Solunars by Aldebaran Sidereal Academy

I will be adding this feature to version 0.5 and I have several questions. I assume the distance from exactness will be measured in time rather than arc. What is a reasonable maximum orb? Clearly less than an hour and more than 15 seconds, but what is reasonable? Do parans only involve the major angles, or is say Ma Mc and Ju Ep valid? Am I correct that we are interested in active parans (planets co-angular at the time of the chart), not in potential parans (planets that will be co-angular sometime during the day but are not currently in orb).

I really dislike parans listed as time instead of degrees. Primarily this is because we are used to thinking in degrees, have our instincts honed in terms of degrees, and the way of finding orbs etc. is in terms of degrees (which can be converted to time, but that's one step removed). Secondarily, I think people get confused about what kind of time it is (clock vs. ST).

Three theories on orb:

• 1° orb is historic and most standard. Probably what I would use myself.
• 2° allows each planet to be within 1° of an angle at the same and is a reasonable concept some would routinely use (I'd use this occasionally, or as a Class 2 on parans)
• Some, like Kenneth Bowser, use parans as I use PV aspects, as their idea of what "mundane aspect" means. To them, this is just another aspect and I've seen orbs out to 5°.

Do parans only involve the major angles, or is say Ma Mc and Ju Ep valid?

That depends on definition entirely. I follow your thinking - I finally fell to calling these other versions co-angularities to avoid confusion. Since the 1950s when the idea took root, the term has tended to apply only to horizon-meridian connections.

Am I correct that we are interested in active parans (planets co-angular at the time of the chart), not in potential parans (planets that will be co-angular sometime during the day but are not currently in orb).

The people that are into parans want the potential parans and tend not to distinguish between them. (I can't think of any practical reason to list only active parans, since they're already evident from what's already in the reports.)

Here is my take-away: Express orb in degrees, allow orbs to five degrees, calculate active and potential parans, major angles only. Basically for each planet we calculate the RAMC when the planet rises, sets, culminates, and anti-culminates. Then we see which of these are in orb. I intend to have parans in a separate optional section. Thanks for the input, I have never calculated parans or used them except as co-angularities visible on the face of the chart, and I don't expect to use them in my personal practice, though I might. I am considering using class two mundane aspects and dropping class three ecliptical aspect (No change in TMSA defaults or legal possibilities.)

This sounds great. (If there is sufficient interest in the future to layer in the other angles, that can be an add-on, I don't know that it is an initial pre-1.0 development detail). - I just got to my office (answered earlier from home), I'll post some samples.

I'd love to see input from others on this - I know Steve has particular interest. The forum has been deadly quiet lately and this question could be one for people to sink their teeth into.

Mike, there's one kind of co-angularity relationship TMSA isn't capturing - no rush, and it's rare but I do think it's important. I'll mention it now because we're on a related area, but I'm not asking for anything now: Given that the MC/EP/IC/WP structure lines along the equator, I've seen in the mundane work that we need to consider (1) two planets, each on one of these angles, (2) they are in partile orb of square in RA, and (3) the orb of that RA square is closer than either ecliptical or PVL (neither of which might exist; or they might). It's really a different subject, but I thought I'd mention it.

Meanwhile, I'll get you some samples.

Solar Fire has a report for Star Parans. If you set the orb to 0°00', it washes out everything except the planets, leaving this nice table. This is the start of identifying parans, but impractical as it exists.

To make this usable, I copy the report and paste it into Excel. I then strip some labels, restructure the columns, fold the columns into one, and sort by the degree value. I end up with a table that looks like this (your natal):
From this, I manually identify all of them that fall in my specified orb. Using 1°, the entire list filtered from your chart looks like this:
From this, I can extract the following. (If there were more than one for the same planet, one theory says to treat these as cumulative - adding points in a way not worth going into now - which makes them stand out more. Normally I just want the closest orb.)

