Reflections & inquiries on angularity

[Jim Eshelman]

I want to start a conversation about a complex inquiry that has baffled me until now. Perhaps some of you have some insights or theories about them.

It begins, however, with something simple - something truly elegant. It may seem complicated until you fully visualize it, after which the pristine elegance shines through: The underlying model of all angularity is sheer simplicity.

In the next four posts, I'll first describe this simplicity and pristine elegance of the underlying model; then I'll raise two questions about it - two things that intrude upon the simplicity. I'll give my current thinking, which (I'm sure) will end in a quandary. Possibly just writing it out will give me insight, or possibly one of you understands (or can be triggered into understanding) the matter better than I do. Please engage!

The questions I will raise are my least favorite kinds of questions in astrology: They are "why" questions - "why is something this way and not that way?" Usually, "why" doesn't get us anywhere except airy intellection abstracted from observation. I've spent most of my time in astrology more concerned with what works than why something works the way it does, but sometimes we have to ask the "why?" questions, too.

[Jim Eshelman]

Our angularity model is three-dimensional. You can infer it looking at a two-dimensional horoscope wheel, but, to really understand it, you need to visualize a simple construct in 3-D: You need to visualize a sphere.

In what follows, please make sure you visualize what I'm saying - don't take it as an intellectual abstraction. I have three suggestions for how to do this: (1) Simply build the construct I describe in your imagination. The ability to do this plus the construct you build will serve you well. (2) Physically stand, facing south, and see what I'm describing about you. (3) Take a small Styrofoam ball and wrap three rubber bands around it to create a physical object like the sphere I describe (or take some other spherical object and draw on it).


The celestial sphere, so far as it relates to your local (mundane, on a particular place on Earth) context, is a sphere of infinite size with three mutually perpendicular circles called the horizon (H), the meridian (M), and the prime vertical (PV). "Mutually perpendicular" means each of them is 90° from the other. - I'll describe these visually: When you have them visualized, you will have the single, simple image that unlocks the rest. (I won't get overly mathematical, so I'll let a few details slide.)

Think of the horizon as similar to the equator on an Earth globe. (If you are making a physical ball, mark [drawing or with rubber bands] an equator-like circle around the ball.) It is approximately what you would see if you were standing at your spot on Earth with completely level ground in every direction and no buildings, trees, or other objects - a completely empty, level field where you can stare at the circle of the horizon about you - all the same - in every direction. (See/imagine this.)

Next, let's build the meridian. Start with the Zenith - the point directly overhead. (Standing, facing south, just observe the point directly over your head: If the horizon is like Earth's equator, the Zenith is it's North Pole.) See a vertical axis drop from straight above you (Zenith), through you, through the center of Earth, and out the other side: Where that comes out the other side is the Nadir. (If you are marking a physical ball, put dots for the "north pole" and "south pole" - the "direct above" Zenith and "direct below" Nadir.)

Now visualize a circle that passes through the Zenith, flows down in front of you to due south on the horizon, passes under Earth through the Nadir, and comes up behind you due north - then continues back up to the Zenith. (Where it crosses the horizon due south and due north are called the Southpoint and Northpoint of the horizon.) This great circle - including Zenith, Southpoint, Nadir, and Northpoint - is called the meridian. (Add a rubber band or draw the circle connecting these dots on your ball.)

Notice - in your imagination, or standing facing south, or looking at your ball - that the circle of the meridian and the circle of the horizon are at right angles to each other, much like Earth's equator and the circle of geographic longitude that is 0°00' E/W through London and 180°00' E/W on the other side of the globe. Notice that the horizon and meridian intersect in two places - at the Southpoint and Northpoint.

Next, we will construct the prime vertical. This is now easy: The prime vertical also passes through Zenith and Nadir, but rotated 90° from the meridian. It rises due east and sets due west. That is, the circle crosses the horizon due east (at Eastpoint), passes through Zenith, crosses the horizon due west (at Westpoint), flows under Earth through Nadir, and comes back up to the horizon's eastern point.

Adding this should now be easy: Add a third rubber band (or draw the third circle): The three circles will now all be at right angles to each other: horizon (H) is square PV in one direction, meridian (M) squares PV in the other direction, and H squares M in a third direction.

Or, stand facing south, arms stretched straight out at your sides (east-west). See (you can gesture as if to call it!) a ring of light rise from where your left hand points to on the horizon due east (Eastpoint). It rises over your head (passes directly overhead: Zenith), continues down the other side to where your right hand points to the horizon (Westpoint), continues underneath your feet (Nadir), and rises back to the horizon at Eastpoint.

Notice that as H and M intersect in two places (Northpoint and Southpoint), PV and M intersect in two places (Zenith and Nadir) and PV and H intersect in two places (Eastpoint and Westpoint). See these clearly.

Secure this visualization. Get it very clear in your mind. Practice walking around visualizing it all the time, consciously recognizing you're never out from under it. Notice as you move about in your life that you're always in the midst of the horizon circle - a personal "magick circle" that always goes with you - always with the meridian flowing between south and north, always with the PV flowing between east and west, no matter which way you turn. Get as used to this as you are to breathing or to detecting whether there is light or darkness around you. It's not only a good mindfulness practice, being aware of this will make almost everything about astrological angles more real to you and more obvious.

[Jim Eshelman]

Once you have that visualization, the hard part is over. The rest is simple. Understanding that you are at the center of an infinite-sized sphere circumscribed by the three mutually perpendicular circles of horizon, meridian, and prime vertical, you are ready to understand what the twelve angles of the horoscope are.

MAJOR ANGLES
The major angles are the three circles themselves. They are not points on the ecliptic that you see written on a horoscope but, rather, the three circles themselves.

The entire circle of the horizon composes Ascendant (the eastern half, where objects rise as Earth turns toward them) and Descendant (the western half, where objects set as Earth turns away from them). - Notice that Ascendant and Descendant are separated by the meridian.

The entire circle of the meridian composes MC (the half above the horizon) and IC (the half below the horizon). - Notice that MC and IC are separated by the horizon.

The entire circle of the prime vertical composes Vertex (the western half, both above and below the horizon) and Antivertex (the eastern half, both above and below the horizon). - Notice that Vertex and Antivertex are separated by the meridian.

This visualization makes clear what we mean by a planet being mundanely on an angle. It has nothing to do with the "degree of Ascendant" (or whatever angle) that you see on the horoscope. It has to do with whether a planet is on or near one of these three circles.

In this simple model, I'm using the term "major angle" to mean an angle that is actually a circle (or half-circle) - not a point.

