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Alcabitius House System

 
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astralwanderer



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Posted: Sun Sep 06, 2015 6:31 am    Post subject: Alcabitius House System Reply with quote

The Alcabitius House System is reckoned to be one of the earliest systems. I am trying to work out how the system is calculated. It actually seems to be quite easy to work out the cusps from a table of ascendants/MCs or using some simple trig to convert RA into longitude.

However, on the web, and in text books, there seems to be varying ways of understanding how the house cusps are constructed. Some say the cusps are actually hour circles, running through the north and south celestial poles and the points that trisect the semi-arcs, and others say that the cusps are position circles (?) running through the north and south points of the horizon.

Is anyone able to clarify which is correct. My calculations seem to suggest the former (hour circles), but I'd just like to clarify this point. The diagram here http://whisperingwood.homestead.com/Astrology---Basic-Astrology-course-Lesson-Eight.html seems to illustrate the situation if the cusps are defined as hour circles. Ralph Holden's diagram suggests cusps running through the north and south points of the horizon (The Elements of House Division, p. 90).

In addition, does anyone understand the logic behind the Alcabitius alternative that is offered in Janus - Alcabitius Declination. Most software seems to offer only one Alcabitius system - the one I have described above, which appears to be called Alcabitius Semi-arc in Janus. The Solar Fire Alcabitius choice offers the same cusps as the Semi-arc version in Janus, as does Astroapp.

Munkasey describes Alcabitius Declination in his Astrological Thesaurus - Appendix B, where he offers the calculations for a variety of systems. He defines the Declination version of Alcabitius as tri-section of the semi-arc projected by hour circles onto the ecliptic, and the semi-arc system as tri-section of the semi-arc projected by vertical circles on to the ecliptic. Deb Houlding also uses this latter definition of Alcabitius houses, but doesn't specify whether the reference is to the semi-arc or declination version (my guess is the former). My understanding is that vertical circles run through the zenith and nadir. Should the semi-arc definition be using hour circles or 'house/position circles (see below)? Confusion abounds. Using his formula, I can re-create the cusps offered by Janus with their Alcabitius Declination choice. (Perhaps they used Munkasey's formula?)

I am taking my interpretation of the definition of vertical circles from 'prime vertical', the great circle running through the e + w points of the horizon and the zenith and nadir. The other fundamental vertical circle in this sense is the meridian, running through the n + s points of the horizon and zenith and nadir. So vertical circles are great circles running through the zenith and nadir perpendicular to the celestial or rational horizon. (Munkasey has this definition of vertical circles.)

Munkasey defines what I am calling position circles as 'house circles', "a great circle which has its poles the north and south points of the horizon, and which is perpendicular to the prime vertical." The north and south points of the horizon are the poles of the prime vertical. The east and west points of the horizon are the poles of the prime meridian.

Hour circles don't seem to be controversial in definition, being great circles perpendicular to the celestial equator and running through a particular body (or point) in space, which have as their poles the north and south celestial pole. (Munkasey's definition paraphrased.)

By the way, he spells the name of the system using Alcibitius. Janus spells the name as Alchabitius.

This probably sounds horribly confused, but if anyone can shed any light on the issues I'd be grateful.

Ed
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astralwanderer



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Posted: Tue Sep 08, 2015 6:14 am    Post subject: Alcabitius Semi-arc House System Reply with quote

Having done some more work on this over the last few days, my conclusion is that Alcabitius houses are created by three equal divisions of each of the diurnal and nocturnal semi-arcs of the rising degree, projected on to the ecliptic by hour circles derived from the poles of the celestial equator. I don't see how they could be constructed from a table of ascendants and MCs if this wasn't the case. I am referring to the system that Janus calls Alcabitius Semi-arc.

To have the cusps created from vertical circles (running through the zenith/nadir or the poles of the celestial horizon) or house/position circles (running through the poles of the prime vertical from the north and south points of the horizon) would involve some complex trigonometry, which isn't required to calculate the cusps by hand.