Moon co. Mercury 0°17'
Sun co. Venus 0°47'
Mercury sq. Uranus 0°48'

(Not bad, I must admit.) Moon-Mercury is closer than your 0°26' mundane conjunction, Sun-Venus is closer than your 1°06' mundane conjunction, and Mercury-Uranus (which I think easily fits you) doesn't exist at all in the other frameworks. So, if parans are selected, these would all collate into your Cosmic State report.

As another example, which shows the more typical multiple occurrences on different angles, here are the paran placements relevant for my chart for birthplace:
These break out as:
From a place of pure aspects, I'd list these (taking the closest) as:
Ju-Ur co 0°12'
Ma-Ju op. 0°37'
Me-Sa co. 0°38'
Ma-Ur op. 0°49'
Ma-Sa sq. 0°53'

All of these are closer than the equivalent aspects by ecliptical or PVL.

A final fun thing - nothing I think you're concerned with here, but something I played with here and there over the years. If you count ALL variations of these aspects (however many angle pairs occur for the same planet pair), it has a tendency to make conjunctions look stronger than the other aspects, oppositions look almost as good, and squares the weakest of the three (just what we'd expect). A simple way to do this is to subtract the orb from the maximum orb (in this case, with only partile orbs allowed, to subtract the orb in minutes from 60) and collate the points. If you do this for my aspects, you get:

Ju-Ur co. 22 + 47 + 48 + 47 = 164
Me-Sa co. 22 + 22 = 44
Ma-Ju op. 23
Ma-Ur op. 11
Ma-Sa sq. 7

There are so many ways to bring parans to the table of what you're doing. Finding them in a single chart, like a nativity, is the start. For those who use them, finding them between two charts (e.g., a natal and a solar) with proper precession corrections will be of great interest.

Probably my greatest interest (either to find that there is a big deal we've been missing, or to rule it out) is transits by paran: for a specified location (latitude), all transiting planet paran aspects to natal planets. I imagine that will have some significant programming challenges, I do know it's Steve's greatest area of interest, and if it turns out to be valid it would revolutionize the entire area of how transits are handled. (Not only using them by paran but sidereally, i.e., with correct precessional adjustments).

Of course, they may not be valid. But I think we need to find out. It might be the single biggest unresolved We Don't Really Know in all of Sidereal astrology.

A variation of this is transit-to-transit parans. Pick the latitude of Washington, DC. and see when planets from Mars or Jupiter outward are forming aspects that nobody knows exist. For example, Russia invaded Ukraine when, for the latitude of Moscow, Pluto set 0°28' from Neptune's culmination. I don't know how long this Neptune-Pluto paran has been hovering over Mioscow, but it might be interesting to find out, In Kiev at the same moment, the parans were:

Moon-Mercury sq. 0°42'
Venus-Pluto co. 0°59'
(Moon had just oved 0°01' out of orb of paran square with Jupiter. Their luck ran out?)

If the theory were strong, we might have seen a sudden Mars paran at Kiev's latitude, which we didn't. Nonetheless, it's a single case just for demonstration, and does suggest that changing relations with their neighbors, though that's a pretty weak, common aspect.

For mundane work, I should also add aspects in RA. It will of course be available for all chart types, with precession correction in returns, etc.

mikestar13 wrote: Thu Mar 24, 2022 8:40 am For mundane work, I should also add aspects in RA.

Conjunctions and oppositions will already be in place, which leaves only the squares.

Conjuctions and oppositions in RA will also almost certainly be conjuctions and oppositions in the prime vertical, but might have different orbs.

mikestar13 wrote: Thu Mar 24, 2022 6:57 am Here is my take-away: Express orb in degrees, allowI am considering using class two mundane aspects and dropping class three ecliptical aspect (No change in TMSA defaults or legal possibilities.)

I do have Class 3 mundane aspects turned on (despite thinking that the default should be Class 1 only so as not to confuse most users).

