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3D Houses: The most accurate method of house placement?
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Michael Sternbach
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Posted: Thu Jul 02, 2020 4:18 am    Post subject: Reply with quote

Well, I think I understand what Walter is getting at: The Prime Vertical (the circle that connects East and West) is the only great circle whose division will result in getting regular sectors of the observer's space. If that's what houses are supposed to be all about.

Anyway, that's why Campanus was Rudhyar's method of choice.
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Cruiser1



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Posted: Thu Jul 02, 2020 5:02 am    Post subject: Reply with quote

Paul wrote:
Well to be specific, with more intent, don't all houses cover 30º of something? For example, Regiomontanus covers 30º of the equator. Campanus covers 30º of the Prime Vertical. Ok not all cover 30 degrees, but a lot do, but they all cover 1/3rd of something.

Indeed, Porphyry houses don't cover 30 degrees of anything, because Porphyry houses simply trisect or take 1/3 of each quadrant seprately. But I agree that every house system in an abstract sense has houses cover 1/12 or 1/3 of something. However, regardless of the internal math used to calculate house positions, only a few house systems end up with equal 30 degree size houses in the end (or 12 equal sized 30 degree wedges when looked at in 3D). Those are the true "equal" house systems, such as Equal (Asc), Equal (MC), Vedic, Whole (and Campanus when looked at in 3D).

Paul wrote:
For example, Regiomontanus covers 30º of the equator.
Indeed, and this raises an interesting point! Thumbs up Regiomontanus is an unequal system, because although it divides the celestial equator into 12 equal 30 degree sections, it then composes wedges which meet at the North and South points on the local horizon, which makes those wedges different sizes. However, if Regiomontanus instead composed its wedges to meet at the celestial poles, then it would be a 3D equal system! It would be like 3D Campanus, just tilted to a different alignment on the celestial sphere. However, this alternate 3D Regiomontanus would not be aligned with the local horizon, and would still (like 2D house systems) sometimes have planets below the horizon be in houses 7-12, or planets West of the meridian be in houses 4-9.

Michael Sternbach wrote:
Well, I think I understand what Walter is getting at: The Prime Vertical (the circle that connects East and West) is the only great circle whose division will result in getting regular sectors of the observer's space. If that's what houses are supposed to be all about. Anyway, that's why Campanus was Rudhyar's method of choice.

Yes, the above is the essence of "3D Equal houses". Also, dividing the prime vertical into unequal sections is how we get 3D versions of other house systems, like 3D Placidus, which produce the same house positions for planets exactly on the ecliptic. Anyway, whether 3D houses produces more accurate astrology than the various simple 2D house systems would be difficult to prove, but it at least seems more precise, and is a useful model to be able to visualize and display.

As the page http://www.quadibloc.com/other/as01.htm says, "To keep things simple for astrologers, however, tables of houses, instead of recording the entire path of the line between houses, give the boundary of each house as a single angular position. That is the location where the line bounding a house crosses the Ecliptic, since the planets always move close to the Ecliptic." That's the essence of 3D houses in general: We no longer need to "keep things simple" as we did in previous centuries, and modern computers can properly see and work with the entire path of the line between houses. Cool
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Cruiser1



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Posted: Fri Sep 17, 2021 12:30 am    Post subject: Reply with quote



A new version of Astrolog has been released, and the new version 7.30 features enhancements to "3D houses" and "chart spheres". Very Happy Astrolog now supports multiple models of 3D houses. Everything described up until now is a 3D model in which houses are arranged along the prime vertical, and have their poles at the North and South points on the local horizon. However, there are other orientations one can use for houses too. Here's a summary of the four models Astrolog supports:
  1. Ecliptic: Houses are arranged along the ecliptic, and have their poles (where the 12 houses meet) at the North and South ecliptic poles. This is classic 2D houses, because signs are also arranged along the ecliptic and use the ecliptic poles, which means only zodiac position longitude is used to determine house placement (and latitude is ignored).
  2. Prime Vertical: Houses are arranged along the prime vertical, and have their poles at the North and South points on the local horizon. Campanus houses combined with this 3D model is a "3D Equal system", in which all houses are equal sized 30 degree wedges of the celestial sphere. As with 2D Campanus and all quadrant systems, the Ascendant will always be on the 1st house boundary line, and the MC on the 10th house boundary line. This can be considered the preferred model for 3D houses (and was the only model available before Astrolog 7.30) since for quadrant systems it ensures that all parts of houses 1-6 are below the horizon, and all parts of houses 7-12 are above the horizon.
  3. Local horizon: Houses are arranged along the azimuth of the local horizon, and have their poles at the Zenith and Nadir points straight up and down on the local horizon. Horizon houses combined with this 3D model is a "3D Equal system", in which all houses are equal sized 30 degree wedges of the celestial sphere. As with 2D Horizon houses, the Ascendant won’t necessarily be on 1st house boundary line, but the Vertex will always be on the 7th house boundary line. As with Horizon houses themselves, stepping across Earth's equator will flip all houses 180 degrees.
  4. Celestial Equator: Houses are arranged along the celestial equator, and have their poles at the celestial poles or the points directly above Earth's North and South poles. Meridian houses combined with this 3D model is a "3D Equal system", in which all houses are equal sized 30 degree wedges of the celestial sphere. As with 2D Meridian houses, the Ascendant won't necessarily be on the 1st house boundary line, but the East Point (i.e. equatorial Ascendant) will always be on this boundary.
The animation above is an example of Porphyry houses displayed in a chart sphere in all four models, in which the 12 signs are in purple, and the 12 houses are in green. The four chart spheres are identical, and it's only the green colored house wedges that differ in orientation. Note how in all four spheres, all house boundaries intersect the ecliptic at the point of the 2D Porphyry house cusps.

