In the words of Tymoczko, "To combine harmonic consistency and conjunct melodic motion is to utilize short-distance line segments between structurally similar chords, and this is possible only if we exploit some unusual feature of the geometry: either the global "twist" by which opposite faces are identified, or the boundaries that act like mirrors" (Tymoczko, 392). To truly understand music and how harmony and melody work in tandem, one must understand how mathematics has been pushed to the extremes. Mathematics allows a boundary in music. The first thing that is taught in a composition class is the necessity of learning the rules before one can learn how to play with them. Mathematics gives a computational foundation to music, which allows creativity to flow within tonal pleasing bounds. Mathematics is the organizational system by which the world runs, and music is no different.