I suspect that the main reason I like Class 3 turned on is my Sun. Without these, my Sun is unaspected. I never really look at the column (rarely), but having it there causes the Cosmic State report to grab them and that's where I see their value: The CS shows the whole run of aspects and the brain doesn't mess with the really wide ones unless they happen to be the closest ones.

mikestar13 wrote: Thu Mar 24, 2022 8:48 am Conjuctions and oppositions in RA will also almost certainly be conjuctions and oppositions in the prime vertical, but might have different orbs.

Exactly right. Actually, I thought you were talking about parans, where the MC-IC parans are simply conjunctions or oppositions in RA.

I seriously doubt squares in RA matter except when both planets are on RA-based angles. But, under the paran theory, they would be as significant as anything else and should be checked.

I'm wondering if a single aspect listing might have the closest of aspects in the ecliptic (no indication), mundane aspects in the prime vertical (M), aspects in right ascension (A), and parans (P). If multiple types are in orb, the last two only considered if the user has selected for that chart type.

Also I may experiment with strength boosts if say Ma co Ju is in orb mutliple ways.

mikestar13 wrote: Thu Mar 24, 2022 9:07 am I'm wondering if a single aspect listing might have the closest of aspects in the ecliptic (no indication), mundane aspects in the prime vertical (M), aspects in right ascension (A), and parans (P).

Yes, it would make sense - I'm thinking of a natal now - to treat them exactly as you've treated them thus far, i.e., of whatever the user has turned on, display only the closest for planet pair (and collate it the same way in CS).

For the typical user, R might be better than A for RA aspects. Another approach - perhaps less confusing, less congested - is to think of RA squares as a variation of parans (in the same sense as indirect midpoints are a separate setting within midpoints). It reduces one category. Only people who know/care enough to go in and turn on parans AND activate the RA squares would encounter it. One cold always have those on and NOT other parans by leaving others blank as in midpoints and other aspect fields.

If multiple types are in orb, the last two only considered if the user has selected for that chart type.

I'm not sure what you're saying. Up until now, if multiple types are in orb you only show the closer (in both the aspect columns and the CS).

Also I may experiment with strength boosts if say Ma co Ju is in orb mutliple ways.

Experimentation is good. I don't think it works that way, though. Multiple parans is one thing (if nothing else, the aspect rotates to the angles four times a day or whatever so it literally 'comes into existence' four times as often). For aspects in general, when they exist in multiple frameworks, it feels like there is this textured tide that rises and falls based on whether the planets are "at an aspect" in a valid plane - but only one tide per planet pair. (I haven't worked out the math - probably don't have enough mat theory training - to articulate the exact way in which midpoints and aspects exist as necessarily linked reciprocal expressions of a single curve-relationship between two circles of position [two planets], but I have an inarticulate intuition about it. Perhaps one day...)

For example, I might consider aspects in RA/Parans in some types of charts (nativity, SSR, Ingresses, etc.) but not in others. Similar to using mundane midpoints in ingresses but not nativities. User will have the option on a per option set basis. Of course it will be possible to have everything on for every chart if the user so desires.

It makes sense to consider aspects in RA as parans. Reducing the abbreviations to (none), M, and P. Basically a planet pair will have four parans a day unless some of them are out of orb or at extreme latitudes the planet doesn't rise or set. Perhaps a weighting of those four occurrences might be possible rather than just taking the closest, though the latter is easier to calculate.

So we have four aspect frameworks: ecliptic (only framework where soft aspects are valid, and then only for nativities and possibly progressions). prime vertical, right ascension, and oblique ascension (the relationship between horizon and meridian distinct from the 90° difference in the prime vertical. The last two are to be treated as parans.

Power score is complicated in the sense of not sure how to get the real life feel of the strength to match up, especially since the parans could be anything from partile-only to "treat like regular aspects with many degrees of orb." I suppose the best approach is to use whatever orb a user selects as the base and arc the curve from there. - This still probably will produce some irregular-looing results but we probably will only figure those out ambulando. - For example, if someone sets partile-only, does it make sense to have a 0°59'60" paran scale to the same % as a 7° ecliptical conjunction? I think not; otoh, it also shouldn't be over-valued by scoring it the same as a partile ecliptical conjunction.

