Prime Vertical Longitude / Rationalized Semi-Arc, Aspects in OA/OD...

[ODdOnLifeItself]

I understand the mathematics behind this, but can you say a few words about the difference between prime vertical longitude and rationalized semi-arc? Which one shows angularity more precisely? Would rationalized semi-arc be more indicative of aspects (as per Marr) in OA/OD? (or am I seeing this incorrectly in a spatial sense?)

One other question, what is the clearest way to explain the special considerations, relative to prime vertical longitude and angularity, to astrologers who normally are only looking at ecliptic longitude to gauge angularity?

Thanks

[Jim Eshelman]

...can you say a few words about the difference between prime vertical longitude and rationalized semi-arc? Which one shows angularity more precisely? Would rationalized semi-arc be more indicative of aspects (as per Marr) in OA/OD? (or am I seeing this incorrectly in a spatial sense?)

I'm not sure what you mean by "rationalized semi-arc," but I suspect you mean what I (very casually) call "Placidus mundoscope" and Solar Fire calls Z-Analogue Prime Vertical, i.e., a proportioning of each planet's semi-arc. Presuming I have the question right:

On the issue of angularity there is going to be very little difference. That is, within close orbs of the angles (horizon and meridian), the values will be nearly identical (as will altitude, for example).

Where their distinctions will be most obvious will be what happens between the angles (in the same sense that Placidus and Campanus house systems (and other so-called "quadrant house systems") have identical angles and everything different between. The usual geometric biases exist where Campanus tends to push things closer to the horizon and Placidus tends to push things closer to the meridian.

And where this really shows is in mundane aspects! One of the greater discoveries/confirmations we've managed in the last decade is the dead-certain confirmation that conjunctions, oppositions, and squares along the prime vertical are important - probably in every respect as important as ecliptical aspects. This was first documented in mundane astrology (in Sidereal solar and lunar ingresses) where we have hundreds to thousands of examples. About a year ago, I caved in on the abundant single case examples in natal charts and admitted the same is true in natals.

In the ingresses, the most general rule of thumb is that only the aspects of foreground planets "count." The one clear, consistent exception is that Moon aspects - both ecliptical and mundane (PV) - are valid whether foreground or not. This (which probably comes from Moon signifying the layer of mass-mind consciousness or subconscious connection that underlies mundane astrology in general) led to my calling them "universal aspects" or "worldwide aspects." There are scores-to-hundreds of examples where ingresses fail to make their point if these are neglected.

That these close-orbed lunar aspects work as smoothly and reliably mundanely as ecliptically established for me the PV aspects beyond any reasonable doubt. (The PV aspects are location distinctive rather than worldwide.) Though I haven't sorted them out for side-by-side comparison with ecliptical aspects (we don't have the raw numbers to do that reliably), one gets a feeling from looking at one chart after the other (by now, many thousands of ingress charts). The aggregate tabulations in the respective chapters of Sidereal Mundane Astrology show how Moon aspects credibly describe the kinds of events studied, such as Moon-Sun for leader deaths and crises (among others), Moon-Mercury for transportation catastrophes, Moon-Venus for peace events and "good feeling" events in general, Moon-Mars for the deadliest disasters on record across categories plus coalmine disasters, fires, assassinations, and more, and on down the list.

It would make an even better comparison to segregate the ecliptical and mundane aspects for comparison and that would be a very large (probably half-year) project. The least I can say is that adding the PV aspects doesn't dilute the ecliptical aspects with random dots. They are signal, not noise.

This is aside from the nagging problem with anything dealing with semi-arcs: They don't exist for circumpolar bodies. You can find a prime vertical longitude (and a Campanus house position with it) for any celestial body at all, anywhere on Earth except exactly at the poles (because there is no way to find an RAMC other than "all RAMCs"), even if you can't calculate Campanus cusps; but there is no gradated semi-arc position for any planet or other body that doesn't have a semi-arc, i.e., doesn't (at its current declination) cover the range of horizon-to-meridian.

