George Packard had always enjoyed music. Strangely, though, his life-long love of jazz and classical music had never intersected with his interest in mathematics.
Sure. The discovery (credited to Pythagorus) that the relationships between the notes of the diatonic scale were directly proportional to the lengths of the strings that created them (as well as to their measured frequencies as we know today) was one of the grand discoveries and revealed an astounding and fundamentally beautiful phenomenon, an epiphany.
Yet George could not take the musical math any further than that. The circle of fifths (pictured below), as well as those geometrical constructions and circular sliderules that transposed all the chord patterns, left George feeling flat (if one could use the use the word flat without striking a bad note!).
The main connection, the common ground between music and math was a system of patterns, mathematics being the science of patterns. There were clear and simple proportions that connected the pieces, the individual notes, with each other. The congruence between these elegant patterns and our aesthetic sensibilities were no longer quite so astounding to George. Octaves, fifths, fourths, relative minor sixths – all of them simple, “rational” proportions – were beautiful to the ear. Then again, the species, the human species, had evolved based on many of the very same mathematical underpinnings (in the genetic code presumably) as the rest of the universe.
The music of the spheres, the order to the universe, the unseen blueprint, the Grand Unified Theory, the TOA, the Theory of Everything – illusion or not – it remains a source of wonder.
That being said (as they say) and all the same, George couldn’t get much of a handle on the doggone circle of fifths thing.