MINOR ANGLES
In contrast, what (for this discussion) I call "minor angles" are all points. They aren't circles or semi-circles: They are single points. Specifically, they are the six points where the two circles cross each other (visualize this): Zenith and Nadir (where M and PV intersect), Eastpoint and Westpoint (where H and PV intersect), and Southpoint and Northpoint (where M and H intersect). Please see these six points on your physical ball and/or in your imagination.

Since these are points and not circles, it would be almost impossible for any planet ever to be exactly on them. Instead, like other points we use in astrology (e.g., planets), we take their celestial longitudes (zodiac positions). It just so happens (the way the math works on a sphere) that their zodiac positions are all exactly 90° from where one of the three circles crosses the ecliptic, i.e., ecliptical squares to major angles. (You can work out the trigonometry or take my word for it: It was the first spherical math problem Gary Duncan gave me to solve 46 years ago.)

What we observe with these points in practice is consistent with them being points, projected onto the ecliptic like a planet, that are capable of forming ecliptical conjunctions and have small orbs.

Another layer with Eastpoint-Westpoint
Eastpoint and Westpoint have a unique characteristic that the other minor angles don't have: They are also on the celestial equator. (They are the two opposing points where the horizon, prime vertical, and celestial equator all intersect perfectly.)

Positions along the celestial equator are measured in right ascension (RA), the equatorial measurement analogous to celestial longitude on the ecliptic. Therefore, another way to say what was in the last paragraph is: Of the six minor angles, EP and WP are the only ones that are also on the celestial equator. The result: We also measure contacts to them in RA, not just in longitude.



That's the whole system! If you aren't already comfortable with it, please take time to become comfortable with it - until it is second nature to you.

[Jim Eshelman]

That's the part I understand. It all fits together. It is satisfyingly whole. But there are two or three issues that seem to derail it a bit.

The first is: Why isn't the prime vertical (and the Vertex family of angles) equal to the other two circles?

It simply isn't. If it were equal to them, then any planets 3°, 7°, and 10° either side of the prime vertical (say, in azimuth, but possibly in PV amplitude) would be comparably as dominant and expressive as planets 3°, 7°, or 10° from the meridian or the horizon. In contrast, when we can track Vertex-Antivertex expressions at all, they are within small orbs - never more than 3°. While their affects seen modestly expressive in nativities, they are utterly worthless in lunar returns and solar and lunar ingresses.

So the first "great problem" about the simple angularity model is: Why aren't the three great circles interchangeable in "angularity" effect?

Your thoughts?

[Jim Eshelman]

The second issue is probably not as important and probably not as hard to understand, but needs to be posed as a seeming complexity - or at least apparent twistedness - of the simple angularity model.

It is this: Given that natal angularity is measured mundanely, why do transits to natal angles and contacts with quotidian angles work ecliptically instead? (This applies not only to natals but to return charts and ingresses.)

One approach to answering this is to question whether the premise is valid in the first place - whether all of the "given" facts I just stated are true. I do think they're true. I also think there are other possible answers to the question (although some of these raise even more questions to be addressed).

Your thoughts?

[Jim Eshelman]

Why isn't the prime vertical (and the Vertex family of angles) equal to the other two circles?

I will give my thoughts on this as a start. Feel free to ignore them, question them, support them, or come up with different approaches.

From what I've observed in practice, and what I've seen in larger and smaller studies: Life would be far simpler if we lived in a world where only the horizon and meridian were operative factors for angularity. And yet, the simplicity of the master model is in the exact way the THREE circles interact geometrically.

Things I believe to be true, based on observation: (1) Realizing that Vx/Av, like other angles, needed to be examined mundanely solved several small mysteries and overall sharpened the approach to Vertex. Proximity to Vx/Av needs to be measured in azimuth. (2) Natal contacts within 3° of azimuth seem relevant (at least much of the time) as if they were weaker angularities. They are strong enough that one can't usually ignore them without loss of information. (3) In SLRs and ingresses, the Vertex is so useless that it comes closer to being an anti-angularity factor. It adds nothing meaningful and runs a serious risk of derailing the correct interpretation. Best practice is to ignore it completely. (4) Prime Vertical Parans (PVPs: mundane aspects formed by planets on the PV itself naturally square planets comparable distances from the meridian or horizon) have proven themselves decisively, but this isn't actually a comment on the Vx/Av as angles, only of the inherent geometry of the three mutually square circles.

Regarding Vx in a natal chart: It has seemed to me for decades that close contacts to Vx/Av showed strong planetary expression that was more or less unconscious. On the (Ascendant-like?) Antivertex in particular, I found many examples of people who strongly expressed certain traits but were pretty oblivious to the fact (e.g., someone with Saturn on Antivertex that had no idea people experienced her as controlling and rigid). Once I learned to calculate these mundanely, it was mind-altering to discover that my own Antivertex is only 2°47' from Pluto. (My early life makes so much more sense considering I had an angular Pluto, but not necessarily something that was in the forefront of my experience of things.) Based on these examples, I'm quite willing to accept that Vx/Av are angles in a natal chart with a forthright (but perhaps subtler) "angular" expression. - It's not puzzling that something would be discernible in a natal but not in returns or ingresses (we have many things like that, probably because a nativity has more primacy and more opportunity to express). It IS still unclear, though, why it would be weaker.

Charles Jayne, who did the largest amount of outright work investigating Vertex, concluded that it shows fated things. I don't believe in fate (in the sense of things that happen in life as if caused by some outside third-party force without our own choice or contribution); but, on reflection, I realized that the same observations could be credited to unconscious causation. This is much more consistent not only with my worldview but with the simple meaning of "it's angular, so we act that way." This interpretation is consistent with (yet also surely contributed to) my "unconscious expression" observations in the last paragraph. It's also consistent with the fact that Vx/Av often fall outside the foreground (as usually defined) and, therefore, would be away from the zone of maximum awareness (foreground). - I should also say that while I am quite solid on the "unaware acting out a planet" of the Antivertex cases, I can't swear that all the examples I've seen of a planet on Ascendant, Midheaven, EP, etc. have any more awareness. (I just realized yesterday that I'd never looked at that half of the question.)

My strongest idea about why the prime vertical angles don't have the same "foregroundness" is because the prime vertical, for some reason, is the actual framework that determines foregroundness. That is, the best modelling of how angularity works with regard to the horizon and meridian has long been that these are measured along the prime vertical. If angularity (strength of expressiveness and conscious awareness) is measured along different parts of the prime vertical, then being on the PV cannot, itself, contribute strength of expressiveness and conscious awareness.

