It may be interesting to propose a careful revision of the term Midheaven with which we usually identify the tenth cusp in an astral figure. The original term in Hellenistic literature, both in astronomical and astrological texts, is the Greek word μεσουράνημα, which later became Latin as «medium coeli». The relevance of this concept lies in the fact that the bitter dispute regarding house systems depends on its definition, especially that between the defenders of domification by counting of signs (house equals sign) versus the defenders of systems by trisection of quadrants (uneven houses).
In the first centuries of our era there were three different concepts of μεσουράνημα, which caused a problem of unsuspected consequences at the time, since these three definitions gave rise to three different ways of thinking about how to distribute the twelve astrological houses. The first conceptualization is the one that understands by Midheaven the complete thirty degrees of the tenth sign counted from the ascending sign in zodiacal order. The second conceptualization is the one that defines Midheaven as the nonagesimal degree of the ecliptic, that is, exactly ninety ecliptic degrees above the ascendant. The third conceptualization is the one that fixes the Midheaven in the exact degree where the ecliptic intersects with the local meridian, that is, with the great circle that travels the north-zenith-south-nadir path.
It becomes clear that the whole sign house system is based on the first definition, the equal house system is based on the second, and the quadrant house systems are based on the third. This is the heart of the whole debate. Well, the reason behind the predilection of Medieval and Renaissance astrologers for systems by division of quadrants is based on a stricter astronomical conceptualization of the «medium coeli», since the Sun, the Moon, the planets and the stars culminate their drag by primary movement when their diurnal arc reaches the intersection of the local meridian in the upper half of the celestial sphere, not when they pass through the tenth zodiacal sign from the ascendant sign, nor when they pass through the nonagesimal ecliptic degree.
The idea behind this precision is that the sky is not something static, but is in permanent motion. As a result, all celestial bodies reach a certain point in their diurnal arc where they attain the highest possible altitude according to their declination. Being the Midheaven, in any of the possible definitions, the place where the stars reach their maximum elevation, it is quite obvious that the ideas associated with the 10th house such as advancement, promotion, profession, vocation, reputation and public image, derive of said elevated condition in the upper part of the celestial vault. Consequently, the exact point of highest elevation for the ecliptic degrees seemed the most logical choice under a more demanding astronomical and observational criteria.
However, it is clear to me from a long experience in traditional astrology that the resolution of the debate is to recognize that full-sign houses are extraordinarily useful for topical delineation purposes (meanings), while houses by division of quadrants are extremely necessary for determine the power or dynamism of the stars (angularity), so that a combined approach of both systems, topical and dynamic, is what gives the best results. The integration of both domifications, in practice, is something that takes time and experience. It is certainly not something recommendable for beginners, because it can confuse and make the learning process quite difficult for students, but for those who have already had more years of practice it is a necessary and beneficial effort. The integration of both approaches has come to generate a lot of consensus among the followers of medieval astrology of Perso-Arabic stamp.
Like many high-level colleagues, I have found in practice that the quadrant division house systems are also very useful in topical delineation, but it is convenient to contrast them with the whole sign house system to enrich and make the interpretation of astral figures more flexible. It can be somewhat complicated to have the same planet in a certain house by quadrant division, and in a different one by counting signs, but the fact that a planet can provide meanings to two adjacent houses enriches the astrologer’s hermeneutics, although at the same time it makes their work quite complex. Naturally, the integration of both systems can be somewhat messy at first, but eventually it is possible to learn to work in a coordinated and coherent way, trying to maintain balance in the midst of this duplicity in the domification.
Faced with the avalanche of misunderstandings and ill-founded criticisms on the part of the defenders of the whole sign house system against the systems by division of quadrants, it must be emphasized, from a traditional point of view, that it is a blunder to prefer only one system and completely discard the other, since the combination of both approaches, in an integrated work, was precisely one of the characteristic elements that distinguished the reform that gave rise to medieval astrology in the days of the Abbasid caliphate of Baghdad. But even before Mash’allah, Sahl ibn Bishr or Abu Ma’shar, some astrologers of the late Hellenistic period, such as Rhetorius of Egypt, had already begun to work with both forms of domification together. Consequently, a joint labor between both forms of houses constitutes a fundamental component in the good practice of our science.
Under a combined scheme of domification by whole signs and by quadrant trisection it will happen many times that a planet will be located in two different houses at the same time. Thus, for example, Jupiter could be in the beneficial 11th house per quadrant and at the same time in the difficult 12th house per whole signs. This would allow distributing the meanings associated with the planet in both locations simultaneously. And although it may seem strange at first, something similar did the Hellenistic astrologers with the meridian Midheaven, which usually transferred meanings of the 10th house to the adjacent places of the 9th and 11th houses. This overlap was common then, as was the superposition of planets on different houses among the Arabs, obtained by counting whole signs and dividing quadrants.