I think parans may need to be one of the later additions to version 0.5, as the ideas seem to need some time to crystalize. I've got transits, quotations, PSSRs, tertieries, and noviens (including enneads) to work on plus a fairly extensive redesign of the option screens to allow new choices. Parans will definitely be a part of version 0.5, researching them is intriguing me. I know how to calculate the RAMC of meridian, horizon, and eastpoint/westpoint crossings, I am not sure about how or whether to calculate zenith/nadir crossings.

For Mc, = RA, for Ic = RA +180°
For Eastpoint, it's RA - 90°, RA + 90° for Westpoint

For horizon crossing adjust the Ep/Wp by the ascension difference (AD)

sin AD = tan decl * tan geo. lat.

If the product is outside the range -1 to +1, the body is circumpolar. A planet with positive AD rises early and sets late, with negative AD the planet rises late and sets early. A value of 0 (planet is on equinox = declination 0 and/or geo. lat on equator) cause the rising/setting to be the same instant as the eastpoint/westpoint crossing.

Yup!

BTW, is 0.4.7 closing out this week?

Oh yes, forgot to mention solar arcs and user selectable rulerships/exhaltations (per program, not per chart type). In principle, anything I want include in TMSA 1.0 except for sysastry (version 0.6). Maybe ready today for TMSA 0.4.7 surely by Saturday barring major catastrophes.

All sounds marvellous.

I am researching how to calculate zenith crossings. Strictly speaking, crossing the celestial longitude of the zenith--Alois Treindl took pains to point out the zenith is a point and crossing it is nonsensical, though I took pains to point out I was looking for the time that a planet has the same celestial longitude as the zenith point. For the Sun or any body on the ecliptic, it's simple if the geographic latitude is between to polar circles: the body crosses the zenith at the same moment as the point 90 degrees counterclockwise rises. I don't know how to allow for celestial latitude or circumpolar degrees.

Zenith crossings (the only way they're relevant astrologically that aren't simply meridian crossings) is the ecliptical square to Asc. The celestial longitude of the Zenith is always the nonagesimal longitude.

So celestial latitude latitude is not relevant.

It would be relevant in another framework, eg conjoining it in RA (same as MC) or in PV (same as MC).

The major angles are all great circles marking a plane. The minor angles are no dimensional points, so either exist as part of another circle they're on or when projected onto a circle such as the ecliptic. The ecliptic is the only available options since the Zenith is on meridian and PV, projected to the equator as MC, and can't be on (is the pole of) the horizon.

The zenith is by definition the celestial longitude of the point with 90° altitude above the horizon. At the North pole, this is always the summer solstice (0 Ca 0 Tropical). As we move further south, the zenith moves in an ever widening circle around the solstice until below the arctic circle, the zenith can be any degree of the zodiac. The process works in the opposite way in the southern hemisphere, the zenith always being the winter solstice at the south pole. The question I have been unable to answer is "does a formula exist for all latitudes that determines when a given body has the same celestial longitude as the zenith point". Internet searches have come up empty. Of course I can start with a seat of the pants guess and refine it iteratively. The celestial longitude of the zenith at a given moment is trivially easy to calculate.

The midheaven crossing is definable as the moment the right ascension of a body coincides with the right ascension of the zenith. The internet must have a million references to how to calculate that.

mikestar13 wrote: Fri Mar 25, 2022 7:11 am The zenith is by definition the celestial longitude of the point with 90° altitude above the horizon. At the North pole, this is always the summer solstice (0 Ca 0 Tropical).

Another way to say this is that, at the North Pole, the horizon is identical with the celestial equator. The Ascendant-Descendant axis (the places where the celestial equator crosses the ecliptic) will always be the equinoxes. The points 90° behind the equinoxes are the solstices and, of the two solstices, the summer solstice point has northern declination.

It's a slightly irregular (but interesting) example, though, because, while it is clear that the summer solstice point is the longitude of the Zenith, it's impossible to determine which of the equinoxes is Ascendant and which is Descendant.