This seems entirely reasonable. However, it leaves the question of why the PV would have that unique role. Would it mean, for example, that each circle has its own distinctive role? That there is a dramatic, fundamental difference between the natures of the meridian and horizon? (If so, what is it? It would need to be of a comparable magnitude, not just a small interpretive difference.) Or is there something that M and H have in common that is different for PV?


I have one theory about this last question. I'm far from being sold on it, but I think it's worth mentioning and it may be true. First, I need to mention a theory about how human evolution has conformed itself to astrological patterns in nature. I don't accept vague theories that "thoughts people have had over the centuries have formed how astrology works" in the sense of forging reality. I do think, though, that the opposite is true, that "how astrology works" (how nature in general works) has, over the centuries, forged how people think, that the human brain (its routine modes of responding and functioning) has been shaped by natural selection. This would mean that the human brain would have been shaped to be responsive to some subtly perceptible things from the cosmos and NOT responsive to others. (This looks a lot like "our metaphors shape reality," but I don't mean that human metaphors shape the actual fabric of nature, only that the fabric of nature, using human metaphors, likely has shaped the organic structures [in the brain, e.g.] that affect human perception of and responsiveness to some details of nature.)

Anyway, on with the metaphors: Of the three circles, the PV is the only one that doesn't obviously divide the sky! The horizon easily divides the sky by distinguishing what's above the horizon from what's below it. The meridian easily divides the sky by distinguishing what's still rising into open sky from what's setting or withdrawing from the open sky. (This is truer of Zenith - which is on the meridian, of course - than MC, but the two are mostly indistinguishable in open sky viewing in moderate latitudes.)

In contrast, the PV doesn't easily or obviously divide the sky. Stand, face south, and visualize: Except in extreme latitudes, all the planets move across the southern sky. The PV is right over your head, yet there is no obvious experience that planets (all above the horizon) on the southern half are all that different from planets on the northern half of the visible sky. (Sure, one can measure and calculate, but there is no intuitive or primitive demarcation evident as we see for horizon and meridian.)

In examining the issue of the PV's independent function, there is also the consideration that aspects along the PV (mundane aspects) have been found enormously valuable, probably equal to ecliptical aspects. This definitely makes the PV a stand-out! (For example, aspects along the horizon haven't proven themselves equally effective unless they happen to show a co-angularity.) Several of these things sound to me like the PV is the most fundamental of the three circles and, therefore, ironically, planets crossing it have much less importance in the same way that planets crossing the ecliptic (changes in celestial latitude) may have some effect - but not much.

[Jim Eshelman]

Some of my thoughts on the second issue.

Given that natal angularity is measured mundanely, why do transits to natal angles and contacts with quotidian angles work ecliptically instead? (This applies not only to natals but to return charts and ingresses.)

Given (premise): Natal angularity is measured mundanely
It is entirely obvious to me that natal angularity works mundanely. ("Natal," for this discussion, includes returns and ingresses, i.e., "in the context of the original chart.")

It remains a fair question whether angularities work both ways - e.g., whether (especially if close) an ecliptical conjunction with an angle has independent significance from its mundane angularity. I think it does not: A few examples here and there have allowed a comparison. (Of course, there is always the other side, an example here or there where you're really excited to see a planet exactly angular, only to learn, on close inspection, that it isn't.)

However, this is at least a valid question, so I open what may be a can or worms.

Given (premise): Transits to natal angles and contacts with quotidian angles work ecliptically.
This is the flip side. My theoretical expectation had always been that these should work mundanely. However, the mundane astrology work - which relies heavily on transits to solar ingress angles and quotidian crossings - kept showing that the ecliptical ones were what worked, to the apparent exclusion of mundane crossings. [I'll retest this from the beginning when TMSA 0.5.x is finished and mature sometime in 2022.]

Taking these conclusions from mundane back to natal/personal work, it seems to work the same way. Admittedly, there are not as many examples with a huge difference, and I've only spot checked (plus watching it in my own life). With personal charts, there is also a possible issue of imprecise birth time (which we don't have with Sidereal ingresses), though my own birthtime is quite exact.

Again, I think I'm right about this premise, but do acknowledge it as legitimately open to challenge. It is possible that both mundane and ecliptical angle contacts "work" in transits and quotidians, and that I have somehow managed to miss this. Even in that case, though, the above issue remains: Given how nativities, return charts, and ingresses work (mundane angularity), why are ecliptical transits and Q crossings valid at all (and, probably, exclusively)?

[Jim Eshelman]

Given that natal angularity is measured mundanely, why do transits to natal angles and contacts with quotidian angles work ecliptically instead? (This applies not only to natals but to return charts and ingresses.)

Continuing my thoughts on this question...

It is completely obvious and intuitively satisfying why angularity in a nativity, return, or ingress would work mundanely. At the time the chart comes into being (time of birth), the question is: How close are the planets to the angles? The actual answer is shown mundanely.

So, this isn't a puzzle.

The main question remaining, though is: Then why do transits (as the simplest case) work ecliptically instead? (This can also apply to other things like synastry interchanges.)

What follows is speculation - thinking aloud - a philosopher of astrology musing on a thought exercise, not a research scientist having actual facts available.

To put it simply: The transits don't exist in the framework of the natal chart. They aren't "in" it. They happen later. At the time they happen, the celestial orientation of the birth chart (the unique mundane framing of the heavens at the time and place of birth) doesn't exist. Therefore, the transits are not "in" that framework.

This view (which isn't strange at all) divorces the transits from the natal mundane framework. Until we go further, it actually seems more likely that transits to major angles wouldn't work at all (if the major angles are entirely mundane things) - though, of course, we know that this isn't true. Transits to angles are enormously important and effective! - However, if houses are astrological realities, this point of view DOES give a very satisfying answer to the question of why transits through houses seem to do nothing, because, again, the transiting planets are never IN that specific mundane framework of the birth chart.

The question remaining, then, is: Why do the ecliptic contacts work at all?

The real answer is: I don't know. But, since we know from abundant observation that ecliptical transits to angles are valid and important (there are hundreds of examples in SMA, plus all the experience we've had with natal transits and SSR transits), then we know that the ecliptical position of the angles MUST be valid (even if the "why" escapes us).