One other question, what is the clearest way to explain the special considerations, relative to prime vertical longitude and angularity, to astrologers who normally are only looking at ecliptic longitude to gauge angularity?

I suppose that depends on the individual astrologer and what they value most, (One needs to talk to people in their own language, in terms that matter to them.) I think the threshold concept, that allows the point at all, is that - contrary to what the majority of astrologers would like to think - astrology simultaneously operates in multiple frameworks. I don't mean this in an "everything works" sense, merely that multiple coordinate systems give simultaneously important information, with the most extreme and obvious example being that the celestial and terrestrial (mundane) are separate "voices" (what some may call the zodiac circle vs. the house circle). For example, (some) aspects work simultaneously along the zodiac and along the PV.

Astrologers who consider parallels and contraparallels valid (I don't) are already using both an ecliptical and equatorial framework, which are quite independent of each other. They have already allowed (usually without knowing it) that they consider two different independent frameworks to be valid.

If they have a mindset that admits the simultaneous voices of different coordinate systems, then the next most important point is that the weight of evidence seems to show that such things as angularity in a natal chart operates not zodiacally but in another framework that actually (one might say visibly) makes clear whether a planet is east or west of the meridian or above or below the horizon. (Astrologers who think that the number of planets in each hemisphere or quadrant of a chart should have some urgency about knowing these distinctions for sure, otherwise they have no reliability on that measurement.)

TMSA routinely shows the difference - by simultaneously displaying ecliptical and mundane positions. There are innumerable charts where this makes a big difference. Below is a snippet my lunar return next month relocated to Chicago, where the clustering around Ascendant looks shocking to astrologers not aware of the ecliptical vs. mundane distinction. (This is a picture of the 12th and 1st houses.)

Then again, this is too technical for most astrologers.

Code: Select all

 12Cp48-----------+
 |                |
 |                |
 |                |
 |                |
 |                |
 |                |
 |tSa 00Aq06 13°31|
 |                |
 |                |
 |                |
 |rMo 27Aq24 21°17|
 |                |
 |tNe 00Pi04 27°48|
 |                |
 |tMo 27Aq24 29°50|
 07Pi49-----------+
 |tMa 04Pi28 00°09|
 |tJu 07Pi25 00°52|
 |                |
 |                |
 |                |
 |tVe 29Pi56 11°37|
 |                |
 |                |
 |                |
 |                |
 |                |
 |tUr 20Ar50 22°09|
 |                |
 |                |
 |                |
 01Ta01-----------+
 

[ODdOnLifeItself]

First, thank you for replying to my questions with such generous detail.

Re: "I'm not sure what you mean by "rationalized semi-arc,..."

This system assigns 0 to 90 degrees to the diurnal semi-arc Ascendant to MC, 90 - 180 degrees to the diurnal semi-arc MC to Descendant, 180 - 270 to the nocturnal semi-arc Descendant to IC, and 270 - 360 degrees to the nocturnal semi-arc IC to Ascendant. Which to me does seem mundoscope like, though the arbitrary numbering scheme is notable and slightly cumbersome and counter-intuitive.

Re: "The one clear, consistent exception is that Moon aspects - both ecliptical and mundane (PV) - are valid whether foreground or not..."

When I was in Italy on vacation, I had time to work up a lot of events' ingresses, approaching your methodology as described in SMA. I found the same thing, that the Moon aspects were relevant, and often definitive for events no matter where the Moon was mundanely.

I think you are also correct in your assertion that astrology "works" in multiple frameworks simultaneously. While routinely checking PVL in the analyzed ingresses, I often noted that important (correctly-symbolized) planets made tight contacts in that measurement system. Using both seems cumbersome, but as each approach is a voice, some important "melody" might just be missed, when not checking...