In summary, there are four "3D Equal systems", in which all houses are equal sized 30 degree wedges of the celestial sphere. They are: (1) Any classic Equal system with 2D Ecliptic model. (2) Campanus combined with 3D Prime Vertical model. (3) Horizon houses combined with 3D Local Horizon model. (4) Meridian houses combined with 3D Celestial Equator model. Equal, Campanus, Horizon, and Meridian are therefore special house systems which could be considered "better" than others, since they are the only systems that can be "3D Equal". I like Campanus in 3D Prime Vertical the best, since it's the only system and model that's 3D Equal but can also ensure all parts of houses 1-6 are below the horizon, and all parts of houses 7-12 are above it.

(Note Regiomontanus houses mentioned in the previous post isn't a "3D Equal" system like the others. Campanus is entirely based on the local horizon, in which houses are simply equal sized 30 degree wedges along the prime vertical. Meridian is entirely based on the celestial equator, in which houses are equal sized 30 degree wedges along the celestial equator. Regiomontanus mixes the two: It divides the celestial equator into 12 equal arc segments like Meridian, however it then draws lines from the North and South points on the local horizon like Campanus, and where those lines intersect the ecliptic forms Regiomontanus house cusps. Mixing the models in this way results in irregular sized Regiomontanus houses in both 2D and 3D.)
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Michael Sternbach
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Posted: Fri Sep 17, 2021 7:14 pm    Post subject: Reply with quote

Cruiser1 wrote:


A new version of Astrolog has been released, and the new version 7.30 features enhancements to "3D houses" and "chart spheres". Very Happy


Awesome animations again, Walter! Very Happy

Quote:
Astrolog now supports multiple models of 3D houses. Everything described up until now is a 3D model in which houses are arranged along the prime vertical, and have their poles at the North and South points on the local horizon. However, there are other orientations one can use for houses too. Here's a summary of the four models Astrolog supports:
  1. Ecliptic: Houses are arranged along the ecliptic, and have their poles (where the 12 houses meet) at the North and South ecliptic poles. This is classic 2D houses, because signs are also arranged along the ecliptic and use the ecliptic poles, which means only zodiac position longitude is used to determine house placement (and latitude is ignored).
  2. Prime Vertical: Houses are arranged along the prime vertical, and have their poles at the North and South points on the local horizon. Campanus houses combined with this 3D model is a "3D Equal system", in which all houses are equal sized 30 degree wedges of the celestial sphere. As with 2D Campanus and all quadrant systems, the Ascendant will always be on the 1st house boundary line, and the MC on the 10th house boundary line. This can be considered the preferred model for 3D houses (and was the only model available before Astrolog 7.30) since for quadrant systems it ensures that all parts of houses 1-6 are below the horizon, and all parts of houses 7-12 are above the horizon.
  3. Local horizon: Houses are arranged along the azimuth of the local horizon, and have their poles at the Zenith and Nadir points straight up and down on the local horizon. Horizon houses combined with this 3D model is a "3D Equal system", in which all houses are equal sized 30 degree wedges of the celestial sphere. As with 2D Horizon houses, the Ascendant won’t necessarily be on 1st house boundary line, but the Vertex will always be on the 7th house boundary line. As with Horizon houses themselves, stepping across Earth's equator will flip all houses 180 degrees.
  4. Celestial Equator: Houses are arranged along the celestial equator, and have their poles at the celestial poles or the points directly above Earth's North and South poles. Meridian houses combined with this 3D model is a "3D Equal system", in which all houses are equal sized 30 degree wedges of the celestial sphere. As with 2D Meridian houses, the Ascendant won't necessarily be on the 1st house boundary line, but the East Point (i.e. equatorial Ascendant) will always be on this boundary.
The animation above is an example of Porphyry houses displayed in a chart sphere in all four models, in which the 12 signs are in purple, and the 12 houses are in green. The four chart spheres are identical, and it's only the green colored house wedges that differ in orientation. Note how in all four spheres, all house boundaries intersect the ecliptic at the point of the 2D Porphyry house cusps.


