Nightlife:

Hans has referenced the bridge that collasped because the wind set up a certain resonance in the suspention wires that built upon itself until....blam.  Because of the nature of atoms, everything has a natual resonance. (I read that but can not recall where)  I believe that Keely, and some others, understood this far beyond what we know of today.

Bill

      Alright after even more research ive found yet more data that confirms that the a432 tuning is the only tuning that will produce creative harmonics. As well this gives the base theory of the diatonic spiral.  Notes and freq for the 432 tuning.

        288 D
        324 E
   360 F
   384 G
   432 A
   480 B
   540 C
   576 D


13.5.1  THE PHI SPIRAL

Fundamental to all studies of spirals is the most important of them all, known as the Golden Mean, Fibonacci or ?phi? spiral. To best understand this spiral, we start with the innately harmonic, vibrational way that it is created through number summing. Essentially, we will see that each new number is the sum of the previous two. Typically we start with one and add it to itself. That gives us a product of two. Then we take two and add it to the number before it, which was one, and that gives us three. Then we take three and add it to the number before it, which was two, and we get five. And on it goes as follows:

    1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89?

So, the numbers continue to expand in a simple, harmonic way, where each new number represents the sum of the two numbers that came before it. If we divide the above pairs of numbers into each other, in the earlier stages we will see all the common Diatonic musical ratios that Pythagoras discovered such as 3/2, 5/3, 8/5, 13/8 and 21/13. This should not surprise us, as music is a vibrational motion, and the summing technique used in phi is a form of vibration as well. The elegant nature of this vibration is easily seen in drawings of the ?phi spiral,? pictured below. To better understand how this spiral works with the Platonic Solids, it should be viewed as a three-dimensional object, as though it were wrapped around a cone with the top point at G and the bottom point at A. This type of three-dimensional spiral shape is called a ?conical helix.?

Fibonacci or "phi" spiral and geometric counterparts.

Although the early stages of the ?phi? number series will form the musical ratios between themselves, as the number pairs get higher and higher, the ratios between them become more and more similar, and the growth process stabilizes. Ultimately, as you go higher every pair of numbers in the series will divide together to form the exact same number, meaning that the ratio between all the numbers remains constant. For this reason, the ratio is called a ?constant? as it will always be the same, and the number, (which continues endlessly,) is:

    1.618033988749894848820?

Another interesting fact is that we can start with any two numbers, regardless of their difference, and begin summing them using the simple formula above. No matter how different they might be, within a short period of time we will again create the constant ?phi? ratio between the two of them. This entire concept has inspired countless generations of mathematicians, musicians, scientists and philosophers, as it mysteriously shows up in many different guises, including the growth proportions of plants, animals and human beings. As we have said, the musical ratios of ?phi? provide the structure for simple geometry in both two and three dimensions, which we now know is another form of vibration. The above diagram demonstrates this, as we can see that there are actually six isosceles triangles of identical proportions represented as the spiral continues to expand. The size ratio between each of the triangles will be the ?phi? constant of 1.618?, given above.