Ok, this is not strictly music based, but urgh, I do get annoyed with all the mysticism and nonsense around the Fibonacci series and the Golden Ratio...and it's time to bust a few myths...
Fibonacci series: 1,1,2,3,5,8,13,21,34,55,89....
Golden ratio = 1.618033..
There's something uniquely special about the Fibonacci series' ability to generate the golden ratio by dividing two consecutive numbers
> There isn't actually anything special about the Fibonacci series' ability to generate the golden ratio in this way. ANY series of consecutively added numbers increasingly approximate the golden ratio as the numbers get bigger:
2/1 = 2
3/2 = 1.5
5/3 = 1.667
21/13 = 1.615
89/55 = 1.618
Lucas' numbers (starting numbers 1 and 3): 1,3,4,7,11,18,29,47,76,123...
18/11 = 1.63
29/18 = 1.611
123/76 = 1.618
Random pair (let's start with 5 & 12): 5,12,19,31,50,81,131,212
212 / 131 = 1.618
So when people measure the Parthenon and the human body and magically find 1,3,5,8 everywhere, it doesn't prove a thing. They could be looking for 1,4,7,11 or 5,12,19. Look hard enough for small enough numbers in hard-to-accurately-measure things and you will find what you're looking for - and that's Numberwang!
There's still something oh-so-special about the Fibonacci series and the Golden Ratio.
The Fibonacci series isn't even the best or most logical series to use if you're really insistent on the whole adding-consecutive-numbers-together-to-get-the-golden-ratio thing. You should be using the Lucas series as shown above, and for a very interesting and cool reason:
> Lucas' numbers (starting numbers 1 and 3): 1,3,4,7,11,18,29,47,76,123...
> Now, let's raise the Golden Ratio to its subsequent powers and round them off:
Phi ^ 1 = 1.618 (phi being the Greek letter for the golden ratio, raised to the power 1)
Phi ^ 2 = 2.618 ~ 3
Phi ^ 3 = 4.23 ~ 4
Phi ^ 4 = 6.85 ~ 7
Phi ^ 5 = 11.09 ~ 11
Phi ^ 6 = 17.94 ~ 18
Phi ^ 7 = 29.03 ~ 29
Look! Raising the golden ratio to subsequent powers produces a series of numbers that approximates the Lucas series.
And if that's not Numberwang I bloody well don't know what is.
Thanks to a chapter in Matt Parker's 'Things to Make and Do in the Fourth Dimension' which the above intel comes from.