Composing in Bach’s Style Using Mathematical Transformations

We propose a new method for music composition in the style of Johann Sebastian Bach, using geometrical transformations of the plane. The method consists of analyzing a classical opus, identifying the motif, and mapping the occurrences of this motif and its transformations throughout the original work. Then compose a new musical motif and use this map to create an entirely new piece while preserving the motivic structure and the style of the original composition. We provide an example in both musical notation and audio format.