The CEG Algorithm (Part I)

Abstract

This chapter presents the Center of Effect Generator (CEG) key-finding algorithm based on the Spiral Array model, starting from the idea of the center of effect (CE), whereby any sequence of notes maps to a point in the interior of the model. The algorithm is illustrated through a simple melodic example, “Simple Gifts” from Copland’s Appalachian Spring. Included are discussions on why the model works, and the principles behind the particular set of model parameters used in the test run. At each step, the algorithm reports the three closest keys, ranked by distance; a step-by-step geometric interpretation of the algorithm and a graph showing the evolution of the closest keys accompany the tabular results. A MATLAB version of the CEG code appears in Appendix B. An evaluation of the CEG algorithm follows in Chap. 5; the CEG method is applied to polyphonic music in MIDI (Musical Instrument Digital Interface) format in Chap. 9, and adapted to music audio in Chap. 11.

This chapter is a minor revision of the first part of Finding Keys (Chapter 5) of “Towards a Mathematical Modeling of Tonality” by Elaine Chew, an MIT PhD dissertation, Cambridge, Massachusetts (2000) https://dspace.mit.edu/handle/1721.1/9139