Originally Posted by Robert Tulip

The division by twelve is far from arbitrary. The diagram I attached at http://www.bautforum.com/attachments...sine-waves.jpg expands on my basic claim that the twelve signs are the next level of physical cycle produced by the equinoxes and solstices. This underpins my objective to argue that the twelve signs are imbedded in the longer precessional cycle. The following explanation shows how the signs are a physical product of the second and third harmonics of the year.

Consider the year as like a bisected guitar string with one half the summer and the other half the winter months. A sine curve of this note (the second harmonic of the string) has wavelength one year. The third harmonic, trisecting the string, produces a curve double the blue curve in the attached, analogous to a regular four monthly rhythm trisecting the year.

Originally Posted by Robert Tulip

The periods of time when this curve is positive and ascending are the fire signs.

Originally Posted by Robert Tulip

Similarly, earth is positive descending, air is negative descending and water is negative ascending. These definitions are simply scientific, although of course the legacy of the elemental labels is unscientific, and as noted in my previous post, the ellipticity of the earth’s orbit produces a complexity regarding the precise location of the cusps. The next musical harmonic, dividing the string in four, similarly produces the pink curve in the attached. Again, the old concepts of cardinal fixed and mutable, known as the qualities, are simple mathematical products of this curve. If each segment of this pink curve is divided in three according to the sign list at the bottom of the table, the cardinal signs are those where the curve is moving away from its axis, the fixed signs are those where the curve stations, and the mutable signs are those where it is moving back to the axis.

Originally Posted by Robert Tulip

The interaction of these two simple waves over the course of the year produces the permanent twelve-fold rhythm which we call the tropical signs.

By contrast, divisions other than twelve are much weaker than even this weak fundamental harmonic composition. The attachment to my opening post http://www.bautforum.com/attachments...sics-signs.jpg makes this same point by another route – showing that the twelve signs arise from the simple main threefold division of the year at harmonic points to the solstices and equinoxes. Why is this not arbitrary? By this method we could also divide the year using higher primes such as 5 to produce 20 signs, 7 to produce 28, or even 401 to produce 1604. My point is that the mathematical rhythms produced by these higher divisions are so much weaker than the twelve-fold rhythm produced by division by three, and in any case the physical effect is so weak, that these higher divisions can be discounted. It is worth looking for empirical confirmation of the twelve-fold division before we say that this observation cannot be real because there are also more complex higher rhythms.