You've given me more food for thought and helped me understand a couple of important things.

Thanks again

[Jim Eshelman]

Using both seems cumbersome

One of the real beauties of Mike's TMSA is how seamlessly ecliptical and mundane aspects are interwoven. You have a couple of mundane aspects (one close, one wider) that simply flow into the rest of the aspectarian. (If the same aspect has different orbs in the two frameworks, the closer is used, i.e., the "aspectivity" between the two planets is at the stronger value). The mundane aspects are marked so we can keep track, but otherwise naturally integrate into the rest of the chart. No need (or, at least less need) to look at two separate charts.

Code: Select all

    Class 1 Aspects         Class 2 Aspects         Class 3 Aspects     
Mo sx Ma 02°39' 86%      Su oc Ur 01°52' 42%       Ve sq Ma 06°55' 14%  
Mo oc Ju 00°56' 85%      Su sx Pl 03°01' 82%       Ve op Sa 09°01' 17%  
Su oc Ma 00°05'100%      Ve sq Ne 04°57' 54% M     Ve co Ur 08°52' 20%  
Su tr Ju 01°39' 95%      Ju op Pl 04°40' 77%                            
Su tr Ne 00°13'100%                                                     
Me sx Ve 00°29'100%                                                     
Me sq Ju 01°31' 96% M                                                   
Ma sq Ur 01°57' 93%                                                     
Ju tr Ne 01°52' 93%                                                     
Sa sq Ne 00°47' 99%                                                     
Ne sx Pl 02°48' 85%

[ODdOnLifeItself]

Re: "No need (or, at least less need) to look at two separate charts."

An elegant, yet simple, solution to be sure.

I do like that Janus (5.5) has the ability for any chart to press one button and see the chart in a different coordinate system in a new window. Not quite as elegant as the TMSA solution, but workable. And I do like seeing the charts!

Options:

Equatorial Right Ascension Degrees
Equatorial Right Ascension Sidereal Time
Equatorial Hour Angle Degrees
Equatorial Hour Angle Sidereal Time
Horizon Astronomical Azimuth
Horizon Astrological Azimuth
Horizon Astrological Azimuth Map (Local Space)
Prime Vertical Longitude
Rationalized Semi-Arc
Galactic Longitude
Invariable Plane

[Jim Eshelman]

Yes, that's a nice Janus feature. AFAIK it's the only astrology program to give galactic coordinates, which are intriguing.

[ODdOnLifeItself]

Why does Jupiter opposite Pluto not show up as a mundane aspect?

Jupiter was on the MC at 22:57:57 and Pluto was on the IC at 22:59:21

How are these mundane aspects being calculated? Is there a time cut-off (exclusion) relative to the actual chart time, relative to the parans' timing?

In the TMSA printout that you shared (above), it lists Mercury square Jupiter 1° 31' and Venus square Neptune 4° 57'. No available coordinate system in Janus, nor any parans list gives me this 1° 31' orb, for instance for the Mercury square Jupiter aspect, as listed in the TMSA printout.

If I look at aspects in Prime Vertical Longitude (in Janus), I see no 4th harmonic aspects between any planets within 5°. (only one between Saturn and Node)

Thanks for any clarification...

[Jim Eshelman]

Why does Jupiter opposite Pluto not show up as a mundane aspect?

Jupiter was on the MC at 22:57:57 and Pluto was on the IC at 22:59:21

That would be the relevant timing if this were being treated as parans. (It isn't. Mike will add parans in the 0.5.x version he's working on over the next few months, but that's not what's being used here.)

That would be relvant if they were both on the meridian at the moment. Yes, to use Solar Fire (since it's convenient), your Jupiter is at RA 344°29' and your Pluto at RA 164°50' (opposite 344°50'), so they are 0°21' from an exact opposition in RA. If one were exactly on MC, the other would be 21' off the angle.

