Wolfram Computation Meets Knowledge

Wolfram Summer School


Michael Dobbs

Summer School

Class of 2017


Michael Dobbs has bachelor’s degrees in physics and applied mathematics with a minor in chemistry from Sonoma State University. He has been working on computer algorithms for the ATLAS b-tagging project with the Stanford group at CERN and a Python program to simulate particle showers. Aside from his ardor for physics, he has a deep passion for combinatorics, philosophy and mathematical art.

His nonacademic interests include improvisation jazz drumming, martial arts and sculpting.

Project: Musical Rule Characterization & Composition

Goal of the project:

Create the rule space of L-scale notes with n neighbouring notes and observe the patterns and distributions created after a number of iterations on the space of initializations.

Additionally, create a list of enumerated primitives that act on musical notes and observe the structure and patterns that emerge when they are applied successively. This list will cover elementary actions such as inversion, retrograde, diminution and scale shifting. Furthermore, these rules will be applied randomly to create a musical composition.

Summary of work:

The note rule space was fabricated and enumerated for n neighboring notes. A histogram of time spent on a note throughout the iteration was created for arbitrary rules in the space.

Additionally, the list of primitives described in the “Goal” section was created and random compositions were made. Some variables implemented include the number of notes, tempo, type of instrument(s), and relative volume between the instruments.

Results and future work:

The 12-note rule space converges to a cyclic group of maximum length L in a maximum number of time steps of L. While the algorithmic composer exhibits musical structure, it is not guaranteed to be aesthetically pleasing.

Generalize the rule for scales of length L, consider chords and implement a probabilistic rule. Additionally, implement chord progression and drums in the algorithmic composer.



Wolfram Summer School | Champaign, IL, USA | July 3 29–July 22, 2022