*nested sine curves*. Maybe someone else would like to play with this?

Here's the basic thing: The five aspects 0°, 60°, 90°, 120°, and 180° are actually

*exact event fourths*of the scaling of a sine wave. That is, measured on the slope of a sine wave (or, turned inside out, a cosine wave, actually), the half-way spot between 0° and 90° isn't 45° - it's 60°! Same with the trine as the "midpoint" of the square and opposition. Here are the cosines of each of those angles.

0° 1.0

60° 0.5

90° 0

120° -0.5

180° -1.0

They are even intervals. First of all, this defines the importance of those angles and the way they form a numerical set. Second, I thought if I could generate another "strength" curve that used the intervals of the cosine curve as its argument, I'd have nested sine waves describing a complete aspect model.

In theory, it's simple; however, getting the bugs out of it is not simple. You can't, for example, multiply the number of degrees before taking the function; rather, you have to use the multiplied cosine itself as the argument of a different formula. But the slope coming off the conjunction and opposition are so slow that it gives gigantic orbs to those two aspects, even though the sextile, trine, and square have quite reasonable orbs that approximate observation.

Here's how far I've gotten: Calculate the cosine of 2 x the angular separation for values 0 through 180. (You could do 0 to 360, but one doesn't need to do that.) This will be a value ranging from -1 to +1. I then want to multiply this by 360 so that the scaling of the sine curve is transferred to a full circle, from which I will

*again*calculate a "strength" score. The formula for all of this is: (COS C +1)/2

You get a graph like the one below. Notice that the five aspects are precisely defined, their strength scaled from 0 to 1 (call it 0% to 100% if you like). For the three central aspects, the orbs are reasonable: a square drops below 99% at about 1°, 90% at about 3°, 75% a little before 5°, and 50% at about 5°. The trine and sextile are similar.

But the conjunction and opposition … whoo! They stay at 99% out to 10°, 90% at 18°(!!!), then drops more rapidly to 75% at 23° and 50% at 31°. This (ahem!) does not match observation!

Anyway, I thought I'd share how far I got in case it catches anyone else's imagination.