Solunars by Aldebaran Sidereal Academy

Recent discussions on the Novien, combined with thoughts on the nature of aspects that I penned in mid-December, converged in the last 24 hours into a new mathematical model that explains, more simply and elegantly, why some aspect distances seem to work and others don't, i.e., why we have the aspects that we have.

As a preliminary, here is my current post on Astrological Structures: Aspects: Specific Harmonics
(This post gives my current best statement on "why some aspects and not others.")
viewtopic.php?f=10&t=1772#p11308

Second, here is a recent post (a theoretical examination of midpoints) in which I explained how aspects are not between points but are the angles between two circles of position. (It starts in the paragraph that begins with "Third -".)
viewtopic.php?f=10&t=5822#p43015

Familiarity with these two prior posts will make what follows easier to understand.

Understanding that probably there are additional aspect "families" based on other prime numbers - at least through division by 7 (since higher prime numbers start overlapping possible aspects too tightly) - we nonetheless know for sure that certain aspects exist. These include the five classic (Ptolemaic) major aspects, the octile series that Cosmobiologists have demonstrated and prove themselves in our own work, and the Novien-based occurrence of aspects every 10° (with very tiny orbs).

Not all of these operate in all contexts. For example, in most forecasting methods only the "2 series" (i.e., "hard") aspects are operative. This likely has to do with different characteristics of the aspect families, with the "2 series" (Opposition Family) having characteristics of action, change, or movement. Nonetheless, the question of "what works where" is separate from the question of what aspects exist.

Notice that the above explicitly excludes the semi-sextile and quincunx. Ancient astrologers called these inconjunct, or "no aspect." Also, my experience has been that they are at best unreliable and, more typically, simply inoperable unless extremely close. When these aspects are extremely close (say, under 0°40') they are examples of the 10° series (tiny blips within a zone of no aspectivity). I entirely embrace the idea that the 30° and 150° aspects are, as the ancients said, "no aspect." I'd like a model that inherently excludes them.

Digression to say a bit more about those aspects: It often has seemed to me that the semi-sextile and quincunx are so thoroughly "no aspect" that they represent null spots where aspectivity (relatedness) between the planets is wiped out - anti-aspects, so to speak. Aspects are all about aspectivity or relatedness between two planets (or sets of needs), so that (for example) an exact aspect between Mercury and Mars means a tight intertwining of information needs and power needs. It may be that the inconjuncts are so thoroughly "no aspect" that they represent a divorce of these planets from each other, an affirmative anti-connection. Early on, I noticed that Moon-Venus semi-sextiles or quincunxes tend to show a divorce from responsiveness to traditionally female matters, Sun-Mars inconjuncts an alienation from elements of masculinity, and so forth. - This all presumes, of course, that the aspect isn't close enough (0°20'-0°40') to be a legitimate aspect in the 10°-multiples series.

Until now, the model that has best described these "available aspects" to me is the one outlined here: viewtopic.php?f=10&t=1772#p11308

In brief: Aspect families are created from dividing the circle by prime numbers. Each family has its own unique "family traits," e.g., the OPPOSITION Family (division by 2: hard aspects) express activity, force, energy, and change, while the TRINE Family (division by 3: soft aspects) are placid, quiet, still, a status quo or lack of visible change.

After dividing the circle by the prime number, successive tiers of aspects are formed by successive halving of an aspect until the effect becomes slight enough to drop off. Thus, the OPPOSITION Family divides the circle by the prime number 2 to get 0° and 180°, halves it to get 90°, halves it to get 45° multiples, then drops off. The TRINE Family divides the circle by the prime number 3 to get 120°, halves it to get 60°, then from a mixture of dropping off and the increasing rigidity and "stuck-ness" of the 3 Family, hits rigid, unmoving effects in the 30° series that adds the 30° and 150° s nearly anti-aspects.

Then, as a third step, I separately note that all 10° multiples are valid as a consequences of Novien effects.

This model is pretty smooth, and yet has a couple of spots that seemed like I had to force things a little. First, the excuse on why the 30° and 150° are so flat is consistent with the nature of the aspect family but did require an extra excuse. Second, the acknowledged 10° series is a tack-on that seems to fall outside the rest of the model, perhaps by the excuse that, "Well, these exist in the Novien, so I guess it's cool." But these are unnecessary soft edges.

The last few days, a different model has been forming in my head. It doesn't require the kludges.

First, though, you have to understand that aspects are angles formed between circles of position, which I described at https://www.solunars.com/viewtopic.php? ... 822#p43015

Planet positions along the ecliptic are formed by a great circle passing through the planet and through the ecliptic poles. (Another way to say this is that the great circle is at right angles to the ecliptic.) But - something usually ignored - this is not a semi-circle but, rather, an entire great circle! It wraps clear around the celestial sphere in the same way that (on an Earth globe) the circle marking longitude 15° East is the same circle (continued around the other side of the globe) that marks 165° West longitude. Or, as another example, the circle that drops through my Moon and crosses the ecliptic at 27°24' Aquarius - since it's a full circle - wraps around the celestial sphere and also crosses the ecliptic at 27°24' Leo. These are the same circle...

There are numerous implications for aspects arising out of this articulation. For example, it means that conjunctions and oppositions are essentially the same aspect - they are formed along the same circle of position. There isn't any need to detail the rest at this point. However, it IS necessary, for the current post, to explain how this impacts midpoints.

Given this understanding, the formula then becomes: Divide the circle by a prime number and then again by the same prime number. This has some surprising (and satisfying) consequences!

OPPOSITION FAMILY. Divide the circle by 2. This gives (alone or in the circles of position view) the 0° and 180° aspects. Divide this again by the same prime number (2) to get the 90° aspect. This can be halved, giving all multiples of 45° (45° and 135°).

TRINE FAMILY. Divide the circle by 3. This gives the 120° aspect and (because this is the angle between two circles of position instead of two points) the 60° aspect. Then, divide this again by the same prime number (3) to get the 40° aspect (and, again, because these are circles of position, this includes all 20°) multiples. This can be halved, giving all multiples of 10°.

In these simple moves - divide by 2, then 2 again, then halve it, and divide by 3, then 3 again, then halve it - we have all aspects listed above. Additionally - something I find very cool - we don't have to explain away the 30° and 150° because they don't even appear in any of the numerical series (except to the extent they are merely on the 10° multiples). Finally, there is the benefit that the Novien-derived aspects simply appear with all the rest without doing anything separate, special, or variant.

That's my theory for now.

(I keep thinking there are clues to the zodiac's structure in this kind of thought, but I haven't cracked it yet.)

This makes sense. I like it.