A honeycomb shaped lattice is the geometrical structure used to represent the recursively expanding relationships between major thirds and perfect fifths, from which a vast set of major and minor harmonic structures can be derived. Pure Tonal Harmonic Structures harmony is described as an outwardly expanding mathematical structure "The ancient Greek philosopher and mathematician Pythagoras, who is generally regarded as the founder of the first pure tonal system, held the outspoken view that the mathematical definition of musical tones was more important than the aesthetic effect when playing them. His chromatic system was based on a repeated stacking of the perfect 5th, which over the course of 7 octaves arrived at a tone that was significantly different from the intended destination, the 7th octave itself. Historically, his approach has been shared by many other great thinkers on the subject, but the emphasis has always been the creation of a cyclical and internally consistent arrangement of a discrete number of tones, which culminated in the invention of the equally tempered scale embraced by Johann Sebastian Bach; since that time, equal temperament has become entrenched as the de facto standard for Western music of nearly all genres."