As we move further south, the zenith moves in an ever widening circle around the solstice until below the arctic circle, the zenith can be any degree of the zodiac. The process works in the opposite way in the southern hemisphere, the zenith always being the winter solstice at the south pole.

Good description.

The question I have been unable to answer is "does a formula exist for all latitudes that determines when a given body has the same celestial longitude as the zenith point".

Yes. Universally, the longitude of the Zenith is 90° behind Ascendant. No exceptions.

(I mean "no exceptions" in the same way that basic math rules like "any number divided by itself equals 1" are universally true except for division by zero. Ironically, the poles themselves might be considered zeroes in the sense that Asc vs. Dsc is ambiguous, since both are ecliptic-horizon intersections but neither is any more rising or setting than the other. In this case, we actually should say that the Ascendant has to be TZ 0° Aries because the Zenith is unquestionably TZ 0° Cancer.)

The poles have to be exceptions because you can't have a Sidereal Time/RAMC at the poles: It is necessarily undefined because all great circles passing through the Zenith necessarily also pass through the North Celestial Pole. But aside from that "define by zero" type exception, there is always some part of the ecliptic intersecting the horizon so there is always an identifiable point 90° behind it.

I think you're making it way to complicated (coming at it from the wrong direction). 47 years ago, this was the first spherical trig problem Gary Duncan gave me to solve. I'm too rusty to do it again, but it was a very straightforward proof at the time. Longitudes of the Zenith and Nadir are determined by a great circle passing through both Zenith and Nadir at right angles to the ecliptic (like the longitude of anything). This great circle will always - always - exactly bisect the 180° of the ecliptic above the horizon. (The ecliptic intersecton above the horizon, by definition, is the Zenith; the other is the Nadir.)

This single rule is enormously valuable because it can be generalized to other situations. Consider as a parallel that the meridian (being a great circle passing through Zenith and Nadir at right angles to the prime vertical) will always exactly bisect the 180° of the PV that is above the horizon. (It's the same math, but easier to visualize.) Or the celestial longitude of Eastpoint will always exactly bisect the 180° of the ecliptic that is east of the meridian (harder to visualize but exactly the same math).

The celestial longitude of the zenith at a given moment is trivially easy to calculate.

And you don't have to calculate is separately if you've already calculated the Ascendant. But yes, at any given moment you know the RA and declination of the Zenith (but doing it that way is almost duplicative).

Am I missing some complexity here? You admit that calculating the longitude of the zenith is trivial and are still asking how to calculate when "a given body has the same celestial longitude as the zenith point." You know how to calculate Zenith's longitude, how to calculate the longitude of the other point, and how to tell when two longitudes are conjunct. (I must be missing something.)

Basically it is dead easy to calculate the longitude of the zenith at a given moment. The issue is calculating when a given position is at the zenith. (I will use the tropical zodiac here for the sake of easy math.) Let's say I'm looking for the moment when 10 Ar 0 is at zenith. In non-polar latitudes, I simply calculate the moment when the ascendant is 10 Cn 0 (dead easy). But at sufficiently high latitudes, 10 Cn is circumpolar, never crossing the horizon and therefor never the ascendant. In that case I must calculate iteratively, starting with an initial guess, calculating the zenith longitude for that moment, refining my guess, and repeating until sufficient accuracy is obtained. Somewhere deep in my memory there is a way to calculate this non-iteratively, but I can't recall it and can't find it on the internet.

An analogous example of the subtle difference in calculation:

A. Calculating the exact longitude of the SVP at this moment in time, vs.
B. Calculating the exact moment the SVP reaches 0 Aq 0 '0.0000".

Closely interrelated but not identical calculations.