This makes the system very interesting, particular in polar regions, where it should be possible to construct houses wherever there is a rising degree, which occurs right up to the north and south celestial poles. This is because it allows for MCs below the horizon (degrees which culminate but don't cross the horizon), which systems like Regiomontanus and Campanus can't accomodate, without some controversial assumptions like calling the IC the MC.

There would be the same issues that occur with Porphyry, where some of the houses become infinitesimally small at certain times, when the Ascendant approaches to conjoin the MC, or when it opposes the MC. There would also be a problem on the arctic circle when the horizon and ecliptic coincide. However, the latter pretty much impacts all systems apart from those calculated from the MC like Meridian/Zariel.

The diagram cited in the previous post is, I am pretty sure, a reliable illustration of the system.
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Paul
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Posted: Tue Sep 08, 2015 9:29 am    Post subject: Reply with quote

astralwanderer

I'm not sure the best way to consider the problem of the houses is to focus on the mathematics of the calculations - after all there may be more than one way to achieve the cusp.

Conceptually the Alcabitius house system is the time it takes for the ascendant degree to culminate on the MC is trisected and projected onto the ecliptic to find the house cusps. There may well be a number of ways to mathematically achieve this.

I would have thought the most straight forward way would be to take the right ascensions of these points and project using hour circles to the ecliptic.
So when you say:
Quote:
Having done some more work on this over the last few days, my conclusion is that Alcabitius houses are created by three equal divisions of each of the diurnal and nocturnal semi-arcs of the rising degree, projected on to the ecliptic by hour circles derived from the poles of the celestial equator.


I agree with this. That's certainly my understanding.
That said, it's entirely possible that people mean different things by Alcabitius, and if we follow the kind of thinking Munkasey espoused then we ought to think that there is more than one Alcabitius system - the semi-arc method and declination method. I've no idea what the difference is between these, and have never seen the declination method used in practice anywhere. Does anyone know which software uses this method?

So when we look at Deb's article, we see she uses the same terminology as Munkasey, and cites this article so is following his lead (is my guess). However I'm not sure that Munkasey is quite right in saying that these positions ought to be passing through the poles of the horizon, but it may well be that there are different ways of calculating this, and in Munkasey's that's how he does it. From what I can see of the notes used by astrodienst they are using the semi arc method and trisecting and using hour circles (through the celestial poles rather than horizon poles):
https://github.com/dwlnetnl/SwissEphemeris/blob/master/swisseph/swehouse.c

If I understand the mathematics behind what Munkasey is doing, and there's really no reason to suspect that I do, it seems that actually for the semi-arc method he is using the right ascension and projecting from there, presumably therefore using the celestial poles. No idea for the declination system. Hopefully someone who is proficient with these calculations can provide some more insight.

What would be more interesting to me is in discovering what formula those ancient authors who used Alcabitius used - did they simply try to calculate when the ascendant degree was on the midheaven, and divide that time by three and take an ascendant for each of those times and use them as the house cusps? Or was there a formula more like what we might use today?

It seems to me that whichever system gives us those house cusps, and for all I know both of them do, is the one to use.

Quote:
This makes the system very interesting, particular in polar regions, where it should be possible to construct houses wherever there is a rising degree, which occurs right up to the north and south celestial poles. This is because it allows for MCs below the horizon (degrees which culminate but don't cross the horizon), which systems like Regiomontanus and Campanus can't accomodate, without some controversial assumptions like calling the IC the MC.


Well we still have the problems with the MC below the horizon as you say. I think either way, the polar regions are just a problem, whether in Alcabitius or not. Personally I prefer to use equal houses for these regions, but even here, we can have the equal 10th beneath the horizon I guess.
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Posted: Tue Sep 08, 2015 5:36 pm    Post subject: Thanks Reply with quote

Hi Paul - thanks for your reply. It was a thoughtful response and very helpful. My interest in house systems dates back many years, because it doesn't take much study of astrology before one realises that it is a hugely problematic area. (And that's before we start on polar horoscopes!)