I highlighted the part that I have a problem with. For Porphyry is simply an equal division of each quadrant along the ecliptic. Are you somehow "back engineering" its houses by dividing other circles in a way that would then result in Porphyry house cusps? Confused

Quote:
In summary, there are four "3D Equal systems", in which all houses are equal sized 30 degree wedges of the celestial sphere. They are: (1) Any classic Equal system with 2D Ecliptic model. (2) Campanus combined with 3D Prime Vertical model. (3) Horizon houses combined with 3D Local Horizon model. (4) Meridian houses combined with 3D Celestial Equator model. Equal, Campanus, Horizon, and Meridian are therefore special house systems which could be considered "better" than others, since they are the only systems that can be "3D Equal". I like Campanus in 3D Prime Vertical the best, since it's the only system and model that's 3D Equal but can also ensure all parts of houses 1-6 are below the horizon, and all parts of houses 7-12 are above it.


It bears repeating: This seems to be an implementation of Rudhyar's vision of a system of 3D houses based on Campanus.

Quote:
(Note Regiomontanus houses mentioned in the previous post isn't a "3D Equal" system like the others. Campanus is entirely based on the local horizon, in which houses are simply equal sized 30 degree wedges along the prime vertical. Meridian is entirely based on the celestial equator, in which houses are equal sized 30 degree wedges along the celestial equator. Regiomontanus mixes the two: It divides the celestial equator into 12 equal arc segments like Meridian, however it then draws lines from the North and South points on the local horizon like Campanus, and where those lines intersect the ecliptic forms Regiomontanus house cusps. Mixing the models in this way results in irregular sized Regiomontanus houses in both 2D and 3D.)


But the meridian always intersects the celestial equator 90 degrees from where the latter rises (at the vertex) and sets. Why would North and South have to be introduced artificially in order to derive the Regiomontanus houses?
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Cruiser1



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Posted: Sat Sep 18, 2021 6:11 am    Post subject: Reply with quote

Michael Sternbach wrote:
Porphyry is simply an equal division of each quadrant along the ecliptic. Are you somehow "back engineering" its houses by dividing other circles in a way that would then result in Porphyry house cusps?
Yes! Very Happy Every classic house system has a corresponding 3D house system, which (in the prime vertical 3D model) is defined by great circles drawn from the due South point to the due North point on the local horizon, passing through each 2D cusp where it intersects the ecliptic. This transformation changes the poles where all 12 houses meet from the ecliptic poles to the local horizon, but won't ever change the house of planets that are exactly on the ecliptic. That allows those who like classic houses to combine their favorite house system with the benefits of 3D houses. For example, see http://www.astrolog.org/astrolog/pic/placidus.gif for "3D Placidus" houses, in contrast to http://www.astrolog.org/astrolog/pic/campanus.gif for "3D Campanus".

Remember that all classic house systems are simply divisions along the ecliptic, even Campanus. Campanus houses uses 3D math to calculate where the equal sized 3D wedges intersect the ecliptic, however once determined the 3D model is discarded and Campanus becomes a classic house system like any other. In other words, all classic house systems still use and define house cusps as positions along the ecliptic, and disregard planetary latitude when determining house placement.

Michael Sternbach wrote:
It bears repeating: This seems to be an implementation of Rudhyar's vision of a system of 3D houses based on Campanus.
Indeed, as Deborah Houlding's article at http://www.skyscript.co.uk/houprob_print.html#6back says:

"Rudhyar also proposed that a future development of the houses could utilize Campanus as the basis of a three dimensional 'birth sphere', in which the effect of planetary latitude could be fully acknowledged; although to do so requires some alternative way of representing this information other than our two-dimensional chart forms which only show measurements along the ecliptic. Those who consider the three dimensional perspective important, argue that defining house positions by zodiacal degree alone can often prove inaccurate since it assumes that the cusps cut through the ecliptic in a straight line whereas in reality the lines are curved..."

Astrolog can do this Rudhyar 3D model (i.e. 3D Campanus with houses arranged along the prime vertical). Astrolog can also do 3D versions of all other classic house systems, by changing the size of the wedges appropriately.

Michael Sternbach wrote:
But the meridian always intersects the celestial equator 90 degrees from where the latter rises (at the vertex) and sets. Why would North and South have to be introduced artificially in order to derive the Regiomontanus houses?
The North and South points on the local horizon have to be introduced to calculate Regiomontanus houses, because that's the definition of that system! I didn't design Regiomontanus, but rather just implement it. Wink As the page http://www.quadibloc.com/other/as01.htm describes it:

"In the Regiomontanus system of house division, the boundaries between houses are also meridians of longitude in the system of coordinates in which the North Point and the South Point on the horizon are the poles. However, instead of being equally spaced, they are determined by dividing the Celestial Equator into twelve equal parts. As this division starts from the eastern horizon, which includes the Ascendant, the eastern and western horizons, and the Meridian, are house boundaries in this system as well as in the Campanus system."

See http://www.astrolog.org/astrolog/pic/regiomon.gif for an animation of 3D Regiomontanus houses in Astrolog. Below is another picture showing the 3D model of Regiomontanus. These wedges are unequal sized, in comparison to http://www.quadibloc.com/other/images/campanus.gif showing the equal sized Campanus wedges:


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