Well, I'll give it a shot. First, though, I was originally inspired to do research on the Fibonacci Sequnce by several posts on this forum by Burger666. Here's a link to one of them.
http://forum.eventide.com/cs/forums/p/6880/30374.aspx
Basically, the Fibonacci Sequence is a series of numbers where the next number is the product of the previous two. Starting with 0, 1, 1, 2, 3, 5, 8, 13, 21, and so forth. The significance of this is that of any pair, dividing the larger number by the smaller number results in a number that approaoches the Golden Ratio with increasing accuracy. This ratio is apparently very pleasing to the senses as it appears in nature (nautilus shells, etc) and has been used since the ancient Greeks in architecture (Parthenon), art, and music, by people such as Pythagorus (math), Kepler (astronomy), and da Vinci (everything), to name a few. It is also used today in advanced search and optimization algorithms, financial analysis and prediction, and audio engineering, among others.
The reason I'm interested in this is because, to my ear, using delay times based on the Fibonacci Sequence result in delays that seem to fit regardless of tempo. Of course, that's just me and your ears may tell you something different. I simply find it as a good place to start.
There's a ton of information about both the Fibonacci Sequence and the Golden Ratio online, including, I'm sure, much better explanations than mine.