My interest in Alcabitius comes out of trying to resolve the issue of houses in the far north and far south of the planet. It seems to me that if one wishes to have the ascendant as the cusp of the first house and the midheaven as the cusp of the tenth house the choices are pretty limited.

My conclusions about the definitions of the angles are presented here:

The Midheaven: http://www.exeterastrologygroup.org.uk/2015/01/the-definition-of-midheaven_18.html

The Ascendant: http://www.exeterastrologygroup.org.uk/2015/02/the-definition-of-ascendant.html

I think that if we are to be intellectually honest, we have to accept that the upper culmination of a degree of the ecliptic can occur below the horizon, creating a sub-horizon MC.

As Norman Blunsdon has written in a classic piece on polar horoscopes: "Let us first consider the MC and its derivation. As this is formed by the Meridian for the subject's birthtime, it is both personal and constant. We use the Local Sidereal Time and usually find the corresponding MC in our house tables: this is the same for all latitudes."

N Blunsdon (1967) Low Thoughts on High Latitudes. Astrological Association Journal: Vol. 8, No. 3, p. 30.

It is reprinted in the AA's compendium of early classic articles from the Journal - An Astrological Anthology: Vol. 1 (1959-1970). Selected and arranged by Zach Matthews.

In this piece, Blunsdon points out that the midheaven is the same at all latitudes, and changing the midheaven to conform to a definition (always above the horizon) transgresses this principle.

In fact it is easy to check Blunsdon's conclusions using a table of houses (remember those!). For any given sidereal time, the midheaven degree is constant, whatever the latitude, and this does not change once we cross the arctic circle.

This means that for a house system to work in polar regions it has to be able to accommodate this fact. I guess I don't think it's very helpful to redefine a perfectly well defined point like the midheaven to accommodate a house system when it breaks down.

Alcabitius, it seems to me, is going to be one (of two?) systems where the first house = ascendant and tenth house = MC will work in polar regions. The other is Porphyry. This seems to me to be an important point - a house system that works from pole to pole, through application of a constant principle of division of the sphere, that has historical lineage. What's not to like?!

The choice between the two is probably a matter of taste, but the use of diurnal motion to define the cusps seems to swing the argument in favour of Alcabitius for me.

Thanks again for your response. I appreciate your time in answering.

Ed
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Posted: Tue Sep 08, 2015 7:33 pm    Post subject: Further thoughts Reply with quote

Hi Paul - a couple of further observations on your post.

It would be very interesting to know the calculation methods of our forebears. My thought is that one of the practical advantages of Alcabiitius, in the sense we have described it, is ease of calculation from tables.

Now that I am practiced I can run up the cusps from a table of ascendants and midheavens in about five minutes. A jobbing astrologer, with hundreds of hand calculated charts under their belts, could probably do it much much quicker. I imagine they also knew the underlying trigonometry as well.

Re. Equal Houses. This is a tempting choice in the polar regions. However, it suffers from one problem and that is the association of the tenth cusp with the nonagesimal degree by most of its advocates. The nonagesimal degree is the degree on the ecliptic with highest absolute altitude above the horizon at any given time and place.

In temperate and tropical regions, this will be tenth house cusp - ninety degrees from the ascendant in a clockwise direction - but in the arctic, with the ascendant in reverse and a sub-horizon MC, the nonagesimal will actually coincide with the fourth house cusp - 270 degrees from the ascendant in a clockwise direction.

For me this is a problem that can only be resolved by giving up the connection between the tenth house and nonagesimal. Given the symbolic association made between height above the horizon and attainment, giving the tenth house symbolism, this seems problematic.

All the best. Ed
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Posted: Thu Sep 10, 2015 8:37 am    Post subject: Re: Thanks Reply with quote

astralwanderer wrote:

My interest in Alcabitius comes out of trying to resolve the issue of houses in the far north and far south of the planet. It seems to me that if one wishes to have the ascendant as the cusp of the first house and the midheaven as the cusp of the tenth house the choices are pretty limited.