So... given everything established and suspected in the posts above, why would ecliptic positions of the angles viably exist at all? I speculate:

First - mostly to rule it out as a relevant consideration to this particular discussion - I want to address the question of whether signs on angles are significant. It is common in astrology to think of Ascendant sign in particular, and Midheaven sign nearly as much, to be meaningful. (More house-driven astrologers consider the opposing angles' signs to be equally important, as part of the larger picture of signs on house cusps.) Over the years, different statistical examinations have seemed to show modest significance for these sign placements - it looks like they work, but that the effect isn't very strong. This matches my subjective experience with the signs on the angles: Ascendant sign seems significant as reflecting a very superficial level of someone's behavior and self-expression, one for which I usually don't need the horoscope (and a level I hope to get almost immediately past). It's no mystery why these signs COULD be significant: Just as planets on angles get greater expression and awareness, we can expect the zodiac on an angle is giving greater expression and awareness. However, the observed level of the sign's expressiveness is quite small.

This use of the zodiac has nothing necessarily to do with whether the ecliptical longitude of the angle is relevant. It's just another (non-planetary) example of something being on an angle. In fact (this is a digression), I've wondered for a while whether the seeming effects of a sign rising or culminating isn't really something more complicated: Perhaps all zodiacal and extra-zodiacal constellations on the rising horizon and culminating meridian are being activated, so we have a mixture of many different independent themes. - Again, that's a digression. My purpose in these paragraphs was to distinguish it from the real question in front of us.

Back to the astronomy of the celestial longitude on an angle: The celestial longitude on the MC, Asc, IC, and Dsc is the intersection of the horizon or meridian with the ecliptic. The nature of the phenomenon, then, is not the same as a planet crossing the plane of the horizon or meridian but, rather, of the intersection of two significant great circles. Astrology has many other examples of these. A simple one is the lunar nodes: There's nothing there, really. The nodes mark the two opposing points of intersection between the ecliptic and the plane of Moon's orbit. I find these to be weak, minor factors - not at all the strength of an angle - but they are similar in their astronomical definition. Another example is the equinoctial points: These are the intersection of the ecliptic with the plane of Earth's equator. Tropical astrologers claim (falsely, evidence says) that these are the basis of the zodiac! But even among Siderealists, there are those who have explored Uranian astrology's treatment of these intersections as valid points, and concluded that they have astrological validity (even if minor). In particular, Sun's crossing of the equinox and solstice points turn out to produce viable mundane charts (though not as strong as the Sidereal ingresses).

Historic mundane astrology is full of all sorts of "plane crossings." C.C. Zain, regarded as one of the greatest mundane astrologers of his day, did a lot of work with these. He more or less held that "every crossing is significant." He would do charts (for example) of whenever any planet reached 0° latitude (crossing the ecliptic) or 0° declination (crossing the equator).

The general point - in theory and perhaps in practice - is that astrologers have long held that intersections of insubstantial planes (and the great circles that mark them) are points of some sort of meaningful alchemy.

However, the difference between these other crossings and the angles is enormous - gigantic! - the angles outweighing essentially everything else. At the moment, I can only think of one reason, which is, simply, that they are angles - that the angles are so enormously powerful (and localized!) that they outpace everything else that might fall into the same category.

That's at least good enough that I can live with it at the moment. It does give a theoretical basis for the ecliptical points intersecting horizon and meridian being ecliptically significant. [NOTE Apr '22: In another post, farther down on this thread, I argue against this "intersection with the ecliptic" theory.]

So... I'm stopping to catch up... where does this leave me in my thought exercise?

I totally see why a transit would not operate in the same (mundane) framework as the natal (see above). I also see why the point where an angle (horizon or meridian) intersects the ecliptic could be significant, and I have a comfortable enough explanation with why these would be so dramatically more powerful than any other "intersections of planes" in a birth chart. So, understanding that all this is conjecture or thought exercise, I guess I have a workable (but not necessarily final) answer to the posed question.

Except... it poses other questions. The most immediate question is: Oh, wait, if suddenly there is a viable ecliptical equivalent to the angles, why can't these be aspected? Isn't this just exactly the sort of thing that we expect to be aspectable? And yet, the body of evidence (a dozen different kinds) suggests to me that angles are not aspectable at all. (C'mon, does anybody here really think that Venus sextile Ascendant 0°27' is one of the strongest expressions of my social behavior? If you do, then I think I should question your judgment )

We can, of course, take a variant view: Looking at all these other examples of "plane intersections," what kind of aspects (if any) do they take? The examples I gave from C.C. Zain's mundane astrology aren't used that way, and the VP as an astrological factor in Uranian and quasi-Uranian astrology is really only used for hard aspects (meaning conjunctions with two equinoctial and two solsticial points), though, of course, they also include octiles).

One could, in fact, answer these concerns by saying that it doesn't seem the other plane-intersection phenomena "take aspects" either (except maybe the square, because of geometrical considerations: the square to the intersection is another significant spot in the relationship of the two circles). The problem comes with Moon's nodes: Most astrologers who work with Moon's nodes think they make aspects. [NOTE 4/7/22: I am less and less persuaded that trines and sextiles to Moon's nodes are valid. (I now think it more likely they do NOT, but still file this as "undecided.")]

[mikestar13]

There are two ways of looking at the six intersection points: where they are in space, and where they project onto the ecliptic (draw a perpendicular line from the point to the ecliptic and note the celestial longitude.) In theory, this would yield effectively twelve points, but for zenith, nadir, north point, and south point, both sets of numbers are identical. However, for the east point and west point, the two different ways of looking at looking at the point produce two different (though close) numbers, baring the occasions when the eastpoint happens to be 90 degrees from the midheaven in both longitude and right ascension. So Jim can reasonably talk about eight points. Evidence suggests the both interpretations of the eastpoint/westpoint are valid. The universe would be slightly neater if they weren't.

[Jim Eshelman]

That's probably why my subconscious mind made the original typo

Something I thought you were saying (but weren't) also reminded me of some interesting thought extensions. These points all appear as MULTIPLE angles, depending on the framework from which you examine them. For example, MC, IC, Zenith, Nadir, NP, and SP all have identical (or opposite: same thing) right ascension; so, in prime vertical longitude (mundoscope) and some ways of looking at a standard horoscope, they are all one axis. Also in the mundoscope, Asc and EP have the same position, as do Dsc and WP. In azimuth, MC and SP (and IC and NP) are the same position.

[mikestar13]

It's obvious that horizon and meridian collectively mean something (we call it angularity) which the prime vertical doesn't. So we consequently measure the proximity to either the horizon or the meridian along the circle mutually perpendicular to them.