If course, if they were at the horizon, they wouldn't be anywhere near opposition. Your Jupiter rises at RAMC 260°46' and your Pluto sets at RAMC 272°00', 11°14' (45m) later. Your Jupiter sets at RAMC 68°13' and your Pluto rises at RAMC 57°33', over 10° apart.

Since your Pluto and Jupiter are somewhere between the horizon and meridian, the distance that they are from opposition along the prime vertical is somewhere between 0° and 11°.

How are these mundane aspects being calculated? Is there a time cut-off (exclusion) relative to the actual chart time, relative to the parans' timing?

They aren't parans. They are aspects in prime vertical longitude. Your Jupiter is PVL 246°06' (6°06' in the 9th house) and your Pluto 60°54' (0°54' in the 3rd house), or 5°12' from opposition.

In the TMSA printout that you shared (above), it lists Mercury square Jupiter 1° 31' and Venus square Neptune 4° 57'. No available coordinate system in Janus, nor any parans list gives me this 1° 31' orb, for instance for the Mercury square Jupiter aspect, as listed in the TMSA printout.

The prime vertical longitudes of these planets in your chart - stated in house notation for ease of seeing the aspect - are as follows (based on SF):

6°06' 9H - Jupiter
7°38' 12H - Mercury

3°17' 2H - Venus
8°13' 5H - Neptune

If I look at aspects in Prime Vertical Longitude (in Janus), I see no 4th harmonic aspects between any planets within 5°.

I'd have to crank up Janus to compare. Here is a copy of your mundoscope (prime vertical longitudes) - I'll remove the diagram when you're through.

JA mundo.png

Compare this to the prime vertical longitudes and consequent strength scores from TMSA:

Code: Select all

Pl PVL    Ang G
Mo  10°21'  74%  
Su 352°59'  87% F
Me 337°38'  15%  
Ve  33°17'  36%  
Ma 318°49'   8%  
Ju 246°06'  10%  
Sa 202°19'  55%  
Ur  45°33'  14%  
Ne 128°13'  28%  
Pl  60°54'   0%  

[Jim Eshelman]

I suggest you go ahead and install TMSA. If nothing else, the Help features on each page usually will explain what's on that page. It's free and lightweight.

[ODdOnLifeItself]

Thanks... that was exactly the information that I was seeking.

When I opened up the aspects' acceptable orb, they were there to see.

Still, there is an anomaly...in that you're showing Jupiter 6° 6' and Mercury 7° 38', where for some reason in Prime Vertical Longitude, Janus is giving 6° 32' and 7° 52'.

Are you using July 3, 1962, 6:16:44 am (CDT), Mount Vernon, IL, 88w54'11 38n19'02?

Re: "I suggest you go ahead and install TMSA."

TMSA doesn't work on my laptop...there are several files missing, or let's say I get a critical warning that says several files are missing. I plan on getting a new Windows 11 machine, within the next weeks and will definitely install TMSA, when I get my new laptop.

[Jim Eshelman]

Still, there is an anomaly...in that you're showing Jupiter 6° 6' and Mercury 7° 38', where for some reason in Prime Vertical Longitude, Janus is giving 6° 32' and 7° 52'.

I can't speak for Janus. I open it so rarely (I find it cumbersome, slow, and enigmatic to get around). The agreement of everything within a minute of arc between TMSA and SF keeps my confidence high (and I know Mike is using the right equations). - I'd expect Janus to have it right also; are the longitude and latitude exactly the same?

Are you using July 3, 1962, 6:16:44 am (CDT), Mount Vernon, IL, 88w54'11 38n19'02?

No, I'm using 6:18 AM (6:18:00) because you said that was the given time IIRC. That's the explanation.

For 6:16:44 AM, TMSA gives exactly the same as you got from Janus.

[ODdOnLifeItself]

Re: "For 6:16:44 AM, TMSA gives exactly the same as you got from Janus."

PERFECT!

Again, thanks!!!