Right, but I think, more to the point, if we wish to have the MC as the point at which the planets gain the most altitude, we have a real problem with polar regions, something you mention in your articles you referenced.

In my opinion there is nothing particular special, symbolically, about south, to make the MC important, except because it is at this point that, normally, the planets reach their highest altitude - in many ways this is how I understand the word culmination to mean anyway. It is like reaching a crescendo or reaching the climax or peak of a thing. When we think of the symbolic associations of the Midheaven with recognition and so on, it makes sense that this astronomical phenomenon be symbolically recognised in this way.

Of course that's a problem in polar regions regardless of how we cut it. The same is true for the equal house system in regards the nonagesimal, but at least has the advantage of having the 10th house cusp overcoming the ascendant by square aspect. Of course it would be better to have the nonagesimal as the 10th house cusp (and not say the 4th), but it's a small step in the right direction.

Quote:
In fact it is easy to check Blunsdon's conclusions using a table of houses (remember those!). For any given sidereal time, the midheaven degree is constant, whatever the latitude, and this does not change once we cross the arctic circle.


Right, the line of the meridian is dependant solely upon the longitude of the observer, not their latitude, so at any latitude it will be the same. In fact we can see the meridian as simply the terrestrial longitude of the observer, and so the MC point will remain consistent irrespective of latitude.

Quote:
This means that for a house system to work in polar regions it has to be able to accommodate this fact. I guess I don't think it's very helpful to redefine a perfectly well defined point like the midheaven to accommodate a house system when it breaks down.


The question for me is less about how might one calculate the MC in polar regions, and more about recognition of the symbolic properties that we associate with the MC and the astrological tradition that has emerged as a result of this. For me that has to do much more with it being a culmination point for planets, it is their high point in the sky, the point at which they gain the most altitude. That we lose this in the polar regions is much more important to me than what ways we should or should not calculate the MC. I agree we should not expect the MC to move, just because we're in a polar region, but to play devil's advocate, that does not mean we shouldn't expect astrologers to adapt to this and to symbolically treat the MC different when it is submerged below the horizon. I am not saying we ought to do this, but just that this is probably the better way, in my view, to consider the problem.

Quote:
Alcabitius, it seems to me, is going to be one (of two?) systems where the first house = ascendant and tenth house = MC will work in polar regions. The other is Porphyry.


Again I think it really depends more on what we expect from the MC. If we just expect it to be a direction, that's fine, I can see that something like Porphyry is just fine. However I struggle to see what Alcabitius would do that, say, Koch houses wouldn't. What is it about Alcabitius that you feel is useful in a way that Koch or Campanus or something isn't?

Campanus at least enjoys the fact that really the focus is on the observer's sky which surrounds them, so may in fact be a better way of approaching the problem as the house cusps will match more or less with what we might expect if we just eyeball the horizon around us, in this sense the tenth house cusp is important because it's the pole of the prime vertical on the horizon, and perhaps one could argue that it's less the case that this is an expectation of the culmination points of planets. Again I'm just playing devil's advocate here so as to allow broader ways of thinking of this problem.

Quote:
The choice between the two is probably a matter of taste, but the use of diurnal motion to define the cusps seems to swing the argument in favour of Alcabitius for me.


Right, but then Koch and Placidus all depend on primary motion, and in fact we can argue that so does something like Regiomontanus too.

Quote:
n temperate and tropical regions, this will be tenth house cusp - ninety degrees from the ascendant in a clockwise direction - but in the arctic, with the ascendant in reverse and a sub-horizon MC, the nonagesimal will actually coincide with the fourth house cusp - 270 degrees from the ascendant in a clockwise direction.


Right, provided we expect the 10th to be the nonagesimal, but we can just instead look at the tenth through the lens of its aspectual relationship to the ascendant. Of course if we expect the nonagesimal to show something about altitude, then the same argument occurs for the MC which will likewise not show us something about altitude in the polar regions. Six of one, half a dozen of the other. But at least equal can be seen to have a strong symbolic foundation just based on the aspects and relationships to the ascendant without recourse to the altitude of a planet at all. It's not how I prefer to see it, as I do prefer to consider the equal 10th as the nonagesimal, but the point is that it's not necessary to do this, and indeed many astrologers don't. Likewise, something like Whole can work for similar reasons.
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Posted: Thu Sep 10, 2015 6:14 pm    Post subject: Initial thoughts Reply with quote

Hi Paul - thanks again for a really valuable response. I want to reply in more detail after I've had some time to consider your ideas.