Similarly,

A. Is the moon rising right now?, vs.
B. When will the moon rise next?

mikestar13 wrote: Fri Mar 25, 2022 10:35 am (I will use the tropical zodiac here for the sake of easy math.) Let's say I'm looking for the moment when 10 Ar 0 is at zenith. In non-polar latitudes, I simply calculate the moment when the ascendant is 10 Cn 0 (dead easy). But at sufficiently high latitudes, 10 Cn is circumpolar, never crossing the horizon and therefor never the ascendant. In that case I must calculate iteratively, starting with an initial guess, calculating the zenith longitude for that moment, refining my guess, and repeating until sufficient accuracy is obtained. Somewhere deep in my memory there is a way to calculate this non-iteratively, but I can't recall it and can't find it on the internet.

You know the celestial longitude and latitude you want. (Longitude is Asc -90°, latitude is 0° because it's a point on the ecliptic.) For known celestial longitude and latitude, you can calculate RA easily. That's your RAMC. (It's exactly the opposite of calculating MC from known RAMC.)

Never realized how much spherical trig I'd need to know when I started this program. I'll have it down pat by the time I'm writing 0.5. Now back to the finishing touches on version 0.4,7! Astrology was so much easier when everything was done in ecliptical l0ngitude (though considerably less accurate).

By the way, Mercury-Uranus is singularly appropriate for a very mathematically inclined astrologer.

i thought so.

Now I have it, it can be so easy to overlook simple things. Parans are intrinsically measured by time, whether expressed in hours or degrees. The latter is Jim's strong preference and mine, as it makes the numbers comparable at a glance to other forms of aspects. So if the ramc when planet A crosses angle B close enough to the ramc when planet C crosses angle D, we have A paran C for any angles be they major or minor. If say 20 Cn Tropical is never the longitude of the ascendant, then 20 Ar Tropical is never the longitude of the zenith (though it come ever so close), and parans involving a planet at 20 Ar Tropical on the zenith never occur. and the simple a planet crosses the zenith when a point 90° CCW rises rule always works (watching for possible 180° flip in polar latitudes).

Are Zenith-Eastpoint parans valid, and if so, by right ascension, celestial longitude, or the closer?

It all comes down to definitions, of course. If we choose to define parans as requiring but the planets are simultaneously angular And form an aspect in Some plane, then the answer is no, because there is no plane where Zenith and EP aspect each other that's any different from any other horizon-meridian square.

That was the way I was thinking. Minor angles only form parans in their own system whether horizon or meridian, so Zenith-Eastpoint and similar would not be valid. An Eastpoint-Westpoint paran would simply be an opposition in RA. Is there any distintion beteween a Zenith-Ascendant paran and an ecliptic square? A Zenith-Nadir paran and an ecliptic opposition? If celestial latitude is involved, there could be, but this is past the edge of my 3D visualization ability.

mikestar13 wrote: Tue May 03, 2022 8:03 am Is there any distintion beteween a Zenith-Ascendant paran and an ecliptic square?

It's slightly complicated.

First of all, if you measure in the mundane framework of Ascendant, the only mundane aspect to Zenith is the PV square to the meridian.

Second, if you look at it ecliptically, the planet that SEEMS to be on Asc may not be actually rising, voiding the whole thing.

Third, OTOH if I'm right about quotidians responding to ecliptical contacts only (except EPa), then the answer becomes yes.

A Zenith-Nadir paran and an ecliptic opposition?

Same thing, right?

If celestial latitude is involved, there could be, but this is past the edge of my 3D visualization ability.

Irrelevant since those angles only respond in celestial longitude.

If we haven't set a consistent standard, I propose that "paran" be defined as a relationship between two planets when both are on angles and they form (in some plane of reference) an actual conjunction, opposition, or square with each other. This is already a wider definition than generally used, but I think warranted. OTOH, if the two planets already form the same aspect by the same or a closer orb, then the paran wouldn't be listed (which takes care of the Z-N and EPa-WPa cases).

So basically, we are looking for conjunctions, squares and oppositions in RA and squares in oblique ascension or oblique descension, none of which exactly duplicate aspects in celestial longitude or prime vertical longitude, though they will be close. If the planets are both sufficiently close to angles, it would be considered and active paran, otherwise a potential paran. It looks like we can pretty much ignore zenith and nadir, as contact to the meridian and Eastpoint axis are not valid, and contacts to the horizon seem to duplicate ecliptic aspects.