In all the research about the vertex in itself we have explored the question of its meaning, but have we looked for:

What does the prime vertical have in common with the meridian but not the horizon? Whatever it is would be measured on the horizon.

What does the prime vertical have in common with the horizon but not the meridian? Whatever it is would be measured on the meridian.

For the horizon and meridian we have a good idea of what angularity means. I would phrase it as the ease of expressiveness of the planetary energy. For the other two things, not so much if at all. This is a question that will require research and interpretation by a better astrologian than me.

[Jim Eshelman]

In all the research about the vertex in itself we have explored the question of its meaning, but have we looked for:

What does the prime vertical have in common with the meridian but not the horizon? Whatever it is would be measured on the horizon.

What does the prime vertical have in common with the horizon but not the meridian? Whatever it is would be measured on the meridian.

This is the sort of line of thinking I was hoping someone would pick up.

I tend to see it from the complementary side: Not "the meridian and horizon share something called angularity, which is measured in the PV," but rather than "the PV is a rheostat showing gradient angularity," which then reflects into spatial relationships to the horizon and meridian. This led to my question, "If this is the distinction of the PV, are there other distinctions for the horizon and the meridian?" (I think these boil down to the same thing you were asking.)

I've also pointed out that mundane aspects between two planes are each measured in the coordinates of the third. Aspects between the meridian and horizon are measured along the PV. Aspects between the PV and meridian are measured in azimuth, i.e., along the horizon. Therefore, aspects between the PV horizon would be measured along the meridian (and I haven't been able to derive formulae to calculate that - which would be an awesome experiment - so I've created ways to cheat and fake it if both points are near the horizon and PV).

For the horizon and meridian we have a good idea of what angularity means. I would phrase it as the ease of expressiveness of the planetary energy. For the other two things, not so much if at all. This is a question that will require research and interpretation by a better astrologian than me.

An obvious starting point for interpretation differences between meridian and horizon, one can probably say that the meridian is more connected to identity and the horizon surroundings and context-relationship. (These may not be true. I'm just sayin' someone could probably be sayin'...) My point is that, even if these are true, they don't feel like the same scale of distinction as saying that the PV is a rheostat regulating expressiveness.

[Jim Eshelman]

I'm not going to worry about the implications of this issue for quotidians right now. If the matter is resolved for other conditions, I'm satisfied the quotidian question will fall in place. (It likely is some variant of the other Issue No. 2 considerations above.)

In any case, I hope many of you will give thought to all of this and engage on these topics.

[mikestar13]

Yes Jim I agree we are expressing the same idea in different words with slightly different emphasis. TMSA will make this a bit easier to explore.

[Patrick Machado]

Not an answer to the question per se, but the reason I never thought issue #2 an issue was that it seemed appropriate that the horoscopic angles had a major, practical importance; otherwise, why acknowledge them at all? (Of course, the answer could be simply, "because astrology conventionally acknowledges them.")

(Thanks for the detailed explanation of the angles. I hadn't taken the time to visualize the whole model in such detail.)

[Jim Eshelman]

BTW, I'm toying (only briefly?) with the idea that the meridian is related to time and the horizon to space. This is probably too simplistic, and I'm not sure how it would solve these problems, but thought I'd mention it.

In the process of facing south, I realized that the direction of the 9th and 10th houses was "in front of me," and the meanings of those houses is consistent with "what's still ahead for me;" while 3rd and 4th houses are clearly associated with "what's behind me." This is useful in a different way of the external-internal polarity I usually use (and avoids confusion of "elevation = external" vs. "angular = external").

Azimuth, of course, comes from a root meaning "the byways" in the sense of "directions" - naturally related to surrounding space, just as the horizon is a reasonable symbol for demarcating "surroundings" (it surrounds us, after all). I wish there were an equivalent, readily usable astronomical term for measurement around the meridian circle.

Again, this is just thinking aloud.

[Danica]

It is this: Given that natal angularity is measured mundanely, why do transits to natal angles and contacts with quotidian angles work ecliptically instead? (This applies not only to natals but to return charts and ingresses.)

I was thinking about this during this past week- it came to awareness as a question, followed by other "can of worms" considerations you mentioned

What seems/feels as an obvious fact is that there is a peculiar Zodiac-related (or: for us as observers on Earth such that it's distinctly zodiac/360*-of-its-eclipto- longitude related) imprint, or position-mark, of an event in time-space, as we experience it on Earth. So the 360* degrees of the zodiac don't only have the quantitative quality, as a measurement-framework (for us to calculate the planet's positions to each other and otherwise, the positions of celestial bodies in space), but also each has its own qualitative distinction, a unique nature/flavor/quality of its own.

So, with charts of a longer-term phenomenon, such as a natal chart -- these are more easy to see over time in practice via how the current-transits to a given set of chart's positions (point-marks-on-ecliptic) operate, than it is with shorter-term phenomena, like Lunar-cycle charts (personal or collective).

Thus, a transit such as tr Mars octile natal Lunar Node can practically work - there is this 'invisible-network', a pattern-of-unique-combination-of-points-mutually-related-on-the-zodiacal-belt, that operatively comes into being with an Event's birth and is present throughout Their (event/person/being's) life.

[Patrick Machado]

I was also thinking along the lines of "perhaps transits are all about the Zodiac," which made me remember that in return charts, even mundane transits to natal planets seem valid. Could it be that mundane transits in general are also valid (whether to planets or angles), similar to how mundane aspects are as equally valid as ecliptical aspects?

[Jim Eshelman]

Could it be that mundane transits in general are also valid (whether to planets or angles), similar to how mundane aspects are as equally valid as ecliptical aspects?

It could be. I haven't seen the evidence that they are EXCEPT when there is an intervening framework such as a return chart.

For example, my Moon culminates about 2° before its ecliptical longitude. Many years ago, when transiting Uranus spent a lot of time around 25° Aquarius (where it had the same RA as my Moon), I had more Uranus-to-Moon phenomena than when it moved 2° further (e.g., significant travel and change in fundamental patterns). However, the key events of that were always when the Uranus-to-Moon was angular in an SLR. (Even if it hadn't been on an angle, that would have shown as a non-foreground partile mundane aspect in the SLR.)

There are astrologers who speak very positively of transiting parans. These have been hard to study because we haven't had the software. (Software that would calculate transiting parans wouldn't precess the natal planets, so they were quirt a bit off.) But with spot-checking I've never been persuaded. (As always, you can find an exciting example randomly here and there.) - They certainly haven't been worth the enormous math required for the smallest of effects.