My initial thought is that that conclusion of my blog piece on the definition of the MC is that its essential quality is not its height above the horizon (or not), nor its direction, but it's proximity to the zenith, the point immediately above the observer at any latitude.

The degree on the MC for any latitude will be the point at which it makes its closest approach to the zenith during the diurnal circle. This remains true even if the MC is below the horizon. Philosophically for me this is about our state in the world, for ever reaching upward but never (except occasionally) making the highest point, marked celestially by the zenith.

There is something telling about the astrologer's oft repeated 'definition' of the MC as 'the highest point in the chart'. It seems as if this yearning is reflected in the common mis-definition of the midheaven.

The definition of the MC that I offer is one that remains true at all latitudes and does not rely on characteristics such as above and below, nor directions such as north and south. These characteristics are neither necessary nor sufficient for an adequate definition of the MC.
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Posted: Sat Sep 12, 2015 6:24 am    Post subject: Construction of Alcabitius Houses Reply with quote

The following image shows the projection of Alcabitius cusps onto a map of the world. The source of the map is Solar Fire's astromapping module. The chart has 12 TA 06 rising and 17 CP 51 culminating, giving a sidereal time of 19H 17M 25S.

The map may be interpreted in the following way.

1. Identify the horizon (green curving line)
2. Identify the ecliptic (orange curving line)
3. The intersection of the two in the east (right hand side of map) is the ascendant.
4. The intersection of the two in the west (left hand side of the map) is the descendant.
5. The meridian of the place is identified as the red vertical line running through the birthplace (just east of London) - this marks the MC where it intersects the ecliptic
6. The parallel of declination travelled by the rising degree is the uppermost purple line. This defines the journey of the rising degree (12 TA 06) from the IC to the MC.
7. The nocturnal semi-arc of the rising degree is identified by the horizontal red arrow running from the meridian identifying the IC to the ASC.
8. Three equal divisions of this semi-arc give the intermediate houses between the IC to the ASC, namely houses 2 and 3. The cusps of these houses are marked by the vertical red lines running through the points of tri-section of the nocturnal semi-arc at their intersection with the ecliptic.
9. The diurnal semi-arc of the rising degree is identified by the red arrow running from the ASC to the meridian identifying the MC along the parallel of declination
8. Three equal divisions of this semi-arc give the intermediate houses between the ASC and the MC, namely houses 11 and 12. The cusps of these houses are marked by the vertical red lines running through the points of tri-section of the diurnal semi-arc at their intersection with the ecliptic.
10. Each vertical red line also marks the longitude of places at noon. Effectively the cusps of the intermediate houses mark not only identify hour circles running through the poles of the equator, but geographical longitude. For instance, in this chart, the Sun at 2 LI 43 is very close to cusp 6. If the chart is relocated to a place very near the geographical longitude of this cusp, the Sun joins the MC.
11. The construction of the cusps west of the meridian is determined by the diurnal semi-arc and the nocturnal semi-arc of the setting degree - 12 SC 06. In effect, the diurnal semi-arc of this degree = the nocturnal semi-arc of the rising degree, and the nocturnal semi-arc of the setting degree = the diurnal semi-arc of the rising degree. This creates a beautiful symmetry between the journeys of the polarity 12 TA/12 SC from IC to MC for the rising degree and from MC to IC for the setting degree. The parallel of declination which determines the semi-arcs of the setting degree is as far south of the equator as the parallel of declination which determines the semi-arcs of the rising degree. Astrologically these degrees are contra-parallel at around 15.5 degrees north and south of the celestial equator. Both parallels define degrees of terrestrial latitude at the same distance from the geographical equator.
12. The cusps of the western intermediate houses are constructed in a similar fashion to the eastern houses, using tri-section of the two semi-arcs.