So my procedure for each planet pair in order:

1. Determine if there is an ecliptic aspect. If so record aspect and the strength, if not set strength to -1 indicating no aspect.
2. Determine if there there is a mundane aspect. If so and it is strength is greater than the current strength, record it, otherwise ignore.
3. If parans are enabled, determine if any exist. If so and the strength of the closest is greater then the current strength record it otherwise ignore.
4. Return the last aspect recorded, or return "no aspect" if the strength is still -1.

I could write the code in Python right now, but first I need to finish the redesign of the chart options page.

I think this is right. It's complicated (as you know) anticipating all the variants.

Thinking this through to double check you (and be sure to triple check me back since I'm simultaneously doing other things here at work), for paran-related exact timings of angularities (in contrast to determinations of angularities in real charts):

• MC/IC/EPa/WPa contacts are measured in RA.
• Asc/Dsc are measured on OA/OD,
• Z/N/EP/WP contacts are measured in celestial longitude.

Of available aspects, therefore:

• MC/IC/EPa/WPa aspects to each other measured in RA.
• MC/IC aspects to Asc/Dsc are measured as specified.
• Asc/Dsc conjunctions/oppositions are measured in OA/OD.
• EPa/WPa to Asc/Dsc make no aspects, therefore have no parans.
• Z/N aspects and EP/WP aspects are simply ecliptical co/op, nothing new to show.
• Z/N aspects to EP/WP have no common circle in which they make an aspect and, in the rare instance of an aspect, it would be the same as an existing ecliptical aspect so noting new.

Therefore, finally, this reduces to a short list of viable parans by the above definition:

• MC/IC/EPa/WPa aspects to each other measured in RA.
• MC/IC aspects to Asc/Dsc are measured as specified.
• Asc/Dsc conjunctions/oppositions are measured in OA/OD.

That's what you said, right?

100% correct.

Mike, as I review old threads (and this an "at your leisure" question) - I'm not sure which TMSA thread is the best to post this, but this one looked reasonable...

In everything we've discussed on parans, are all the main points from the following thread covered? (I'm discovering today just how much I've forgotten I ever wrote on this forum lol.)

viewtopic.php?f=15&t=431

This is a fairly good summary. I remember you had a formula somewhere (not fully worked out IIRC) for calculating meridian longitude which would be the correct method to measure horizon-vertex axis contacts (meridian-vetex contacts would be measured in azimuth).

Yes I'll dig it. As far as I can tell it's correct except for quadrant accuracy, and there's a kludge for that.

Thanks. Yeah, that's where it is

As far as I can tell, this gives accurate results though I don't know how to throw things into the right quadrants. I think that's OK - that it doesn't matter because of a work-around. (Exact positions don't matter so much as orbs.)

There are two separate issues here:

First, for actual parans - things that would go in the paran report - this isn't what you need. The task is to find the RAMC for which a planet is at azimuth 90° or 270°. You then (if the option is selected) fold it into the table and if it matches (within orb) the orb when another planet is exactly on the horizon or meridian, you have this variety of paran. - I don't know the formula for determining azimuth, but it could be worked backwards, I'm sure.

Second, though, is for determining (for an aspectarian) what I've called prime vertical parans (PVP). I don't know if that should be a permanent name (and, from one point of view, it's just another mundane aspect). In a static chart (natal, return, ingress), a PVP exists when a PV to horizon/meridian mundane square exists. So far, I'm considering these only when "on the angles" since they're based on the idea that the horizon, meridian, and PV are always square each other. - My proposed working definition, therefore is:

1. One planet is within Class 1 angularity orb of horizon or meridian in PVL.
2. Another planet is within Class 1 angularity orb of 90° or 270° azimuth [maybe a separate orb setting should be defined for this, with default 3°].
3. If meridian-to-PV or PV to PV, then the mundane aspect is measured in azimuth.
4. If horizon-to-PV, then the mundane square is measured in meridian longitude.

