Harmonics

Referring to my previous post on fundamental harmonic structures, here's an example of how harmonics are related visually, as in art and architecture, and as the structure of music. Bach's Tocatta and Fugue in D Minor in this example. There's an underlying logic and meaning to creative patterns as shown in this piece. Others are at the Music Animation Machine. It's about patterns and how they construct themselves with wave interference such as one uses to create holograms. I'll leave out the Quantum Physics discussion for now. Or grab a copy of the Dancing Wu Li Masters that will take you through all of these concepts without laying any math on you.

Hint: just think of it as infinitely small bitmaps like you see in a pixellated photo. That's calculus...scary, huh? It's all patterns, which relate to each other in orderly fashion; refer to the Fibonacci sequence for the ordering principles in nature - and music!

Postscript: There's a great article and series at the New York Times that lays out the fundamentals of mathematical tools to describe what happens to numbers when they are manipulated in a very functional and graphic way.