More easily calculated and to the point, transiting planets mundanely crossing natal angles just don't show as well as ecliptical ones. (From back when Pluto was farther from the ecliptic, I'll never forget the night that we had some kind of party at my place and in the middle of the party a woman attending announced she was now lesbian. It wasn't just a coming out, it wasn't that she had just found a particular person to whom she was attracted - she said she'd been thinking about it and had decided it made more sense <?> and today seemed the day. We pulled up her chart and transiting Pluto was 0°01' from her natal Ascendant in longitude.)

[Jim Eshelman]

BTW, it's a fair question, "If transiting mundane aspects aren't valid, then why not?" One of the ideas that emerged in the writing above is that mundane aspects have to exist within a specific mundane framework. Transits (for example) don't exist within the natal chart - they exist atop the natal chart.

Transits have mundane aspects within a current transit chart - a chart for the current moment and place - because they're native within the chart. They exist within a return chart because they are native within that chart.

This, of course, presumes that the theory articulated above is correct. Testing transiting parans with proper precession correction would be the way to rule that in or out.

[mikestar13]

Jim, when my solunars module is complete, the natal planets will be precessed to the date/time of the return. When the synastry module is completed, it will be possible to precess any chart's planets to any other chart's date/time. This will actually be rather significant in traditional synastry (putting one person's planets in the angles/cusps of the other) when there is a meaningful age difference between the parties.

But what is exciting is what else we can investigated with this capability: for example "synastry" between the chart of the moment and the nativity, etc.

[Jim Eshelman]

This will be a great tool for experimenting, Mike. I don't know if any of these things is correct, Mike, but we really should find out - and this is a way to do it. This alone could open up 20 years of new research since we really need to go back and re-examine every pair of charts we've ever seen.

For the kind of transits Patrick was talking, though, we'd need something else - an internal speculum tabulation (RAMC for when each planet crosses each angle at a given latitude - one set precessed to the other's epoch) and then (the easy part) finding the aspects (the conjunctions, oppositions, and squares all show as 'conjunctions').

[mikestar13]

Somewhere along the way (likely for version 0.4) I will calculate a speculum and add a user option to print it in the chart file. I will need to review the procedure for calculating one. When the user checks the option, shall I mix parans into the aspectarian (presumably marked P)?

[Jim Eshelman]

When the user checks the option, shall I mix parans into the aspectarian (presumably marked P)?

I wouldn't - primarily because I'm all but completely disenchanted with "potential parans." Nonetheless, I recognize that this is a topic well-represented in historic Sidereal literature, usually without the benefit of anyone actually being able to test it well.

It would be nice to be able either to find out that my disenchantment is misplaced and we should be watching these, or to once and for all times lay to rest people's concern with it - and that can only be done by actually studying the matter.

[Jupiter Sets at Dawn]

I think mixing parans into the aspectarian gives them too much legitimacy without the data to back that up. I'd rather see them separated out. I'd rather see Eris and the rest separated out as well. THIS is known. THAT is speculative.

Some people may want to use the charts printed out for clients, relatives and friends. They shouldn't have to explain Eris or parans to people who know little to nothing about astrology while already explaining, no you're not a Gemini, you're a Taurus, but when you read your horoscope in the newspaper, you're still a Gemini, Aunt Bee.

[Jim Eshelman]

If they want to print them out, then of course then can remove Eris before doing it if they want. - And, while I think of Eris now as a known quantity (despite much more to learn about it), there are times I'll turn it off myself just to have a simpler look at things (especially if it's one of those charts that has a LOT of close aspects).

Sedna, to me, is different. I think I have a strong handle on it, but I can't say something concrete about it even half the time, so I'm happy to see it turned off by default, but able to be turned on when desired.

[mikestar13]

I will start a thread "suggestions for version 0.4" for this, as I will not be doing anything paran related until the next version. I will continue the discussion there.

[SteveS]

I have got to spend more time studying this thread for better understanding, but for now I need to know one thing for looking at charts for different locations: I guess we always allow more potency for the MC vs the Zenith when looking at the same planet on these chart points? For example: If I see Jupiter on MC for one location, and see Jupiter on Zenith for another location I always choose Jupiter MC---correct? And if correct, how much more potency with a % number?

[mikestar13]

Steve raises interesting questions. IMO, within a chart Jupiter exactly on the Zenith is precisely as strongly angular as Jupiter exactly on the MC, but the fall off is faster as the orb widens for the zenith case. In transits where the major angles take aspects, the Zenith is a square to the ascendant, a major dynamic aspect, presumably equal in strength to a conjunction to the MC given the same orb. An interesting question: are transits to the eastpoint valid? after all, it in not in aspect by longitude with the MC save by coincidence.

[Jim Eshelman]

I guess we always allow more potency for the MC vs the Zenith when looking at the same planet on these chart points? For example: If I see Jupiter on MC for one location, and see Jupiter on Zenith for another location I always choose Jupiter MC---correct?

This is a great question. Mike gave part of the answer: One difference in, say, a birth chart (rather than transits) is that the "slope" of the angle is more acute - Zenith contacts rise up from zero to maximum strength with shorter orbs, i.e., a faster rise and faster drop-off. A 2°-wide Zenith contact in a natal is at about the same strength as a 7° contact with the MC.

However, it does seem that, at the point of exact contact, their strengths are the same. Also, when it comes to transits, I can't see any difference at the close orbs. The mundane work has been invaluable for this: Over and over, Saturn "square Ascendant" (by which we really mean "conjunct Zenith" is as likely to trigger an event as Saturn crossing a major angle, and both within about the same orb.

I know that intuitively it feels like the major angle should be a bigger deal. Based on examples I've seen, though, I can't confirm that it's a bigger deal.

I'll dig out some mundane examples later as examples.

[Jim Eshelman]

In transits where the major angles take aspects, the Zenith is a square to the ascendant, a major dynamic aspect

I disagree. Though I allow that I'm wrong about this, I don't think angles ever take aspects. The transit to Zenith or Nadir is 90° from Ascendant in longitude, but it is also the conjunction with Zenith or Nadir.

That is, if you drop a great circle through the Zenith, perpendicular to the ecliptic, it will always cross the ecliptic 90°00' from the longitude of Ascendant. This is the same way you determine the longitude of a planet (or anything else in the chart) - it's the actual longitude of the point.

An interesting question: are transits to the eastpoint valid? after all, it in not in aspect by longitude with the MC save by coincidence.