By defining it in terms of angularity Class orbs, it makes it less arbitrary than I said before. In fact, the definition starts to be barely different from how mundane aspects are calculated:

Currently, mundane aspects are determined by: (1) Planets allowed to be considered depends on the "Show Aspects" setting. (2) Allow the orb set for mundane aspects.

This could be the same definition for Vertex (PV) contacts, except I'm loathe to give as large an orb as we do for horizon and meridian. This is most easily overcome (without adding some new layer) be always using Minor Angle orbs for Vx/Av.

The method then starts simplifying: (1) Considering only conjunctions with horizon, meridian, and prime vertical, determine that the two planets are each on an "angle." (2) Use Major Angle orbs for angularity on meridian and horizon, Minor Angle orbs for angularity on PV. (3) Any aspect (of allowed planets: both on an angle) between any Plane X and Plane Y is measured in the coordinates of Plane Z. (PV to PV are measured in azimuth, horizon to horizon or meridian to meridian are measured in PVL as currently.)

That is, horizon-to-meridian is measured in PVL, horizon-to-PV in meridian longitude, and meridian-to-PV in azimuth. The definition is consistent.

If we prefilter the allowed planets for these PVP meridian longitude aspects, it overcomes the quadrant problem. That is, it rules out planet combinations that are disallowed without worrying about getting the quadrant right. Everything valid comes out as a conjunction or opposition, you label it a square, and all you really want is the orb.

This has settled into making sense to me. Have I explained it so that it makes sense to you?

Summary for Aspectarian

• Horizon-to-meridian mundane squares are measured along the prime vertical (prime vertical longitude).
• Horizon-to-prime vertical mundane squares are measured along the meridian (meridian longitude).
• Meridian-to-prime vertical mundane squares are measured along the horizon (azimuth).
• Horizon-to-horizon or meridian-to-meridian mundane conjunctions and oppositions are measured in PVL.
• PV-to-PV mundane conjunctions and oppositions are measured in azimuth.
• PVL aspects are deemed proven across the board (no matter where they fall in the quadrant), so we use these interchangeably with ecliptic aspects.
• Azimuth and meridian longitude aspects have not proven themselves valid except when "near the angles," i.e., when actually reflecting the innate squares between the planes. Therefore, they are only needed in these specialized cases.
• We have learned so much so fast in this regard the last few years that, as always, any "final conclusion" is subject to change or evolution. That doesn't mean we should stop ourselves by refusing to draw a (current) "final conclusion."

PS - The plane-to-itself definitions could be defined in different ways that made for a more cross-plane consistency. I'm not going to worry about that right now (especially since the obvious substitutes give nearly identical results).

This won't make into the next release, I need additional thought and study time to fully grasp everything, but I'm pretty sure I get the direction your going in a general sense.

Jim wrote:

I know Steve has particular interest.

Indeed!!! Relative to my personal research only with my charts using the major angles, there is no doubt in my mind Fagan nailed it when he stated Parans are the most potent aspects known in Sidereal Astrology. I did weeks of relocation work with locating where I could put myself under any kind Moon-Jupiter Paran for Gambling in a Casino, 1 degree partile orbs. I was working with the DOS Nova Program (slow tetious work) and a Matrix Printer.

I had a friend who told me to pick any week in the year and he would pay for all expenses to any Casino in the US for me/him to personally experiment with Moon-Jupiter Parans for myself. For 4 days I limited myself to only 5 $ bets playing a 5 card card game (forgot the name). On an evening under a Moon-Jupiter paran set-up, forgot exactly the type chart used, I made my friend sit down next to me to witness the Moon-Jupiter Paran experiment and was dealt 4 7’s in a 5 card deal which paid 500 $ on a 5 $ bet.

Came home a 1600 $ winner never betting more than 5 $ on any dealt hand---four days of playing app 4-5 hours a day. Again, no doubt in my mind Parans using 1 degree partile orbs are the most potent aspect I have ever witness applying Sidereal Astrology.