http://www.projectavalon.net/forum/s...ead.php?t=9877
This is a link to Gregor Arturo posting of Fibonacci reborn, for some reason it did not copy his graphs and illustrations so go to the link to find out more. Phiedpiper did not know if you would have time to always look through all other postings on Avalon and thought this might be of interest to you.

made some interesting discoveries about the Fibonacci sequence recently that I think many of you may enjoy. I am pretty sure Marko Rodin has already discovered this but from what I have gathered myself, he doesn't share all of his work out in the open. First off, the sequence is not linear moving toward positive infinity. It is cyclical and actually consists of 24 numbers. Here's another one of those grand ole charts:

What's cool about this is the 24 number pattern is absolutely perfect and balanced, much more than what people had imagined. I'll explain that a little bit more on.

Anyways, as you move up the fibonacci sequence with any two consecutive pairs, that ratio of those pairs approaches phi (1.618), the golden ratio. However, in MOD9 (Marko Rodin's Quantum Numerology), it creates 24 unique ratios that are not approaching any constant/irrational number. If you take these ratios and apply them to a fundamental frequency, say 256 hertz (a perfect C), you get a full set of 24 unique frequencies. However, many of these frequencies are overtones of each other. Under the column "modified frequency" you can see where I take all the frequencies and their overtones and put them into the same octave of between 256 hz and 512 hz. When you do this you discover only 13 unique frequencies, while the rest are duplicates. With these new frequencies you can make a ratio of them with the fundamental frequency of C256 which creates a unique and interesting 13 note tonal scale. I'm going to rewrite the pattern here with the ratios changed a little to complete the pattern (compare with the set above and you'll see what I mean with the fractions).

256 1/ 1

288 9/ 8

292.57 8/ 7

298.67 7/ 6

307.2 6/ 5

320 5/ 4

341.33 4/ 3

384 3/ 2

*Right here the pattern changes over, which is the exact halfway point (384hz) in between C256 and C512

409.6 8 / 5

426.67 10/ 6

438.86 12/ 7

448 14/ 8

455.1 16/ 9

I've had one friend (ucan on Avalon) play around with them so far and he was rather delighted with the sound. Hopefully someone can make a piece of music from this and see what we can get out of it.

Now onto further patterns. The cyclical sequence consists of four 1s and 8s, and two of each other numbers of 2-9 (no 8 obviously). What I noticed is after the first 9, 3 appears twice before the next nine evenly spaced, as so with 6 twice on the latter half evenly spaced. And then it clicked. This furthered Marko Rodin's notion of 3 and 6 oscillating between nine and I realized the true origins of the infinity symbol.

In doing so, it inspired me to make a piece of art which the clever mind can easily decipher. Enjoy!

http://www.troubledeye.com/other/Fibonacci.jpg
You can create a triangles inside each circle of the infinity sign if you connect the trinity numbers (3,3,9 & 6,6,9).

Now if you look at the symbol, you will see that each number in one of the circles is the exact opposite of the other when in relation to Marko Rodin's circle of life.

1-8

2-7

3-6

4-5

9 stands alone as the central axis.

Now if you take the circle of life and connect the 24 number fibonacci sequence in sequential order so you draw a line from a 9 to a 1 (technically you pause on the 1), to a 2 to a 3 to a 5 and so on it creates a perfect symmetrical image.

It's interesting in that 4 and 5 are the only consecutive numbers that do not connect. If you do a diagram with just the first 12, then the second 12, they create opposite mirrors of each other.

Now if you connect the fibonacci numbers in a different technique by adding each one to the next (so it starts at 0, goes to 1, then 2, then 4, then 7, then 3, always going clockwise on the circle) instead of connecting to the actual number, it also creates the same perfect symmetrical image. However, this one does not line up on the nine axis, but instead it points to the eight (shifted to the left one step) but it still ends and starts on the nine.

Metaphysically, this shows the roots of how the yin and yang, masculine and feminine energies came from in how energy fields on a basic level oscillate. Marko Rodin talked about this but outside of his simple number patterns, I am not sure if he discussed this.

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