I see why you would ask this if you consider that (in transit) these have stopped becoming conjunctions with the minor angles. But the answer in practice is clear: Transits to Eastpoint are effective both in longitude and RA. Some of the most stunning exact timings of the events in mundane astrology have been from exact transits in RA to EP-WP.

[Jim Eshelman]

Looking at the question of whether contacts with major angles are stronger or more impactful than those with minor angles, using Sidereal mundane astrology. I'm not going to calculate more charts, I'm just going to take the data already compiled in my book, Sidereal Mundane Astrology.

I'll start with earthquakes. Though earthquake patterns are complex (at least three different "flavors" of earthquakes), across all those types Saturn is the most commonly angular planet in solar and lunar ingresses, quotidians, and transits to solar ingress angles. Saturn was especially angular in final daily timing - crossing CapQ or CanQ angles or transiting Capsolar or Cansolar angles. It was also the most commonly angular planet in lunar ingresses and (behind Mercury!?) Saturn and Mars tied for the second most common angularities in solar ingresses.

I will list which angle Saturn was on for all of these. If I've already listed the orb or which angle was involved in SMA, I'll give that also. We can see if any patterns become obvious.

RHODES EARTHQUAKE CanQ MC = s Saturn

1693 SICILY EARTHQUAKE CapQ Asc sq. s Neptune (Dsc +0°10') and Saturn (Nadir -0°13'). Transiting Saturn was also in orb (0°46')

GENROKU EARTHQUAKE Caplunar Saturn on IC (1°43'). Canlunar Saturn sq. Asc (0°59').

LISBON EARTHQUAKE Cansolar on Dsc (1°22'). Caplunar Saturn on EP-a 1°09'. Canlunar Saturn on IC 3°13' (opposite culminating Moon). CanQ IC = s Saturn 0°51'.

FORT TEJON EARTHQUAKE Caplunar Dsc = Saturn 1°22' (opposite Sun across horizon).

MANILA EARTHQUAKE CapQ MC = t Saturn 0°00'

1902 GUATELMALA EARTHQUAKE Arisolar EP-a = Saturn 2°00'. Caplunar Asc = Saturn 2°07.

1906 SAN FRANCISCO EARTHQUAKE Capsolar Asc sq. Saturn 1°15'. CapQ Asc = t Saturn 1°43'.

AVEZZANO EARTHQUAKE Capsolar Asc = Saturn 0°14'. CapQ Asc = s Saturn 1°19'

GREAT KANTO EARTHQUAKE Capsolar MC = Saturn 2°09'. Arisolar Asc sq. Saturn 1°37'. Caplunar EP-a = Saturn 1°00'. Transiting Saturn on Capsolar MC 1°29'.

XINING EARTHQUAKE Capsolar Asc = Saturn 2°19'. Transiting Saturn = Capsolar Asc 1°06'.

LONG BEACH EARTHQUAKE Cansolar MC sq. Saturn 1°26'. Transiting Saturn to Cansolar Dsc 1°16'.

ERZINCAN EARTHQUAKE CapQ Dsc = t Saturn 1°16'. Transiting Saturn = Cansolar WP-a 1°25'.

OLYMPIA EARTHQUAKE Capsolar Asc sq. Saturn 2°10'. Transiting Saturn = Cansolar EP-a 0°30'.

TEHACHAPI EARTHQUAKE Caplunar Asc sq. Saturn 1°59'. Transiting Saturn to Capsolar EP-a 0°49'. CapQ MC sq. s Saturn 1°08'.

KAMCHATKA EARTHQUAKE CanQ Asc = Saturn 0°07'

AGADIR EARTHQUAKE Transiting Saturn = Cansolar IC 1°31'

GREAT CHILEAN EARTHQUAKE Arisolar Asc = Saturn 1°56'. CapQ MC = t Saturn 1°26'.

BUIN ZAHRA EARTHQUAKE CanQ Asc sq. t Saturn (0°27'), CanQ IC = s Saturn (0°18').

SYLMAR EARTHQUAKE CanQ MC sq. s Saturn 1°32'

TANGSHAN EARTHQUAKE Capsolar EP-a = Saturn 1°03'. Caplunar Asc = Saturn 0°45'.

1985 MEXICO CITY EARTHQUAKE CanQ WP-a = s Saturn 0°05'

NORTHRIDGE EARTHQUAKE Liblunar Asc = Saturn 1°39'

SUMATRA-ANDAMAN EARTHQUAKE Caplunar IC = Saturn 0°55'. CanQ Dsc = t Saturn 0°18'

CHRISTCHURCH EARTHQUAKE CanQ Asc sq. t Saturn 1°13' (with CanQ MC = s Mars 0°17')

TOHOKU EARTHQUAKE Transiting Saturn sq. Cansolar MC 0°40'

NEPAL EARTHQUAKE Caplunar: Saturn sq. Asc 0°33', on IC 2°28'. Transiting Mars & Saturn on Cansolar angles (I didn't note which ones)

SULAWESI EARTHQUAKE Arilunar IC = Saturn 3°

[Jim Eshelman]

My broad conclusion from this, as across the whole mundane range, is that it doesn't really matter what angle something touches. If it's a valid angle, they're all the same. However, this conclusion (casual observation over the years) was based more on looking for thematic differences (MC vs. Dsc for the kind of event, etc.), not for distinguishing whether MC vs. Zenith is more important.

Of all these perfectly valid hits of the most perfect planet to angles for this category of event, is there any real difference? Let's tabulate which were more common.

MC 5
IC 8
Asc 10
Dsc 5
EP-a 6
WP-a 2
sq. Asc 10
sq. MC 4

There isn't a lot of difference here. (Remember to divide "sq. Asc" and "sq. MC" by 2, since they represent two different angles.) There IS an interesting preference of Ascendant ahead of all the other angles - not sure this is that big of a deal, or if it would hold up across other types of events. There may simply have been something that biased Saturn toward the eastern half of the chart instead of the western, since Asc + Dsc = 15 and MC + IC = 13 (about the same).

But - for the original question - there doesn't seem to be a lot to separate the major angles from the minors. (We expect the minor angles to have fewer contacts in the solar and lunar ingresses, since they have narrower orbs, but they should be about the same for daily timing, i.e., transits and quotidians.) Consider the axes:

Asc + Dsc = 15
MC + IC = 13
sq. MC (long + RA) = 12
sq. Asc = 10

[Jim Eshelman]

We get a more even playing field if we use only the daily timers - quotidian angle hits and transits to solar ingress angles. However, we have a lot fewer examples. Let's see if we have enough to draw any conclusions:

MC - 4
IC - 3
Asc - 4
Dsc - 3
EP-a - 2
WP-a - 2
sq. Asc - 4
sq. MC - 3

These are remarkably even. It's a small number, so tiny differences don't mean anything. Once you halve the squares to the angles, the major angles may have a small preference (14 total vs. 11 for the minor angles), but I don't think that means anything.

