In my Astrological Nativity:
In Sidereal Zodiac
Sun/Mercury in 17'29 Libra (11'50 Scorpio in Tropical)
Jupiter/Uranus in 17'26 Libra (11'47 Scorpio in Tropical)
I have these midpoints in conjunction.
Two Midpoints in conjunction or opposition is what David Cochrane refers to as an Isosceles Trapezoid
Iso-Trap for short
An Iso-Trap is a life-building structure. It has a double-resonance. It is impossible to have a single resonance. As soon as there is one resonance (two pairs of planets having the same angle), there are automatically two resonances.
An IsoTrap is an extremely powerful harmonic pattern and is very important in astrological interpretation!
ISOSCELES TRAPEZOID:
An isosceles trapezoid is a four-sided figure which has two opposite sides of the same length, and the shape is vertically symmetrical. Note that an isosceles trapezoid is similar to a parllelogram, but has very different properties from a parallelogram. A parallelogram has 4 parallel sides and does not have symmetry, except in the case of a rectangle. A rectangle is simultaneously a parallelogram and an isosceles trapezoid.
One can view the double pairs of angles in an isosceles trapezoid as a huge resonance; from the viewpoint of wave theory, then, there is as a double-resonance, which in turn creates a huge astrological resonance. One can argue that this double resonance, from the standpoint of wave theory (or harmonic astrology, which is founded on the concept of waves), is far more powerful than the usual application of wave theory to support the concept of minor aspects.
The isosceles trapezoid is an elegant concept that integrates many seemingly disparate astrological concepts, such as midpoints, antiscia and solstice points, Jonas birth control, Vedic tithi returns, the traditional aspect patterns of grand trines, grand crosses, mystic rectangles, and yods, and even the very popular composite chart that was introduced in the 20th century. The isosceles trapezoid was identified by the founder of the Hamburg school of astrology Alfred Witte. Witte referred to isosceles trapezoids as planetary pictures. Rather than find the fourth point that makes an isosceles trapezoid (an Arabic Part), Witte interpreted isosceles trapezoids that occur in the chart. He did not, to my knowledge, emphasize the geometric shape or the fact that planetary pictures and Arabic Parts are mathematically identical; he was more intrigued by the symmetry that planetary pictures have. Symmetry is always created when there is planetary resonance, so Witte is correct; whether one prefers to focus on the symmetry or the resonance, one is actually identifying the same phenomenon. Planetary resonance is based on wave theory, which allows an even wider number of astrological influences to be integrated into a single conceptual framework.
An isosceles trapezoid mathematically is simply a midpoint conjunct or opposition a midpoint, and a list of midpoints conjunct and opposition midpoints is a good way to view them. My observations indicate that an orb of only about 1/2 degree is used for aspects to Arabic Parts and for midpoints conjunct midpoints, so I look at them up to about a 1 degree orb but pay close attention to only those configurations that are within about 30 minutes orb. Evidently the planetary resonance occurs only when the angular distances are nearly identical.
astrosoftware.com/ArabicParts.htmDistance between Mercury and Jupiter - 19'56
Distance between Uranus and Sun - 20'02
Distance between Sun and Jupiter - 32'56
Distance between Uranus and Mercury - 33'02
Astrologically, what makes an Isotrap very powerful, not only is the Uranus-Sun angle the same as the Mercury- Jupiter angle by definition that's what makes it an isotrap, but the Uranus-Mercury angle is the same as the Sun-Jupiter angle so it's this powerful force of nature that whenever to planets have this resonance between them (resonance created by the angular distance being the same), there's another resonance. You always get a double resonance.
My Isotrap is made up of two Golden Mean midpoint structures, and so I have a Silver Isotrap.
The distances that I listed are actually aspects.
Mercury seminovile Jupiter - '03
Sun seminovile Uranus - '02
Sun undecile Jupiter - '12
Mercury undecile Uranus - '19
Seminovile is 20'00 aspect, and it is 18th harmonic aspect. It is half a novile. It will appear as a conjunction in the 18th harmonic chart and an opposition in the 9th harmonic chart.
Undecile is 32'43 aspect, and it is 11th harmonic aspect. It will appear as a conjunction in the 11th harmonic chart.
Sun at the Golden Mean point of Jupiter and Uranus - .37
Mercury at the Golden Mean point of Jupiter and Uranus - .57
The orb is 1 percent based on proportion of angle.
Sirius Astrology software:
Suppose that "Proportion of angle" is selected with an orb of 1 percent. In the example given above of two planets separated by 30 degrees, the orb at the points along the shorter angle of 30 degrees is only 18 minutes while the orb along the larger angle of 330 degrees is 3 deg 18 min. Proportionate orbs ensure that the focal planet is relatively close to the golden ratio point regardless of how large the angular distance is between the two other planets. If "Same for all" is selected, then all golden ratio midpoint structures have the same allowable orb. If proportionate orbs are selected, then the orb is displayed as the percent from exact, where a value .00 indicates an exact golden ratio midpoint structure and a value of 1.00 indicates a golden ratio midpoint structure that has the maximum allowable orb.
Jupiter at the golden mean point of Moon and Uranus - .23
Moon in golden mean aspect (137'30) Uranus - '22
Moon in golden mean of golden mean aspect (84'58) Jupiter - '08
I drew in blue lines to show Sun at the GM point of Jupiter and Uranus.
I drew in green lines to show Mercury at the GM point of Jupiter and Uranus.
There is a yellow line to show Moon and Uranus in GM aspect.
I drew in red lines to show Jupiter at the GM point of Moon and Uranus.
A golden mean aspect indicates that the two planets work together in a way that feels natural and instinctive. The energies of the golden mean aspect are so instinctive and natural that they are often taken for granted by the person.
The person expresses the GM Midpoint Structure in a way that is natural and easy. There is an instinctive talent for expressing the energy, but the person may channel the energies in a constructive way and positive way or a destructive and negative way. The person may not be motivated to pursue a path symbolized by the planets in the GM structure but rather more often use the facility given by the golden mean midpoint structure in some other area of interest. The GM midpoint structure indicates a way of being and a way of thinking, but not necessarily an area that person is motivated to master. The GM midpoint structure is deeply ingrained in the person and typically utilized in whatever interests and pursuits the person has.