In many cases the houses of both systems will be fairly close to coinciding, especially if the ascending degree is at the beginning of a sign and if, at the same time, the latitude of the location is neither too far north nor too far south. But if the degree of the ascendant is very late in the sign, then the difference between the two forms of domification will be radically noticeable. To avoid making the work of combining systems too confusing, it may initially be easier to use whole sign houses for topical delineation issues and quadrant houses to determine the dynamism or angularity of the planets. This would be the simplest option to solve the matter, and it is the one that many tend to promote today, but it is not the best or the most complete. With a little practice it is possible to go further, and also give topical capacity to domification by division of quadrants, since there are thousands of examples in interrogations and nativities where the whole sign house system does not seem to reflect very well the reality of the horary figure or the natal chart.
Now, one wonders which of the numerous options for domification by division of quadrants should be used in conjunction with the whole sign house system. Obviously I do not pretend to give an absolute answer for a topic that causes so many discussions and differences of opinion, but we can say with certainty that a good answer to this question will always involve an astronomical understanding of how the intermediate cusps are calculated and distributed in the celestial sphere, so that we can make a decision based on the knowledge of the mathematical and astronomical structure of each system, and having in view the logic of the algorithm behind each proposal, in order to assimilate the literal and symbolic meaning of each one of the possible options. What does not seem very smart is to use a certain house system simply because it is the one our teacher used, or because it is the fashionable one.
While the Porphyry system simply divides the ecliptic segments of each quadrant into equal parts, being a pretty straightforward option to calculate, the Alchabitus system trisects the segments of the diurnal semi-arc of the ascendant for each quadrant, so that the division is based in ascensional time and not in a division of local space. In contrast, the Campanus system trisects every quarter of the prime vertical equally, that is, of the great circle that goes from the east point to the west point, passing through the zenith and the nadir, and then projects the division onto the ecliptic. The Regiomontanus system trisects every quarter of the celestial equator in equal parts, projecting the derived circles onto the ecliptic, while the popular Placidus system places the cusps in every sixth of the ascensional time of the ecliptic degrees, thus linking the houses with the division of planetary hours.
In my personal case, the Alchabitus system is by far the chosen one since, by dividing the diurnal arc of the ascending degree equally, it maintains the same logic of time displacement that we use in the Primary Directions, thus being an ideal domification scheme to be used in conjunction with this classic prognosis technique in a functional and consistent way. In addition, the division of houses by ascensional times of the diurnal arc of the horoscope or hour marker, gives us a work with a system based on a fundamental symbolic sense, since every astral figure starts from the ascendant, and the notion of angularity of the houses depends precisely on the primary movement of the celestial sphere, being the angular houses those that move from the four angles, the succeeding ones those that come from behind in the primary movement, and the cadent ones those that have already passed through the angles and lost their angularity condition. In these three positions lie the differences in strength or dynamism offered by the three types of houses to the planets positioned within them.
Now, to adopt a house system, it is necessary to get head first into the astronomical architecture of each proposal. Once it is well understood how the intermediate cusps are constructed, the symbolism behind each particular algorithm begins to be gradually clarified. And if in parallel a historical review of its origins is carried out, sooner or later it ends up finding the most suitable domification model for the function that corresponds to houses in astrology, which on the one hand is topical, but on the other it is dynamic, that is, it encompasses both meanings and angular force. And in the latter lies the key to understanding what is important when choosing, because between the end of the Hellenistic period and the beginning of the Middle Ages, all this disquisition reached its point of maturity and good sense. But from then on, and especially since the Renaissance, everything was confused and deformed, so it is necessary to investigate the origins of the problem.
Recapitulating what has already been said, there are three successive steps in the process of integrating the house system by whole signs with a house system by quadrant trisection. For students, first it is necessary to work with a single system in order to avoid confusion and unnecessary entanglement in the learning process. Then, for more advanced practitioners, proceed to work with the whole sign house system for topics related to accidental significators (topical function) and with a quadrant division system to determine the force or angularity of the planets (dynamic function). Finally, for astrologers with more experience, it is beneficial to move towards the full integration of both domification systems to interpret the topical or qualitative function, so that the meanings for a planet located in different houses are extracted under each of the two systems. At the same time, the domification of houses by quadrant trisection is also used to determine the dynamic or quantitative function. The latter is the way of working that the ancients used, but it requires agile handling and discrimination criteria that can only be acquired after a long time of practice.
To conclude, it should be noted that other options for the division of quadrants that differ from the one I have suggested are perfectly valid, insofar as they are based on a good understanding of the calculation and geometric structure of domification, together with the elaboration, from of this, of a logical argumentation and a symbolic interpretation that gives a reasonable basis to the preference, or at least an explanatory criterion that goes beyond the blind imitation of a house system whose formulation is unknown as much as that of its possible competing alternatives. And so, going back to the beginning of the question, it is essential to understand that the three historical definitions of the Midheaven do not have to throw us into an insoluble dilemma. Rather, they should invite us to carry out the task of studying in detail the astronomical coordinate systems and the reference points in the celestial sphere on which the different algorithms are built to domificate an astral figure.