory of Mapping

   2. Mapping of Inversions of One Triad

   3. Mapping Chord Progressions

      1. One Chord in Different Positions

      2. Two Chords in Root Position

      3. Three Chords in Different Positions

   4. Use of System in Writing

      1. Examples of Compositions

      2. Applying the System to Blues

      3. Coordination, Harmony, and the Piano

NOTE: Some links are to music examples while other links are to ResearchGate for papers and GeoGebra for music theory. 

Lab Notes