This system is of some interest because Gettings' description of it suggests that it prefigures Carter's Poli-Equatorial system (see separate post on this site). Gettings' says that the Halyian system is "A method of house division...whereby the projected arc was defined by the passage of two hours of right ascension for each house, measured from the Ascendant." (p. 224)
This is exactly the procedure described by Carter to determine the cusps for the Poli-Equatorial system. Carter does not refer to this medieval system in his description of Poli-Equatorial houses. However, Gettings' reference to the Halyian, or Albohazen, system, does seem to suggest an historical precedent for Carter's modern, and unjustly neglected, method of house division.
Carter writes that for the poli equatorial method “...the houses are demarcated by circles passing through the celestial poles and dividing the equator into twelve equal arcs, the cusp of the 1sthouse passing through the ascendant. This system, therefore, agrees with the natural rotation of the heavens and also produces, as the Ptolemaic (equal) does not, distinctive cusps for each house....” 1
Calculation of the cusps is a relatively simple affair. The ascendant degree is converted to right ascension in degrees. Thirty degrees (or two hours) of right ascension is then added for each subsequent cusp. The right ascension so found is, for each cusp, then converted back to celestial longitude and expressed in zodiacal degrees. The tenth house cusp will not generally coincide with the MC degree. The second cusp is opposite the eighth cusp, the third opposite the ninth and so on.
A brief biographical reference to Albohazen Haly may be found in James Holden's Biographical Dictionary of Western Astrologers. Albohazen Haly is also likely to be called Haly Abenragel by some sources.
Gettings might have mis-described the derivation of Halyian houses. However it is impossible to check his source for the description as he does not identify it. It should be noted that the house system known as Abenragel is derived differently.
The Abenragel house system finds its modern expression in the Dutch method called Ascendant-Parallel-Circle (APC), which creates twelve houses by six equal divisions of the parallel of declination traveled by the ascendant degree above the horizon and six equal divisions of the parallel of declination traveled by the same degree below the horizon. The divisions of the parallel of declination are referred to the ecliptic through the north and south points of the horizon. The cusps of the first and seventh house are formed by the great circle of the rational horizon.
1. Charles Carter (1947, 2nd ed. 1978) Essays on the Foundations of Astrology. Theosophical Publishing House, London. p. 158-159.
The full blog post on Carter's Poli-Equatorial system can be found at Charles Carter's Forgotten House System
For information on the A-P-C house system see http://www.ingmardeboer.nl/php/apcmoden.php