[mikestar13]

Thanks for the clarification Jim. So angles never take aspects. A square to the ascendant as such means nothing but since such a square is concurrently a connection to the zenith or nadir, it is valid for that reason. I think there needs to be a new term to indicate transits to the angles to indicate this difference. For example, a transiting square to the natal sun is valid whether or not there is a concurrent transiting conjunction to something 90 degrees away. I will propose calling the transiting contacts to the angles crossings, or transit crossings if context doesn't distinguish them from say Quotidian crossings. Thoughts?

[Jupiter Sets at Dawn]

Why not leave out everything but the conjunctions and call the angle being transited by it's own name? We don't need "square to the Asc" when we have conj the zenith. They are actually more accurate, because there's conj either the zenith or nadir.

[Jim Eshelman]

Thanks for the clarification Jim. So angles never take aspects. A square to the ascendant as such means nothing but since such a square is concurrently a connection to the zenith or nadir, it is valid for that reason.

Yes, that is my position. I know we confuse it because it's easier to communicate with "square to Ascendant" than with "on Zenith," and my clarifying the relationship and introducing the distinction EP-alpha and EP-lamba etc. was an incremental effort to resolving it.

My best effort at solving it will probably when I write the big book and simply define everything consistently from page 1 forward.

I think there needs to be a new term to indicate transits to the angles to indicate this difference... I will propose calling the transiting contacts to the angles crossings, or transit crossings if context doesn't distinguish them from say Quotidian crossings. Thoughts?

I don't object to the term, since it is correct; but I'd suggest that it's equally correct when a planet conjoins (say) Sun. - As a writer, I often use multiple words or phrases for the same thing, simply because they're all equally correct and good writing often means finding many ways to say the same thing; though, OTOH, that can also confuse people learning their way around.

Using far less letters, I have often used the word "on." Instead of saying "Planet X conjunct Ascendant" (or, your word, "Planet X crossing Ascendant"), I say "Planet X on Ascendant." Fewer letters, fewer mental syllables, fewer characters to type "on" than "co." or "conj." It also moves it away from the aspect idea of even the humble conjunction.

Having said all that, I think the most important thing we can do is to stop saying "squares to angles" (or stop saying it without clarifying modifications). I'd already decided that I need to rewrite Sidereal Mundane Astrology we weed out the several hundred instances of it, but probably won't do that quickly since it involves recalculating every chart that had a "square to Asc or MC" in it.

[Jim Eshelman]

Why not leave out everything but the conjunctions and call the angle being transited by it's own name? We don't need "square to the Asc" when we have conj the zenith. They are actually more accurate, because there's conj either the zenith or nadir.

Yes. I read this after I wrote the last answer but, yes, that's what I ended up saying at the end I would do.

Sometimes we have to say "square" in context, e.g., someone posts wanting relocation advice. The software they're using will keep referring to squares to angles, so we need to use that language at least long enough to add, "by which I mean conjunction with the Nadir." That's not too burdensome if we don't have to repeat it more than five or six times per person. (And gradually slide it to, "on the Nadir (what your software shows as square Ascendant.")

[mikestar13]

I'm thinking specifically for how to list them in TMSA transit listings (version 0.4 onward) . Perhaps Ju on Ze or Ma on Ep either with a sub indication in the Ep case (by longitude or RA) or perhaps two different abbreviations for Ep (and correspondingly with Wp). Perhaps El and Ea. Will add all the abbreviations to the relevant help files.

[Jim Eshelman]

I'm thinking specifically for how to list them in TMSA transit listings (version 0.4 onward) . Perhaps Ju on Ze or Ma on Ep either with a sub indication in the Ep case (by longitude or RA) or perhaps two different abbreviations for Ep (and correspondingly with Wp). Perhaps El and Ea. Will add all the abbreviations to the relevant help files.

Something like this, yeah. I'd go with Z and N for Zenith and Nadir (Ze would make some people think you were including the Uranian hypothetical Zeus), then EP/WP for the ecliptical aspects and EP-a/WP-a for the RA contacts.

I could see EP-l and WP-l if you could generate the lamba. In English letters, it's confusing. I lean toward no tag on the longitude versions to retrain people that the squares to MC are Eastpoint and Westpoint, whereas the -a forms (however important) are the clear "alternative model" hits. (Or something like that.)

[Jim Eshelman]

I have a new way to explain why major angles aren't contacted ecliptically (i.e., don't have a longitude) while minor angles are taken ONLY in longitude.

This is so simple... I've nearly said it many times but never quite landed the hammer on the head of the nail. It's crazy simple.

As I said at the very top of this thread, the Asc-Desc is the ENTIRETY of the circle of the horizon. When astrologers list a longitude for it, we take the point where the horizon Intersects the ecliptic. But this isn't how celestial longitude is determined. (In no other case is it determined this way.) Celestial longitude is determined by dropping through a point a great circle that is perpendicular to the ecliptic. (Always.)

Since the angle is the ENTIRE great circle of the horizon, note that there is NO part of the ecliptic that is perpendicular to the ENTIRE horizon (except for two brief moments a day in some locals). All of this is true of the meridian as well.

To give an ecliptical expression of a major angle, astrologers have had to create a new, special-purpose definition of it having a longitude. That's a red flag.

Minor angles OTOH are points, not circles. Points have celestial longitudes. The minor angles aren't the exceptions; they're the standard rule! It's the major angles that have been treated be variant, kludgy rules historically.

It's so damn simple that it never occurred to me to say it or, perhaps, even to think it.

[Jim Eshelman]

This may also be the best explanation for why angles don't have aspects. A true "aspect to Asc or MC" would have to aspect the ENTIRE great circle. The only thing that can do this is another great circle! The only great circles that form 60° or 120° angles to horizon or meridian are... Campanus house cusp circles! If aspects to angles exist at all (If!), they would be formed by planets conjunct a house cusp in the Mundoscope (i.e., in prime vertical longitude).

I'm still skeptical aspects exist... But that's what they'd have to be. (I think it more likely that phenomena that are great circles aren't the kind of thing that make aspects - things that cross the ecliptic like the horizon, meridian, Moon's orbit/Moon's nodes, or celestial equator/equinoxes).