The integration of Alcabitius with geographical co-ordinates opens up some powerful interpretative avenues. For example, in this chart you will notice that Neptune lies very close to the southern parallel of declination defining the setting semi-arc. This means that the journey of the setting degree along it's parallel of declination is closely identified with Neptunian energy. This might not be surprising, given that Neptune lies close to the descendant. However, notice that other planets - Venus and Moon in particular - also lie close to the northern parallel. In essence, this suggests that the individual's fixed t-square - Venus, Neptune, Moon - is closely integrated with the two semi-diurnal (12 hour) arcs that define the house cusps in Alcabitius. Sun near the autumn equinox on the equator completes the picture. Saturn and Jupiter might considered slightly wide of orb for declination.

Another interpretative avenue might be identifying parans that lie on or close to the parallels. For example, in this case, the Mercury/Node parans and the Pluto/Node parans lie close to the latitude of the declination circles.

Please note that the map projection means that the hour circles that define the cusps of the houses run parallel north-south on the map. If shown on a sphere they would meet at the north and south poles.

A small version of this map is shown below.



The following link takes you to a large version of this map.

http://i.imgur.com/M6uaTLF.png
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Posted: Sat Sep 12, 2015 8:44 am    Post subject: Response Reply with quote

Hi Paul - here are some thoughts for you.

Quote:
if we wish to have the MC as the point at which the planets gain the most altitude, we have a real problem with polar regions, something you mention in your articles you referenced


I think the point I am trying to make is that the definition of the MC is about proximity to the zenith, rather than altitude above and below the horizon. Of course, the two are linked, when in temperate and equatorial latitudes, the MC degree is generally close(r) to the zenith and above the horizon.

However, this link is broken at the polar circles, when the midheaven falls below the horizon. For me, this reveals the general truth that the midheaven's principle relationship is with the zenith, the pole of the rational horizon, in the way that the ascendant's principle relationship is with the plane of the rational horizon itself.

This point also raises questions for me about whether the plane of rational horizon has much to do with house systems, apart from identifying the ascending degree. This, I know, will be extremely controversial, but it follows from my observation that most (all?) houses systems that use the plane of the rational horizon to define the cusps of the 1st and 7th houses and the upper meridian to define the 10th cusp, fail beyond the polar circles when the MC goes below the horizon.

Quote:
In my opinion there is nothing particular special, symbolically, about south, to make the MC important


Yes - because the MC is about proximity to the zenith rather than compass directions on the horizon. I hope this comes through in my blog piece.

Quote:

Of course it would be better to have the nonagesimal as the 10th house cusp (and not say the 4th), but it's a small step in the right direction.


Or perhaps, in polar regions, a large step in the wrong direction!

Quote:
For me that has to do much more with it being a culmination point for planets, it is their high point in the sky, the point at which they gain the most altitude. That we lose this in the polar regions is much more important to me than what ways we should or should not calculate the MC.


This is the point about proximity to the zenith again. The midheaven is not, I believe, essentially about altitude above the horizon but proximity to the zenith. This removes the requirement by definition to be above the horizon, because the MC degree will always be at its closest to the zenith when it is on the meridian, whether or not it is above the horizon.

Quote:
However I struggle to see what Alcabitius would do that, say, Koch houses wouldn't. What is it about Alcabitius that you feel is useful in a way that Koch or Campanus or something isn't?


Alcabitius holds together at all latitudes whereas Koch and Campanus do not.

Quote:
But at least equal can be seen to have a strong symbolic foundation just based on the aspects and relationships to the ascendant without recourse to the altitude of a planet at all.


With equal houses in polar latitudes we have to do this (let go of the altitude of the tenth house cusp) as the defining factor of its symbolism. I guess that has implications for the equal tenth house in temperate and equatorial latitudes.

Thanks again for your detailed and thoughtful response. I appreciate your interest in the thread Paul.
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